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October 30, 2001 A&AE 451 - Fall, 2001 1
Critical Design Review
Brian BarnettRob BennerAlex FleckRyan SrogiJohn Keune
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October 30, 2001 A&AE 451 - Fall, 2001 2
Preliminary Design• Initial Weight Estimation (Historical Data)
– Payload = approx 1.18 lb• 3 Battery Cells• Rate Gyro
– Weight = approx 5 lb.
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October 30, 2001 A&AE 451 - Fall, 2001 3
Preliminary Design• Equations of Constraint (Roskam)
– Loiter Velocity
– Turn Radius
– Climb Angle
cruisep VqCd
S
W
P
W
****550
S
WVCdq
S
WK
rg
V
VP
W cruiseocruise
cruise
p ***
*2*
)**(**550
2
3
19*
***
9.
2/3
2
Cl
eAR
ClCd
S
W
RCP
P
W
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October 30, 2001 A&AE 451 - Fall, 2001 4
Preliminary Design
ClVS
Wstall ***
2
1 2
2
max
)(*0148.0*13.8/
*87.0*
TOPTOPRollOT
SW
CTOP
P
W L
• Equations of Constraint (Roskam)– Ground Roll
– Stall
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October 30, 2001 A&AE 451 - Fall, 2001 5
Preliminary Design• Constraint Diagram
W/P = 23 lb/hp
W/S = 0.55 lb/ft2
With AR=6, S = 9.1 ft2
b = 7.4 ft c = 1.2 ft
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October 30, 2001 A&AE 451 - Fall, 2001 6
Aerodynamics• Airfoil Selection
– Best endurance when CL3/2/CD is maximized
– Selig airfoils for low Re flight– 2-D Data readily available online (www.nasg.com)– Compared 13 Selig airfoils
• Roskam method used to generate CL and CD values
eAR
CCC
d
d
S
SCCC
CCC
LDD
htLLL
LLoL
hwf
2
0
1
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October 30, 2001 A&AE 451 - Fall, 2001 7
AerodynamicsCL
(3/2)/CD
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12
Alpha (deg)
CL
(3/2
) /CD
S1210
S2048
S2048
S2055
S2091
s3010
S3016
s3014
Selig S1210 Airfoil
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October 30, 2001 A&AE 451 - Fall, 2001 8
Aerodynamics• Twist for elliptical loading
22
14)()(
b
y
CC
yCyC
L
l
.,),( constCCyC L
Elliptical Lift Distribution
-10
-8
-6
-4
-2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2y/b
Cl ,
(
deg
)
Cl
Alpha (deg)
• Elliptical Loading• 12º total twist• Very high d/dy near wing tips• Twist for elliptical loading very
difficult to manufacture
• Linear Twist• 3º twist is sufficient to ensure initial
stall at root
• Angle of incidence• CL
3/2/CD peaks at 3º
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October 30, 2001 A&AE 451 - Fall, 2001 9
Aerodynamics
• Vertical Tail Sizing
v
vv x
SbVS
292.0 ftSv
(Roskam)
Aerodynamics
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October 30, 2001 A&AE 451 - Fall, 2001 10
Longitudinal Xplot
SM = 15%
Horizontal Tail Area = 1.7 ft2
Xcg = 0.37c
Xac = 0.52c
Aerodynamics
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October 30, 2001 A&AE 451 - Fall, 2001 11
Propulsion
•Power Analysis
• Preq= Ppout= Ppin* p
• Ppin= Pgout
• Pgout= Pgin * g
• Pgin = Pmout
• Pmout = Pmin * m
• Pmin = Pbout
Battery SpeedController Motor Gearbox Propeller
pgm
Ppout
Pgout = PpinPmout = Pgin Pbout = Pmin
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October 30, 2001 A&AE 451 - Fall, 2001 12
•Propeller Selection
• Power required from aerodynamics• 8.6 ft*lbf/sec
• Gold matlab code
• 15 x 10 propeller was chosen
42 *** DnCP ppout
n = RPM/60 = HzD = propeller diameter
p = .766
Propulsion
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October 30, 2001 A&AE 451 - Fall, 2001 13
PropulsionEffect of Differing Prop Diameter with Pitch = 10”
Pro
p
Eta
Power Out (ft*lbf/sec)
RPM =1910
Eta =.766
Ground Clearance Constraint (15”)
D=8”
D=18”
D=16”D=14”
D=12”
D=10”
Power Required=8.6
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October 30, 2001 A&AE 451 - Fall, 2001 14
•Gearbox Selection
• Ppin= Pgout = 11.23 ft*lbf/sec
• Pgin = Pgout / .95 = 11.82 ft*lbf/sec
• Gear ratio = 3:1
g = .95
Propulsion
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October 30, 2001 A&AE 451 - Fall, 2001 15
•Propeller Selection
•Power required from aerodynamics
•8.6 ft*lbf/sec
•Gold matlab code
•15 x 10 propeller was chosen
Propulsion
42 *** DnCP ppout n = RPM/60 = HzD = propeller diameterJ = V/(n*D)
p = Ct*J/Cp = .766
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October 30, 2001 A&AE 451 - Fall, 2001 16
•Motor Selection• Pgin = Pmout = 11.82 ft*lbf/sec
• RPM = 1910• Matlab script was run for 615 motors• Motor was chosen for highest efficiency using three
battery cells
Propulsion
•Efficiencies
m = .519 g = .95 p = .766 tot = .378
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October 30, 2001 A&AE 451 - Fall, 2001 17
•Motor Performance
Motor Current (amperes)
Propulsion
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October 30, 2001 A&AE 451 - Fall, 2001 18
•Battery Selection
•3 x Panasonic NiMH batteries•3000 mAh•1.2 V/cell•57.4 g/cell
Propulsion
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October 30, 2001 A&AE 451 - Fall, 2001 19
PropulsionMaxx Products Cobalt 400 14T•Kv = 2290 RPM/V•Io = 2.5 A•Imax = 20 A•Rm = .108 Ohm•$70.00
Maxx Products Ball Bearing Gearbox•Ratio 3:1•$22.50
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October 30, 2001 A&AE 451 - Fall, 2001 20
Finite Element Methods Modeling
Moment of Inertia: I = 2(Aflange x d2) + 1/12 (bweb x h3web)
3/8”
1/8”
3/8”All Spars
Structures
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October 30, 2001 A&AE 451 - Fall, 2001 21
Bending Load Carried in Spars
•Huge percentage of bending moment transmitted to all spars
•Max stress: max = Mmaxy
IUniform Pressure Load:
2.5 lbs x 2.5 g’s = 6.25 lbs
6.25 lbs x 1.5 safety factor =
Applied Load = 9.38 lbs
Divided by ½ Wing Area:
9.38 lbs / 648 in2 = Distributed Pressure Load = .0145 psi
Structures
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October 30, 2001 A&AE 451 - Fall, 2001 22
FEM Calculated Weight:
.56 lbs for ½ wing
Exaggerated Wing DeflectionFEM Results:
max = 273.3 psi
max = .34”
Balsa Properties:
yield = 1725 psi(WT team, Spring ’99)
Structures
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October 30, 2001 A&AE 451 - Fall, 2001 23
Buckling Load:
•FEM calculates Eigenvalue of stability problem
•This value is a load multiplier for buckling to occur
Wing Spar Buckling Point
Evalue = 5.443
Applied Load = .0145 psi
Buckling Load = .0789 psi
Structures
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October 30, 2001 A&AE 451 - Fall, 2001 24
Fuselage Structure•Employing bulkheads/stringers for ease of manufacturing
•Tail-boom to be captured through reinforced bulkheads
•Terminates at wing bolt-down block
•Pinned to prevent rotation
•Removable at fuselage
junction
Structures
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October 30, 2001 A&AE 451 - Fall, 2001 25
Tail Structure•Built on a box design
•Hole drilled into box to allow tight fit of tail-boom
•Pinned design prevents rotation
•Stabilizer assembly removable
from boom
•Stabilizers manufactured from
sheet balsa with lightening holes
Structures
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October 30, 2001 A&AE 451 - Fall, 2001 26
Landing Gear Structure•Steerable nose-wheel mounted to internal firewall
•Main gear mounted to internal/external sandwich plate
•Bolt holes run vertically
between stringers
•Minimize damage if shear-off occurs
•Easily replaceable
Structures
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October 30, 2001 A&AE 451 - Fall, 2001 27
•Control Surface Sizing
41.h
e
S
S
081.S
Sa
38.v
r
S
S
Class I sizing based on historical data
235.2 ftSh
292. ftSr
209.9 ftSa 274. ftSa
235. ftSr
296. ftSe
Dynamics & Control
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October 30, 2001 A&AE 451 - Fall, 2001 28
Dihedral and Static Margin
• 2º dihedral recommended for high-wing model aircraft with ailerons and no sweep.– ‘The Basics of R/C Model Aircraft Design’
• 15% Static Margin– Mark Peters recommends 18%– Previous 451 designs have gone as low as 10%– Adjustable by moving internal components
Dynamics & Control
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October 30, 2001 A&AE 451 - Fall, 2001 29
Loop Closure
K Hg(s)
Rate GyroTransfer FunctionFeedback Gain
He(s) q(s)/e(s)
ServoTransfer Function
AircraftTransfer Function
+ -
e(s) q(s)
PilotInput
Dynamics & Control
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October 30, 2001 A&AE 451 - Fall, 2001 30
Transfer Functions
98.432.15
95.6375.6
)(
)(2
11
21
1
ss
s
MU
MZsM
UZ
MsU
MZZMsMZMU
s
sq
e
eeee
Aircraft Transfer Function (Short Period Approximation)
Natural Frequency and Damping Ratio
= 6.63 rad/s = 1.146
Dynamics & Control
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October 30, 2001 A&AE 451 - Fall, 2001 31
Transfer FunctionsFutaba S-148 Servo Transfer Function (2nd Order Approximation)
22
2
2)(
servoservo
servo
nnservo
ne sSH
21
21
1)(
GG
GGSH e
40
9501 s
Gs
G1
2
Airtronics SG-1 Gyro SystemGain K (abs value) < 1.3 deg/(deg/sec)
Dynamics & Control
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October 30, 2001 A&AE 451 - Fall, 2001 32
Root Locus
Dynamics & Control
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October 30, 2001 A&AE 451 - Fall, 2001 33
Bode Plot
Dynamics & Control
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October 30, 2001 A&AE 451 - Fall, 2001 34
Nyquist Plot
Dynamics & Control
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October 30, 2001 A&AE 451 - Fall, 2001 35
30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21-25 26-29 30 1 2 3 4 5Construction
WingTail
FuselageAssemblyChanges
Component TestingWing Strength
Boom StrengthLanding Gear
MotorControl Surface
Flight TestingPhase 1Phase 2Phase 3Phase 4Phase 5Phase 6
First FlightFinal PresentationThikol Final Report
NovemberOctober December
Flight Testing•Schedule of Events
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October 30, 2001 A&AE 451 - Fall, 2001 36
Component Testing•Test boom for structural strength with point load at end of boom•Test wing with uniform load distribution•Landing gear test for impact load carrying
•Provides time to add strength if needed before flight•Engine test on stand, check operation•Control Surface test, check operation
Flight Testing
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October 30, 2001 A&AE 451 - Fall, 2001 37
Ground Testing•Phase 1 (AR 106)
•Ground Stability Check•Phase 2 (Black IM Fields)
•Running takeoff, feedback off, turns, climbs, descents, approaches to landing
Rolling Takeoff•Phase 3 (Smooth Surface Strip)
•Stabilizing feedback on, turns, climbs, descents, approaches to landing•Phase 4 (Smooth Surface Strip)
•Destabilizing feedback, turns, climbs, descents, approaches to landing•Phase 5 (Smooth Surface Strip)
•Confined space practice, endurance test•Phase 6 (Mollenkopf)
• Stabilizing and destabilizing feedback, indoor endurance test
Flight Testing
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October 30, 2001 A&AE 451 - Fall, 2001 38
• Approximate cost for boom $25•This is available at Hobby Time
• Approximate cost for landing gear $20• This is available at Tower Hobbies
Item # Quantity Description Price Item # Quantity Description PriceGPMQ3900 1 NYLON CONTROL HORNS 0.85$ TOWR1395 1 1/4x3x36 BALSA SHEET 7.99$ GPMQ3702 1 FLEXIBLE CABLE PUSHRODS 2.99$ TOWR1500 1 1/8x1/8 BALSA STICK 3.29$ GPMQ3920 1 NYLON BELLCRANKS 1.05$ TOWR1505 1 1/8x1/4 BALSA STICK 2.99$ GPMQ3710 1 ACCU-GLIDE NYLON PUSHRODS 3.99$ TOWR1520 1 1/4x1/4 BALSA STICK 3.79$ GPMQ3750 1 THREADED PUSHRODS 2.79$ TOWR1535 1 3/8x3/8 BALSA STICK 4.79$ GPMQ3840 1 BALL LINKS 1.39$ TOWR1650 1 1/4x1/4 BALSA STICK 2.59$ GPMQ4260 1 STEERABLE NOSE GEAR 4.49$ TOWR1760 1 1/4x1-1/2 AILERON STOCK 3.49$
DAVQ5030-5530 2 LITE FLITE WHEELS 3" 9.98$ TOWR1560 1 1/2x1 BALSA STICK 4.49$ HAYQ1105 1 HINGES (20) 1.80$ TOWR1850 1 1x2 BALSA BLOCK 1.89$ TOWR3800 1 BUILD-IT CA THIN GLUE 7.99$ TOWR1920 1 1/4x6x12 PLYWOOD 1.79$ TOWR3807 1 6-MINUTE EPOXY 5.99$ TOWR1905 3 1/16x6x12 PLYWOOD 4.47$ GPMR8070 1 SILVER SOLDER 6.99$ TOWR1910 3 1/8x6x12 PLYWOOD 5.37$ GPMR1054 1 FIBERGLASS TAPE 3.99$ NHPR2211 1 BALSA MICRO-FILL 4.09$ TOWR1305 1 1/16x3x30 BALSA SHEET 4.49$ XACR4317 1 XACTO KNIFE W/ 5 BLADES 4.29$ TOWR1355 2 1/8x3x36 BALSA SHEET 10.98$ TOPQ0304 1 MONOKOTE TRANS. BLUE 12.99$ TOWR1360 1 1/8x4x36 BALSA SHEET 7.98$ TOWQ1008 1 TOWERKOTE CUB YELLOW 6.99$
TOTAL (MINUS LANDING GEAR AND BOOM: 153.04$
Brings total cost to approximately $198
Cost & Economics
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October 30, 2001 A&AE 451 - Fall, 2001 39
Man-hours devoted
0
20
40
60
80
100
120
140
160
180
200
Te
am
To
tal H
ou
rs
1 2 3 4 5 6 7 8 9 10 11Week Number
Team Time Spent
Includes time spent in classroom.
• Total hours spent: 985 hrs
•Man hours per person per week: 17.9 hrs
• Project 600 man hours for construction
Cost & Economics
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October 30, 2001 A&AE 451 - Fall, 2001 40
• Prototype Cost: $119,073985 design hours + 600 construction hours 1585 prototype development hours
• Further Production Cost: $257.54Sell 2000 aircraft kitsPrototype costs/2000 kits + kit price
• $75.00 per hour labor cost• Kit Price = $198.00
Cost & Economics
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October 30, 2001 A&AE 451 - Fall, 2001 41
Questions?
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October 30, 2001 A&AE 451 - Fall, 2001 42
Appendix
• 3-View Drawing
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October 30, 2001 A&AE 451 - Fall, 2001 43
Appendix
• Roskam Method:
eAR
CCC
KKKd
d
CKC
d
d
S
SCCC
CCC
LDD
chA
LwfL
htLLL
LLoL
wwf
hwf
2
0
19.1
4/ )(cos44.4
1
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October 30, 2001 A&AE 451 - Fall, 2001 44
AppendixCdo AR e Lift/(Weight) (lb) Rho(slug/ft^3) d (ft) b (ft) Kwf K= Beta etaH de/da i (deg) Power Req'd
0.018 6 0.85 5 0.002378 0.5 8.7 1.000611 0.875065708 0.9999 0.97 0.544138 2.5 8.630929352
K (1/piARe) Sht (ft^2) W/P (lb/hp) W/S (lb/ft2) i (rad)0.062414 2.03 23 0.55 0.043633231
S (ft2) b cVh: 0.63 xh: 3 Sh: 2.349928464 1.7??? 9.0909091 7.385489 1.23091491Vv: 0.041 xv: 3 Sv: 0.917591115
S1210ALPHA AlphRAD Cl Cd ClAlpha CLAlphaW CLAlphaWF CLAlphaH CLAlpha AlphaZL (Rad) CL0 CL CD CL^(3/2)/D Velocity (ft/s)
-5.1 -0.08901 0.294 0.0203 5.4982 0.266086039 0.266248629 4.1238602 4.12386 -0.1646 0.055408 -0.434 0.029756 #NUM! #NUM!-4.1 -0.07156 0.447 0.0148 -0.33803 0.025132 #NUM! #NUM!
-3.05 -0.05323 0.586 0.0116 AlphaZL (Deg) -0.23728 0.021514 #NUM! #NUM!-2.03 -0.03543 0.698 0.0116 -9.430885308 -0.13939 0.019213 #NUM! #NUM!-1.03 -0.01798 0.796 0.0126 -0.04343 0.018118 #NUM! #NUM!0.02 0.000349 0.904 0.0135 0.057327 0.018205 0.753958612 89.827661141.01 0.017628 1.005 0.0138 0.152329 0.019448 3.056991716 55.105981672.09 0.036477 1.116 0.0146 0.255968 0.022089 5.862676418 42.51064263.1 0.054105 1.217 0.0151 0.352889 0.025772 8.133963637 36.2052234
4.13 0.072082 1.316 0.0157 0.45173 0.030736 9.877997552 32.000080595.15 0.089884 1.409 0.0158 0.549611 0.036853 11.05617431 29.011009286.17 0.107687 1.493 0.0163 0.647492 0.044167 11.79659549 26.728423747.13 0.124442 1.571 0.0172 0.739615 0.052142 12.19886093 25.008498258.23 0.143641 1.66 0.0183 0.845173 0.062583 12.4153991 23.39471139.14 0.159523 1.721 0.0195 0.932498 0.072272 12.45953497 22.27237359
10.23 0.178547 1.778 0.0224 1.037096 0.08513 12.40637314 21.1193682211.27 0.196699 1.812 0.0273 1.136896 0.098672 12.28537184 20.1711195512.27 0.214152 1.835 0.0339 1.232858 0.112865 12.12858842 19.37019092
S1223ALPHA AlphRAD Cl Cd ClAlpha CLAlphaW CLAlphaWF CLAlphaH CLAlpha AlphaZL (Rad) CL0 CL CD CL^(3/2)/D Velocity (ft/s)
-2.68 -0.04677 0.642 0.04 5.0126 0.264844364 0.265006196 4.1238602 4.12386 -0.2519 0.07827 -0.15619 0.019523 #NUM! #NUM!-1.02 -0.0178 0.961 0.0168 -0.01097 0.018008 #NUM! #NUM!0.48 0.008378 1.131 0.0164 AlphaZL (Deg) 0.120264 0.018903 2.206368695 62.018750212.05 0.035779 1.282 0.0187 -14.43280686 0.257617 0.022142 5.905302011 42.374329573.6 0.062832 1.429 0.02 0.393221 0.027651 8.917663024 34.298247015.1 0.089012 1.548 0.0212 0.524451 0.035167 10.80001185 29.69874064
6.61 0.115366 1.671 0.0232 0.656555 0.044904 11.84727582 26.543291748.21 0.143292 1.8 0.0257 0.796533 0.057599 12.34208384 24.098411199.7 0.169297 1.91 0.0281 0.926888 0.071621 12.4595064 22.33967008
11.22 0.195826 2.016 0.0307 1.059867 0.08811 12.38367855 20.8912605112.84 0.2241 2.116 0.0336 1.201595 0.108115 12.18293575 19.6205554214.74 0.257262 2.175 0.0371 1.367819 0.134772 11.8698312 18.3897585716.38 0.285885 2.217 0.0454 1.511297 0.160554 11.57186685 17.49506218
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October 30, 2001 A&AE 451 - Fall, 2001 45
Effect of Differing Prop Diameter with Pitch = 6”
Power Out (ft*lbf/sec)
Pro
p
Eta
RPM =2430
Eta =.757
Ground Clearance Constraint (15”)
D=8”
D=18”
D=16”
D=12”D=10”
D=14”
Power Required =8.6
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October 30, 2001 A&AE 451 - Fall, 2001 46
Effect of Differing Prop Diameter with Pitch = 8”
D = 8”
D=12”D=1
0”
D=18”D=1
6”D=14”
Power Out (ft*lbf/sec)
Pro
p
Eta
RPM =2140
Eta =.765
Ground Clearance Constraint (15”)
Power Required=8.6
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October 30, 2001 A&AE 451 - Fall, 2001 47
Effect of Differing Prop Diameter with Pitch = 12”
Power Out (ft*lbf/sec)
Pro
p
Eta
Ground Clearance Constraint (15”)
D=8”D=10”
D=12”
D=14”
D=16”
D=18”
RPM =1750
Eta =.760
Power Required=8.6
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October 30, 2001 A&AE 451 - Fall, 2001 48
Dimensional Derivatives
490.42 1
2
UF
CqScq
Myy
mq
9.1811
m
CCqSZ Dl
236.8yy
m
I
qScCM e
e
25.13
m
qSCZ e
e
L
443.22 1
2
UI
CqScM
yy
m
866.6yy
m
I
qScCM
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October 30, 2001 A&AE 451 - Fall, 2001 49
Stabilizing Root Locus
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October 30, 2001 A&AE 451 - Fall, 2001 50
Stabilizing Bode Plot
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October 30, 2001 A&AE 451 - Fall, 2001 51
Stabilizing Nyquist Plot
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October 30, 2001 A&AE 451 - Fall, 2001 52
Step Response