Where’s The Fireby

Larry Rice

All

IntroductionAs a Cartographer you will be making maps from photos taken by satellite and airplane so that you can:

name specific locations on the map,

estimate how much of the ground area has been burnt by fire (or where there is fire), and

plan how you will fly your plane closer to the ground to take multiple smaller photos that will combine to show more detail.

Fly the plan, take the photos

Your work will be used by the community to estimate risk to residents, where to fight the fire, and to plan the recovery of natural resources. All

Topics CoveredMapping Basics

Estimating Map Areas

Digital Camera Basics

Aerial Photos

Unit conversions

Compass Directions

Flight Algorithm

Flight Plan

Mapping Basics

All

When combined, these are perpendicular

Lines for A GridA

vertical Line is

up-down

A horizontal line is left-

right

A map grid is made up of multiple

vertical lines, equally spaced (parallel)

And multiple equally-spaced horizontal lines

(parallel)

4th GradeHands-on: make vertical, horizontal, parallel, and perpendicular lines on paper

Labels on a MapNotice that our

map, as with most all maps, has

several labels and symbols...

The Compass Rose shows which way is north, always up on

maps, and it sometimes shows other directions:

south, west, east.

There are many other types of compass

rose, for example...

The scale shows us how far a distance on a map is, in this case, 2.5 Km (Kilometer) is

as far as the white line is long...

And a map may have titles explaining areas or points of interest

AllHands-on: Draw map labels and titles on photos or in GIS software

How Big is the PhotoBefore we draw our

grid, we need to pick an origin, the starting

point,

and determine the dimensions (width and height) of our photo-map, using the scale.

Km is Kilometer

The Origin is often the bottom left

corner

This is 20 Km high

8 x 2.5km

This is 30 Km wide

12 x 2.5km

AllHands-on: use scale on map to determine dimensions or distance between things

A quick Check on Terminology

AA

BB CC

__ Vertical Line__ Horizontal Line__ Compass Rose__ Scale__ Label__ Perpendicular__ Parallel

DD

EE

FFGG

AllHands-on: Identify on an actual map

Laying out a GridWe can now draw different grids.

(Remember, this photo map is 20Km high by 30Km wide)

A large grid has 3 horizontal, 4 vertical

lines (10Km apart)

A medium grid has 3 horizontal, 7 vertical

lines (5Km apart)

A small grid has 9 horizontal, 13 vertical

lines (2.5Km apart)

You should note that each area drawn is a square, all sides are of equal length and are perpendicular, since all grid lines are equally

spaced.All

Hands-on: Draw differing grids on actual maps

Coordinates for the Grid

We will now select our Origin to be the upper left corner

So we can now use letters going

down to label the vertical direction,

numbers going left to label the

horizontal direction, these

can be shown on two sides or all

four sidesLetters

BB

AA

Numbers

11 22 33

The Grid location name becomes the letter-number combination

A1A1 A2A2 A3A3

B1B1 B2B2 B3B3

All

Can you Label a Different Sized Grid ?

Using the same

method, type in the label and each grid location

____

____

____

____

__ __

__

__

AllHands-on: add labels on grids created previously

Estimating Map Areas

All

Estimating Fire Damage

4th Grade

To estimate how much forest is damaged by fire,

we will use different shapes that each have an area of 10 square miles

Use any number of shapes to cover all the areas in the

photo map that are dark red. You can rotate the shape to complete the

puzzle. Once all dark red is covered, count how many

shapes have been used, did you get 15 to 20 ?

The area burned is about 150 square miles

(15 shape x 10 square miles each)

Hands-on: Complete area estimate on actual maps / photos with cut-out shapes

Chart the Areas

4th Grade

You have made pie charts before, can you complete this chart,

showing how much area is burned (dark red), forest (green), rock

(dark brown), and other.

Fire Damage

______________

_______Hands-on: Draw Pie chart on paper

Estimating Fire DamageTo estimate how much

forest is damaged by fire, we will count the

number of squares that include mostly bright red areas (3 here),

then divide it by the total squares in the grid, in this case 6

If the photo map is 20Km by 30Km, then the area covered by

the map is the product of these, or 600 Square

Km

Mostly all dark

red

Three of the six squares2 / 6 = 1 / 3

33% of the area is burnedis our estimate, this is

about 200 Square Km (Km2)

7th Grade, High

School

Estimating Fire Damage

We can get a more detailed, or more

accurate, estimate by using a smaller

grid, in this case our grid with 8 vertical

labels and 12 horizontal labels,

this map has 8 x 12 squares, 96 total

27 of the 96 squares27 / 96 =

28% of the area is burnedis our estimate here, a little less

than 33% from before7th Grade,

High SchoolHands-on: On paper grids made previously

Can you complete an Estimate of the Fire

DamageGiven this grid,

what is your estimate of the fire-damaged

area?

Is it close to the previous

estimates?__ of the 24 squares

__ / 24 = __% of the area is burned,

this is __ Km2

7th Grade, High

SchoolHands-on: On paper grids made previously

Digital Camera Basics

7th Grade, High

School

Photo & Viewing Sizes

Media Horz Vert

DVDs 16 9

35mm Camera 3 2

Digital Cameras,

Monitors, TVs4 3

Photos, TVs, DVDs and other displays are generally not

square in size, they all have a specific ratio, horizontal to

vertical, sometimes called an aspect ratio. This is noted as a

ratio, Horizontal:Vertical

Digital Photos usually have a 4:3 ratio

7th Grade, High

School

Horizontal

Vertical

Hands-on: Measure distances on TV, computer monitor, DVD being played

Pixel ResolutionCamera Rating

HorzPixels

VertPixels

12 MP 4000 3000

6 MP 2828 2121

3 MP 2048 1536

7th Grade, High

School

The MegaPixel (MP) rating on a digital camera is a

specification of the number of pixels created / captured by

the camera, Mega referring to 106

With the aspect ratio at 4:3, the pixel dimension of the

longest side of a digital photo is

43

* MP

Hands-on: make calculations with calculator

Please note, a doubling of the MP rating only results in a 40% increase in pixels

(resolution)

Check your Understanding

What are the pixel dimensions of an 8 MegaPixel digital camera?

_____ X _____

7th Grade, High

SchoolHands-on: make calculations with calculator

Camera Lenses

7th Grade, High

School

Hands-on: for multiple zoom settings on the digital camera, measure multiple distances and photo width, calculate angles, make summary table.

The angle of photo captured from a camera is dependent

upon the length of the lense focal

length, measured in

mm

AngleLenseArea in Photo

Film or CCDs

The digital camera we will use changes lense length

through zoom, from 45mm to 55mm, we will use 50mm for this activity, a common sized

lense.

Some example angles by lense size include:

Lense Size (mm)

20 35 45 50 55 100

Horizontal Angle

83 53 45 39 36 20

Reference: Lense angle chart

Aerial Photo Resolution

7th Grade, High

School

Camera

Rating

HorzPixels

VertPixels

12 MP 4000 3000

6 MP 2828 2121

3 MP 2048 1536

In order to see fire areas in a photo, endangered species, or invasive species, we need to create aerial photos with a minimum resolution. There should be at least one pixel for every foot on the ground. It would be best if we have photos that have 10 or more pixels per foot. The MP resolution of the camera effects this, remember the table we had before.

Pixels per foot

Horz Distance

VertDistance

1 4000 ft 3000 ft

4 1000 750

12 333 250

In order to determine how high to fly our plane with the digital camera, we need to determine how much area should be covered by the camera on the ground.

If we use a 12 MP camera, there are 4000 x 3000 pixels captured, if we need 1 pixel per foot, then the area on the ground should be 4000 ft x 3000 ft, easy yes? How about four pixels per foot (divide distance by 4), twelve pixels per foot (divide distance by 12), what is the ground area for these?

Aerial Photo Resolution

7th Grade, High

School

Camera

Rating

HorzPixels

VertPixels

12 MP 4000 3000

6 MP 2828 2121

3 MP 2048 1536

Can you complete a table for a 3 MP camera ?

Pixels per foot

Horz Distance

VertDistance

1

4

12

Flying Height Calculations

High School

Hands-on: make calculations with calculator, Sine, Cosine, and Tangent

Given the table you completed for a 3 MP camera with a 50 mm lense. We will calculate the distance above the ground the Plane needs to fly in order to get 12 Pixels per foot resolution. This will take some Trigonometry...specifically Tangent

390

Height

512 Ft

Trig provides several functions to help in determining the length of sides on a right triangle, given an internal angle is known.So we create a right triangle between the camera and the ground. This bisects the lense angle (39/2) and the width of the photo area on the ground (512/2).

256 ft

Height

19.50

Please note, since two internal angles are known for this right triangle, the third angle can be found, all three angles in a triangle sum to 180. That angle is 70.50.

Height = 256 /Tan-1(19.50) =240 Feet

Tan (19.50) = 256 / Height

A Check on Understanding

High School

Hands-on: make calculations with calculator (TI83 or HP50, for example)

Pixels per foot

Horz Distanc

e

VertDistanc

e

Height above

Ground

1 2048 1536 2891

4 1024 768 722

12 512 384 240

Can you calculate the height above ground for this 3 MP camera with a 50 mm lense, given pixel resolutions of 4 per foot and 1 per foot.

Unit Conversions

7th Grade, High

School

Units and Conversions

7th Grade, High

School

So far we have used several types of unit measurements: KiloMeters, Milimeters, Feet, and Pixels. We will also be using Miles, so we need to review how to make distance unit conversions between Metric (meters, Km, mm) and English (Miles, feet).

References: Unit Conversion, Metric prefixes and Metric Conversions

Unit conversions can be made within the English or metric systems:

1000 meters = 1Km1000 mm = 1 MeterIn these cases, move the decimal three places.

Within the English system it is a bit more difficult, conversion factors must be used, for distance5280 ft = 1 mile, use the conversion factor of 5280 ft/Mi.

Show some example conversions and have student complete some conversions.

Aerial Photos

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Photo RC Plane Flight PlanTo plan a flight path of an RC plane we will first assume a 3MP camera with a 50mm lense, this is a common digital camera you can buy in most any electronics store.

We require a resolution of 3 pixels per foot on the ground so that we have photos with sufficient detail for analysis (10X the detail of satellite photos).

This means we must fly the RC plane 250 feet above the ground while taking the photos. The photos will therefore cover a path of about 500ft wide by 375ft.

We will be flying over two new areas: Bone Creek Reservoir and Crawford Wildlife area. Both satellite photos are 1 mile in one dimension, about 5000 feet. On one we will calculate the area of water and on the other the forested area (no fires in either).

Above numbers are rounded for ease of calculation.

All

What is an ArrayThe map grid we

completed previously can also be thought of as an

array.

An array is pattern of shapes (squares in this

case), number of shapes high by wide: A 2 x 3

Array

Our RC plane photos are rectangles, not squares.

The ratio of width to height is 4:3. We will

create an array of photos using these rectangles.

2

3

All

What is the Flight Path?

Hands-on: Grade 4 - place photo-sized cutouts in two patterns over the photo map. Grade 7, High School - measure photo map and calculate array.

All

Can you create an RC Plane array of photos over this area? You can fly the plane in two directions, one up / down (North / South), the other left / right (West / East).

The full area needs to be covered, so the photo array from the plane would be 10 x 10 or 8 x 14Which is better (less photos, less flying, more accurate) ?

500’

375’

5000’

3750’

All

10 x 10(100 Photos)

(Best)

8 x 14(112

Photos)

How much area is covered by forest ?

66 photos x 500’ x 375’= 12.4 Million Sq. Ft.

What is the Best Flight Path?

All

5000’

6700’

500

375

Can you determine how many photos need to be taken for this area, to determine the area of water at the reservoir?

10 x 18 (180 photos ) (west <-> East Flight Path)

or 14 x 14 (196 Photos) (South <-> North Flight

Path)

Compass Direction

All

Angles on a Compass

N

S

W E

NNE

ENE

ESE

SSE

SE

NE

SW

SSW

WSW

WNW

NW

NNW

Example: ENE“East North East”at 150 increments

4th Grade?7th Grade,

High School

3600 / 00

450

900

1350

1800

2250

2700

3150

Zero is at the top, angles in degrees going clockwise, 360 degrees total

How about another Direction?

Hands-on: Grade 4 - place photo-sized cutouts in a pattern, at an angle. Measure the angle. Convert the angle to compass direction.

5000’

6700’

How about flying at a diagonal, could this require less photos, flying, and be more efficient ?

What angle (or compass direction) would be best?

Can you do better than 6 paths, 72 photos, at 75 degrees, ENE ?

4th Grade?7th Grade,

High School

Flight Algorithm

7th Grade, High

School

What is the Flight Algorithm?

An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, sometimes named a method, procedure, or technique (Wolfram).

7th Grade, High

School

As you can see from the last two examples, the method to create the smallest flight array could be on the longest or shortest dimension, dependent upon the product of the array dimensions. And the number of photos needs to cover an equal or greater area, not less (round up of the number).

So how would you explain the steps?

Hands-on: Can this be done electronically? Possibly only on paper?

Your Procedure ?

7th Grade, High

School

Ls

Ws

Lp

Wp

Step 1: divide Ls by Lp, round up answers to the nearest integer. Divide Ws by Wp, round up the answer to the nearest integer. Step 2: State the Array ratio. Step 3: Reverse the calculations (Ls / Wp and Wz / Lp), a flight path perpendicular to the first calculation.

Step 4: Select the lowest product of each, lowest total number of photos.

Hands-on: Can this be done electronically? Possibly only on paper?

Flight Plan

7th Grade, High

School

Flying the RC Plane

7th Grade, High

School

5000’

3750’

5000’

6700’

The final calculations to be made for the flight plan are time required to fly one path, all paths, with turns and time between photos. We will assume the RC plane flys at 15 MPH and a single-engine plane flys at 75 MPH (5X faster).

500

375

Unit conversions will be required to find travel times. 5280 ft/mi and 3600 s/hr (60 s/min X 60 min/hr) are to be used.

15 MPH x 5280 ft/mi = 22 ft/s, RC Plane 3600 s/hr

75 MPH x 5280 ft/mi = 110 ft/s, Plane 3600 s/hr

Flying the RC Plane

7th Grade, High

School

5000’

3750’

To fly 3750’

- The RC plane would take

3750 ft / 22 ft/s = 170 sec = 2.8 minutes to fly one pass. With 10 paths, this would take 28 minutes to fly (not counting the turns). Photos would need to be taken every 375 feet, or every 17 seconds (375 ft / 22 ft/s).

- The single-engine plane would take

3750 ft / 110 ft/s = 34 sec = 0.57 minutes to fly one path. With 10 paths, this would take 5.7 minutes to fly (not counting turns). Photos would need to be taken every 375 feet, or every 3.4 seconds (374 ft / 110 ft/s).

Flying the RC Plane

7th Grade, High

School

5000’

3750’

When we include the turns, 9 total, we need to determine the distance for the turn. Assuming it is circular, the diameter is 500 ft, Circumference = diameter x pie, 1/2 the circumference is used for the turn, so the turn is 250 ft x Pie = 785 ft, for 9 turns, 785 ft x 9 = 7070 ft total distance in turns.

For the RC plane (22 ft/s), the turns will add 320 seconds (7070/22) or 5 minutes. Total time is 28 + 5, 33 minutes total flying time (check the RC battery).

For the plane (110 ft/s), the turns will add 64 seconds, or 1.1 minute. Total flying time is 5.7 + 1.1, or 6.8 minutes total.

500’

Turn

Check your Calculations

7th Grade, High

School

5000’

6700’

500

375

Can you determine the total flying time for this photo, both the RC plane and single-engine plane. How many seconds between photos?

Topics CoveredMapping Basics

Estimating Map Areas

Digital Camera Basics

Aerial Photos

Unit conversions

Compass Directions

Flight Algorithm

Flying Plan

Final Project 12 Miles

8 Miles

For the satellite photo of Pittsburg, determine the following RC plane plan details, given a 12MP camera with a 55mm lense and 12 pixels per foot resolution:

Grade 4- Create labels for the photo- If the RC plane flys over the area and takes a photo 1 square mile, what is the minimum number of photos required for the full photo.-Show the path you would fly to cover just the city area with pictures- How big is Pittsburg in square miles- Draw a pie chart of the types of areas in the map (City (buildings/houses), farming, forest)

Hands-on: Assemble and fly the RC plane over an area, take photos by plan (camera MP and lense, flight direction, height, time between photos, distance between paths)

Grade 7 & High School- Determine minimum photos to be taken (array) for the full area, just the city, flying direction, % area is city (buildings and houses), farming, size of the city, total flight times.High School- How high should you fly the RC plane- How often, number of seconds, should you take photos over the area- Total flight time for RC and single-engine

SummaryAs a Cartographer you are now able to make maps from photos taken by satellite and airplane to:

name specific locations on the map,

estimate how much of the ground area has been burnt by fire (or where there is fire), and

plan how you will fly your plane closer to the ground to take multiple smaller photos that will combine to show more detail.

Fly the plan, take the photos

Your work will be used by the community to estimate risk to residents, where to fight the fire, and to plan the recovery of natural resources. All

Where’s The Fireby

Larry Rice

All