1. Purdue University AIAA Design Build Fly Team 2007-2008
Electric Propeller Driven RC Aircraft Constraint Analysis/Weight Estimation/Flight Simulation/Optimization
Purdue University
AIAA Design Build Fly Team

2. Electric Propulsion Model
Measures of efficiency:
Battery
Motor
Propeller
Battery Energy Density: 2

3. Quantifying the target design space
CONSTRAINT ANALYSIS

4. Definition
Performance requirements imply a functional relationship between Power to Weight ratio ( ) and Wing Loading ( ).
For each phase of flight, the power to weight ratio is calculated in terms of wing loading.

5. Code Structure Turns input.dat constraint.m
(can rename as required)
Calculate
C_D, K, L/D
constraint.m
(Run this file to run code)
Takeoff
Landing
Ceiling
Rate of
Climb
Max
Speed
Turns
Turns

6. Aircraft Input Parameters

7. Takeoff
Note: Velocity taken to be mean velocity till take-off (=70% of take-off velocity)
(Brandt Eqs 5.52 and 5.77)

8. Landing
(Brandt Eqs 5.52 and 5.77)

9. Ceiling

10. Rate of Climb

11. Maximum Speed

12. Turn

13. 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.

14. The altitude is MSL (Altitude above Mean Sea Level).
The input file is called contraint_input.dat (You can rename it to whatever you want). Here is an example set of inputs:
airplane
aspect ratio
Cdo
propellor efficiency
motor efficiency
oswald efficiciency
take off
altitude (ft)
Clmax
takeoff distance (ft)
landing
altitude (ft)
landing distance (ft)
reverse force fraction
ceiling
altitude (ft)
rate-of-climb
R/C (ft/sec)
max speed
airspeed (ft/sec)
turn
altitude (ft)
airspeed (ft/sec)
load factor
Edit as required
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 Legs
Edit as required

15. Sample Output

16. Estimating aircraft weight/size
WEIGHT ANALYSIS

17. Take-Off Weight Computation
Empty
Weight
Payload
Weight
Battery Weight
for each flight leg
Rearrange terms
Mission Input
Mission
Output
Empirically
Derived
Computed for
each flight leg

18. SLUF Battery Weight Fraction
Brandt p42

19. Flight Segments Aerodynamic Model: Take-off:
Reference: Aircraft Design: A Conceptual Approach, Daniel P. Raymer
Flight Segments
Aerodynamic Model:
Take-off:
Cruise (Type 1 – Best Range; Type 2 – Velocity Specified)
Loiter (Max. Endurance)
Sustained Turn:

20. 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

21. 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.

22. The altitude is MSL (Altitude above Mean Sea Level).
The input file is called weight_input.dat (You can rename it to whatever you want). Here is an example set of inputs:
airplane
aspect ratio
Cdo
span efficiency
propeller efficiency
motor efficiency
wing loading (oz weight/ft2)
power to weight (Watt/lbf)
energy (Joules) / Battery Weight (lbf)
empty weight fraction (emperical)
payload weight (lbf)
take-off
altitude (ft)
Clmax
climb
alitude above ground to climb to (ft)
delta (% of max power) c1
altitude (ft)
cruise distance (ft) c2
cruise velocity (ft/s) lo t1
turn angle (degrees)
clmax t2
turn velocity (ft/s)
turn angle (degrees)
Edit as required
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 Legs
Edit as required
Note: Climb module available, but current version requires improvement and is not recommended for use.

23. Sample Output

24. Estimating aircraft performance
FLIGHT ANALYSIS

25. 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.

26. The altitude is MSL (Altitude above Mean Sea Level).
The input file is called flight_input.dat (You can rename it to whatever you want). Here is an example set of inputs:
airplane
aspect ratio
Cdo
span efficiency
propeller efficiency
motor efficiency
Energy (Joules) / Battery Weight (lbf)
payload weight (lbf)
empty weight (lbf)
battery weight
wing planform area (ft^2)
motor power (watts)
take-off
altitude (ft)
Clmax
climb
alitude above ground to climb to (ft)
delta (% of max power) c1
altitude (ft)
cruise distance (ft) c2
cruise velocity (ft/s) lo t1
turn angle (degrees)
clmax t2
altitude (ft)
turn velocity (ft/s)
turn angle (degrees)
Edit as required
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 Legs
Edit as required
Note: Climb module available, but current version requires improvement and is not recommended for use.

27. Sample Output

28. Iterating through the feasible design space
PERFORMACE OPTIMIZER

29. 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

30. 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.

31. 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 competition and will require to be tailored for each year’s requirements.

32. PAYLOAD MISSION T/O WEIGHT EMPTY MISSION T/O WEIGHT
Example: Flowchart
INPUT:
Wing Loading (WTO/S) & Aspect Ratio (AR)
MAIN PROGRAM LOOP
Drag
Coefficient:
Take-off
Weight:
TAKE-OFF
Take-off
Velocity:
Distance:
CRUISE
Min. Power
Cruise Point:
Battery Weight
Fraction:
TURN
Iterate load factor (n) and turn velocity.
Minimize Battery Weight Fraction:
PAYLOAD MISSION T/O WEIGHT
MISSION 2 SCORE
EMPTY MISSION T/O WEIGHT
MISSION 1 SCORE

33. Sample Output

34. Sample Output

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