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Transcript of RC Model Aircraft Design Analysis Notes ??Web viewRC Model Aircraft Design Analysis Notes

RC Model Aircraft Design Analysis Notes

RC Model Aircraft Design Analysis NotesNotes and Formulas Useful In Analyzing the Performance of Model Aircraft

William B. Garner1/1/2017

Rev 1 Notes: Revised Aircraft Lift and Drag section, adding measurement units for metric and English systemsProvides notes and formulas for the evaluation of model aircraft performance. Subjects included are aerodynamics, propellers and electric power systems.

Expanded drag equations to include fuselage and tail contributionsRemoved or modified most formulas containing English unitsCorrected several errors

Table of ContentsIntroduction2Measurement Conversion Tables3Aircraft Lift and Drag4Wing Pitching Moment (Torque)5Angle of Attack5Reynolds Number & Drag Estimating5Fuselage Drag Estimating5Climb Rate & Angle of Climb6Wing Aerodynamic Center & Mean Chord7Air Density, Standard Atmosphere7Air Foils8Flight Duration10Center of Gravity and Neutral Point12Propellers13Propeller equations15Propeller Noise17Glow Engines and Matching Propellers18Electric Power Systems19Battery Resistance19Electronic Speed Controls20ESC and Electric Motor Combined20Relationships22Newtons Method Solution25Matching motor to prop & estimating flight performance at max throttle26Bending Moment29Stress Analysis30

Introduction

Over the years I have collected a number of programs and descriptions related to the design and performance of RC model airplanes. They are scattered in various books, notebooks, document files and computer programs, making finding some particular subject sometimes a challenge. This document attempts to remedy that condition by assembling a lot of them in one place. It is limited to a set of subjects that are of most interest to the author.

Topics included are various aspects of aerodynamics, propellers and electric power systems. There is a section on in-flight performance combining the aerodynamics and electric power system to estimate flight duration as a function of power setting as well as climb performance.

The subjects are mostly presented without explanations as to their use or derivations. It is assumed the reader has some understanding of these subjects and does not need further explanations. Many of the explanations can be found in the literature, but there are a few that the author developed for a specific purpose. The section on in-flight performance was developed by the author and does contain some more detailed explanations.

The application of the formulas and other information requires the use of a consistent set of measurement units. Any set can be used; in this case the foot pound second system is used throughout. Tables are included giving conversions from this system to the metric system.

The formulas and other types of numerical information are approximations to the real world. For instance, wing profile drag coefficients change with air speed and angle of attack but it is very difficult to include these changes in any straight forward analysis. The result is that there are differences between computed results and actual results that can be quite large. It makes no sense, then, to carry out computations to 3 decimal places when the actual results may be no better than no decimal places.

There are three books that were especially helpful in understanding how models work and perform.

#1: Lennon, Andy, R/C Model Aircraft Design, Air Age, Inc., 2002.

The best source for detailed explanations of just about every RC airplane subject with math models for many of them. Much of the formulae in this document came from this source.

#2: Simmons, Martin; Model Aircraft Dynamics, Fourth Edition, Special Interest Model Books, Dorset, UK, 2002.

More qualitative than quantitative, many excellent chapters on the underlying principles of aerodynamics as applied to models. There is a large appendix devoted to airfoils and one with example calculations of aerodynamic properties.

#3: Smith, H.C. Skip, The Illustrated Guide to Aerodynamics, 2nd Edition, 1992, Tab Books (McGraw Hill),

This book was written for a private pilot so is written in a more general manner than the other books. It has lots of illustrations and photos that help in understanding the descriptions. It is a good starting book.

Measurement Conversion Tables

English Measurement Equivalents

To Convert From

Symbol

Multiply By

To Get

Symbol

Foot

Ft

12

Inches

In

Inch

In

1/12

Feet

ft

Pound

lb

16

Ounces

oz

Ounce

Oz

1/16

Pound

lb

Square foot

Ft2

144

Square Inches

In^2

Square Inches

In2

1/144

Square feet

Ft2

Foot-pound

Ft-lb

192

Inch-ounces

In-oz

Inch-ounces

In-oz

1/192

Pound-feet

Ft-lb

Brake Horsepower

BHP

746

Watts

W

Watts

W

1/746

Brake Horsepower

BHP

Revolutions/minute

Rpm

1/60

Revolutions /second

Rps

Slug

Slug

1

Lbf-sec2/ft

Lbf-sec^2/ft

English to Metric Equivalents

To Convert From

Symbol

Multiply By

To Get

Symbol

Foot

Ft

0.3048

Meters

m

Inch

In

2.54

Centimeters

cm

Inch

In

1/39.37

Meter

m

Inch

In

25.4

millimeter

mm

Mile

Mi

1.60934

Kilometers

km

Square foot

Ft2

0.092903

Square meters

M2

Square Inches

In2

6.4516

Square centimeters

Cm2

Ounces

Oz

28.3495

Gram

Grm

Pound

Lb

0.45392

Kilogram

Kg

Pound Force

Lbf

4.44822

Newton

N

Pound-force-foot

Lbf-ft

1.355818

Newton-meter

N-m

Pounds/cubic foot

Lb/ft3

16.0185

Kilograms/cubic meter

Kg/m3

Degree Fahrenheit

F

(F-32)*5/9

Degree Celsius

C

Millibar

Mb

100

Pascals

Pa

Inches Mercury

inHg

33.8639

Millibar

Mb

Inches Mercury

inHg

3386.39

Pascals

Pa

Aircraft Lift and Drag

Symbol

Description

Metric Units

British Units

b

Wing Span

m

ft

Cl

Lift Coefficient

Cdi

Wing Induced Drag Coefficient

Cdw

Wing Profile Drag Coefficient

Cdf

Fuselage Drag Coefficient

Cdt

Tail Drag Coefficient

g

Gravity Constant

9.81 m/sec^2

32.2 ft/sec^2

h

Height above sea level

m

ft

L

Lift Force

Kg-m/sec^2

Lb-ft/sec^2

Drag

Drag Force

Kg-m/sec^2

Lb-ft/sec^2

W

Mass

Kg

Lb

V

Air Speed

m/sec

ft/sec

Sw

Wing Area

m^2

ft^2

Sf

Fuselage Effective Drag Area

m^2

ft^2

St

Tail Area

m^2

ft^2

o

Air Density at Sea Level

1.225 Kg/m^3

0.00765 Lb/ft^3

Air Density Correction for Height Above Sea Level

1-8.245E-05*h

1-2.519e-05*h

Air Density = o*

Kg/m^3

Lb/ft^3

For level steady state flight, lift force must equal weight force

Lift:L = g*W

W =

The lift coefficient required to sustain an air speed of V:

Cl =

Air speed at a given lift coefficient:

Stall

Drag = Dwprofile + Dwinduced + Dfuselage + Dtail + Dother

Wing Profile Drag:

Wing Induced Drag:

,Aspect Ratio:

Fuselage Drag:

Tail Drag:

Dother:Allowance for prop wash or margin for errors. Suggest multiplying total by some factor.

Wing Planform Taper Ratio

Tau, AoA correction

Delta, Cdi correction

0

0.16

.12

.125

0.045

0.045

.25

0.01

0.02

.275

0.01

0.01

.5

0.035

0.01

.625

0.065

0.015

.75

0.10

0.025

.875

0.13

0.04

1.0

0.16

0.05

Wing Pitching Moment (Torque)

Ch = mean chord length

Angle of Attack

The actual angle of attack is a function of the lift coefficient, wing planform and the aspect ratio.

0 is angle of attack from airfoil infinite aspect ratio plot at given Cl.

Degrees

Reynolds Number & Drag Estimating

Re = =

V is the fluid velocity

L is the characteristic length, the chord width of an airfoil

is the fluid density

is the dynamic fluid viscosity

v is the kinematic fluid viscosity

v = 1.511E-05, m^2/sec at sea level

v = 1.626E-04, ft^2/secat sea level

Divide v by for other altitudes.

A tapered wing has chords that decrease in length from root to tip. This means that the Reynolds number decreases in proportion and the corresponding drag coefficient increases. The drag area will decrease with chord decrease, and since drag is proportional to area and drag coefficient, the net drag