electric propeller driven rc aircraft constraint analysis/weight estimation/flight...
DESCRIPTION
Electric Propeller Driven RC Aircraft Constraint Analysis/Weight Estimation/Flight Simulation/Optimization. Purdue University AIAA Design Build Fly Team 2007-2008. Electric Propulsion Model. Measures of efficiency:. Battery. Motor. Propeller. Battery Energy Density:. - PowerPoint PPT PresentationTRANSCRIPT
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 ([email protected])Kyle Noth ([email protected])