Getting Startedengtech.weebly.com/.../ftrc_2_getstarted_2010-11_v2_r.pdf · 2018-09-12 · Team...

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FastTrack Racing Challenges Curriculum © 1080 Education Inc.

As a part of the FastTrack RC National STEM League, your team will earn points for competing in race events, investigating, designing & developing, building public relations and managing team efforts.

This FastTrack RC STEM League handbook includes rules & guidelines, season schedule, points system, forms, track layouts and more.

Teams should understand, sign and return the FTRC Rules & Guidelines with their annual registration form.

Good luck. May you keep the sunny side up!

Grades 6 - 12Booklet #2

A NASCAR Youth Initiative

Getting Started

www.FastTrackRC.com FastTrack RC Curriculum: Getting Started © 1080 Education Inc.

Getting Started Booklet ContentsFirst Things FirstFirst Steps as an FTRC Team Member.................................................................................................................. 4

FastTrack RC Integrated Curriculum ...................................................................................................................... 6

Certification Process & RequirementsTeam Coach Procedure ...................................................................................................................................................... 11

Certification Process & Requirements .................................................................................................................. 9

Driver CertificationTeam Coach Procedure .....................................................................................................................................................12

Driver Certification Procedure.....................................................................................................................................12

Driver Certification Table ................................................................................................................................................ 13

FastTrack RC Driver Certification Data Table ............................................................................................... 14

Driver Certification Challenges .................................................................................................................................. 15Driver Certification Challenge #1: Turtle vs. Hare ........................................................... 15Driver Certification Challenge #2: Slightly Faster............................................................ 15Driver Certification Challenge #3: Hit Your Marks, Drag Strip ...........................16Driver Certification Challenge #4: U-Turn, Right & Left ...........................................16Driver Certification Challenge #5 & #6: Oval, Standing & Flying..................... 17Driver Certification Challenge #7 & #8: Slalom, One Way & U-Turn ......... 18

Mechanics CertificationTeam Coach Procedure .................................................................................................................................................... 19

Mechanics Certification Procedure ........................................................................................................................20

Mechanics Certification Table.......................................................................................................................................21

Mechanics Certification Challenge #1: Identify Components ........................................................22

Mechanics Certification Challenge #2: Characterize Components .........................................23

Mechanics Certification Challenges #3 - #8: Common Repairs .................................................24

Mechanics Certification Challenge #9: Gear Ratios ...............................................................................27

Mechanics Certification Challenges #10 - #18: Preventive Maintenance ...........................29

FTRC Fundamentals CertificationTeam Coach Procedure .................................................................................................................................................... 31

FTRC Fundamentals Certification Table ............................................................................................................32

Challenge Assessment Rubric .....................................................................................................................................33

Professor Pi Notes on FTRC Fundamentals ...................................................................................................34

Background on Math2Go Challenges .................................................................................................................37

Math2Go Challenge #1: How Fast is Fast? ..................................................................................................38

Math2Go Challenge #2: Are We There Yet? ..........................................................................................48

Math2Go Challenge #3: Optimal Power ......................................................................................................57

FTRC Fundamentals Certification Challenges #4: Gear Ratios ....................................................76

Getting Started in the

www.FastTrackRC.com

First Things First

Section ContentsFirst Steps as an FTRC Team Member ............................................................. 4Step 1 for Everyone ................................................................................................................................................................. 4

Step 2 for Everyone ............................................................................................................................................................... 4

Next Steps for Everyone .................................................................................................................................................... 4

Individualized Next Steps ................................................................................................................................................... 5

FastTrack RC Integrated Curriculum ............................................................... 6FTRC Projects & Investigations .....................................................................................................................................7

10-11, Getting Started FastTrack RC © 1080 Education Inc.

Step 1 for EveryoneRead the FTRC Rules & Guidelines in the FTRC STEM League Handbook. The adult Team Coach must sign and return a copy to the FTRC Sanctioning Body.

Step 2 for EveryoneMake copies of the Pre-Assessment for everyone (photocopy from the Curriculum & Program Design insert or download and print from the FTRC team web site). Take it to see where you need to reinforce your fundamental science, math and race engineering skills.

Next Steps for EveryoneIf you are a new team, the first real step is to create a Business plan as outlined in the Business Planning, Project Planning & Public Relations (Biz, Project & PR) booklet. This doesn’t mean that team members can’t get started on fundamental tasks before it is done by following these steps:

Read excerpts from a sample team business plan to better understand the vision of a FastTrack RC team and commitment required. Find them in the Business Planning section of the Biz, Project & PR booklet and download at the Business section of the FTRC team web site. Business plan excepts include the typical team organization and work breakdown structure (WBS) shown below and on the next page. A WBS shows typical products of an organization. An individual can do several of the proposed jobs.

Read the sample job descriptions for a FastTrack RC team. Go to the Project Planning section of the Biz, Project & PR booklet for some context and of the FTRC team web site to download them.

Begin with the Individualized Steps outlined on the next page using the curriculum outlined in the following pages.

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Major strategy, budget and systems questions are answered through open discussion with the whole team then ultimately by the Executive Directors who are elected by the team. The Team Pi board is made of the team coach, Executive Directors, team mentors, school principal and major sponsors. Sub-teams are responsible for each major points category.

Team Pi Board Executive Directors: Finance, Strategy, Operations

STEM Projects Manager

Chassis Setup

Aero- dynamics

Alt. Energy Project

Creative (Mech)

Engineer.

Driving & Maint.

3-D CAD Team

Public Relations Dir.

Graphic Design

Media Relations

Web & Media

Copy-writer

Events & Fundraising

Sub-teams

Example FTRC Team Organization DiagramShows the major jobs and how they relate to one another.

First Steps as an FTRC Team Member

(10-11) First Things First FastTrack RC, Getting Started © 1080 Education Inc.

Example FTRC Team Work Breakdown StructureShows the major products of a FTRC team.

Competitive FTRC TeamLevel 1

Public Relations

Executive Management

Chassis Setup

Aero- dynamics

Solar Charge Station

Creative Eng. Project

3D-CAD Designs

Licensed Drive/Mech

Licensed Drivers

Certified Mechanics

Hitting Your Marks Data on Tracks 1-10

Wing Design

Body Design

FlowSim Data

Concept

Design

Model

Presentation

Battery Profile

Solar Data

Charging Station

Tracking System

Presentation

Baseline

Wing Design

Wing

Car Body Design

Car Body

Track Maps

Gear Ratio Models

Geometry Models

Traction Models

Business Plan

Team Project Plan

Inventory Control

Budget Control

Quality Control

Strategy

Plan

Materials

Web Sites

Meetings

Fundraisers

Media

Level 3

Individualized Next StepsIf you’ve identified a job you’re interested in, you may have to apply for it. Talk to your team coach and executive team about how. Once hired, here are some generalized next steps for each job.

Job First Individualized Steps

STEM TeachersReview Curriculum & Program Design booklet to help you plan the FTRC integration into your course of study.

Team Coach, Adult LeaderHelp team executives build a Business Plan and Team Project Plans then help them implement those plans over the season.

Team Executive

Build a Business Plan then a team project plan as outlined in the Biz, Project & PR booklet. The business plan includes targets for budget, season performance, and community involvement. Once the document is ready, work on how to present it and work with project manager team members to build a team project plan.

Project ManagerBuild a team and sub-team project plans as outlined in the Project section of the Biz, Project & PR booklet. Implement and control those plans.

Race EngineersChassis Setup & Mechanical EngineeringAerodynamics teamCreative EngineeringAlternative Engineering

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Become certified in Race Engineering Fundamentals in this Getting Started booklet.

Once certified, begin working on your investigations and projects using the curriculum booklets and your team’s project plan as guide for timing. If you don’t have one, make a sub-team project plan as outlined in the Biz, Project & PR booklet. Samples are provided.

Also refer to the FTRC Points System and Rules & Guidelines to help prioritize work.

3-D CAD Designers Take SolidWorks tutorials including Flow Simulation tutorial at the FTRC team web site

Drivers

All good drivers are also good communicators of what needs to be fixed on their car. This is why drivers must get certified in Driving, Mechanics & FTRC Fundamentals as outlined in this Getting Started booklet. Once certified, practice the league tracks outlined in the FTRC STEM League Handbook and help the Race Engineering teams gather data.

MechanicsBecome certified in Mechanics as outlined in this Getting Started booklet. Once certified, continue to practice fast diagnosis and repairs and to maintain the car as outlined in the project, Preventive Maintenance & Repairs (download from web site).

Graphic ArtistsBuild a team identity as outlined in the Biz, Project & PR booklet. Once that’s complete, help the PR team create PR materials like fliers, banners and business cars. After that, work with others on your team’s car decal design.

Public Relations & Fundraising

Build a public relations strategy and plan as outlined in the Biz, Project & PR booklet. Once that’s complete, implement it by setting up meetings, planning fundraisers, etc.

Web DesignersFind out about what web sites and social networking sites your school or organizational leadership allows. Build them and update them frequently to earn points as outlined in the FTRC Points System.


FastTrack RC Integrated CurriculumPrint Pack Includes Booklets 1 - 6 and MS 1 - 3

e-Curriculum at FTRC Team Web Includes All Booklets, Videos, Presentations, etc.

1. FTRC National STEM League Handbook

Project Manager

CFO

Marketing

WebDesigner

3. Business Planning, Project Planning & Public Relations

6. Mechanical Engineering (Creative Engineering Ideas)

5. Aerodynamic Projects

7. P.I.T. Now: Alternative Energies download from FTRC web site

9. Applied Physics LessonsAero Drag

Rolling Drag

Motor Thrust

Normal Force = 0.5gm

Normal Force

gm

MS 1 - 3. FTRC for Middle Grades

4. Chassis Set-Up Investigations

www.FastTrackRC.com FastTrack RC Curriculum & Fundamentals © 1080 Education Inc.

Insert: Curriculum & Program Planning

8. Applied Math Lessons download from FTRC web site

2. Getting Started

(10-11) First Things First FastTrack RC, Getting Started © 1080 Education Inc.

FTRC Projects & InvestigationsTo reach any goal, students and educators must first define them. Once you understand your goals, you can plan how to achieve them. The Project Management & Marketing booklet will help you through this process that is critical for success in any organization.

A major goal for any FTRC team is to perform well in races. The FTRC car comes ready-to-run, but is doesn’t run as well as you need it to. Only through race engineering can you get the high performance you want. Race engineering can boil down to two types of activities:

Set-up: adjust and optimize settings through investigation

Modification: design and modify parts through projects

Set-up means you are choosing the right setting or type for an existing part (like gears or springs). Modification means you’re changing the part or building a new one altogether.

A goal in all setup and modification is to improve energy efficiency, but where will that energy come from? FTRC cars are fueled by electrical energy that can come from conventional power plants (plug into the wall), solar, bio or wind sources. The P.I.T. Now! projects help you solve one critical aspect of creating Petroleum Independent Transportation: establishing refueling (recharging) sites.

You can drive the FTRC car the moment it arrives but there are over 14 million answers to the question, “How will you set it up?”. A “set up” is the combination of gear set, spring settings, camber, toe angles, etc. The right one depends on track layout, conditions and score. Chassis Set-Up investigations help solve the ‘set up’ problem.

There are an infinite number of ways you can modify the car to improve speed, handling and energy efficiency. If you sketched a concept car, it probably wouldn’t look like the stock car you received. It might be sleek for low drag like full-sized electric cars. It might have an upside-down wing to add down force like a Sprint or Formula 1 car. Aerodynamic Projects guide you through designing & engineering your concept car body.

With all the added down-force you’ll get from your new or improved car body, parts like the lower control arm might need to be reinforced to keep from snapping. The Mechanical Design & Fabrication book guides you through the process of evaluating and engineering improved parts. (Optional) You’ll save time and resources by using 3-D CAD to make sure you fabricate only effective designs.

A curriculum specifically for middle grades is provided.

Reinforce and extend core standards-based concepts from FTRC projects with lessons from the Math and Science on the FastTrack books. Share them with science and math teachers in your school.

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Calibrate CAD Model

Wings

Car Body

Aerodynamic Design

Fabrication

Lower Control Arm

Chassis Plate

Car-Wing System

Mechanical Design

& Fabrication

Cap & Trade

Solar Power

Wind Power

PIT Now!Alternative

Energies

Driver Skill

Gear Ratios

Traction

Energy Use

Chassis Geometry

Chassis Set-Up Investigations

Problem Solving through Math

Modeling

6-8 Grades

Math on the FastTrack

Science on the FastTrack

Power Up

Set Up

Modify

FTRC Curriculum Context (continued)


www.FastTrackRC.com

Certification Process & Requirements

Certification Process

Procedures for certification in each of the three areas are outlined in separate sections.

For all three certifications, there is a table to fill in as you complete each section. Your team coach must sign off that each one has been completed satisfactorily.

Once you’ve completed all sections, your team coach will sign and present you with a certificate indicating you can proceed with investigations and projects that will optimize performance and prepare your team for FastTrack RC competition.

Driver Certification RequirementsAll good drivers are also good communicators of what needs to be fixed on their car. Therefore, to drive, you must be certified in:

DrivingMechanics FTRC Fundamentals (may be required by team coach).

Mechanics Certification RequirementsA good mechanic understands his or her car not just as it sits on the table, but as it moves on the track. To fully be able to diagnose problems, keep it maintained and optimize setup, you must be certified in:

DrivingMechanics FTRC Fundamentals.

Race Engineer Certification RequirementsTo be a race engineer, you have to be certified in the FTRC Fundamentals which are basic STEM concepts and investigation skills. Though everyone is encouraged to get certified in all areas, to be a part of any race engineering sub-team, you must be certified in:

DrivingMechanics FTRC Fundamentals.

Race engineers include everyone working on: Chassis Setup & Mechanical EngineeringAerodynamics DesignCreative EngineeringAlternative Engineering

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Certification Requirements

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(10-11) Certification Process & Requirements FastTrack RC, Getting Started © 1080 Education Inc.

Mechanics Name: Jeffrey Farmer

Activity Logbook Page(s) Date Challenge Met Team Coach Initials

1. Identify Components 12 Oct - 15 PP2. Characterize Components 14 Oct - 18 PP3. Replace the Pulley Set

4. Replace Front Dogbone & Wheel Axle

5. Replace Rear Dogbone & Wheel Axle

6. Replace the Front Belt

7. Replace the Rear Belt

8. Modify the Suspension

9. Gears & Gear Ratio

10. Prevent Tire Pins from Falling Out

11. Motor Mount Screws Come Off

12. Motor, MF & Rear Differential Get Dirty

17. Electrical Connections Overheat

Sample Certification Table Mechanics

Sample Certificate Race Engineer

FastTrack RC Certif cate

Awarded To:

On This Date:

Awarded By:

Certified FastTrack RC Race Engineer

________________ Date


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Driver Certification

Team Coach Procedure

Administer the certification process as follows:

Decide if drivers need to be certified in Race Engineering.

Periodically (or frequently, your choice) observe as s/he completes the challenges in this section. Because an unskilled driver can cause real damage and ‘contaminate’ race engineering data with bad driving, it is important that drivers take a break (relinquish their turn on track) after violating the challenge terms (like driving out of the track more than twice). Because drivers should also be certified mechanics, after ‘losing their turn’, drivers should work on another task then come back to try again later. After each challenge is completed, review logbooks and provide feedback if necessary. When it is completed successfully, sign off on the Challenge table and move to the next step.

Section ContentsTeam Coach Procedure ...................................................................................11

Driver Certification Procedure .......................................................................12

Driver Certification Table ...............................................................................13

Driver Certification Challenges ......................................................................15Driver Certification Challenge #1: Turtle vs. Hare ..................................................................................... 15

Driver Certification Challenge #2: Slightly Faster ..................................................................................... 15

Driver Certification Challenge #3: Hit Your Marks, Drag Strip .................................................... 16

Driver Certification Challenge #4: U-Turn, Right & Left .................................................................... 16

Driver Certification Challenge #5: Oval, Standing .....................................................................................17

Driver Certification Challenge #6: Oval, Flying.............................................................................................17

Driver Certification Challenge #7: Slalom, One Way ..............................................................................18

Driver Certification Challenge #8: Slalom, U-Turn....................................................................................18


Your natural urge is going to be to drive fast and drive NOW! Our Ten80 team of engineer-educators has however designed a well-tested, centuries-old method of training that keeps your car safe and cultivates your patience and systematic thinking. Whether you are a NASCAR driver, football player, politician or FastTrack RC team member, these skills are just as important as aggressive competitiveness.

There is a parallel between being a good driver, engineer, business leader and martial arts master. Becoming a martial arts master, like becoming a professional driver, engineer or business executive, requires you perfect both the art and science of your craft.

The practices of yoga and martial arts are very popular today for fitness; however, they are also the cause of a lot of injuries. Consensus is that modern people don’t have the patience or create the time needed to learn them the way the ancients did. People used to learn by practicing until they ‘hit a wall’, then go home for the day and return later to try again. Eventually, your body opens up and you master that move. Only then do you graduate to the next stage of development.

To avoid injury to your kit and to help cultivate both the art and science of driving, you will follow this more ancient method in learning to drive a FastTrack RC car. Here is the procedure:

Run a driving challenge until:

You successfully complete the challenge or

Your track time is over,

You ‘hit a wall’ and violate one of the challenge rules

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Driver Certification Procedure

IF, THEN:

IF you successfully meet the driving challenge, THEN your team coach will review the acticity data, sign off on it and you can continue to the next one.

IF your track time is up, THEN pick up again where you left off next time it is your turn. Meanwhile, work on the next mechanics or race engineering certification activity. The one you choose to work on may depend on the tools that are available (i.e. 1:10 car, small car, neither).

IF you ‘hit a wall’ and violate the challenge rules, THEN relinquish your turn on track and work on the next mechanics or race engineering certification activity. The one you choose to work on may depend on the tools that are available (i.e. 1:10 car, small car, neither). When you’ve completed an activity, return to the driving challenge.

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Driver Certification Table

ChallengeTrack

Length (ft.)

Best time (seconds)

Total laps to meet target

Date Challenge

Met

Team Coach Initials

1. Turtle & Hare

2. Slightly Faster

3. Hit Your Marks, Drag Strip

4. Left U-Turn

4. Right U-Turn

5. Oval, Standing

6. Oval, Flying

7. Slalom, One Way

8. Slalom, U-Turn

School / Organization: __________________________________________________ City, State: _________________________________

FastTrack RC Team Name: ________________________________________________________

Driver Name: _______________________________________________________________________

By initialing each Challenge, the team coach certifies that he or she has reviewed the Challenge data for driver candidate. In signing below, the team coach certifies that the driver candidate has completed all driver certification challenges satisfactorily and is hereby certified to drive the FastTrack RC car for our FastTrack RC team.

By signing below, the driver candidate certifies that he or she has completed all driver certification challenges and that all data from the challenges was recorded accurately and truthfully.

Team Coach Name: __________________________________________________

Team Coach Signature: _________________________________________ Date: _________________

Driver Name: __________________________________________________

Driver Signature: _________________________________________ Date: _________________


Driver Certification Challenge: _________________________________________________________

Driver: Team Name: Date:

Surface: Car No: Track L:

Battery: Full Charge at start Geometry: Neutral, Stock Gear Ratio:

Units of Time: _____________ Units of Length: _____________ Units of Speed: _________________

Lap Enter from 3 people measuring time. Average of 3 Times

Average Speed

Lane Penalty?Time 1 Time 2 Time 3

Ex. 13.52 sec 13.75 sec 14.01 sec 13.76 sec 5.45 ft/sec No had to slow down

FastTrack RC Driver Certification Data TablePage _____ of ______


Driver Certification Challenge #1: Turtle vs. HareChallenge Introduction: Your strategy for some FTRC race events may require a slow and steady speed along the whole track. First you find the top speed around the tightest curve and you drive that speed the whole time. This would be a good one if the score rewards you for going farther than you are going fast --- it works because accelerating uses A LOT more energy than driving a constant speed. Your first challenge is to consistently drive at a very specific average speed.

Performance Target to Meet: Drive the drag strip 5 times in a row with a drive time that is between 14 and 15 seconds without slowing down along the track.

Drag Strip: Mark a start line then mark a finish line 75 feet away. Drive in a single line from start to finsh.

Challenge Violation: You complete the course in under 12 seconds OR drive outside of the track lanes more than once.

Strategy Suggestion: To begin with you’ll probably speed up and slow down a few times along the track. Figure out where to pull the throttle controller to give you a steady acceleration to hit the target time. Put in a ‘throttle block’ so you can hit that every time. See the image below.

Challenge Summary: Target Performance: Hit target speed 5 times in a row without slowing down

Track: Drag strip, 75 feet long (50 if not enough room)

Target Drive Time: 15 seconds (10 seconds on a 50 foot track)

Target Average Speed: 75 feet / 15 seconds = 5 feet per second (What is target speed on a 50 foot track?)

Start Type: Standing

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Driver Certification Challenges

Driver Certification Challenge #2: Slightly FasterChallenge Introduction: Transfer what you learned in Challenge #1 - prove you can control the FastTrack RC car. Repeat with a slightly higher target speed.

Performance Target to Meet: Drive the drag strip 5 times in a row with a drive time that is between 9 and 10 seconds without slowing down along the track.


Challenge Violation: You complete the course in less than 7 seconds OR you drive outside of the lanes more than once.

Strategy Suggestion: Again seek out the throttle position and insert a ‘throttle block’ so you can hit that every time.

Challenge Summary: Target Performance: Hit target speed 5 times in a row without slowing down

Track: Drag strip, 75 feet long

Target Drive Time: 10 seconds

Target Average Speed: 75 feet / 10 seconds = 7.5 feet per second


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Start Line

Finish Line

Acceleration

Constant Speed

L = 50-75 ft.t = drive time


Driver Certification Challenges (continued)

Driver Certification Challenge #3: Hit Your Marks, Drag StripChallenge Introduction: Now you can drive consistently. Begin this challenge driving consistently fast, and increase your speed until driving as fast as you can while staying consistent.

Performance Target to Meet: Drive as fast as possible, 5 times in a row with a spread of only 1 second. For example, you’ll meet target with times of 4.1, 4.4, 4.9, 3.9 and 4.3 seconds. The lowest and highest number are less than 1 sec. different.


Challenge Violation: You drive outside of the track lanes more than once or 15 laps without hitting target performance.

Strategy Suggestion: Start slow and speed up as you feel more comfortable with the speed. If graphing your drive time for every lap, you should see a consistent improvement toward the best possible time.

Challenge Summary: Target Performance: Drive fast and 5 times in a row with a spread of only 1 second

Target Drive Time: Your lowest

Target Average Speed: Your highest


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12

0 5 10 15 20 25

Ave

rage

Driv

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me

(sec

)

Trial/Lap Number

Drive Consistently: Set 1

Tim e

Driver Certification Challenge #4: U-Turn, Right & LeftChallenge Introduction: Now add a turn. There are a lot of paths to drive a U-Turn and over time you’ll gather data to show you which is best for a surface type. Today, your challenge is just to pick a path then drive it smoothly and consistently.

Performance Target to Meet: Drive the U-Turn 5 times in a row with a spread of only 1 second. For example, you’ll meet target with times of 7.1, 7.4, 7.9, 6.9 and 7.3 seconds. The lowest and highest number are less than 1 second different.

Once complete, do it again but this time, turn in the other direction. If you turned to the left first, now turn to the right.

U-Turn Track: Mark a start-finish line and place a turn-around point (cone, chair) 50 feet away. Drive from the start-finish line, around the point and back.

Challenge Violation: You drive outside of the track more than twice or 25 laps without hitting target performance.

Strategy Suggestion: Start slow and speed up as you feel more comfortable with the speed. Choose a drive path that feels good, put tape down to mark that path and attempt to hit the marks on every run.

Challenge Summary: Target Performance: Drive 5 times in a row with a spread of only 1 second; turning left then right.

Track: U-Turn, 50 feet long




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Driver Certification Challenge #5: Oval, StandingChallenge Introduction: Now add turns in both directions and drive the oval track consistently.

Performance Target to Meet: Drive the oval track 5 times in a row with a spread of only 2 seconds.

Challenge Violation: You drive outside of the track more than twice or 20 laps without hitting target performance.

Strategy Suggestion: Start slow and speed up as you feel more comfortable with the speed. Choose a drive path that feels good, put tape down to mark that path and attempt to hit the marks on every run.

Challenge Summary: Target Performance: Drive 5 times in a row with a spread of only 2 seconds

Track: Oval track with 50 feet between turn points



Start Type: Standing - do one lap, stop and repeat

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Driver Certification Challenge #6: Oval, FlyingChallenge Introduction: Now add drive many laps in a row without stopping.

Performance Target to Meet: Drive 5 laps on the oval track with a spread of only 1 second between laps. Do not stop between laps. Do not measure time for the first lap, only the 2nd lap and beyond.

Challenge Violation: Drive outside of the track more than three times or 20 laps without hitting target performance.

Challenge Summary: Target Performance: Drive 5 laps without stopping with a spread of only 1 second

Track: Oval track with 50 feet between turn points



Start Type: Flying - Do not stop after the first lap. Keep going for 5 timed laps (6 total, 1 to accelerate and 5 timed)

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Driver Certification Challenge #7: Slalom, One WayChallenge Introduction: Now drive a slalom track consistently.

Performance Target to Meet: Drive 5 laps on the slalom track with a spread of only 1 second between laps. Begin by driving only one direction (like a drag-strip with big pot holes).

Challenge Violation: Drive outside of the track more than three times or 20 laps without hitting target performance.

Challenge Summary: Target Performance: Drive 5 laps with a spread of only 1 second

Track: Slalom track, 50 feet long, laid out as shown below with 20 feet in between turn points.



Start Type: Standing - One way race

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40 ft

Start-Finish Line

60 ft20 ft

Driver Certification Challenge #8: Slalom, U-TurnChallenge Introduction: Now drive a slalom track consistently, in both directions like a U-Turn track.

Performance Target to Meet: Drive 5 laps on the slalom track with a spread of only 1 second between laps. Drive one-way then turn around like a U-Turn and drive back to the start-finish line.

Challenge Violation: Drive outside of the track more than three times, hit a turn point more than 5 times or 20 laps without hitting target performance.

Challenge Summary: Target Performance: Drive 5 times with a spread of only 1 second

Track: Slalom track, 60 feet long, with 20 feet between cones, both directions



Start Type: Standing at start line, around final turn-around point and back to start-finish line

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40 ft

Start-Line

60 ft20 ft

Finish-Line


www.FastTrackRC.com

Mechanics Certification



Periodically (or frequently, your choice) observe as s/he completes the challenges in this section. After each challenge is completed, review logbooks and provide feedback if necessary. When it is completed successfully, sign off on the Challenge table and move to the next step

Carefully stage a ‘broken’ car that needs repair. If s/he diagnoses and repairs it successfully, move to the next step.

Give a short test with a blank component identification form from this section. If 90% or better, move to the final step.

Give a final short test by presenting a pinion and spur gear. If s/he installs it and calculates the gear ratio properly, certify!

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Section ContentsMechanics Certification Procedure ...............................................................20

Mechanics Certification Table .......................................................................21

Mechanics Certification Challenge #1 ..........................................................22Mechanics Certification Challenge #1: Identify Components ........................................................22

Mechanics Certification Challenge #2: Characterize Components .........................................23

Mechanics Certification Challenges #3 - #8: Common FTRC Repairs .................................24

Mechanics Certification Challenge #9: Gear Ratio .................................................................................27

Mechanics Certification Challenges #10-#18: Preventive Maintenance ...............................29


As a mechanic, your team will count on you to keep the car in good operating shape and make emergency repairs when preparing for and during competition. You need to be very familiar with every part of the car because you can practice common repairs, but you need to be able to diagnose new problems that may arise.

To gain your certification, you’ll:

Complete each of the 18 challenges, documenting each one in your logbook and filling in the Certification Table after each one.

Pass a test in which your team coach will stage a problem with the FTRC car and you successfully diagnosis the problem and repair the car. If your team coach is unfamiliar with the car, another student will stage it with the oversight of your team coach.

From memory, complete the component identification diagram.

Pass a test in which you’re given sets of gears by your team coach and you successfully install them and record the gear ratio.

If you do not have a spare car, schedule time in between driving trials to work on these challenges.

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Mechanics Certification Procedure


Mechanics Certification Table

Activity Logbook Page(s) Date Challenge Met Team Coach Initials

1. Identify Components

2. Characterize Components

3. Replace the Pulley Set

4. Replace Front Dogbone & Wheel Axle

5. Replace Rear Dogbone & Wheel Axle

6. Replace the Front Belt

7. Replace the Rear Belt

8. Modify the Suspension

9. Gears & Gear Ratio

10. Prevent Tire Pins from Falling Out

11. Motor Mount Screws Come Off

12. Motor, MF & Rear Differential Get Dirty

13. Battery Wires Get Damaged

14. Radio Receiver Falls Off

15. Gears Grinding

16. Electronic Speed Control Wires Get Cut

17. Electrical Connections Overheat

18. Chassis Screws Fall Out



Mechanics Name: _______________________________________________________________________

By initialing each Challenge, the team coach certifies that he or she has reviewed the Challenge logbook entries for mechanic

candidate. In signing below, the team coach certifies that the driver mechanic has completed all mechanic certification challenges

satisfactorily and is hereby certified to maintain, repair and modify the FastTrack RC car for our FastTrack RC team.

By signing below, the driver candidate certifies that he or she has completed all mechanic certification challenges and that all

data and images from the challenges were recorded accurately and truthfully.

Team Coach Name: _____________________________________________________________________

Team Coach Signature: _______________________________________________________ Date: _________________

Mechanic Name: __________________________________________________________________________

Mechanic Signature: _______________________________________________________ Date: _________________


______ Motor ______ Spur Gear

______ Pinion Gear ______ Electronic Speed Controller

______ Servo ______ Adjust Toe Angle

______ Battery ______ Lower Control Arm

______ Frequency Chip ______ Body Mount

______ Shocks / Springs ______ Chassis

______ Tire ______ Upper Deck

______ Rear Drive Belt ______ Receiver

______ Front Drive Belt

Use your car to help match part names to the letter. Answer as many as you can then use the manual or internet search. to look up the rest. Find the answer key inside the cover of the ‘Getting Started’ booklet.

Mechanics Certification Challenge #1Identify Components of the FTRC 1:10 Scale Car

B

Q

E

F

A

C

I

JL

K

N

M (hidden from view; part

that rotates pinion gear)

P

G

H

D

O


Research each part or feature using your FTRC car manual, the internet and glossary of car parts. Download the manual and glossary at the FTRC team web site.

In your logbook: (1) Record its purpose. (2) Identify it on your FTRC car and sketch it.

Example Notebook Entry for the Suspension Arm (Control Arm)

Suspension Arm: A part of the car to which the uprights, hub carriers, shocks and/or steering knuckles are attached. It will swing up and down as it is absorbing bumps or lowering into dips. It is usually in the shape of a capital “A”, which is where the name “A Arm” comes from.

Features on the ControllerSteering Trim

Throttle Trim

AM Transmitter Crystal Also called the “Frequency Chip”

1.

2.

3.

Steering Dual Rate Nob is labeled D/R. What does D/R stand for? What is it for?

Servo Reverse Switch What do the abbreviations stand for? ST and TH, N and R

4.

5.

PartsElectronic Motor How many turns is yours? What is the trade-off between a higher vs. lower turn motor.

Electronic Speed Controller (ESC)

AM Receiver

Chassis

Suspension Arm Also called control arms

Gear Differential

Bulkhead

Upper Deck

Shock Tower

Dogbone Also called drive shaft

Wheel Axle

Front Urethane Belt

Rear Urethane Belt

Ball Bearing

Spur Gear

Pinion Gear

Heat Sink

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4.

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6.

7.

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11.

12.

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15.

16.

17.

Mechanics Certification Challenge #2Characterize Features & Components of the FTRC Car & Controller


Use the FTRC car manual to practice each of these common repairs. Take the part off and replace it (or fix the broken part). Take and paste/tape pictures into your logbook so your team coach can certify the repair was completed and to help you do that repair faster in the future.

#3. Replace the Pulley SetUse your hands to turn the wheels (while car is off) and watch how the parts move. Follow instructions on page 11 of the car manual to remove then replace the pulley set then. Make sure to test that it works right (no grinding, skipping, etc.) when done.

#4. Replace the Front Dogbone and Wheel AxleFollow instructions on page 12 of the car manual to remove then replace the front dogbone (also called drive shaft) and wheel axle.

This repair requires that you remove lots of parts so take pictures as you remove them so you know how to replace them.

Make sure to test that it works right (no grinding, skipping, etc.) when done.

#5. Replace the Rear Dogbone and Wheel AxleFollow instructions on page 13 of the car manual to remove then replace the rear dogbone and wheel axle.

#6. Replace the Front BeltFollow instructions on page 14 - 16 of the car manual to remove then replace the front urethane belt. As you replace the parts, pay close attention to the direction. It matters!

#7. Replace the Rear BeltFollow instructions on page 17 - 18 of the car manual to replace the rear urethane belt.

Pulley Set

Wheel Axle

Dogbones or Drive Shafts

Front Urethane Belt

Mechanics Certification Challenges #3 - #8Common FTRC Car Repairs

(10-11) Mechanics Certification FastTrack RC, Getting Started © 1080 Education Inc.

#8. Modify the SuspensionWatch the FTRC Pi Note video on chassis geometry then:

Read descriptions below and page 19 of the car manual.

Practice changing each type of setting. If you are a certified driver, perform the U-Turn after each change and record the drive time and how it felt. If you are not a certified driver, get a team-mate to test after changes. Record his/her drive time and comments.

8A. Camber

Seen from the front and rear of the car, the angle of the tires in relation to the ground is called the camber angle. Tires that are perfectly perpendicular to the ground (90 degrees) are at ‘zero camber’. If the tops of the tires lean toward each other, the tires have negative camber. If they lean out, the tires have positive camber.

Camber links on the FTRC car are made of a turnbuckle (threaded rod) and ball cup at each end. The camber link fits into one of three holes at the bottom of the Shock Tower labeled E, C and D in the car manual.

Change the camber angle on the tires by connecting the camber link to different holes.

8B. Shock Pick-Up Points

Change the spring tension and distance the shock travels up and down by changing the pick-up points. Pick-up points are holes the shock body connect to.

In the front suspension, the top of the shock body fits into one of three holes labeled 1 - 3 in the manual.

In the rear suspension, the top of the shock body fits into one of four holes labeled 1 - 4 in the manual.

The bottom of the shock body fits into one of two holes on the lower control arm (also called the suspension or ‘A’ arm) labeled A or B in the car manual.

Change the pick-up points to see how the shock tower and spring change.

1.

2.

Camber Links

Shock Tower Body

Front Shock Pick-Up Points

Camber Angle

Mechanical Certification Challenges (continued)


Toe Angle

Toe angle refers to the direction the tires face when steering is straight ahead and the car is seen from above. There are both front and rear toe angles.

Usually, most drivers use one or two degrees of toe-in on their car’s front wheels. The FTRC car comes with two or three degrees of toe-in.

Slight toe-in (1° or 2°) at either end helps to stabilize the car, but higher toe-in (3°, 4° or more) reduces your speed because tires are scrubbing the track. There is a trade-off in stability and speed.

Toe-out on the front end gives increased steering which is useful for quick turn-ins, but you’ll sacrifice cornering speed and straight-line stability. Toe-out at the rear gives twitchy handling and is NOT recommended.

To adjust the toe of the front wheels make the tie rods longer (toe in) or shorter (toe out) and measure the toe angle of the front wheels with each adjustment.

Rear Toe-in Block

Front C-Hub & Knuckle Arm Set (4˚ and 6˚)

Rear hub Set (2˚ and 3˚)

Zero Toe (Neutral)

Toe-Out

Adjust front toe angle by making tie-rods longer or shorter.

Front Tie RodAdjust Here



1. Read about gears and gear ratios below. 2. Change the gears on your car using the table on the next page (or make one in your notebook) to record which gears you use and calculate the gear ratio.

Pinion Gear

About Gears and Gear Ratios

There are two gears in most RC cars, a spur gear and a pinion gear. The pinion gear is attached to the motor shaft and is smaller than the spur gear. The spur gear is attached to the wheels and is larger than the pinon gear.

The choice of gears will set your car’s top speed and acceleration rate. A higher acceleration rate (zippier car) means you have a lower top speed. Higher top speed means lower acceleration.

For an “open course” of sweeping turns you’d install a big pinion gear and a small spur. This combination gives a high top speed for straight-aways but the trade-off is lower acceleration out of the corners.

There are two measurements for each gear: Pitch and Teeth. The pitch of a gear is the distance between teeth. For two gears to mesh they must have the same pitch. A common FTRC spur gear is 48 P 78 T which means 48 pitch and 78 teeth.

You usually compare gear sizes using gear ratios. The gear ratio is the relationship between the number of teeth on two gears that are meshed together. In the picture to the left, the spur gear may have 72 teeth and the pinion gear, 28 teeth. The gear ratio is therefore:

For every one revolution of the pinion gear attached to the motor, the spur gear attached to the wheels makes 1/2.57, or 0.39, revolutions.

7228

= 2.57 : 1Gear Ratio =

Spur Gear

Some gears have the number of teeth printed right on them. If not, mark the 1st tooth with a piece of tape and count.

Pinion Gear with 31 teeth.

Set screws are on the side of a pinion gear.

High Top Speed

High Acceleration

Low Acceleration

Low Top Speed

Gear Ratio

Mechanics Certification Challenge #9Gears & Gear Ratios


Changing Gears

Page 8 in the FTRC car manual shows you how to remove and replace spur and pinion gears. To keep gears from grinding, make sure the gears mesh properly by adjusting the motor position.

Make a table like the one below in your notebook.

Using the gears you have, change them out. For each new set, record the number of teeth and calculate the gear ratio.

Top: Allen Wrench in kit Bottom: Integy Hex Wrench, 1.5mm

The Right Tool

Figuring out the right tool for the job is an important skill to acquire. Changing gears is a good example. The typical Allen wrench like the one in your kit, is torsionally too soft to remove the set screws in the pinion gear. This means that when you turn it, the key twists rather than removing the screw. The In-tegy Tool Hex Drivers are one example of a nitride hardened driver that will effectively remove the screws. Be SURE to use the correct size. A 1 mm hex can strip a 1.5 mm set screw.

Gear Ratio Chart

Spur GearNumber of Teeth

Pinion GearNumber of Teeth

Gear RatioSpur Gear : Pinion Gear

If you have 2 spur gears and 2 pinion gears, you

can get 2 x 2 = 4 different gear combinations.

If you have 3 spur gears and 2 pinion gears, how many gear combinations

can you get?



You don’t just fix things when they’re broken, you should work to prevent things from breaking. This kind of activity is called ‘preventive maintenance’. Do the activities listed here and be prepared to

demonstrate them as part of the certification process.

#10. Prevent Tire Pins from Falling Out(FTRC car manual p. 10) When changing tires, you remove the flanged lock nut and tire. Underneath the tire is the shock cap and a silver pin. You’ll find that the silver pins fall out pretty easily. Ahead of a race, you can consider using a light glue to adhere the pins. Don’t use something too strong because you’ll have to remove them later for maintenance.

#11. Motor Mount Screws Come OffThere are two purple plates that hold the motor in. There are four 3 mm mounting screws on each one that come loose a lot. Locate them so you can check after each set of runs.

#12. Motor, Mounting Frame & Rear Differential Get Dirty, Motor Burns UpWhen you drive the car, the magnetic motor picks up stuff from the track. Look out for dust, paper clips, carpet fuzz and other things that can overheat the motor and ultimately ruin it. If you fail to keep these parts clean and the gears are resisting movement, the motor will put out maximum current and eventually BURN UP! Search the internet for articles and videos on how to clean the motor using Q-tips and/or compressed air. Clean the car after every set of runs by team driver(s).

#13. Battery Wires Get DamagedThe battery wires can drag on the ground when you drive. That’s bad for a lot of reasons. Make sure you get them out of the way each time you install the battery. Fix this by looping them under the motor leads (the wires that go from speed control to motor).

Standard Battery Wire Routing Modified Battery Wire Routing

Mechanics Certification Challenges #10 - #18Preventive Maintenance & Diagnostics


#14. Radio Receiver Falls OffIt just happens. Always does. Secure it to the upper deck with a simple zip tie.

Zip Tied Receiver

Rerouted Speed Control Wires

#18. Chassis Screws Fall OutTurn the car over. There are several phillips screws that will eventually fall out. There are two suggestions to handle this:

Replace the Phillips screws with Hex Socket Screws

Secure the screws with green Loctite. Do NOT use red because you’ll never get the screws out without cracking the chassis around them.

1.

2.


#17. Electrical Connections OverheatThere is a lot of resistance in the electrical connections so heat builds up quickly, especially those between the motor and ESC. Most electronics can handle higher intermittent loads (current jumps up then back down quickly) better than they can sustained high currents.

There are usually some insulated wires inside the electronic systems and that insulation melts when the wires are hot. If those bare wires touch then the system shorts out and you’re done for!

Frequently check to see that they are tight because they’ll overheat if loose. If possible, replace them with soldered connections (splice in a heavy gauge wire if necessary).

#15. Gears GrindingAlignment and gear meshing is critical. The gear teeth should overlap each other by about two-thirds of tooth depth, but not bottom out. If the spur gear is white then you can see if the wear from the pinion is uniform over the gear tooth width. Be prepared to diagnose this problem and fix it.

#16. Electronic Speed Control Wires Get CutWhen you quickly open the battery compartment (like during a Pit Stop), you can easily cut the speed control wires. This one is a little more advanced, but you should re-route them behind the controller.


www.FastTrackRC.com

FTRC Fundamentals Certification



Give the pre-assessment from the Curriculum & Program Design insert.

Periodically (or frequently, your choice) observe as s/he completes the Math2Go Challenges After each is completed, evaluate using the Challenge Assessment Rubric and sample Think About It answers in the ‘Curriculum’ insert. When it is completed successfully, sign off on the Challenge table.

After all challenges are completed successfully, re-administer the pre-assessment as a post-assessment.

Observe as s/he works with a driver on the Chassis Setup Investigation, Hitting Your Marks. Evaluate the data table, calculations and graphs. If completed successfully, certify!

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Section ContentsTeam Coach Procedure ...................................................................................31

FTRC Fundamentals Certification Procedure ...............................................32

FTRC Fundamentals Certification Table .......................................................33

Challenge Assessment Rubric ........................................................................34

Professor Pi Notes on FTRC Fundamentals ..................................................35Good Investigation Practices (GIP) .............................................................................................................35

Trial & Model ..................................................................................................................................................................37

Background on Math2Go Challenges ...........................................................38

Math2Go Challenge #1: How Fast is Fast? ..................................................39Overview & Objectives ..........................................................................................................................................39

Prepare for the Challenge ..................................................................................................................................39

Procedure ........................................................................................................................................................................... 41

Review Averages..........................................................................................................................................................42

Organize and Understand Data ....................................................................................................................43

Data Sheet ........................................................................................................................................................................46

Think About It Questions ....................................................................................................................................48

Math2Go Challenge #1: How Fast is Fast? ...........................................................................................48

Math2Go Challenge #2: Are We There Yet? ...............................................49Overview & Objectives ..........................................................................................................................................49


Procedure ........................................................................................................................................................................... 51

Organize and Understand Data ....................................................................................................................52

Think About It Questions ....................................................................................................................................57

Math2Go Challenge #3: Optimal Power .....................................................58Overview & Objectives ..........................................................................................................................................58

Pose the Challenge ...................................................................................................................................................58

Review Speed, Work, Power and Power ................................................................................................59


Procedure ........................................................................................................................................................................... 61

Organize & Understand Data .........................................................................................................................62

Analysis Step 1: Model Time, Speed & Weight ...............................................................................64

Analysis Step 2: Model Weight, Work & Power ............................................................................68

Data Sheet ........................................................................................................................................................................72

Optional Calculation Sheet ................................................................................................................................73

Think About the Data .............................................................................................................................................76

FTRC Fundamentals Certification Challenge #4: Gear Ratio ......................77


FTRC Fundamentals Certification Procedure

There are a literally tens of millions of ways to set up and modify your FastTrack RC to perform optimally in race events. The world is waiting for new creative ideas and clever yet viable developments, especially in the field of alternative energies. No matter which type of FastTrack RC project or investigation you’re working on, there are some fundamental skills and concepts you must possess. This certification indicates you have demonstrated them. From there, it is up to you to apply them in new and interesting ways.

This certification is suggested if you are engaging in:

Chassis Setup Investigations

Mechanical Engineering Projects

Aerodynamics Design

Creative Engineering Projects

Alternative Engineering Projects

To gain your certification, you’ll:

Read the Professor Pi Notes on FTRC Fundamentals

Do a pre-assessment activity (from the Curriculum & Program Design Insert)

Complete the three Math2Go Challenges, documenting each one in your logbook, answering the ‘Think About It’ questions and filling in the Certification Table after each one.

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1.

2.

3.


Challenge Logbook RequirementsLogbook

PagesDate Met

Team Coach Initials

Pre-Assessment Complete sections 1 and 2•

Math2Go Challenge #1

Completed data table with circles, etc.

Graph with three series

Answers to Think About It Questions

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Completed data table

Graph of distance vs. time with best-fit line

Graph of distance vs. speed with best-fit line


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Completed data table from testing at least 3 different weights.Graph of time vs. weight with best-fit lineGraph of speed vs. weight with best-fit line

Gr. 6-8: Slope of the best-fit linePre-Algebra: Speed of a zero-weight car

Algebra: Equation of the lineGraph of weight vs. work with best-fit lineGraph of weight vs. power

Gr. 6-8: Turn around point and best scoreBonus, Algebra: Quadratic equation


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Gear Ratios Completed gear ratio table•

Hit Your Marks Completed table and learning curve graph•



Race Engineer’s Name: _______________________________________________________________________

By initialing each Challenge, the team coach certifies that he or she has reviewed the Challenge data for race engineering candidate. In signing below, the team coach certifies that the race engineering candidate has completed all driver certification challenges satisfactorily and is hereby certified to work on race engineering activities for our FastTrack RC team.

By signing below, the race engineering candidate certifies that he or she has completed all certification challenges and that all data from the challenges was recorded accurately and truthfully.

Team Coach Name: __________________________________________________

Team Coach Signature: _________________________________________ Date: _________________

Race Engineer’s Name: __________________________________________________

Race Engineer’s Signature: ______________________________________ Date: _________________

FTRC Fundamentals Certification Table

FastTrack Racing Challenges © 1080 Education Inc.

Process Not Satisfactory

Below Expectations

Meets Expectations

Excellent Profes-sional

Rating

1. Has clear vision of final product 1 2 3 4 5

2. Properly organized to complete project 1 2 3 4 5

3. Managed time wisely 1 2 3 4 5

4. Acquired needed knowledge base 1 2 3 4 5

5. Communicated efforts with teacher 1 2 3 4 5

Problem Solving

6. Used Data during investigations to make decisions

1 2 3 4 5

7. Adequate sample size used 1 2 3 4 5

8. Conclusions accurately based on data 1 2 3 4 5

9. Demonstrates comprehension of content material

1 2 3 4 5

10. Limitations of data discussed 1 2 3 4 5

11. Measurements/Observations are accurate 1 2 3 4 5

Teamwork

12. Helping: The teacher observed the students offering assistance to each other

1 2 3 4 5

13. Listening: The teacher observed students working from each other’s ideas.

1 2 3 4 5

14. Participation: The teacher observed each student contributing to the project.

1 2 3 4 5

15. Persuading: The teacher observed the students exchanging, defending, and rethinking ideas.

1 2 3 4 5

16. Questioning: The teacher observed the students interacting, discussing, and posing questions to all members of the team.

1 2 3 4 5

17. Respecting: The teacher observed the students encouraging and supporting the ideas and efforts of others.

1 2 3 4 5

18. Sharing: The teacher observed the students offering ideas and reporting their findings to each other.

1 2 3 4 5

Outcome Didn’t Complete

Was Not

Competitive

Continued Attempts to

Improve

Very Competitive

Scores

Won the Challenge

19. Clearly Defined Goal for Challenge 1 2 3 4 5

20. Obtained Goal 1 2 3 4 5

TOTAL SCORE

PERCENT SCORE (Total / 100)

To complete a challenge, you should receive a score of 85% or more. Repeat the challenges, learn and improve until you achieve that score. Your event scores should increase every time too because your data set is growing.

Challenge Assessment Rubric


Here are a few definitions and tips on running investigations. Read carefully and embody these ideas from the very frst moment. Once bad habits are formed, they’re hard to break ... so form the good ones instead.

Logbooks: Team & IndividualEverybody on a team has his or her own log book. Though you work as a team, each person MUST record the team data. When one person is responsible for submitting team data, all members must initial the version being submitted so that EVERYONE takes responsibility for the outcomes.

Never Miss a Chance to Collect Data: Even if you’re ‘messing around’, take advantage of all that energy you’re wasting (yours and the battery’s). Keep stopwatches, measuring tapes, paper and pen with you to make sure you can easily capture information anytime. Even if you make a bad run, record the time and put down a note about why the time was ‘off’. Even bad runs drain the battery and you should know how many you’ve made.

Control Variables:In every investigation, you examine the effect that changing only ONE variable has on performance. That means you need to pay very close attention to making sure that everything other than that one variable stays exactly the same between trials in the investigation.

Once you’re more comfortable with problem solving or begin using ‘multi-variant’ software, you can change several variables at a time.

Pay Attention to Energy Use:Every run drains the battery a little. The drain will have little effect until it hits a critically low level. After it gets that low, performance will plummet (drive times get really long). Keep in mind that this happens and recharge when it does.

Good Measurement Practice (GMP): Account for human error by taking several measurements for each trial then finding their average value. Usually, you run any trial more than once. For example, 3 trials with 3 measurements in each will give you 9 total measurements for any setup.

Take Care of Your Tools: Make sure your driving surface is swept clean of debris. The motors are magnetic so pick up metal along the way. Dust and rocks can actually cut drive belts, break control arms and/or overheat the system. Use the Preventive Maintenance & Repair guide to make sure your car stays in good working order. For example, make sure the mounting screws aren’t coming unscrewed after every set.

Professor Pi Notes on FTRC Fundamentals

Good Investigation Practices (GIP)

(10-11) Race Engineering Certification FastTrack RC, Getting Started © 1080 Education Inc.

Whether you’re a professional scientist, motorcycle designer or FastTrack RC team, collecting, keeping and organizing your data is critical. Below is the anatomy of a data table like the ones you’ll use in these Chassis Setup Investigations.

Put GIP Into Practice

Definitionsdata: factual information such as measurements that is used as a basis for reasoning, discussion, or calculation. Information you collect like gear ratio and drive time is data.

trial: a single event or test

set: a collection of identical trials. You do more than one to account for human error.

variable: a symbol that stands for a value that may vary. The symbol can be letters like X, Y, t, V, d or spelled-out words like ‘gear ratio’.

Sets & Trials

Trials are individual tests, or runs. A set is made up of several identical trials (‘do-overs’) aimed at making sure you get a good average measurement. For example, if you’re testing to find the best tire, one set would include 4 trials (runs) with a foam tire and a second set would include 4 trials with a rubber tire.

Table Rows & Columns

Make sure to name each trial (a single event) then write all the data from that one trial in the same row. Information for the next trial (a ‘redo’) goes on the next line.

In the example below, Time 1, Time 2 and Time 3 are three different times that three different people measure while watching the same event. If you only have two people measuring time, leave the cell under Time 3 blank.

Trial Tire Type Time 1 Time 2 Time 3 Avg. Time

Foam - 1 Soft Foam 6.21 sec 6.34 sec 6.15 sec 6.23 sec

- 2 “ 6.13 6.12 6.20 6.15

- 3 “ - 4 “

Rubber-1 Slick Rubber

-2 “-3 “

Notes: Write down things that may help you understand the data. For example, if you realized half way through that a tire was loose, write it here to help explain odd drive times.

A Set of four identical runs {

Record all information someone else would need to recreate what you’re doing. What gears are

installed? What surface? Etc.

As you’re learning to problem solve, change only one variable between sets. In this example, only the tires are different.

{Record units in at least one place. Use the same ones for the whole inves-tigation.

You can say ‘ditto’ with a quotation mark. It the info from above is copied here. You can also use an arrow, but don’t get sloppy!

Everything in a row is from the same run.

This is the average of Time 1, 2 and 3 from the same trial.

Professor Pi Notes on FTRC Fundamentals (continued)


It’s natural. We want to drive the RC cars as fast as possible as soon as possible! Performance Now!

The problem is, there are about 14 million different ways to set up your FastTrack RC car and a very small fraction of them will give high performance in a race. If your plan to find the best possibilities is trial and error, you’re likely to meet with frustration rather than the checkered flag. You’re playing the technology lottery and the odds against you are 14 million to 1.

In FastTrack RC we want everyone to be as innovative as he or she can be. Think outlandishly. Think outside the box, outside the sphere and the pyramid too. The real thrill of science, engineering and technology is to tackle something that seems “impossible”; whether it is the ability to fly, orbit the earth, talk to someone 15,000 miles away or decrease your lap time by 1/10th of a second.

Pushing the envelope of what’s possible means there are lots of failures. Every good engineer has a closet full of stories about building things that crashed, blew up or caught fire (even better if it happens all at once); however, why things fail matters a lot. There is a huge difference in seeing all the wheels fall off your RC car because you:

Simply drilled a bunch of holes in it to lighten the load, or

Went just 8% too far in your plan to improve the ratio of sprung to un-sprung weight

The former makes you want to give up; the latter sends you back to calculating because you know what happened, you know what to do next and you know your car will outperform the others (and maybe you’ll get another spectacular wreck in the bargain)!

To make the seemingly impossible happen, we need to encourage one another to ask questions and investigate to find answers; to design for improvement. We need to create a culture that celebrates incremental progress (baby steps forward); a culture of finding the best possibilities through trial-and-model. Trial-and-model doesn’t mean you avoid errors. It means your results aren’t considered errors because you’re building something through them: a model of your car’s performance. You’re finding answers to the endless array of questions instead of just more questions.

So how do you go from seat-of-the-pants playing to leading the pack? Start simple. Start by learning the basics of performance that matter most (see the Race Engineering Certification activities) . Model speed and acceleration for various gear ratios. Once you understand the things that impact performance the most, investigate more subtle input like suspension and chassis geometry settings (c-rings in the springs, suspension points and toe settings). You’ll improve greatly in the beginning then continually squeeze out improved performance.

Start simple and start now. Build a dynamic team of innovators, dreamers, rigorous thinkers and achievers. Start channeling your innovation; I think you’ll be amazed at what you can achieve in just six months.

A.

B.

Having things fail when you don’t know why is frustrating. Having things fail in a calculated pursuit of excellence is inspiring; it drives you to work even harder.

- Jeff Thompson, a.k.a. Professor Pi of Ten80 Education

Changing things on the car just because they can be changed usually gets you nowhere…and gets you there over and over and over.

Trial & ModelProfessor Pi Notes on FTRC Fundamentals (continued)


What is Math2Go?Math2Go is a ‘feeder league’ for the FastTrack Racing Challenges. It is a series of Challenges that students begin using as early as the 3rd grade and continue using through Calculus. In Math2Go Challenges, you’ll use a 1:16 or 1:18 scale that is A LOT easier to handle than the larger 1:10 scale RC car. You can get much cleaner data from these ‘small cars’ which means you will be better prepared to make great improvements in performance once you begin working with the FTRC car.

Background on Math2Go Challenges

You’ll find that graphs tell stories if you speak the language of mathematics!

(09-10, 2-B) Fundamental FTRC Skills

How does Math2Go Work?Why do you collect data? You collect data to solve problems; to answer questions. In these activities, you’ll be given a question to answer or a scenario to optimize using the Math2Go car.

In the Math2Go Challenges, you will ultimately set up an experiment in which you vary the weight of your car, placement of the weight or length of the track. These terms are used frequently in Math2Go experiments so make sure you understand them by the time you complete the 2nd challenge:

Independent Variable: What YOU change is called an independent variable. X-axis of graphs.

Dependent Variable: The measured outcome is the dependent variable; its value depends on the choice you made in setting the independent variable. Y-axis of graphs.

In every Challenge, the best approach is to gather enough data to make a graph. The graph describes how your independent variables effect the outcome of your investigation. In other words, making a graph will help you understand what’s going on and what you should do to increase your scores.

Gathering data for at least three points is often the fastest way to make a graph that helps you answer the question. For example, if you are changing the weight of the car and measuring run-time, make a graph with weight on the x-axis and time on the y-axis. Test the full range of possibilities by measuring time for:

one car with very little weight,

one car with a lot of weight,

a couple of cars with a weights somewhere between the two extremes.

•

•

•

•

•


Math2Go Challenge #1: How Fast is Fast?

Overview & ObjectivesEssential Question: How long does it take to go 180 inches?

Objectives: To compare three different methods of motion: walking, running, driving the car.To determine the range of times required to walk, run, and drive a 180 in. track.To gain an understanding of the concept of averaging data.

Time Requirement: 2 x 60-minute periods

1 x 60 min: Introduce and gather data.

1 x 60 min: Graph data and discuss. Homework Option: Answer questions in logbooks.

Materials:Math2Go Small CarTape measureTape / ChalkStopwatches, 3 or more

Additional Resources:Presentation (PPT): How Fast is Fast? (FTRC Team Web Site)VIDEO: How Fast is Fast? (FTRC Team Web Site)Sample Answers for Think About It questions (Curriculum Insert)

Final Product to Deliver:(1) Logbook entries with raw data, notes, graphs and conclusions. Your performance on this challenge will be evaluated using the Challenge Assessment Rubric. (2) Answers to Think About it Questions.

•••

•

•

••••

•••

Prepare for the ChallengePose the Challenge: How fast is your car? How fast do you walk? You have the idea that one is faster than the other, but a less than / better than comparison isn’t good enough in science. You have to measure and get real numbers. As a warm-up activity to get used to using measurement tools and data tables, you are challenged to:

Measure the top speed of your RC car, Measure the speed of walking Measure the speed of you running top speed.

You’ll need to recruit a few volunteers to help measure time; it won’t take long.

1.2.3.


Layout a Race Track:

Use chalk or tape to mark a Start line.

Mark a Time-Start line where you will begin to measure time. Your car should be at top speed once crossing this line. For small RC cars, it should be 8 - 15 feet in front of the Start line.

From the Time-Start line, measure and mark a Finish line 180 inches away.

1.

2.

3.

Listen to the engine to make sure the car hits top speed before crossing the Time-Start line.

‘t’ stands for time‘L’ stands for track length

AccelerationTop, Constant Speed

time, t = 0 sec

Time-Start Line

Drive Start Line

Finish LineL = 180 inches

Math2Go Challenge #1: How Fast is Fast? (continued)

Track Length: 180 inches

Set 1, Walker: Terri

Trial NameTime 1

(sec.)

Time 2

(sec.)

Time 3

(sec.)Average Time

(sec.)Trial Range

(sec.)

Walk - 1Walk - 2Walk - 3

Set 2, Runner: Terri

Trial NameTime 1

(sec.)

Time 2

(sec.)

Time 3

(sec.)Average Time

(sec.)Trial Range

(sec.)

Run - 1Run - 2

Prepare Data Tables:

Make a copy of the data table and tape it into your logbook, recreate your own version in the logbook or build the table in a spreadsheet. Sample table is at the end of this challenge.

Enter notes about the experiment like track length, walker name, etc.

1.

2.

The stopwatch here displays hours : minutes : seconds. hundredths of a second

Read your stopwatch using the decimal point. Any number after the last decimal point is part of a second, called a fraction of a second. This stopwatch shows two numbers to the right of the decimal that represent hundredths of a second.

Start and stop the timer by pressing the same button, Start 1 as shown here.

Reset the timer to zero by pressing the opposite button, Start 2 as shown here.

1.

2.

0:00:02.34

This watch shows 2 seconds and 34 hundredths of a second. This value represents two full seconds and one fraction of a second.

Practice Using a Stopwatch:


Procedure

1 x Walker / Runner / Driver: Stand at the Start Line.

2-3 x Timers: Set Stopwatches to zero.

Data Collector: Prepare data tables

READY! SET!

GO!

Walker / Runner / Driver: (1) Set One: Start casually walking. Try to walk the same speed along the track. (2) Set Two: Start running and don’t slow down until you cross the finish line. (3) Set Three: Start driving and do not stop until you cross the finish line.

2-3 x Timers: Start the timer when the walker, runner or car crosses the Time-Start line. Stop the timer when she/he/it crosses the Finish line.

Data Collector: Watch to ensure the timing is done correctly. Assure the quality of data.

RECORD

Walker / Runner / Driver: Rest.

2-3 x Timers: Read the times from stopwatches to the data collector.

Data Collector: Enter measurements and units from each timer into the table. For one trial, all times go into the same row.

REPEAT

In Science, once is never enough. Repeat the test for a total of 3 trials using the same walker, runner or driver.

CALCULATE

Data Collector: Calculate the average walk, run or drive time for each trial. You may first need to review averages as outlined later in this section.

Recruit 2-3 people to measure time. Anyone can do the walking, running and driving. The race engineering candidate must be the data collector (collect, record and analyze the data).

Follow this procedure for three sets. In the 1st set, walk the track. In the 2nd set, run the track and in the 3rd set, drive the ‘small’ RC car along the track.



Review AveragesCalculate then Check for “Reasonableness”

An average is a single number that represents a set of unequal numbers. A batting average is one popular use of this helpful number. One hitter will take his or her turn at the plate many times; however, you never hear an announcer list the result of each one. They count a hit as 1 and a non-hit as a zero and find the average for every at-bat. Baseball statisticians calculate the average just like you will for drive times.

To find the average for a set of quantities, calculate the sum of all quantities then divide that sum by the number of quantities in the set. Here is the formula.

Take the baseball batter and remember that a hit is equal to 1 and a non-hit is equal to 0. The batter’s record for the last ten at-bats is as follows: 0, 1, 0, 0, 0, 1, 0, 0, 1, 0. The batters average is calculated by adding all of the numbers then dividing by 10.

Now its your turn ‘at bat’. Practice calculating an average then check your answer to make sure that it is reasonable.

Find the average of this set of numbers: 3.1, 3.6, 3.5.

Check the reasonableness of your answer using the seesaw test. Once you understand what a reasonable answer is, you can do this test in your head.

Make a number line for the numbers between 3 and 4. Because the numbers you’re averaging are precise to the tenths place, divide your line into tenths.

Put two dots on the line; one for the smallest and one for the largest of the numbers you’re averaging.

Place an arrow along the line for the average.

Check that the average falls between the smallest and the largest of the numbers.

1.

2.

3.

4.

5.

6.

values)of (number

values)of (sumAverage =

0.310

0)10010001(0Average =

+++++++++=

Use The Seesaw Method to Check for Reasonable Averages.


3 3.5 4


Track Length: 180 inches

Set 1, Walker: Terri

Trial NameTime 1

(sec.)

Time 2

(sec.)

Time 3

(sec.)Average Time

(sec.)Trial Range

(sec.)

Walk - 1 4.01 4.11 3.98 4.03 0.13Walk - 2 4.09 4.29 3.88 4.09 0.41Walk - 3 4.34 4.38 4.06 4.26 0.32

Set 2, Runner: Jeannie

Trial NameTime 1

(sec.)

Time 2

(sec.)

Time 3

(sec.)Average Time

(sec.)Trial Range

(sec.)

Run - 1 0.74 0.77 0.68 0.73 0.10Run - 2Run - 3

Set 3, Driver: Beverly

Trial NameTime 1

(sec.)

Time 2

(sec.)

Time 3

(sec.)Average Time

(sec.)Trial Range

(sec.)

Drive - 1

Organize and Understand Data

Calculate the average time for each walking, running & driving trial (a spreadsheet would help).

Calculate the average time for walking by finding the average of all times for walking. You can also do this by finding the average of average times from each trial (If it sounds confusing, just think about it).

Repeat by finding the average time for running and driving.

Calculate the Trial Range to see how much measured times can differ even when people are looking at the same event. The Trial Range is equal to the minimum time subtracted from the maximum time in a trial. Trial Range = Maximum Time - Minimum Time

Example: Trial Range for Walk-1 = 4.11 - 3.98 = 0.13 sec.

1.

2.

3.

4.

Average = (sum of values)

(number of values)Average Time

for trial, Walk-1

(4.01 + 4.11 + 3.98)

3= 4.03 sec.=

Average Time, Walking

(4.03 + 4.09 + 4.26)

3= 4.13 sec.=

Put a circle around the minimum average time for each set.

Put a square around the maximum average time for each set.

5.

6.



Create a GraphIllustrate Your Findings Visually

† Blank graphing pages are available on the FastTrack RC Team Web Site for reprint

Graphs are used to understand information by making a picture out of numbers. Use graph paper or the sample graph at the end of this challenge to plot the times from each trial.

Label the horizontal line at the bottom of your graph, the X-axis, with the trial numbers.

Label the vertical line along the left side of your graph, the Y-axis, with a range of times in seconds. Repeat the same process, but build your number line vertically.

Plot the first point to show one of the time measurements from trial one for walking. Look to the trial number at the bottom, then move up in a straight line from that point until you are even with the correct time on the left. Use a circle to mark the point that’s above the trial number and even with the time. If possible, choose a color to use only for this set.

Label the series of points as Set 1: Walk.

1.

2.

3.

4.

Data PointSeries Label: Set 1X-axis Value for Trial Number = 1Y-axis Value for Time = 4 seconds

This point shows that trial number 1 of Set 1 had a time measurement of 4 seconds.

•••

Measured Times to Walk, Run and Drive 180 inches

0

1

2

3

4

5

6

7

0 1 2 3 4Trial Number

Tim

e (s

econ

ds)

S et 1 : W a lk

s)

X - axis

Y - axis

Series Label

Graph Title

Choose the lowest and the highest value that should be shown on the line. The lowest is often zero but doesn’t have to be. The highest number can be higher than your maximum measured value.

Make a number line along the bottom that counts from the lowest to the highest number. In this example, you can fit a line for all whole numbers from zero to four, but this isn’t always true. If the difference between the first and last number on the line is large, you will need to group the numbers to fit them all onto the axis. For example, you might show only multiples of ten.

A.

B.




0

1

2

3

4

5

6

7


Tim

e (s

econ

ds)

S et 1 : W a lk

S e t 2 : Run


0

1

2

3

4

5

6

7


Tim

e (s

econ

ds)

S et 1 : W a lk


0

1

2

3

4

5

6

7


Tim

e (s

econ

ds)

S et 1 : W a lkS e t 2 : RunS e t 3 : D rive

Plot the remaining time measurements for walking in each trial from Set 1. Use the same shape and color for all points in this Set

Plot the measured times for running in each trial from Set 2. Use a diamond for each point. If possible, choose a different color to use only for this set.

Label the series as Set 2: Run.

Plot the measured times for driving in each trial from Set 3. Use a square for each point. If possible, choose a different color to use only for this set.

Label the series as Set 3: Drive.

5.

6.

7.

8.

9.



Track Length: inches

Set 1, Walker:

Trial NameTime 1

(sec.)

Time 2

(sec.)

Time 3

(sec.)Average Time

(sec.)Trial Range

(sec.)

Average Walk Time (sec.)

Set 2, Runner:

Trial NameTime 1

(sec.)

Time 2

(sec.)

Time 3

(sec.)Average Time

(sec.)Trial Range

(sec.)

Average Run Time (sec.)

Set 3, Driver:

Trial NameTime 1

(sec.)

Time 2

(sec.)

Time 3

(sec.)Average Time

(sec.)Trial Range

(sec.)

Average Drive Time (sec.)

Follow the Challenge Guide instructions to collect and enter the data into the table. Record any notes on the back of this sheet or in your log book. Calculate the Average Time for each trial.Calculate the Average Time for walking, running and driving.Calculate the Trial Range: Trial Range = Maximum Time - Minimum TimePut a circle around the minimum average time for each set. Put a square around the maximum average time for each set.

1.

2.3.4.5.6.

Data SheetMath2Go Challenge #1: How Fast is Fast?


Gra

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Mat

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#1,

How

Fas

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Fas

t?D

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___

____

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D

ate:

___

____

____

____

Tea

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____

____

____

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Oth

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:___

____

____

____

____

____

____

____

____

____

____

____

Tria

l Num

ber

Time in _________________________

Series

D

efin

ition

s:


Have you ever walked on a treadmill? What can you measure on this machine?

What is a variable? What variables exist in this investigation?

Why use the same walker in each walking trial?

Why perform more than one trial in each set?

What were the minimum times for walking? For running? For driving?

As the runner’s speed increases, what happens to time? What does that look like on a graph?

Which activities have similar times?

What does the trial range represent?

1.

2.

3.

4.

5.

6.

7.

8.

Think About It QuestionsMath2Go Challenge #1: How Fast is Fast?


Overview & Objectives

Essential Question: What is speed and how is it calculated?

Objectives: Measure average time and speed using three different distances.Gain an understanding of speed and how it is calculated.

Time Requirement: 2 x 60-minute periods

1 x 60 min: Introduce and gather data.

1 x 60 min: Graph data and discuss. Discuss balance and unbalanced forces. Homework Option: Answer questions in logbooks.

Materials:Math2Go Small CarTape measure

••

•

•

••

Tape / ChalkStopwatches, 3 or more

••

Additional Resources:Presentation (PPT): Are We There Yet? (FTRC Team Web Site)VIDEO: Speed (FTRC Team Web Site)VIDEO: Are We There Yet? (FTRC Team Web Site)Sample Answers for Think About It questions (Curriculum Insert)


••••

Math2Go Challenge #2: Are We There Yet?

Prepare for the ChallengePose the Challenge:

The Bristol Motor Speedway is only a little over half a mile long. The Talladega Superspeedway is over 2.6 miles long; almost 5 times as long. The target lap times differ greatly between these tracks so it is hard to compare performance between tracks by comparing lap times. You can however compare average speeds between tracks.

Though race teams can calculate the average speed for each lap, real race cars don’t have speedometers so drivers don’t know how fast they’re going at any one time. The teams measure performance by measuring only the lap time down to the millisecond! They know within fractions of a second what their target time is.

In this activity, you are challenged toMeasure the top speed of your RC car along three different track lengths, Show that when you’re driving at a constant speed the distance driven increases proportionally with time driven, andGraphically show that the top speed doesn’t depend on track length.

1.2.

3.


‘t’ stands for time‘L’ stands for Length, or distance traveled


time, t = 0 sec

Time-Start Line

Drive Start LineFinish Line 1

Finish Line 2

Finish Line 3

Finish 1, L = 120 in

Layout a Race Track:


Mark a Time-Start line where you will begin to measure time. Your car should be at top speed once crossing this line. For small RC cars, it should be 8 - 15 feet in front of the Start line. If using the

FTRC 1:10 scale car, it should be 50 - 75 feet in front of the Start line.

From the Time-Start line, measure and mark three finish lines.

Finish Line 1 at 120 inches (FTRC car, 30 feet)



1.

2.

3.

»»»

Listen to the engine to make sure the car hits

top speed before crossing the Time-Start line.

Math2Go Challenge #2: Are We There Yet? (continued)

Driver Wayne Surface: parking lotBattery: full recharge at start Gears: 96:32

Trial Name

Length (inches)

Time 1(sec.)

Time 2(sec.)

Time 3(sec.)

Average Time (sec.)

Average Speed

(inches/sec.)120 - 1 120120 - 2 120120 - 3 120

180 - 1 180180 - 2 180180 - 3 180

Record all information someone else would need to recreate what you’re doing. What track length? Walker or Driver? Etc.

A Set of three identical trials {

Record units in at least one place. Use the

same ones for the whole investigation.

Everything in a row is from the same trial (run).

The average of Time 1, 2 and 3

from the same trial.

A Set of three identical trials

that are different from trials in the

first set.

{Notes: Write down things that may help you understand the data. For example, if

you tripped half way through, make a note of it here to help explain odd times.

Prepare to Collect Data:

Make a copy of the data table and tape it into your logbook, recreate your own version in the logbook or build the table in a spreadsheet. Sample table is at the end of this challenge.

Make sure you think about where your measurements are supposed to be written. Think about it as you record. The anatomy of this data table is shown below. Review the definition of trials and sets from the Pi Note on Good Investigation Practices.

Enter the information you already know like track surface, driver name, exact track lengths, etc.

1.

2.

3.


Procedure

Driver: Stand at the Start Line.

Timers: Set Stopwatches to zero.

Data Collector: Prepare data tables.

READY! SET!

GO!

Driver: (1) Set One: Start driving and don’t slow until Finish line 1. (2) Set Two: Start driving and don’t slow until Finish line 2. (3) Set Three: Start driving and don’t slow until Finish line 3.

Timers: Start the timer when the car crosses the Time-Start line. Stop the timer when it crosses the correct Finish line.


RECORD

Driver: Retrieve the car on foot. Driving it needlessly drains the battery.

Timers: Read the times from stopwatches to the data collector.

Data Collectors: Enter measurements and units from each timer into the table.

REPEATIn Science, once is never enough.

Repeat the test for a total of 3 trials using the driver and going to the same finish line.

CALCULATE

Data Collector: Calculate values for this set (finish line). Examples are given in the Organize & Understand Data section.

(1) Calculate the average drive time for each trial in this set.

(2) Calculate the average drive time for this set.

(3) Calculate the average top speed of the car in this set.

Recruit 2-3 people to measure time. Anyone can do the driving. The race engineering candidate must be the data collector (collect, record and analyze the data).

To evaluate how distance, time and speed are related, measure drive time over three different drive distances then graph your findings. The challenge is dealing with the car’s top speed so don’t measure time along the track until its already at its top speed. This is called a Flying Start.

Follow this procedure for three sets. In the 1st set, drive to finish line 1. In the 2nd set, drive to finish line 2 and in the 3rd set, drive to finish line 3.



Organize and Understand DataFor each sets 1, 2 and 3, calculate average times and speed as follows.


Calculate the average time for each trial.

For each set, calculate the average drive time for Finish Line 1, Finish Line 2 and Finish Line 3.

For each set, calculate top average speed of the car: Track distance divided by average drive Time

1.

2.

3.

Average = (sum of values)

(number of values)Average Time for trial, 120-1

(1.50 + 1.62 + 1.44)

3= 1.52 sec.=

Average Speed = 120 in.

1.52 sec.= 78.9 in/secSpeed =

distance

time

Example Data Table

Trial Name

Length (inches)

Time 1

(sec.)

Time 2

(sec.)

Time 3

(sec.)Average Time

(sec.)Average Speed

(inches/sec.)

120 - 1 120 1.50 1.62 1.44 1.52 78.9120 - 2 120 1.46 1.58 1.40 1.48 80.9120 - 3 120 1.48 1.60 1.42 1.50 79.9180 - 1 180 2.20 2.37 2.11 2.22 80.92

Set Number Track Length (inches)

Average Set Time (sec.)

Average Set Speed (inches/sec.)

1 1202 180

Create Graphs

Label the horizontal line at the bottom of your graph, the X-axis, with drive distances.

Label the vertical line along the left side, the Y-axis, with a range of times in seconds.

Plot the first point to show the average drive time for finish line 1 by finding the distance for the first finish line along the X-axis, then moving up in a straight line from that point until you are even with the correct time on the left. Use a circle to mark the point.

Repeat to plot average drive times for the other two finish lines.

1.

2.

3.

4.

Average Times to Drive Varied Distances

0

0 .5

1

1 .5

2

2 .5

3

0 4 0 8 0 1 2 0 1 6 0 2 0 0

Drive Distance (inches)

Tim

e (s

ec.)

Distance vs. Time: To show you that the time and distance driven increase (and decrease) proportionally when driving at a constant speed, make a graph of distance driven vs. drive time over that distance.


Average Times to Drive Varied Distances

0

0 .5

1

1 .5

2

2 .5

3

0 4 0 8 0 1 2 0 1 6 0 2 0 0

Drive Distance (inches)

Tim

e (s

ec.)

Add a ‘best-fit’ line to the Distance-Time Graph. Starting at the left side of the graph, draw a single straight line that runs as close to all points as possible. This line represents all points on the graph. You can use the best-fit line to predict drive times for distances that you didn’t test. In the example here, you can estimate that it would take 5 seconds to drive 140 inches.

5.

Notice that the low number on each axis is not zero. Beginning the axis at a higher number let’s you see more detail and helps you to be precise when making and using your graph.

The first graph represents a magnified view of detail in the graph to the left. You can see how they fit together. The area represented by the first graph above is shown shaded.

Average Speed Over Varied Distances

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0Drive Distance (inches)

Spee

d (in

ches

/ se

cond

)


5 0

5 5

6 0

6 5

7 0

7 5

8 0

8 5

9 0

1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0Drive Distance (inches)

Spe

ed (i

nche

s / s

econ

d)


5 0

5 5

6 0

6 5

7 0

7 5

8 0

8 5

9 0

1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0Drive Distance (inches)

Spee

d (in

ches

/ se

cond

)

Label the X-axis with the range of drive distances in inches. Label the Y-axis with a range of average speeds.

Plot the average speed for finish lines.

Add a ‘best-fit’ line (or a trendline) to the graph.

1.

2.

3.

Distance vs. Speed: Show that the top speed of a car doesn’t depend on the distance driven. A graph of average top speed vs. drive distance should show a horizontal line or something close to it.

Discuss what these graphs show: The drive time graph does show that the relationship between drive time increases proportionally with distance. The relationship is therefore linear. This is true because the speed is constant, it isn’t changing.

The speed graph shows a straight line showing that the speed is indeed constant. If this line were not horizontal (or very close), the drive time vs. distance graph wouldn’t be linear. If you need convincing, run trials in which the car starts from a speed of zero and accelerates along the track.



Math2Go Challenge Data Table: Are We There Yet?Your Name: Date:

Surface: Gears:

Battery Charge:

Enter your units of measure. In the future, you must remember to label them on your own.

Units of Time: _____________ Units of Length: _____________ Units of Speed: _________________

Driver Name Track Length

Trial Name Enter from 3 people measuring time. Average of 3 Times

Average SpeedTime 1 Time 2 Time 3

Notes: Set Number Track Length Average Set Time Average Set Speed

1

2

3

Mat

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#2:

Are

We

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Are

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Dri

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Fun

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Dri

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Drive Time (seconds)

Drive

Dis

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(en

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units

) __

____

____

____

___

Mat

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Are

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Are

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Top

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Drive

Dis

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(en

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____

____

____

___

Top Speed in (enter units) ____________________________


Think About It QuestionsMath2Go Challenge #2: Are We There Yet?

Why perform more than one trial in each set?

On the graph with speed, what axis shows length? What axis shows speed?

What is speed?

What two measurements are required to calculate speed?

What are the units of speed on a highway sign in the United States?

Use graphs to compare your drive times over different tracks. What happens to the times as the track length increases?

Use graphs to compare your speeds over different tracks. What happens to the speed as the track length increases?

Use the Time vs. Distance graph to predict how long it would take to drive 150 inches. Test your prediction (use the same driving surface and battery charge).

1.

2.

3.

4.

5.

6.

7.

8.


Overview & ObjectivesEssential Question: What weight maximizes power?

Objectives: Model how weight affects speed, work and power.Gain an understanding of forces, work and power.

Time Requirement: 3-4 x 60-minute periods

1 x 60 min: Understand forces, work and power.

2-3 x 60 min: Gather data, graph and repeat until you get the best score. Homework Option: Answer questions in logbooks.

Materials:Math2Go Small CarTape measureTape / ChalkStopwatches, 3 or moreWeights to add onto the car (metal screws, washers, filled water bottles, etc.)Digital weigh scale

Additional Resources:Presentation (PPT): Optimal Power (FTRC Team Web Site)VIDEO: Optimal Power (FTRC Team Web Site)Sample Answers for Think About It questions (Curriculum Insert)


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••••••

•••

Math2Go Challenge #3: Optimal Power

Pose the ChallengeRace tracks are very different from one another in many ways. Look at difference between the road courses in Sonoma, California and Watkins Glen, NY. Though the tracks are similar in some ways, cars travel around the NY track at much higher speeds. This is because the Sonoma track has an elevation change of 300 feet. The cars have to do work to lift themselves that 300 feet on each lap. The time in which they do that work is measured as power.

Understanding how weight changes the power can make a big difference in lap time. That’s important to understand when the difference between teams that qualify and teams that go home can be less than 3/10 of a second in a lap time of 25 seconds.

In this challenges you’ll calculate work and a score proportional to the power (PowerF). By modeling how

work and power change as weight changes, you’ll choose the car weight to maximize the PowerF.

Though the independent variable changes, NASCAR teams are constantly asking themselves this same question. What is the best setting to optimize power?


Review Speed, Work, Power and PowerF

Create a story-graph to illustrate the relationship between speed and weight.

(Talk to your team coach - there are sample answers in the ‘Curriculum’ insert.)

Create an X-Y graph without numbers in your logbook. Label X-axis as weight and Y-axis as speed.

Plot points to go along with this story (no numbers, just points that are relative to each other): You’re wearing a back-pack with nothing in it and have to run to class. Put a point on the graph to show how heavy the load is and how fast you can run. Now someone puts three books in your bag. Plot a point to show if you faster or slower with the added weight. Finally, they pile your bag as full as it can go with really heavy books. Plot that point.

Write down in a full sentence what happens to the speed as weight increases or decreases.

Can you predict just as easily what happens to the work in this scenario? Probably. Can you predict what happens to the power in this scenario? Probably NOT!

“My mother works on the computer at least eight hours a day.”

This sentence illustrates a common use of the term ‘work’; however, this time spent at the keyboard isn’t work according to scientists, mathematicians or engineers. The term ‘work’ has this simple but very specific definition: work is defined as a force acting upon an object to cause a displacement.

A force is the push or pull on an object by another object. That force directly causes a movement, but not just any movement. That force causes a displacement. Displacement implies that the object ends up in a place different than where it started. A simpler version of our definition for work might go like this: work is done whenever there is a push or pull on something that causes it to move from one place to a different place.

Examples of work being done by this definition are everywhere. If you push a salt shaker to your friend, you’ve done work on the shaker. You pushed it and as a result, it moved. If the plate that your friend was seasoning fell off of the table, work was done on the plate because gravity pulled it from the table onto the floor.

Calculate the work done using the following formula:

Work = F x dwhere F is the force in the direction of movement and d is the distance that the object is displaced. Notice that the force used in this equation is only the force in the direction of the displacement. The variable F is in bold because it is called a vector quantity; meaning it indicates a number and direction.

Though we’ve described how much work is done, we haven’t described how fast it is done. Two runners who weigh the same do equal amounts of work when competing in a race; however, the more powerful runner will be the winner. Power describes the rate at which work is done (how fast it is done).

Power = Work / time, or because work=Fd, Power = Fd/t

Notice also that speed is equal to d/t so you can also calculate this way:

Power = Force x speed.

Math2Go uses a power factor. Calculate the power factor using our simple formula for how much work is done by the RC car.

The PowerF = Weight x Speed, or Power

F = Weight x Distance ÷ Time

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Math2Go Challenge #3: Optimal Power (continued)

Think About the Challenge. Make a Plan.

Your challenge is to find the weight that gives the most power so weight is the independent variable. Your score, the PowerF, is the dependent variable. The PowerF depends on the drive time (another dependent variable), the weight (the independent variable) and track length (unchanged in this activity).

First, you’ll find the general pattern between weight and the score by testing cars with different weights. Every time you change the weight is a new data set. You’ll use the model to choose the best weight.

Track Length: 180 inches Driver: WayneBattery: full recharge at start Surface: parking lot

Trial Name

Exact Weight (oz.)

Time 1(sec.)

Time 2(sec.)

Time 3(sec.)

Average Time (sec.)

Avg. Speed

(inches/sec.)

Work

(inch-oz)

PowerF

(inch-oz/sec)

W3 - 1 70.1W3 - 2 70.1W3 - 3 70.1

Set 3: W3Set 4: W4Set 5: W5

Prepare Your Data Tables:

Make a copy of the data table and tape it into your logbook, recreate your own version in the logbook or build the table in a spreadsheet. Fill in the information you already know.

‘t’ stands for time‘L’ stands for track length


time, t = 0 sec

Start Line

Finish LineL = 180 inches

Prepare for the ChallengeLayout a Race Track: Use a standing start in this activity. The start and time-start line are the same so you begin measuring time right when the car begins to move.


From the Start line, measure and mark a Finish line 180 inches away.

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Prepare Your Car:

Decide what is a good lower weight to test (no added weight?) and a good high weight to test (try one that is ALMOST so heavy the car doesn’t move).

1.

Add weights to the car. Try taping washers or filled water bottles to the car.

Use your scale to weigh the car with added weights. Measure in ounces (oz.).

Read the weight to the hundredths place. Round the weight to the nearest tenth of an ounce and record that ‘Exact Weight’ in the team data table.

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Drivers: Place the Car at the Start Line.

2-3 x Timers: Set Stopwatches to zero.

Data Collector: Prepare data tables

READY! SET!

GO!

Drivers: Start driving and do not stop until you cross the finish line.

Timers: Start the timer when the driver crosses the Start line. Stop the timer when the driver crosses the Finish line


RECORD

Drivers: Retrieve the car on foot. Driving it needlessly drains the battery.

Timers: Read the times from stopwatches to the data collector.

Data Collectors: Enter measurements and units from each timer into the table.

REPEAT

In Science, once is never enough. Repeat the test for a total of 3 trials using the same weight.

CALCULATE

Data Collectors: When you’ve completed all trials for this set, calculate the average drive time and the average speed for each trial. Calculate Work and PowerF for each trial.

Recruit 2-3 people to measure time. Anyone can do the driving. The race engineering candidate must be the data collector (collect, record and analyze the data).

Follow this procedure for at least three sets - try to do more. Each set is a car with a different weight. Test a low weight, very high weight and middle weight. Ex. 22 oz, 60 oz and 90 oz.

Procedure

DO SETS 2, 3, 4...

Set 2: Repeat these steps for a second, different weight.Set 3: Repeat these steps for a third, different weight.

Sets 4+ Time permitting, test other weights.



Because the amount of work done changes when the car weight changes, we say that work is a function of weight. Similarly, because the power changes with weight we say that power is a function of weight. Your model will describe both work and power as functions of weight.

Use your team or class data from Challenge 3 to understand how work and PowerF change as the car weight changes. Re-enter the values for car weight, average set speed and average set time in each table under the correct heading.

Organize & Understand Data


Trial Name

Exact Weight (ounces)

Time 1(sec.)

Time 2(sec.)

Time 3(sec.)

Average Time (sec.)

Avg. Speed

(inches/sec.)Work

(inch-oz)PowerF

(inch-oz/sec)

W1 - 1 70.1 3.37 3.42 3.34 3.38 53.31W1 - 2 70.1 3.44 3.49 3.38 3.44 52.38W1 - 3 70.1 3.51 3.58 3.49 3.53 51.04

Set Car Weight (ounces)



Work (inch-oz)

PowerF

(inch-oz/sec)

W1 70.1 3.45 52.24

W2


Fill in the data table by calculating average trial and set values. Follow this example for trial W1-1 and set W1 shown here.


Calculate the average time for each trial. Enter that time into the data table.

Calculate and record the speed for each trial. Because the time is an average value, the speed is also an average value.

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Work = Weight x Distance

From our Math2Go formula for work, all you need is the weight of the car and the distance traveled to calculate the work done. Use the weight in ounces and the track distance in inches to calculate the work done in each set from the previous challenge. Work will have the units of inch-ounces.

Average Time for trial, W1-2

(3.44 + 3.49 + 3.38)

3= 3.44 sec.=Average =

(sum of values)

(number of values)

Speed = distance

timeAverage Speed =

180 in.

3.44 sec.= 52.4 in/sec



Trial Car Weight (ounces)

Average Speed (inches/sec.)

PowerF (inch-ounces/sec.)

W1 - 1 70.1 x 53.31 = 3,737

Trial Work (inch-ounces)

Average Time (sec.)

PowerF (inch-ounces/sec.)

W1 - 1 12.618 ÷ 3.38 = 3,733

You’ve already calculated speed and work from your data on weight, distance and time so any of the three formulas make sense to choose. Try calculating PowerF using more than one formula.

Differences in the final values are due to rounding in earlier steps.

Calculate PowerF using weight and the average speed.

Calculate PowerF using work and the Average Set Time.

Calculate and record the work done in each trial.

There are a few ways you can calculate Power and your PowerF score for each trial. The units will be inch-ounces per second, regardless of method.

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For each set, calculate the average set time, speed, work and PowerF by averaging all values for that weight or by averaging the average trial values.

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Trial Name

Exact Weight (ounces)

Time 1(sec.)

Time 2(sec.)

Time 3(sec.)

Average Time (sec.)

Avg. Speed

(inches/sec.)Work

(inch-oz)PowerF

(inch-oz/sec)

W1 - 1 70.1 3.37 3.42 3.34 3.38 53.31 12,618 3737W1 - 2 70.1 3.44 3.49 3.38 3.44 52.38 12,618 3672W1 - 3 70.1 3.51 3.58 3.49 3.53 51.04 12,618 3578

Set Car Weight (ounces)



Work (inch-oz)

PowerF

(inch-oz/sec)

W1 70.1 3.45 52.24 12,618 3,661

W2


Work = Weight x Distance Work = 70.1 oz. / 180 in. = 12.62 inch-oz.

PowerF = Weight x

Distance

Time

Average Set Speed

(53.31 + 52.38 + 51.04)

3= 52.24 sec.=

Because Speed = Distance ÷ Time

PowerF = Weight x Speed Power

F = Work ÷ Time

Because Work = Weight x Distance


Make a scatter plot to describe the average speed versus total car weight.

Label the X-axis with the range of total car weights in ounces.

Label the Y-axis with a range of speeds in inches per second.

Plot average speed vs. weight for every trial (1 point / trial).

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Average Speed at Various WeightsL = 180 inches, On a parking lot

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10

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0 10 20 30 40 50 60

Total Car Weight (ounces)

Ave

rage

Spe

ed

(inch

es p

er s

ec.)

Make a plot to describe the average drive time versus the total car weight. You can make graphs by hand, with a graphing calculator or using software like a spreadsheet.

Label the X-axis, with the range of total car weights in ounces.

Label the Y-axis, with a range of times in seconds.

Plot the average drive times vs. weight for every trial (1 point / trial).

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2.

3.

Average Drive Times at Various WeightsL = 180 inches, On a parking lot

0

0 .5

1

1 .5

2

2 .5

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0 10 20 30 40 50 60Car Weight (ounces)

Ave

rag

e D

rive

Tim

e (s

ec.)

(sec

.)

Analysis Step 1: Model Time, Speed & Weight

Get Help to Get it Right: If it will help, work with a math and science teacher to hone these skills that are fundamental to problem solving in many careers including marketing, business and engineering.


Graph then Analyze Using the Grade Appropriate Lesson



Draw a best-fit line that runs as close to all points as possible. This line approximates all of the possible points. You can use the best-fit line to predict the speed for weights that you didn’t test. In this example, you can estimate that the car would travel 67 inches per second if it weight a total of 40 ounces. Use it to predict the speed for a 25 ounce car.

Determine the slope of the best fit line on your graph.

A linear relationship is one of the most basic types of relationships. The relationship between speed and weight is linear. The slope of the line is a ratio that describes how much the speed changes as the weight changes. In this Challenge and in this graph, speed is the Y value and weight is the X value.

Use any two points that lie on the best fit line. Each point is in the format of (X,Y) where X is a value for the weight and Y is a value for the speed. For this example, you can choose these points that the line passes through (19.0, 79.3) and (50.0, 61.0).

The change in speed (Y) is from 79.3 to 61.0; a change of -18.3 inches per sec.

The change in weight (X) is from 19.0 to 50.0; a change of 31.0 ounces.

The slope of the line is equal to -18.3 / 31.0 = -0.6

What does this slope of (-6⁄10) mean for our car? It means that if you increase the weight by 10 ounces, the car slows by 6 inches per second. The negative sign means that the speed and weight are inversely related. If one increases, the other decreases.

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You have defined a mathematical relationship for how weight affects speed. Adding more data points to the model will make it more accurate. With a more accurate model, the equation of the best-fit line will better match the real system which means that you can make better predictions.

(Rise) The change in Y, Speed

(Run) The change in X, Weight

The slope is also equal to this ‘rise’ divided by this ‘run’; each is twice the distance.

Grades 6-8: Define a Relationship Using Slope

Slope = ‘rise’

‘run’

change in Y

change in X=

Average Set Speed vs. WeightL = 180 inches, On a parking lot

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10

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50

60

70

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90

100

0 10 20 30 40 50 60 70


Ave

rage

Spe

ed

(inch

es p

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ec.)


First follow the 6 - 8 Instructions then use your own data points to determine the speed your car would run if it could weigh nothing.

Of course, a zero weight car is fictional - there is no such thing. It is however an interesting concept. There are two ways you can estimate the speed that a zero-weight car would travel: graphically and using a known point and the calculated slope.

The example graph to the right shows the trendline extended backwards to the Y-intercept where X = 0. If the weight is zero (X=0) then the speed is estimated as 92 in/sec.

Here’s an example using the point and slope.

The slope of 0.6 means that for every ounce removed, this car’s speed increases by 0.6 in/sec.

One known point is (40,67). It means that a 40 ounce car has a speed of 67 in/sec.

If the 40 ounces are removed to give the zero-weight car, each ounce removed adds 0.6 in/sec to the speed. The zero-weight car gains 40 x 0.6 in/sec. or 24 in/sec.

Approximate the speed of a zero-weight car by adding 24 in/sec to 67 in/sec to get 91 in / sec. This is VERY CLOSE to the 92 in/sec you’d estimate using the graph shown here.

Creating a model such as this one is often the first step in problem solving. Because you cannot afford to test every possibility, mathematical models make it possible to examine many possibilities on paper.

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Pre-Algebra: Create Math Models to Predict Outcomes

Average Set Speed vs. WeightL = 180 inches, On a parking lot

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0


Ave

rage

Spe

ed

(inch

es p

er s

ec.)

First follow the 6 - 8 and Pre-Algebra Instructions then find an equation to describe the relationship between data on speed and weight.

For the sample data, the slope of the best-fit line is -0.6 and a zero-weight car would have a speed of approximately 92 in/sec. These are helpful pieces of information about the relationship between speed and weight, but finding the equation of the best-fit line would describe the relationship completely.

Any time data seems to fall into a straight line, it may mean that a linear relationship will define the system. Every straight line on a graph can be described with the linear equation

Y = a X + b.In this case, Y is the speed of the car, the dependent variable X is the weight of the car, the independent variable b is the Y-intercept; the value of Y when X=0, This is the speed (Y) of a zero-weight car (X=0) a is the slope of the line; the ratio of the change in speed (Y) for every change in weight (X)

Define the equation of our best-fit line using the slope (a) of -1.8 and the Y-intercept (b) of 120. The equation of the line becomes:

Y = -0.6 X + 92

Every point on this line shares this description. Test the equation using other known points.

Algebra: Describe What You Observe with a Linear Equation


Technology: Create an Accurate Math Model


You have calculated a linear equation to describe the relationship between weight and speed of your Math2Go car. Do the following using the technology available to you.

Create a graph in a spreadsheet or in a graphing calculator.

Generate a best fit line for your data and see the equation that describes it. Do this by creating a trend line in the spreadsheet or finding the linear regression equation in the calculator.

Trace along the line to see other points and run tests to see if they are accurate. The more data you input the more accurate your model will become.

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Set No. Trial No. Weight (oz.)

Length (inches)

Time 1 (sec.)

Time 2 (sec.)

Time 3 (sec.)

Avg. Time (sec.)

Avg. Speed (in/sec.)

1 1 19 180 2.20 2.37 2.11 2.22 80.92

1 2 19 180 2.25 2.43 2.16 2.28 78.95

1 3 19 180 2.28 2.46 2.19 2.31 77.96

2 1 33.8 180 2.45 2.51 2.39 2.45 73.47

2 2 33.8 180 2.62 2.69 2.56 2.62 68.66

2 3 33.8 180 2.32 2.38 2.27 2.33 77.34

3 1 52.1 180 2.79 2.72 2.63 2.71 66.34

3 2 52.1 180 2.93 2.86 2.76 2.85 63.18

3 3 52.1 180 2.56 2.52 2.47 2.52 71.35



Make a graph of work done as a function of weight.

Because you changed the weight, it is the independent variable along the X-axis.

Because the work changed with the weight, it is the dependent variable along the Y-axis.

Total Car Weight vs. Work DoneL = 180 inches, On a parking lot

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0Total Car Weight (ounces)

Wo

rk (

inch

-ou

nce

s)W

ork

(inch

-oun

ces)

Make a graph of PowerF as a function of weight.

Because you changed the weight, it’s the independent variable along the X-axis.

Because the PowerF changed with the weight, it is the dependent variable along the Y-axis.

In this example, data from lower weights shows an increasing trend so if you only ran low weights, you might think adding more would be the best.

By testing high weight cars, you know that there is a point where its too heavy and your score starts to dip. What is that point because it is the one that gives you the highest score?

Total Car Weight vs. Average PowerF

L = 180 inches, On a parking lot

0

500

1000

1500

2000

2500

3000

3500

4000

0 10 20 30 40 50 60 70 80Total Car Weight (ounces)

Pow

erF (i

nch-

ounc

es /

sec.

)

?

??

Pow

erF

(inch

-oz/

sec)

You’ve created a model to help answer the question, which weight gives the best score, but may need to know more about the relationship between PowerF and weight to choose the best weight. Improve your model with more data points.

Analysis Step 2: Model Weight, Work & Power

Get Help to Get it Right: If it will help, work with a math and science teacher to hone these skills that are fundamental to problem solving in many careers including marketing, business and engineering.

Graph then Analyze Using the Grade Appropriate Lesson


Make a graph of Total Car Weight vs. Average PowerF. Notice that a line would not go very close to all of the points so add a best-fit curve instead.

Just as you did with the best-fit lines, start at the left side of the graph and draw a single curve that runs as close to all points as possible. This curve represents all points on the graph, but with so little data it is impossible to know its exact shape.

Graphs tell stories. They may not always be exciting, but they are often helpful.

Total Car Weight vs. Average PowerF

L = 180 inches, On a parking lot

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2000

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3000

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0 20 40 60 80 100Total Car Weight (ounces)

Pow

erF (

inch

-oun

ces

/ sec

.)

Grades 6-8: Find the turn-around point

Make a graph of Total Car Weight vs. Work. Add a best-fit line to this graph just as you did in the previous Challenges.

You can see that work increases with weight. The relationship shows a line meaning they increase proportionally. Double the weight, the work is pretty close to doubled. Triple gives triple and so on.

Total Car Weight vs. WorkL = 180 inches, On a parking lot

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Total Car Weight (ounces)W

ork

(inch

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ces)


At first the data seems to say that adding more weight increases the PowerF just as it continues to increase the work done. However, collecting a few more data points using high weights shows that this isn’t true. In fact, if too much weight is added then the speed becomes zero and the PowerF goes down to zero. There is a point where the PowerF begins to go down with added weight. In this example, the PowerF looks at its maximum around 75 ounces.

Use your own graph to identify the weight that will give you the highest possible PowerF. Make a final run in this Challenge to test your prediction against predictions made by other teams.

Remember that more data points will improve your model. You can get closer and closer to the maximum value for PowerF by adding more data points to your graph. You could continue to improve this graph and your ability to predict by collecting more data points around the maximum, perhaps between 65 and 80 total ounces. You could also choose another very high weight to fill out the high end of the X-axis.


Algebra: The Goldilocks Story and Quadratic Equations


Complete the analysis for 6-8 from this Challenge to create Work and PowerF graphs.

Follow instructions from Analysis Step #1 for Pre-algebra and Algebra with two points from your data set.

Use the example below to find the linear equation that describes the relationship between weight and speed for your data. Use this form: Y = aX + b

Points: (33.8, 73.16) and (70.1, 52.24)

The Slope (a) equals –0.58 meaning that for every added ounce, the car slows by 0.58 in/sec

The Y-intercept (b) is the theoretical speed of a zero-weight car, or 92.5 in/sec.

The linear equation describing speed as a function of weight is Y = -0.58X + 92.5 If my goal is to earn money by moving the most weight of some object in the shortest time then speed multiplied by weight (the PowerF) is a good way to define success. Imagine that your company is paid an amount equal to the PowerF. A large PowerF means you generate a high income. At what weight does the company earn the most money?

From the data table you can see that adding more weight is the best way to make more money at first. However, when a really heavy weight is posted the income or PowerF goes down.

This story is like the Goldilocks tale. One chair is too small, one is too large and one is just right. Somewhere along the range of possible weights, the curve turns around. Finding that point in business, in sport or in household chores can be very important.

Algebra Bonus

Because Power = (Speed) x (Weight), you can use your equation for speed as a function of weight to estimate the equation for Power as a function of weight.

From the formula just generated, the speed in this example is equal to 92.5 - 0.58 W if W stands for the weight. If income is defined as weight multiplied by speed (PowerF) then the formula would be:

PowerF = W (92.5 -0.58W) or

PowerF = 92.5W – 0.58 W2.

Weight (oz.) Avg. Set Time (sec.)

Avg. Set Speed (in/sec.)

Work (inch-ounces)

PowerF (inch-ounces / sec)

19.0 2.27 79.28 3420 150633.8 2.47 73.16 6084 246752.1 2.70 66.96 9378 348070.1 3.45 52.24 12618 366180.0 3.89 46.27 14400 3702

100.0 5.32 33.83 18000 3383


In reality, no zero-weight cars exist so the best fit curve does not go through the origin. This means that one other term is also part of the math equation to describe this curve. That point is on the X-axis where the best fit curve really crosses the Y=0 line. This Y-intercept is not zero but 11.21. The X coefficients are different because out time measurements are not perfect, but are imprecise. Even a tenth of a second difference in time can change the calculated value for PowerF significantly.

You can get an equation to describe the data set by putting all data points into a spreadsheet or Graphing calculator. Once you’ve built the list then you generate a quadratic regression. Here is an example of the results from a spreadsheet and from a graphing calculator. Y is the PowerF while X is the weight of the car.

Y = -0.62X2 + 96.2 X + 11.21

The maximum weight is about 77 ounces with a score of about 3703.

Weight (oz) PowerF (in-oz/sec)

Speed (in/sec)

20.0 1621 81.130.0 2260 75.340.0 2813 70.352.1 3480 66.860.0 3427 57.170.1 3639 51.980.0 3781 47.390.0 3721 41.3

100.0 3325 33.3110.0 2824 25.7120.0 2557 21.3130.0 1892 14.6140.0 561 4.0

Total Car Weight vs. PowerF

Track Length=180 inches; Surface = parking lot

Y = -0 .6228X 2 + 96 .196X - 11 .21

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Pow

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Technology: Create an Accurate Math Model



Trial Name

Exact Weight Time 1 Time 2 Time 3 Average Time

Avg. Speed Work PowerF

seconds seconds seconds seconds

Set Name

Exact Weight Average Time Avg. Speed Work PowerF

seconds

Follow the Challenge instructions to collect and enter the data into the table. Record any notes on the back of this sheet or in your log book.

Calculate the Average Drive time, Average Speed, Work Done and PowerF for each trial.

Calculate the Average Drive time, Average Speed, Work Done and PowerF for each set.

1.

2.

3.

Track Length: Driver:

Battery: Surface:

Data SheetMath2Go Challenge #3: Optimal Power


Because the amount of work done changes when the car weight changes, we say that work is a function of weight. Similarly, because the power changes with weight we say that power is a function of weight. Your model will describe both work and power as functions of weight.

Calculate the work you did.

Trial or

Set Name

Track Length Car Weight Work Done

x =

x =

x =

x =

Try calculating PowerF using more than one formula.

Calculate PowerF using weight and the Average Speed.

Calculate PowerF using work and the Average Time.

Trial or

Set Name

Car Weight Avg. Speed PowerF

x =

x =

x =

x =

Work = Weight x Distance

Trial or

Set Name

Work Done Avg. Time PowerF

÷ =

÷ =

÷ =

÷ =

PowerF = Weight x Speed

PowerF = Work ÷ Time

Optional Calculation SheetUse as an exercise in calculating Work and PowerF

Mat

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o Ch

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al P

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Wor

k ve

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Car

Wei

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(Wor

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f Wei

ght)

Tota

l Car

Wei

ght

in _

____

____

____

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Serie

s D

efin

ition

s:

Work Done in _________________________

Mat

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o Ch

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Ave

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Pow

erF v

s. C

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vg. P

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Tota

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Wei

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in _

____

____

____

__

Serie

s D

efin

ition

s:

PowerF in _________________________________


What is the difference between work and power?

How do the graphs illustrate the difference clearly?

What was the car weight that you would choose to race next time? Why?

Examine your graphs. Discuss conclusions you could make about weight and PowerF by looking only at the first half of the X-axis. Contrast those to conclusions you would make by looking only at the second half of the X-axis. Finally, Contrast those to conclusions you would make by looking at the entire picture.

Extension Question: How does the story of Goldilocks and the Three Bears relate to the Power Challenge?

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Think About the DataMath2Go Challenge #3: Optimal Power


1. Read about gears and gear ratios below. 2. Change the gears on your car using the table on the next page (or make one in your notebook) to record which gears you use and calculate the gear ratio.

Pinion Gear

About Gears and Gear Ratios

There are two gears in most RC cars, a spur gear and a pinion gear. The pinion gear is attached to the motor shaft and is smaller than the spur gear. The spur gear is attached to the wheels and is larger than the pinon gear.

The choice of gears will set your car’s top speed and acceleration rate. A higher acceleration rate (zippier car) means you have a lower top speed. Higher top speed means lower acceleration.

For an “open course” of sweeping turns you’d install a big pinion gear and a small spur. This combination gives a high top speed for straight-aways but the trade-off is lower acceleration out of the corners.

There are two measurements for each gear: Pitch and Teeth. The pitch of a gear is the distance between teeth. For two gears to mesh they must have the same pitch. A common FTRC spur gear is 48 P 78 T which means 48 pitch and 78 teeth.

You usually compare gear sizes using gear ratios. The gear ratio is the relationship between the number of teeth on two gears that are meshed together. In the picture to the left, the spur gear may have 72 teeth and the pinion gear, 28 teeth. The gear ratio is therefore:

For every one revolution of the pinion gear attached to the motor, the spur gear attached to the wheels makes 1/2.57, or 0.39, revolutions.

7228

= 2.57 : 1Gear Ratio =

Spur Gear

Some gears have the number of teeth printed right on them. If not, mark the 1st tooth with a piece of tape and count.

Pinion Gear with 31 teeth.

Set screws are on the side of a pinion gear.

High Top Speed

High Acceleration

Low Acceleration

Low Top Speed

Gear Ratio

FTRC Fundamentals Certification Challenge #4Gears & Gear Ratios


Changing Gears

Page 8 in the FTRC car manual shows you how to remove and replace spur and pinion gears. To keep gears from grinding, make sure the gears mesh properly by adjusting the motor position.

Make a table like the one below in your notebook.

Using the gears you have, change them out. For each new set, record the number of teeth and calculate the gear ratio.

Top: Allen Wrench in kit Bottom: Integy Hex Wrench, 1.5mm

The Right Tool

Figuring out the right tool for the job is an important skill to acquire. Changing gears is a good example. The typical Allen wrench like the one in your kit, is torsionally too soft to remove the set screws in the pinion gear. This means that when you turn it, the key twists rather than removing the screw. The In-tegy Tool Hex Drivers are one example of a nitride hardened driver that will effectively remove the screws. Be SURE to use the correct size. A 1 mm hex can strip a 1.5 mm set screw.

Gear Ratio Chart

Spur GearNumber of Teeth

Pinion GearNumber of Teeth

Gear RatioSpur Gear : Pinion Gear

If you have 2 spur gears and 2 pinion gears, you

can get 2 x 2 = 4 different gear combinations.

If you have 3 spur gears and 2 pinion gears, how many gear combinations

can you get?


B

Q

A

C

I

JL

K

N

M (hidden from view; part

that rotates pinion gear)

P

G

H

______ Motor ______ Spur Gear

______ Pinion Gear ______ Electronic Speed Controller

______ Servo ______ Adjust Toe Angle

______ Battery ______ Lower Control Arm

______ Frequency Chip ______ Body Mount

______ Shocks / Springs ______ Chassis

______ Tire ______ Upper Deck

______ Rear Drive Belt ______ Receiver

______ Front Drive Belt

M K

Q G

C P

B O

I F

N A

E D

L J

H

FastTrack RC 1:10 Scale CarIdentify Components


The Science of MotorsportsLogin to the FTRC Team Web Site for More Resources

Drivers can ‘bump’ one another without actually making contact. They can push and pull each other by manipulating the air between them. Understanding Bernoulli’s Principle will help

you avoid crashes like this one.

Cyclists draft. Professional drivers draft. What does that mean and why does it help?

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Login to your FTRC Team Web Site to check out the Pi Notes and lessons on this pressure principle.

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