Electric Propeller Driven RC AircraftConstraint Analysis/Weight Estimation/Flight Simulation/Optimization

Purdue UniversityAIAA Design Build Fly Team

2007-2008

Battery Motor

Propellerm

p

pmelec

elecmshaftp

available

requiredopellerPr

TvPPTv

PTv

PowerPower

Efficiency

battbatt W

EK

propmotoroverall

Electric Propulsion ModelMeasures of efficiency:

battK

Battery Energy Density:

CONSTRAINT ANALYSISQuantifying the target design space

DefinitionPerformance requirements imply a functional relationship between Power to Weight ratio ( ) and Wing Loading ( ).

WP

SWTO

0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

100

120

140

160

180

200 Constraint Analysis

W/S - Wing Loading (oz/ft2)

Wat

ts/W

- P

ower

Loa

ding

(Wat

ts/lb

f)For each phase of flight, the power to weight ratio is calculated in terms of wing loading.

Code Structure

input.dat(can rename as required)

constraint.m(Run this file to run code)

TurnsTurnsMaxSpeed

Rate ofClimb

CeilingLandingTakeoff

Calculate C_D, K, L/D

Aircraft Input ParametersThe following parameters must be estimated based on the type of aircraft and past experience.

Aspect Ratio Span Efficiency Factor

Zero Lift Drag

The drag for any condition is: 2LDD KCCC

o

)/(1 eARK

The maximum lift/drag ratio is oD

MAXMAX KC21E)D/L(

A sample input is provided below. This is representative of a typical conventional aircraft.

Computer Program Input aircraft (This must be the first line) 5.0 Aspect ratio (AR) 0.8 Span Efficiency (e)

TakeoffFrom Brandt et. al. Equation 5.52, the takeoff velocity is found by:

StallTO

LSL

TO

Stall

VV

CS

W

VMAX

2.1

2

The Power/Weight (Watts/lbf) ratio is given by:

gd

VWPmp

TO

*550*27.0/

3

Computer Program Input Takeoff 500. Altitude (ft) 1.5 Cl_max 75. Take off distance (ft)

Note: Velocity taken to be mean velocity till take-off (=70% of take-off velocity)

(Brandt Eqs 5.52 and 5.77)

LandingThe take off velocity is again calculated:

MAXLSL

TO

TO CS

W

V

22.1

The Power/Weight (Watts/lbf) ratio is given by:

gdVWP

mp

TO

550/

3

Computer Input Landing 500. altitude (ft) 1.5

MAXLC 100 landing distance

(Brandt Eqs 5.52 and 5.77)

CeilingThe Coefficient of lift (at minimum drag/velocity) is given as:

kCC do

l3

l

To

y CS

W

V

2

The Power/Weight ratio is given by:

gV

WPmp

y

*550*866./

Computer Input Ceiling 500. Altitude (ft)

Rate of ClimbThe Coefficient of lift (at minimum drag/velocity) is given as:

kCC do

l3

l

To

power CS

W

V

2min

The Power/Weight ratio is given by:

max

min

866.*5501/

DLV

RofCWP power

mp

Computer Input Ceiling 500. Altitude (ft)

Maximum SpeedBy definition, the dynamic pressure is:

2

21 Vq

The thrust to weight ratio is calculated by the equation:

))(1(qS

Wk

SWqC

WT

TO

TO

do

The power to weight ratio is:

mp

WTV

WP*550

)(/

Computer Input max speed 500. Altitude (ft) 100 Airspeed (ft/s)

TurnThe Power/Weight ratio for turns is determined the same way as that of the Maximum Speed function but with a load factor (dependent on bank angle) in the thrust-to-weight ratio equation.

2

21 Vq

))(1( 2

qS

Wkn

SWqC

WT

To

To

do

mp

WTV

WP*550

/

Computer Input turn 35000. Altitude (ft) 660. airspeed (ft/sec) 1.15 load factor – n

Running the Constraint Program• Download and unzip the constraint analysis code(s) from Team Center. • In the folder, you will see a program called constraint.m. This is the

master program, and it calls all of the other .m files as functions.– There is no need to edit the master program, but feel free to take a look at the

program and its functions to understand how it works.– Run constraint.m in MATLAB, it will prompt you for an input file

(contraint_input.dat).– Desired constraints can be analyzed by updating the aircraft parameters and

flight segments in the input file (contraint_input.dat).• The program will output (to the MATLAB command screen) some various

values (mostly the data you have input). If you wish to see additional numerical data, feel free to change the program to print out the data.

• A graph of Wing Loading (oz/ft2) vs. Power to Weight Ratio (Watts/lbf) will be created, showing the energy required for each of the legs of the mission. An example of the output follows.

The input file is called contraint_input.dat (You can rename it to whatever you want). Here is an example set of inputs:airplane 5.00 aspect ratio 0.08 Cdo 0.60 propellor efficiency 0.60 motor efficiency 0.80 oswald efficiciencytake off 1300. altitude (ft) 1.2 Clmax 75. takeoff distance (ft)landing 1300. altitude (ft) 1.2 Clmax 100. landing distance (ft) 0. reverse force fractionceiling 1400. altitude (ft)rate-of-climb 1400. altitude (ft) 5. R/C (ft/sec)max speed 1400. altitude (ft) 42. airspeed (ft/sec)turn 1400. altitude (ft) 50. airspeed (ft/sec) 1.15 load factor

• Each of the numbers in the input file must have a decimal in it. For example, 1.2, or 75. (not 75).

• Do not change the order of the different variables. Don’t change anything but the numbers!

• The altitude is MSL (Altitude above Mean Sea Level).

• You can repeat certain legs, for example, you can have multiple turn segments, ceilings, etc. To do so, simply add the new flight profiles to the input file. Sequence of flight segments is not important.

Mission LegsEdit as required

Edit as required

Sample Output

0 10 20 30 40 50 60 700

20

40

60

80

100

120

140

160

180

200 Constraint Analysis

W/S - Wing Loading (oz/ft2)

Wat

ts/W

- S

peci

fic P

ower

(Wat

ts/lb

f)

TakeoffLandingCeilingR of CMax VelTurn

WEIGHT ANALYSISEstimating aircraft weight/size

Rearrange terms

TO

B

TO

E

PLTO

WW

WW

WW1

Take-offWeight

EmptyWeight

PayloadWeight

Battery Weightfor each flight leg

BPLETO WWWW

Mission Input

EmpiricallyDerived

MissionOutput

Computed foreach flight leg

Take-Off Weight Computation

SLUF Battery Weight Fraction

)D/L(Kx

WW

PWK

W)D/L(P

vtxdtdxv

PWKt

WtPK

W)D/L(P

vWLDD...but...

DP

v

PDv

PTv

PowerPower

DT__&WLSLUF

battpmTO

B

elec

Bbatt

TO

pmelec

elec

Bbatt

B

elecbatt

TO

pmelecTO

pmelec

elecmShaftActual

quiredRep

TO

Brandt p42

Flight Segments

cbattmp

C

TO

B

D/Lkx

WW

maxL

TOstallLO C

S/W22.1v2.1v

)W/P(gv7.0x

TOmp

3LO

TO

oD

TOBR C

kS/W2v

Take-off:

Cruise (Type 1 – Best Range; Type 2 – Velocity Specified)

Sustained Turn:

2LDD kCCC

o

oDmax C

ARe21D/L

Aerodynamic Model:

Lbattmp

L

TO

B

D/Lkx

WW

oD

TOL C3

kS/W2v

Loiter (Max. Endurance)

maxL D/L866.0)D/L(

S/WCq

v)W/P(

S/Wkqn

TO

DmpTO

TO

o

ARe1k

1ngk

v)W/P(2WW

2batt

TTO

TO

B

Reference: Aircraft Design: A Conceptual Approach, Daniel P. Raymer

q)S/W(kqC

)S/W()D/L( 2TO

Do

TOc

Assumptions• The weight fraction is known and achievable

– 0.23 for most competitive AIAA D/B/F aircraft– 0.40 for AIAA D/B/F competition average

• The motor and propeller efficiencies are constant (not true!)• Known 2 term aircraft aerodynamic drag model is applicable

– Estimate and update based on wind-tunnel testing• Wind speeds/directions not considered

– Increased power requirement for upwind flight segments with a headwind are not offset by reduced power requirements on the downwind flight segment.

• Human-in-the-loop – Pilot cannot always operate aircraft at optimal design point!– Safety factor required to achieve design performance specification

Running the Weight Program• Download and unzip the constraint analysis code(s) from Team Center. • In the folder, you will see a program called weight.m. This is the master

program, and it calls all of the other .m files as functions.– There is no need to edit the master program, but feel free to take a look at the

program and its functions to understand how it works.– Update to input file (weight_input.txt) to include desired aircraft parameters

and define different flight segments.– Run weight.m in MATLAB, it will prompt you for an input file

(weight_input.txt).• Aircraft weight break-up and performance summary for each flight leg will

be output to the Matlab screen. An example of the output follows.

The input file is called weight_input.dat (You can rename it to whatever you want). Here is an example set of inputs:airplane 5. aspect ratio 0.08 Cdo 0.65 span efficiency 0.60 propeller efficiency 0.60 motor efficiency 22. wing loading (oz weight/ft2) 45. power to weight (Watt/lbf) 70000. energy (Joules) / Battery Weight (lbf) 0.40 empty weight fraction (emperical) 7.2 payload weight (lbf)take-off 1300. altitude (ft) 1.2 Clmaxclimb 100 alitude above ground to climb to (ft) 1. delta (% of max power)c1 1400. altitude (ft) 7000. cruise distance (ft)c2 1400. altitude (ft) 7000. cruise distance (ft) 40. cruise velocity (ft/s)lo 1400. altitude (ft) 7000. cruise distance (ft)t1 1400. altitude (ft) 720. turn angle (degrees) 1.8 clmaxt2 1400. altitude (ft) 31.05 turn velocity (ft/s) 720. turn angle (degrees)

• Each of the numbers in the input file must have a decimal in it. For example, 1.2, or 75. (not 75).

• Do not change the order of the different variables. Don’t change anything but the numbers!

• The altitude is MSL (Altitude above Mean Sea Level).

• You can repeat certain legs, for example, you can have multiple turn segments, ceilings, etc. To do so, simply add the new flight profiles to the input file. Sequence of flight segments is not important.

Mission LegsEdit as required

Edit as required

Note: Climb module available, but current version requires improvement and is not recommended for use.

Sample Output

FLIGHT ANALYSISEstimating aircraft performance

Running the Flight Program• Download and unzip the constraint analysis code(s) from Team Center. • In the folder, you will see a program called flight.m. This is the master

program, and it calls all of the other .m files as functions.– There is no need to edit the master program, but feel free to take a look at the

program and its functions to understand how it works.– Update to input file (flight_input.txt) to include desired aircraft parameters

and define different flight segments.– Run flight.m in MATLAB, it will prompt you for an input file (flight_input.txt).

• Aircraft performance summary for each flight leg will be output to the Matlab screen, including energy requirements and surplus. An example of the output follows.

The input file is called flight_input.dat (You can rename it to whatever you want). Here is an example set of inputs:airplane 5. aspect ratio 0.08 Cdo 0.65 span efficiency 0.60 propeller efficiency 0.60 motor efficiency 70000. Energy (Joules) / Battery Weight (lbf) 7.2 payload weight (lbf) 7.96 empty weight (lbf) 4.75 battery weight 14.48 wing planform area (ft^2) 895.95 motor power (watts)take-off 1300. altitude (ft) 1.2 Clmaxclimb 100 alitude above ground to climb to (ft) 1. delta (% of max power)c1 1400. altitude (ft) 7000. cruise distance (ft)c2 1400. altitude (ft) 7000. cruise distance (ft) 40. cruise velocity (ft/s)lo 1400. altitude (ft) 7000. cruise distance (ft)t1 1400. altitude (ft) 720. turn angle (degrees) 1.8 clmaxt2 1400. altitude (ft) 31.05 turn velocity (ft/s) 720. turn angle (degrees)

• Each of the numbers in the input file must have a decimal in it. For example, 1.2, or 75. (not 75).

• Do not change the order of the different variables. Don’t change anything but the numbers!

• The altitude is MSL (Altitude above Mean Sea Level).

• You can repeat certain legs, for example, you can have multiple turn segments, ceilings, etc. To do so, simply add the new flight profiles to the input file. Sequence of flight segments is not important.

Mission LegsEdit as required

Edit as required

Note: Climb module available, but current version requires improvement and is not recommended for use.

Sample Output

PERFORMACE OPTIMIZERIterating through the feasible design space

Program Format

• Software Platform: Matlab• Flight Profiles: mission1.m, mission2.m

– Specify flight segment types, distances, etc. for each flight mission

• Main program: optimize.m– Define design space, aircraft constants and scoring

parameters• Program Output: Matlab screen

– No output file

Mission Profiles (missionx.m)• Place blue text in mission files in any sequence and any number of times. Required

inputs are placed in <> and outputs include flight segment name (leg(i,:)), battery weight fraction (wb_wto(i,:)), velocity (v(i,:)) in ft/s, time (t(i,:)) in seconds and distance (x(i,:)) in feet. Input units are feet and degrees.

• Take-off:[leg(i,:) wb_wto(i,:) v(i,:) t(i,:) x(i,:)]=takeoffp((<altitude>, <Clmax>)

• Straight & Level Flight– Cruise Type 1 (Min. Power Consumption)

[leg(i,:) wb_wto(i,:) v(i,:) t(i,:) x(i,:)]=cruise1p(<altitude>, <distance>);– Cruise Type 2 (Specified Velocity)

[leg(i,:) wb_wto(i,:) v(i,:) t(i,:) x(i,:)]=cruise2p(<altitude>, <distance>, <velocity>);– Loiter (Max. Endurance)

[leg(i,:) wb_wto(i,:) v(i,:) t(i,:) x(i,:)]=loiterp(<altitude>, <distance>);• Turns

– Turn Type 1 (Min. Power Consumption)[leg(i,:) wb_wto(i,:) v(i,:) t(i,:) x(i,:)]=turn1p(<altitude>, <angle>);

– Turn Type 2 (Velocity Specified)[leg(i,:) wb_wto(i,:) v(i,:) t(i,:) x(i,:)]=turn1p(<altitude>, <velocity>, <angle>);

Note: Climb module available, but current version requires improvement and is not recommended for use.

Main Program (optimize.m)• Input aircraft parameters• Establish mission constraint to obtain required specific power

requirements– Usually take-off distance requirement

• Size aircraft for heaviest payload mission• Evaluate aircraft performance for other missions• Iterate through wing loadings and aspect ratios to optimize

parameters of interest!• File provided is based on 2007-2008 competition and will

require to be tailored for each year’s requirements.

Example: 2007-2008 FlowchartINPUT:

Wing Loading (WTO/S) & Aspect Ratio (AR)

MAIN PROGRAM LOOPDragCoefficient:Take-offWeight:

TAKE-OFFTake-off Velocity:

Take-offDistance:

PAYLOAD MISSION T/O WEIGHT

2TO

2B

TO

E

2PL2TO

WW

WW1

WW

BPLETO WWWW

)AR(eCCC

2L

DD o

maxL

TOLO C

S/W22.1v

)W/P(g

v7.0xTOmp

3LO

TO

CRUISEMin. Power Cruise Point:

Battery WeightFraction:

TURNIterate load factor (n) and turn velocity.Minimize Battery Weight Fraction:

maxbattpp

cruise

TO

B

D/Lkx

WW

)AR(eqS/Wn

S/WqC

kx

WW TO

2

TO

D

battpp

turn

TO

B o

oD

max C)AR(e1

21D/L

EMPTY MISSION T/O WEIGHT

1TO

1B

E1TO

WW1

WW

MISSION 2 SCORE

MISSION 1 SCORE

2BEloading2 WWt

1Score

1B

laps1 W

nScore

2007-2008 Sample Output

2007-2008 Sample Output

Contacts

Pritesh Mody (pcmody@purdue.edu)Kyle Noth (knoth@purdue.edu)