UCSD MAE 155A Lecture # 5

Prepared by H.Altmann

18 January, 2005

Lecture # 5 - T/W , W/S, Flt Performance

• Historical overview of the different categories of aircraft.

• Mission Analysis

• Performance Analysis

– Level Flight

• Range / Endurance

– Steady Climb / Descend

– Takeoff / Landing

– Turn rate

– Specific excess power, Ps

Historical Summary Overview

• Aircraft Categories T/W; W/S, AR Mission Peculiar Attributes

• Historical developments / improvementsGas turbine improvements – TSFC , Thrust, ReliabilityMetallurgyAircraft system reliability Use of high strength compositesImproved aerodynamicsFlight Control – RSS, TVCStealth

Historical Summary Overview

• Notes• US and Russian fighters favor conventional aft tail configurations.• Latest European designs are canard-delta• T/W average: 0.63 ; Capability increased over time

•Ability to super cruise, achieve VSTOL and VSTOL in a single airframe• TVC added as an essential for agility and air superiority

• W/S average: 102 lbs/ft2 ; AR average : 2.7• Stealth forces internal carry

• A-10 is in between a bomber and fighter for the Close Air Support role.• Needs tight turning radius, thus a higher T/W and sustained load factor ( n) capability at low subsonic speed

•Bomber designs reflect the philosophy of strategic deterrence during the time period.•The Vulcan , flying wing design, reflects nuclear delivery at high speed / high altitude both- ingress and egress

Historical SummaryRough Aircraft Data - from Internet Open Sources ( Probably up to 15 % percent variation )

Payload Fraction

MTOW (lbs)

Empty Wt (lbs)

Wing area ( ft2)

Wing Span (ft)

Wing Aspect

ratio

W/S ( lbs / ft2)

Sea Level Thrust (

Dry, lbs)

T/W or for prop

P/W

Load Factor Nz(Gs)

Max Speed Mach (Kts)

Range (Nmi) / Endur ( hrs)

Service Ceiling

(ft)Manned

FightersMulti-role F-35 JSF 0.53 50,000 23,500 460 35 ft 1 in 2.67 108.7 18 K / 35 K 0.7 9? 1.5 1080

Air to air F-22 0.47 60,000 31,670 840 44 ft 6 in 2.36 71.42 X 18 K / 2 X 35 K wet 0.6 9+

2.2 / 1.5+ supercruise 50 K ft

Su-37 0.46 74,960 40,565 667.4 48 ft 2 in 3.5 112.3 2 X 34,200 0.91 9

1782 hi-alt/

1960 59 K ftTyphoon 0.52 50,715 24,244 538 35 ft 11 in 2.2 94.3 2 x 20,000 0.79 9 2 2000 55 K ftDassault Rafale 0.54 42,990 19,975 491.7 35 ft 9 in 2.6 87.4 2 x 11,240 0.52 9? 2.00

1189-1800 50 K ft

SAAB JAS-39 Gripen 0.48 27,562 14,332 275 26 ft 3 in 2.76 100 1 X 18,000 0.65

9 sustained

1.15 Low Alt 2.0 at 46 Kft > 50 K ft

2000 ft take off;> 200 deg/s roll

rateMulti-role F-16 0.48 37,500 19,520 356 32 ft 8 in 3 105 1 X 17,000 0.45 9 2 @ alt > 50 K ft

Dassault Mirage-

2000 0.54 36,382 16,758 441 29 ft 5 in 1.96 82.5 1 X 14,330 0.391.2 Low Alt 2.2 Hi Alt

Dual role F-15C 0.59 68,000 28,000 608 42 ft 9 in 3 133 2 X 29,000 0.85 9 / -3 2.5 + 65 Kft

MiG-31 0.47 90,500 47,500 730 46 ft 2.9 124 2 X 22,000 0.48 2.4 75 K ft Hi alt interceptorCAS

A-10 0.51 51,000 24,959 506 57 ft 6 in 6.53 101 2 X 9,065 0.36 70.56

(300-380) 500 -695 45 K ftTrainersBombers

B-2 0.52 336,500 162,000 > 5000 172 ft < 5.9 < 67 4 X 17,300 0.21 hi-subsonic 6000 50 K ft

B-1B 0.60 477,000 190,000 1950 137 ft / 79 ft 9.6 / 3.2 244 4 X 17,000 0.141.2 - 1.4

@ SL4000 - 5600 > 30 K ft Swing wing

B-52H 0.62 488,000 185,000 4000 185 ft 8.55 122 4 X 17,000 0.14 0.86 8,800 50 K ftAvro-

Vulcan Mk 2 0.54 200,180 92,600 3964 111 ft 3.11 50.5 4 x 20,000 0.4

0.75 Low Alt 0.95 55 K ft 65 K ft

1700 0.50

Historical Summary Overview

• Notes• Commercial aircraft data ( most reliable in the spread sheet), suggests that: AR average= 8.5; W/S average=130; T/W average=0.28 for medium to long range transports. Also notice due to metallurgy and reliability improvements, engine diameters increased considerably and thrust increased. This allowed for fewer engines and considerable reduction in spares cost. To reduce direct operating and training costs the cockpits / avionics are practically the same for Boeing’s and Airbus’ aircraft. • Military transports are high wing configurations (more efficient) AR average =8.2; W/S average=140; T/W average=0.24 (reflects then available technology)• Cruise Missile: T/W average=0.20; W/S=250. This illustrates what the embedded penalty is for having conventional takeoff and landing capability

Historical Summary - continued

Payload Fraction

MTOW (lbs)

Empty Wt (lbs)

Wing area ( ft2)

Wing Span (ft)

Wing Aspect

ratio

W/S ( lbs / ft2)

Sea Level Thrust (

Dry, lbs)

T/W or for prop

P/W

Load Factor Nz(Gs)

Max Speed Mach (Kts)

Range (Nmi) / Endur ( hrs)

Service Ceiling

(ft)Transports

C-17 0.54 585,000 269,000 3800 169 ft 10 in 7.6 154 4 X 40,440 0.276 0.74

2430 W/ 172K

payload 45 K ft

C-5B 0.55 840,000 374,000 6200 229 ft 11 in 8.5 135 4 X 43,000 0.205 0.77

2985 w/ 261 K

payload 36 K ft

28 wheels, each can be raised separately

An-124 0.57 892,872 384,653 6760 240 ft 6 in 8.55 132 4 X 51,590 0.23

2376 w/ 150 ton payload 35 K ft

Commercial Blended wing- body designs aiming for L/D = 20 -23B-777 /

200 0.45 545,000 297,250 4883 199 ft 11 in 8.18 109 2 X 77,000 0.28 0.845210 @ 34 K ft

200 ER 7730 Nmi

A-340 / 200 0.53 606,300 284,400 3892 197 ft 1 in 9.98 155 4 X 31,200 0.2 0.86 8000

B-727; 4 K hrs in windtunnel

Approx.14 K hrs in windtunnel

B-747 / 100 0.49 710,115 358,000 5500 195 ft 8 in 6.96 129 4 X 46,500 0.26 0.84 5300

Approx 25 K hrs in windtunnel

B-767 / 200 ER 0.47 345,056 181,250 3045 156 ft 1 in 8 113 2 X 50,000 0.29 0.8 6600

A-300 / 600 0.45 363,825 198,600 2800 147 ft 1 in 7.73 130 2 X 56,000 0.31 0.82 4100

A-310 / 300 0.46 330,743 178,200 2360 144 ft 8.78 140 2 X 52,000 0.31 0.84 8050

Strategic ISR

U-2 0.62 41,300 15,500 992 103 ft 10.7 41.7 1 X 17,000 0.41 373 Kts 5427 >70 K ft

UnmannedGlobal Hawk 0.61 25,600 10,000 540 116 ft 25 47.4 1 X 7600 0.3 340 Kts

12 K 35 Hr 65 K ft

Predator-B 0.586400 (

v2 10K) 2650 234 64 ft 17.5 27.3 700 SHP 0.11 220 Kts >24 hrs 45 K ftTactical ISR

Predator-A 0.49 2250 1130 122 48 ft 8.4 in 19.4 18.4 100 SHP 0.045

70 Kts cruise / 112

Kts maxup to 400 25 K ft

Heron I 0.59 2430 1000 138 54 ft 6 in 21.5 17.6 100 SHP 0.041 40 Hr 30 K ftFighter/ Bomber J-UCAS Characteristics : Stealth - Tailless- Autonomous

Cruise Missiles

d=20.4 in l=18.25 ft

Tomahawk BGM 109

up to 1000lbs payload 2800 12 8 ft 7.2 in 6.16 233 1 X 600 0.21

0.73 460 Kts 600-870 Sea launched

d=24.5 in l=20.75 ft

ALCM AGM-86B 3150 13.1 12 ft 11 240 1 X 600 0.19 460 Kts 1300 Air launched

d=27.75 in l=20.83 ft

ACM AGM-129 stealth 3700 13.6 10 ft 2 in 7.6 ? 272 1 X 732 0.2 1620 Air launchedJASSM stealth Air launched

Mission Analysis

• Understand the Customer Needs• Challenge the customer needs if appropriate• Establish / Manage Expectations

• Understand the real world constraints• Infrastructure compatibility• National and International Rules and Regulations• The physical environment

• Natural• Induced

• Technology• Competition

Strategic ISR - Mission Profile

Climb

Cruise-climbLoiter

Descent

Approx 50 - 55 K ft

RANGE RANGE

ENDURANCE

CONSTRAINTS ( additional)• Affordable System Cost / Unit Price• Infrastructure compatibility • Manufacturing size

Mission Effectiveness: Min. number of aircraft to assure continuous XX –day surveillance/ reconnaissance over a designated area at YY Nmi distance

Utility / AC = f( reliability, maintainability, L/D, TSFC, Empty wt fraction, sensor capability)

Basic Equations for Sizing and Performance

T cos( + ) – D – W sin = mV

T sin( + ) + L – W cos = mV

T

T

Along velocity vector

Normal to velocity vector

W = - C T Time rate of change of weight; Specific Fuel Consumption X thrust

C = C V Piston Engine Fuel Consumptionbhp

550 p

T = 550 bhp / V Propeller Thrust p

(Simplified Equations)

T – D – W sin = mV

L – W cos = mV

Steady Level Flight

T = D = q S ( Cdo + K CL )

L =W = q S CL

2

CD

K = 1 e AR

Breguet

R= V t ; W= -C.T t

R = V ; L=WW - C.T T=D

T= W L/D

R = V (L/D) W -C W

dR= V (L/D) dW -C W

R= V (L/D) ln ( Wi / Wf) TSFC

C= TSFC

E= (L/D) ln ( Wi / Wf) TSFC

( Range)

( Endurance)

Where, i = initial and f = final weight

R= V (L/D) ln ( Wi / Wf) BSFCE= (L/D) ln ( Wi / Wf) BSFC

( Prop Range)

( Prop Endurance)

p

p

Weight Fractions

W0 - rough sensitivity to L/D & Endurance

W0 sensitivity to L/D & Endurance

0

10

20

30

40

50

35 40 45

L/D

W0,

( x 10

00 lb

s)

E=42 hrs E=36 hrs

Assumptions for Sizing Example• Payload Weight = 2000 lbs• TSFC = 0.65= C (Raymer’s nomenclature)

Wo

guessWe/Wo Wo

Calc

24000 0.391423,724

24001 0.391823,838

23,838 0.391723,809

L/D= 40

Wo = W payload

1 - Wf / Wo – We / Wo

(-E C / (L/D))W1/ Wo = e ; Wf / Wo = 1.06 ( 1- W1 / Wo)

Climb & Unuseable Fuel

38,805 0.3743 38,768 L/D=35

17,466 0.4032 17,430 L/D=45

12,875 0.4148 12,866 L/D= 45

16,086 0.4063 16,097 L/D= 40

22,401 0.3939 22,430 L/D= 35

E=42 hrs

E=36 hrs

Design Lift Coefficient, CLdesign

1.0

1.5

2.0

3.0

2.5

3.5

4.5

4.0

5.0

5 6

5.5

87 13 14129 10 16 18 2011 22 24 26 28Wing Aspect Ratio ( AR)

Extrapolated

f(CL )design

f( CL )design = CL (AR) / Ca cos

design

0.5

( Source :L.R.Jenkinson,P.Simpkin,D.Rhodes, Civil Jet Aircraft design, p163, AIAA Education series. SAWE, paper No.2228, May 1994)

M CL design Ca

0.65-0.70 0.14-0.60 1.100.70-0.75 0.30-0.55 1.070.75-0.85 0.30-0.45 1.050.85-0.95 0.20-0.30 1.02

Global Temp Profile & ISA model

Picture 001.jpg

(Source: M.E.Eschelby, Aircraft Performance: Theory and Practice, pp 15-16, AIAA Education Series)

First Rough estimate of (T/W), (W/S)

(Level un-accelerated flight)T-D = 0L=W

T = D = 1W L (L/D) cruise

T SLS = 1 W (L/D) cruise

TSLS

x

FN =FNSL

x

Density ratio

; x 0.7 troposphere x =1.0 stratosphere

V = 2 W CL S

L = W = q S CL

Sref = S

NOW ONE CAN LAYOUT A FIRST ROUGH SKETCH START FINDING ENGINES IN THE APPROX.THRUST CLASS

Min Thrust Required

(Level un-accelerated flight)L = W = q S CL

T = q CDO + W KW ( W/S) S q

T = D = q S ( CDO + K CL )2

(T/W) = VCDO – W 2 K = 0 V W/S S V

30.5

(T/W) = - CDO + K = 0 CL CL2

CL min thrust/ = min drag

CDO

K

(T/W) = CDO + K CL CL

V min thrust/ = min drag

K CDO

2WS

D min thrust/ = min drag

q S (CDO+CDO)

Summary of L/D values for max Range and Endurance

Tactical ISR / CAS - Mission Profile

Climb

Cruise-climbLoiter

Descent

Approx. 25 - 30 K ft

RANGE RANGE

ENDURANCE

CONSTRAINTS• Affordable System Cost / Unit Price• Transportability ( Tactical ISR UAV)• Set up time – aircraft / system• Infrastructure compatibility• Icing• Winds / turbulence ( for the slow flyers)

CHALLENGES• Manned / Unmanned Teaming

•Cooperation / Collaboration

Global max horizontal wind profile

Picture 001.jpg65 K ft

0 K ft

150 Knots1000

( Source: Internet – University of York presentation on Hi- Alt Airships)

50

Thrust required and Thrust available

Thrust and Power

Transport - Mission Profile

RANGE

Climb

Altitude Hold

25 - 35-45 K ft

Loiter

Main Destination

AlternateTakeoff

TRIP FUEL

DIVERSIONFUEL

RESERVES

CONSTRAINTS

• RUNWAY LENGTH• RUNWAY LOAD CAPABILITY• RUNWAY WIDTH• TAXI WIDTH• NOISE• EMISSIONS• ICAO SPAN LIMIT• FAR 25 / JAR 25 REGULATIONS

• RATE OF CLIMB• BANK ANGLE • etc

Total Direct Operating Cost

• Standing Charge = 35 %• Crew Cost = 17 %• Airport Charge = 7 %• Fuel Cost = 27 %• Maintenance Cost = 14 %

• Total DOC = 100 %

Depreciation costInterest on investment costInsurance cost

Block time• Seat Mile Cost

• Dispatch Reliability• Passenger Load Factor

Source: L.Jenkins, P.Simpkin,D.Rhodes, Civil Jet Aircraft Design, AIAA Education Series

2005 prediction 30 40 %

Unit Price vs OEW ROI

Picture 001.jpg

( Source: L.R.Jenkinson,P.Simpkin,D.Rhodes,Civil Jet Aircraft Design, pp 303, 309, AIAA Education Series)

World Airport Runway Analysis W O R L D A I R P O R T R U N W A Y A N A L Y S I S ( S o u r c e f r o m I n t e r n e t W e b s i t e )

R u n w a y L e n g t h ( K f t )

N u m b e r o f

A i r p o r t s

P e r c e n t w i t h i n 2 0 0 0 f t

b a n d C u m u l a t i v e

R u n w a y L e n g t h

( K f t )

N u m b e r o f

A i r p o r t s

P e r c e n t w i t h i n 1 0 0 0 f t

b a n d C u m u l a t i v e

< 4 2 1 2 . 2 4 % 2 . 2 4 % 0 t o 1 0 0 . 0 0 % 0 . 0 0 %4 t o 6 1 1 8 1 2 . 5 8 % 1 4 . 8 2 % 1 t o 2 0 0 . 0 0 % 0 . 0 0 %6 t o 8 2 0 0 2 1 . 3 2 % 3 6 . 1 4 % 2 t o 3 6 0 . 6 4 % 0 . 6 4 %

8 t o 1 0 2 8 5 3 0 . 3 8 % 6 6 . 5 2 % 3 t o 4 1 5 1 . 6 0 % 2 . 2 4 %1 0 t o 1 2 2 2 3 2 3 . 7 7 % 9 0 . 3 0 % 4 t o 5 5 5 5 . 8 6 % 8 . 1 0 %

> 1 2 9 1 9 . 7 9 % 1 0 0 . 0 0 % 5 t o 6 6 3 6 . 7 2 % 1 4 . 8 2 %6 t o 7 8 6 9 . 1 7 % 2 3 . 9 9 %

T o t a l 9 3 8 7 t o 8 1 1 4 1 2 . 1 5 % 3 6 . 1 4 %8 t o 9 1 4 3 1 5 . 2 5 % 5 1 . 3 9 %

9 t o 1 0 1 4 2 1 5 . 1 4 % 6 6 . 5 2 %1 0 t o 1 1 1 3 2 1 4 . 0 7 % 8 0 . 6 0 %1 1 t o 1 2 9 1 9 . 7 0 % 9 0 . 3 0 %

D e n v e r ' s 6 t h r u n w a y = 1 6 , 0 0 0 f t l o n g 1 2 t o 1 3 5 5 5 . 8 6 % 9 6 . 1 6 %A l l o w s f u l l y l o a d e d j u m b o j e t s t o t a k e o f f 1 3 t o 1 4 2 7 2 . 8 8 % 9 9 . 0 4 %T h e o t h e r r u n w a y s a r e 1 2 , 0 0 0 f t l o n g 1 4 t o 1 5 6 0 . 6 4 % 9 9 . 6 8 %

1 5 t o 1 6 2 0 . 2 1 % 9 9 . 8 9 %1 6 t o 1 7 1 0 . 1 1 % 1 0 0 . 0 0 %

9 3 8

T y p i c a l r u n w a y w i d t h : 1 5 0 t o 2 0 0 f t

C i t y

R u n w a y E l e v a t i o n

( f t ) W o r l d C i t y P a i r

G r e a t C i r c l e D i s t a n c e

( N m i )L o n d o n t o S i n g a p o r e 5 8 5 7

D e n v e r m i l e h i g h L o s A n g e l e s t o S y d n e y 6 5 5 1N a i r o b i 5 3 2 7 L o s A n g e l e s t o S i n g a p o r e 7 6 0 0J o h a n n e s b u r g 5 5 5 9 N e w Y o r k t o S i n g a p o r e 8 2 9 1B o g o t a 8 3 5 5 N e w Y o r k t o S y d n e y 8 6 4 2Q u i t o 9 2 1 0 L o n d o n t o A u c k l a n d 9 9 1 2L a P a z 1 3 , 3 5 4 R i o d e J a n e i r o t o T o k y o 1 0 , 0 3 3

CL max

e.g Transports

The higher the CL max an aircraft needs( due to takeoff and landing) the more complex the design implementation solution. Try to keep it simple !!!

Steady Climb and Descend

(Simplified Equations)

T – D – W sin = mV =0

L – W cos = mV =0

sin =T - D WL= W cos

sin T - 1 W L/D

-1(rad)

Vv = V sin = V (T – D) = V T - l W W L/D

Vertical climb rate

Climb angle

Takeoff Analysis

a= g T- D - (W – L) W

Integrate twice to get SG

SR = 1 to 3 seconds x velocity *

n= L = S(0.9CLmax)(1.15 Vstall) = 1.2 W SCLmax Vstall

0.5 0.5 2

2

n= 1.0 + VTR =1.2 Rg

2

R = VTR 0.205 V stall

0.2g

2

hTR = R(1-cos climb)

STR = R – ( R- hTR ) 22

2

These are safety factors. Imposed by FAR / JAR & MILFAR/ JAR = 35 ftMil = 50 ft

Note *: SR - almost all aircraft rotate for takeoff. But some have hiking nose gears to set the wing at an angle of attack and don’t rotate.

Takeoff Performance

Takeoff Distance Estimate

LANDING

Typically = -3 deg.

Landing Performance

Bomber - Mission Profile ( Hi-Lo-Hi / Hi )

Climb

Cruise-climb

Descent

Up to 65 K ft

RANGE

Low

HighHigh

Mission Profile reflected the philosophy of the period.

Cruise Missile

Fighter - Mission Profile

Climb

Max. Energy climb Up to 65 K ft

RANGE

Subsoniccombat

High Supersonic dash / cruise

Min. Energy Descent

WVR - Within Visual Range

BVR – Beyond Visual Range

BVR domain / reqmts• High Altitude • Supersonic Speed• Need adequate fuel• Good radar / missiles• Stealth

WVR domain / reqmts• Low- Medium Altitude • Subsonic / Transonic Speed• Be agile – geometry control

Agility : Ability to change state rapidly and get the first shot off

Agility

Airframe agility

Turn rate

Maneuverability

Accel / Decel Roll perf Yaw Thrust / DragPitch Roll

Controllability (RSS)

Engagement < 10 sec

Observe Orient Decide Act

Human

( Source : Eidetics )

TVC

Speed

BrakesINFRASTRUCTURE• Runway length ( push to STOVL & VTOL)

RelaxedStaticstability

Turn Rate and Load Factor Equivalence(Level flight, steady turn )

L=nW

Lcos

Lsin

W

V

RHorizontal plane

= L sin = mV = mV R

2

= n Wsin = g n sin mV V

2

nWcos = W

ncos = 1; n cos =1 ; n ( 1 – sin ) = 1

n sin = n - 1

2 22

2 = g n - 1 V

2

= V R

R = V g n - 12

( Steady State Turn rate )

( Turn Radius )

Turn Rate and Load Factor Equivalence

Energy Maneuverability

Specific Excess Power and Turn Rate

Name of the game : Have MARGIN over your adversary

T=D=qS(CDo + K CL ) ; CL = nW / qS

T - CDo = K CL = K n (W/S)qS q

2

2 2 2

2n = q T - CDo K (W/S) qS

2

2

2

Minimum time to Climb – Low Thrust Fighter

Lift=Weight

Lines of constantSpecific energy, he(same for any aircraft)

e.g F-4

Tangency point = max he for particular Ps

Need to diveTo enter theSecond “ bubble”

Min Time to Climb – High Thrust Fighter

Constraints

Operating Envelope

Minimum Fuel to Climb

Constraints

Fighter Performance

Cruise Missile - Mission Profile

Climb

Cruise-climb

RANGE

Low

Climb

Cruise-climb

RANGE

Low

High- Alt Launch

Low- Alt Launch

SEA LAUNCH

AIR LAUNCH

End game

End game

CONSTRAINTS

• LAUNCH DEPTH • HANDLING WEIGHT• HYDRAULIC PRESSURE

CONSTRAINTS

• LAUNCH ALTITUDE• LAUNCH BAY SIZE• PYLON CONSTRAINTS

CONSTRAINTS

• LENGTH / DIA • FORM FACTOR• SHOCK• WING DEPLOYMENT TIME• ENGINE START TIME• ICING• TERRAIN ROUGHNESS• END GAME REQMTS

Mission Effectiveness = f( Payload, Range, P c, P arrival, P survival, P k/h, unit cost )

A Final Thought

“There is real magic in enthusiasm. It spells the difference between mediocrity and accomplishment. “

Norman Vincent Peale