October 30, 2001A&AE 451 - Fall, 20011 Critical Design Review Brian Barnett Rob Benner Alex Fleck Ryan Srogi John Keune.

October 30, 2001 A&AE 451 - Fall, 2001 1

Critical Design Review

Brian BarnettRob BennerAlex FleckRyan SrogiJohn Keune

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.

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

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

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

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

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

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

October 30, 2001 A&AE 451 - Fall, 2001 9

Aerodynamics

• Vertical Tail Sizing

v

vv x

SbVS

292.0 ftSv

(Roskam)

Aerodynamics

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

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

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

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

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

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

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

October 30, 2001 A&AE 451 - Fall, 2001 17

•Motor Performance

Motor Current (amperes)

Propulsion

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

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

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

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

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

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

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

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

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

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

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

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

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

qq

e

eeee

Aircraft Transfer Function (Short Period Approximation)

Natural Frequency and Damping Ratio

= 6.63 rad/s = 1.146

Dynamics & Control

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

October 30, 2001 A&AE 451 - Fall, 2001 32

Root Locus

Dynamics & Control

October 30, 2001 A&AE 451 - Fall, 2001 33

Bode Plot

Dynamics & Control

October 30, 2001 A&AE 451 - Fall, 2001 34

Nyquist Plot

Dynamics & Control

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

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

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

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

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

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

October 30, 2001 A&AE 451 - Fall, 2001 41

Questions?

October 30, 2001 A&AE 451 - Fall, 2001 42

Appendix

• 3-View Drawing

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

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

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

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

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

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

October 30, 2001 A&AE 451 - Fall, 2001 49

Stabilizing Root Locus

October 30, 2001 A&AE 451 - Fall, 2001 50

Stabilizing Bode Plot

October 30, 2001 A&AE 451 - Fall, 2001 51

Stabilizing Nyquist Plot

October 30, 2001 A&AE 451 - Fall, 2001 52

Step Response