2013 Chapter 7.Wing and Tail Aerodynamic Design

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Wing and tail design

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Elements of the Airfoil Lift Curve

cl

cl,max

cl,α

α0 0 α0 αcl,max α

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Evolution of NACA airfoil sections

The historical evolution of airfoil sections, 1908 1944.

The last two shapes (N.A.C.A. 661 -212 and N.A.C.A. 74 7A315) are low-drag sections designed to have laminar flow over 60 to 70 percent of chord on both the upper and the lower surface.

Note that the laminar flow sections are thickest near the center of their chords.

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Airfoil Configuration Characteristics

Chord line

Mean camber line

Leading edge

Trailing edge

Upper surface

Lower surface

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Upper surface, cl=0.22

Lower surface, cl=0.22

(v/V)2

x/c

Velocity ratio over upper and lower surfaces

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Typical Airfoil Data (NACA TR 824)

Split flap δF=60o

No flap

cl

cM,c/4

Drag bucket

cm,a.c.

Angle of attack Angle of attack

3 million<Re<9 million; std.roughness at Re=6 million

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High Lift Devices: The Flap

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0 20 40 60 δf (degrees)

Cl,max

3.2

2.8

2.4

2.0

1.6

Increase in CL,max: 2- Slot Flap Cl,max=1.6[1 + (δf /45)]

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Airfoil with Slat

slat Separation is delayed, thereby increasing the stall angle

slot

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Effect of Slat on Lift

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High Lift Devices for Maximum CL

Cl,max

Flaps Slat

Plain airfoil

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Supercritical Airfoils

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Conventional & supercritical airfoils Pressure distributions

Strong shock wave

Weak shock wave

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Integral supercritical airfoil, t/c =11%

NACA 641-212 airfoil, t/c =12%

Slotted supercritical airfoil, t/c 13.5% .02

.012

0

0 .72 M .84

Supercritical Airfoil Drag Compared to NACA Airfoil Drag

Cd

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Supercritical Airfoil, t/c=11%

NACA 641-212

Airfoil, t/c=12%

1.4

1.0

Cn

.4

0 .64 .72 M .84

Normal Force Coefficient of Supercritical Airfoil vs. NACA Airfoil

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b

c

V

Lift on a Finite Wing

2-D Lift Distribution

3-D Lift Distribution

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Wing Trailing Vortex System and Associated Downwash Field

Bound Vortex

Trailing Wingtip Vortex

Trailing Wingtip Vortex

Downwash

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Boeing 727 Trailing Vortex

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centerline

root chord, cr

tip chord, ct

half-span, b/2

Wing with high-lift devices

leading-edge slats

trailing edge flaps

inboard aileron

outboard aileron

Wing area S is found in the engine selection process

A=b2/S is selected, thereby determining span b

Λle

mean aerodynamic chord, MAC

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1/ 222 2/ 2

2 2

2

tan2 1 4

L

c

CA A

α π

βκ β

= Λ

+ + +

Lift characteristics of the 3-D wing

21 Mβ = −

Lift curve slope of the wing

4 1tan tan1LE nc

nA

λλ

− Λ = Λ + + Taper ratio: λ=ct / cr

Prandtl-Meyer function

Sweepback angles:

Airfoil lift curve slope: κ = cl,α / 2π

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max max

maxmax max max

max

max0L L

LL L

LC C

L

CC c Cc

CC

α

α α α

= + ∆

= + + ∆

Untwisted, Constant-Section Wings

wing maximum lift airfoil maximum lift

from Fig. 4.1.3.4-21a

Mach number correction from Fig. 4.1.3.4-22

(extrapolation to M=0.8 required)

wing α for maximum lift

Wing lift curve slope

Mach number correction from Fig. 4.1.3.4-21b

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Condition Typical Flap Deflection (in degrees) Take off 15<δTE<25; δLE<20 Landing 40<δTE<50 or 60; δLE<20

CL,max in Landing and Take-off Configurations

( )max 1 2 3 max basec k k k c∆ = ∆

airfoil with trailing edge flaps

(∆clmax)base is the section maximum lift increment for 25 percent-chord flaps at the reference flap-deflection angle from Fig. 6.1.1.3-12a,

k1 is a factor accounting for flap-chord-to-airfoil-chord ratios other than 0.25 from Fig. 6.1.1.3-12b,

k2 is a factor accounting for flap deflections other than the reference values from Fig. 6.1.1.3-13a, and

k3 is a factor accounting for flap motion as a function of flap deflection from Fig. 6.1.1.3-13b.

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,max ,maxWf

L

SC c K

S Λ∆ = ∆

∆CL,max for the Wing with Trailing Edge Flaps

( )( )

0

2 3/ 4/ 4 / 4

,max ,max ,max

1 0.08cos cos

/ 2

f f

c c

L L L

K

C C C

yb

δ δ

η

=

Λ = − Λ Λ

= + ∆

=

22

,max / 4

/1.28 cos

0.18f slat

L ce

c c bCb

∆ = Λ

trailing edge flaps

leading edge slats

(Note that leading edge flaps are rarely used. See p.251-258 in Torenbeek regarding high lift devices)

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centerline

half-span, b/2

Wing with high-lift devices leading-edge slat span ratio bslat/be =(b1+b2)/be

trailing edge flaps mean aerodynamic chord, MAC

b1 b2 be

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Airfoil Choice : NACA 64,-212 (ROOT) NACA 64,-209 (TIP) Aspect Ratio : A = 6.25 Taper Ratio : λ = .333 Flap Type (cf /c) : Fowler, (23%) Spanwise Extent (ηi and ηo) : 16.4% and 76.0% Rated Area (SWf /S) : 0.53

Summary of Design Lift Characteristics of the Wing

Configura-tion

Flap deflection in degrees

Slat deployment

CL,max Low speed M=0.2

CL,max cruise M=0.8

Cruise 0 no 1.23 0.99

Take-off 25 yes 1.64 -

Landing 40 yes 1.92 -

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Horizontal tail sizing lh

0.05MAC

Sh, horizontal tail planform area

Vh=Shlh/S(MAC)

Volume coefficient of the horizontal tail

L1011 Vh=0.93

CMAC/4 point

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lv

Vv=Svlv/S(MAC) Volume coefficient of the vertical tail L1011 Vv=0.59

Sv, vertical tail planform area

Sizing the Vertical Tail

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Tail Arrangement

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T-Tail: DC 9

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T-Tail: B 727

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Cruciform Tail: B1-B

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H Tail: T 46

http://aeroweb.brooklyn.cuny.edu/specs/fairchil/t-46a.htm�

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H-Tail: A 10

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H-Tail: E2-C

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V-Tail

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V-Tail: F117

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Y-Tail

F-4

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Y-Tail

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Twin Tail: F-14

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Twin Tail: F-15

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Twin Tail: F-18

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Twin Tail: F-22

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Twin Tail: MiG-25

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Boom Mounted Tail: Cessna Skymaster

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Boom Mounted Tail

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Boom Mounted Tail: JM-2 race plane

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Canard

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Canard: EF2000

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Canard: i42

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Canard: JAS

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Canard

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Canard: SU-37

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Tail Arrangement for Spin Recovery

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05-09-2012

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Tail Geometry

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The Included Material Refer to:

http://www.ae.utexas.edu/ASE261KChaput/Chapters/chapter20.ppt

http://www.ae.utexas.edu/ASE261KChaput/Chapters/chapter20.ppt�

http://www.ae.utexas.edu/ASE261KChaput/Chapters/chapter20.ppt�

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Design of UAV Systems

Air vehicle geometry c 2004 LM Corporation

Lesson objective - to discuss

Air vehicle geometry

including …

• Fundamentals

• Design drivers

• Geometry models

Expectations - You will understand how to define an air vehicle without having to draw it

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Editorial comment

Not drawing a configuration is generally a bad idea

- Air vehicles are highly integrated machines and good geometry is what makes them work

- Drawings bring multi-discipline teams together

But drawing and analyzing airplanes takes time

- Up front trade studies need to address a wide range of concepts and time is always at a premium

And sometimes design teams (especially designers) fall in love with their concepts

- Alternate concepts don’t get much attention Therefore we will develop simple analytical geometry models for initial trade studies and concept screening

- Physically capture the important design variables but minimize the time and effort required to assess them

- Use it to develop the “best” configuration concept

- Then we will draw the airplane

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Notation and constraints

In this section, some notation could be confusing - For geometry, L and D represent length and diameter. - In previous sections, they represented lift and drag

- The differences should be obvious but be alert L/D (Length/Diameter) vs. Lift/Drag could also be confusing - Both are primary parametrics, one for geometry, the other

for aerodynamics Diameter (D) typically is an equivalent, not a true value - It is calculated from cross sectional area (Ac) where

D = Deq = 2∗sqrt(Ac/π) Acceptable values of Lth/Deq vary with speed range and application - For low subsonic speeds, fuselage Lth/Deq ≥ 7, nacelles

and pods Lth/Deq ≥ 5 - For higher speeds, higher values are required

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Fundamentals

Air vehicle geometry is not just about aerodynamics, structures and signature - it is also about packaging • Efficient arrangement of pieces, parts and systems to

maximize performance and minimize penalties (cost, weight, drag, etc.)

Surface (wetted) area - the most powerful design driver • For any given volume nothing has less wetted area

(albeit at high drag) than a sphere where

V(sphere) = (4/3)*π*R^3 and Swet(sphere) = 4*π*R^2

Veff(max theoretical)* = V/Swet = R/3

• Cylinders are reasonably efficient but not at high fineness ratios. “Flattened” cylinders are inefficient

or

*Note - Volumetric efficiency (Veff) increases with size regardless of shape

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Parametric cylinder comparison

For purposes of comparison consider a family of cylinders with hemispherical end domes so that Vol = (4∗π/3)∗(D/2)^3 + π∗[(D/2)^2]∗(L-D) = (π/12)∗(3∗L/D-1)∗D^3 = 100 cuft Swet = 4∗π∗(D/2)^2 + π∗D∗(L-D) = (π∗L/D)∗D^2

Sphere (Lth/D = 1) D = 5.76 ft; Swet = 104.2 sqft Cylinder (Lth/D = 4) D = 3.26 ft; Swet = 133.7 sqft Cylinder (Lth/D = 8) D = 2.55 ft; Swet = 163.6 sqft Cylinder (Lth/D = 16) D = 2.01 ft; Swet = 203.2 sqft

or

Side View L End

View D

Study this carefully – it is a generalized cylindrical tank geometry model. • The required inputs are Volume or D and Lth/Deq (or fineness ratio)

Later we will develop similar models for fuselages, wings and tails

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- Minimize Swet, keep forward and aft facing slopes < 5 -15° Provide optimum “moment arm” for control surfaces

• Length-to-span ratios range from 0.5 to 2.5 - Slow vehicles have low Lth/b

20-5



Overall geometry drivers

• Speed and L/D drive what an air vehicle looks like - Very high speeds require high fineness ratio while low

speed vehicles can be significantly “blunter” - (L/D)max establishes the allowable span (b) and Swet

• Aerodynamic “rules” focus on wings and tails - E.g. maximize span (b) to minimize induced drag

• Fuselage rules are subjective with few parametrics Length to span ratio

0.0

0.5

1.0

1.5

2.0

2.5

0 300 600 900 1200

Vmax (Kts)

Raw data sources - Roskam and Janes All the World’s Aircraft

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Fuselage and pods

For minimum drag, we want to minimize wetted area and select shapes that match the design speed regime

- Subsonic - ogive or elliptical forebodies with tapered aftbodies (See RayAD 8.2) or shapes based on symmetrical NACA-4 Digit series

- Transonic - Sears-Haack bodies of revolution (See RayAD Fig 8.3)

- Supersonic - Modified Sears-Haack bodies per RayAD Eq. 12.46

For minimum weight, minimize wetted area and use simple geometry and “load paths”

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Payload volume

• Varies widely with application - People + baggage ≈ 5 lbm/ft^3 (ppcf) - Typical cargo ≈ 10 ppcf - Typical useable area / fuselage cross section ≈ 0.67

• UAV payloads vary with type - Density typically ≈ 25 ppcf (as is almost everything else!)

Payload density

0

2

4

6

8

10

0 10 20 30 40 50

Weight (Klbm)

Prop - passJet - pass Cargo only

2.5 ppcf 5 ppcf

10 ppcf

Fuselage cross sectional area

10

40

70

100

10 40 70 100

Nominal external area (sqft)

Nom

inal

inte

rnal

are

a (s

qft)

Raw data sources - Janes All the World’s Aircraft

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Wings and tails

During pre-concept design, the most critical design issues are area and span - Sweep, thickness and taper are also important but less

critical - See RayAD 4.3 (Wing Geometry)

Wing design drivers - Wing area establishes wing loading (W0/Sref)

- Slow flight or high flight (subsonic) means low W0/Sref - The other parameters drive weight and drag

- Thin wings have lower profile drag, but higher weight - Induced drag is driven by span, not aspect ratio

Di = (Cl^2)*q*S/(π*e*AR) = (Cl^2)*q/(π*e*b^2) Horizontal and vertical tail geometry is another consideration - For pre-concept design, we only need to know tail type

(conventional, “V”or tailless) and area Parametrics provide inputs for initial sizing

What does this say about big vs. small vehicle efficiency?

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Wing parametrics

Wing loading parametric(jet aircraft except as noted)

10000

20000

30000

40000

50000

60000

70000

0 40 80 120 160 200

Wing loading (PSF)

Initial cruiseFinal cruiseGlobal HawkPredator

Thickness ratio parametric(jet aircraft except as noted)

0

5

10

15

20

25

1 3 5 7 9 11

Aspect ratio

RootTip RootTip

Aspect ratio parametric(jet aircraft except as noted)

2

6

10

14

18

1 3 5 7 9 11

Aspect ratio

Speed parametric(jet aircraft except as noted)

2

6

10

14

18

200 600 1000 1400 1800

Maximum speed (Kts)

(a) (b)

(c) (d)

Reasonable tip t/c upper limit = 13% (RosAD.2,pp 156)

Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources

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Wing and tail parametrics

Tail area parametric

0.100 0.150 0.200 0.250 0.300

Av erage

Fighter

Jet Transp

Biz Jet

SE-prop

Exposed area/Sref

VerticalHorizontal

Speed parametric(jet aircraft except as noted)

0

10

20

30

40

50

60

70

200 600 1000 1400 1800Maximum speed (Kts)

t/c > 10%5 < t/c < 10t/c < 5%

Sht/Sref Svt/Sref

Single engine - prop 0.20 0.14 Multi engine -prop 0.26 0.14 Business Jet 0.24 0.16 Regional Turbprop 0.25 0.19 Jet Transport 0.29 0.17 Military Trainer 0.23 0.13 Fighter 0.25 0.13 Average 0.246 0.151 (b)

See RayAD Fig’s 4.20 for ΛLe vs. Mmax and 4.24 for wing taper ratio (λ) vs. Λ.25c

(a)

ΛLe

(deg

rees

)

Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources

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Geometry models – why?

Drawing and analyzing airplanes takes time - Up front trade studies need to address a wide range

of concepts and time is always at a premium And sometimes design teams (especially designers) fall in love with their concepts

- Alternate concepts don’t get much attention Therefore we will develop simple analytical geometry models for initial trade studies and concept screening - Physically capture the important design variables but

minimize the time and effort required to assess them - Use them to develop the “best” configuration concept - Then draw the airplane and analyze it to confirm the

geometry model estimates

From Chart 20-2

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Analytical geometry model

Objective - to capture key pre-concept design variables (See RayAD 7.8-7.10) 1. Independent variables

- Wing reference area (Sref) - Wing span (b) or aspect ratio (AR) - Wing taper ratio (λ) - Wing thickness ratio (t/c) - Fuselage length (L,Lf or Lth) and diameter (D,Df or Deq) - Horizontal tail exposed area ratio (Kht) - Vertical tail exposed area ratio (Kvt) - Engine length (Leng) and diameter (Deng)

2. Dependent variables - Total and component and wetted areas (Swet-wing,

fuse, ht, vt) - Component volumes (V-wing,fuse)

We will do this without making a configuration drawing

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Fuselage model

• Geometry model – Similar to cylindrical tank models except we use elliptical fore and aft bodies

L L1 L2

D

V-fuse = (π/4)*[(L/D)*D^3]*[1-(k1+k2)/3] (20.1)

Swet-fuse = [(π/2)*D^2]*{1+(L/D)*[k1*(fe1-2)+ k2*(fe2-2)+2]}

Where (20.2)

k1 = L1/L, fe1 = arcsin(ε1)/ ε1, ε1 = sqrt(1-(D/L)/(2*K1))^2)

k2 = L2/L, fe2 = arcsin(ε2)/ ε2, ε2 = sqrt(1-(D/L)/(2*K2))^2) Note - arcsin(ε) is expressed in radians

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Example - TBProp

Calculate Vfuse and Swet for example TBProp UAV - If the 720 lbm payload has a density of 27.1 lbm/cuft (calculation from Chapter 11 to be covered later) and is installed in a constant area fuselage center section, the required installation volume will be 26.55 cuft

- At an assumed center section packing efficiency (Pf) of 70% (30% not useable), volume required is 37.7 cuft

- If we assume (1) minimum overall fuselage Lth/Diam = 7, (2) the forebody transitions to maximum diameter over a length of one diameter and (3) the aftbody transitions in 2 diameters, then Lcyl/Dcyl = 4 and the diameter (Dcyl) of the cylindrical section will be given by Vcyl = (π/4)*(Lcyl/Dcyl)*Dcyl^3 or Dcyl = 2.29 ft

2.29 ft 2.29 ′ 9.16′ 4.58′

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Example – cont’d

From the resulting dimensions, we calculate: k1 = 1/7 = 0.143, k2 = 2/7 = 0.286 ε1 = sqrt(1-(0.143/(2*0.143))^2) = 0.866 fe1 = arcsin(0.866)/0.866 = 1.209 ε2 = sqrt(1-(0.143/(2*0.286))^2) = 0.968 fe2 = arcsin(0.968)/0.968 = 1.361

Swet = ((π/2)*2.29^2)*(1+(0.143)*(0.143*(1.209-2) + 0.286*(1.361-2)+2) = 106.3 ft^2

Vol = (π/4)*[(7)*D^3]*[1-(.143+.286)/3] = 56.5 cuft Of the total fuselage volume available of 39.7 cuft - 26.55 cuft is allocated to payload, leaving 13.1 cuft

available for fuel and systems

2.29 ft 2.29 ′ 9.16′ 4.58′

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Fuselage/nacelle model

Combined Swet≈ fuselage Swet+Kswet ∗nacelle Swet (20.4)

Multi-engine prop

Front L

D

Dnac

Top

Lnac

Combined Swet ≈ fuselage Swet + neng∗Kswet∗nacelle Swet Note - 0.0 < Kswet < 1.0 - Dnac ≈ 1.25∗Deng - neng = Number of engines

(20.3)

L

D

Dnac

Side

Front

Single engine prop Lnac

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Example – nacelle (prop)

• We estimate TBProp nacelle diameter from engine size required using uninstalled parametric engine weight = 100.7 lbm (chart 19-27) and density = 22 pcf

- Engine volume = Wprop/density = 100.7/22 = 4.58 cuft and nominal Leng/Deng = 2.5. Therefore, - Deng = [4*Vol/(π*Lth/Deng)]^1/3 ≈ 1.33 - Dnac, therefore, ≈ 1.33*1.25 = 1.66 ft

• We assume a minimum Lth/Dia = 5 for the pod mounted nacelle (Lth = 8.29 ft), K1 = .2 and K2 = .4 - L1 and L2 are estimated at 1.66 and 3.32 ft and … Swet-nac = 38.6 sqft

• We also assume that nacelle volume is allocated entirely to the propulsion subsystem

- No other systems or fuel will be accommodated within

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Fuselage/nacelle model

Multi-engine jet

Single engine jet

L

D

Lnac Dnac

Top

Front

Combined Swet≈ fuselage Swet+neng∗Kswet∗π∗Dnac∗Lnac Note - 0.0 < Kswet < 1.0 - Dnac ≈ 1.25∗Deng - neng = Number of engines

(20.5)

Combined Swet≈ fuselage Swet+neng∗Kswet∗π∗Dnac∗Lnac (20.6)

Kswet≈0.5 D

Lnac

Dnac

Side

Front L

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Fuselage/nacelle - cont’d

Combined area ≈ fuselage area + 5*Aeng Note - Aeng = Engine area at front face (20.7)

Integrated jet

L

D Dnac

Top Front Deng

Swet-fuse = [(π/2)*De^2]*{1+(L/De)*[k1*(fe1-2)+k2*(fe2-2)+2]} *sqrt[h/w+w/h]/sqrt(2) (20.8) De = sqrt(w∗h)

Non-circular cross section

h

Front

Top w

L

L1 L2

where

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Example – nacelle (jet)

• Jet engine nacelle diameters are also estimated from engine size required but use engine airflow (WdotA) to calculate diameter using Raymer’s engine size parametric (chart 18-18)

- Deng(ft) = WdotA/26 • Nacelle Lnac/Dnac is assumed to equal engine

Leng/Deng - Leng/Deng is determined parametrically from BPR

- See the lower right hand plot in chart 18-17 • Jet engine nacelle volume is also assumed to be

allocated entirely to the propulsion subsystem

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Pods, stores and multi-fuselages

……with non-circular cross sections

h

Front

Top w

L

L1 L2

Model as multiple ellipse-cylinders per Eqs. 20.1 and 20.2

Apply Eq. 20.8 as correction factors

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• Fuselage volume and area data not widely published - RosA&P Table 5.1 has Swet-fuse data for some general

aviation (GA) aircraft and jet transports - Data correlates reasonably well with Eq’n 20.2 (+/- 10%)

- Eq 20.1 predicts Raymer Fig 7.3 fuselage volume (+/- 10%)

Data correlation

Fuselage wetted area

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000

Swet - Roskam (RosAP) Table 5.1

Total wetted area

0

2000

4000

6000

8000

10000

0 2000 4000 6000 8000 10000

Swet – Raymer Fig 7.3

Swet

-fuse

from

Eq

20.2

Swet

-fuse

from

Eq

20.2

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WIngs and tails

During pre-concept design, the most critical design issues are area and span

- Sweep, thickness and taper are important but are less critical

- See RayAD 4.3 (Wing Geometry) Wing design drivers

- Wing area establishes wing loading (W0/Sref) - Slow flight or high flight (subsonic) means low W0/Sref

- Other parameters drive weight and drag - Thin wings have lower profile drag, higher weight

- Induced drag is driven by span, not aspect ratio

Di = (Cl^2)*q*S/(π*e*AR) = (Cl^2)*q/(π*e*b^2) Horizontal and vertical tail geometry is another consideration

- For pre-concept design, we need to know tail type and area

Parametrics provide inputs for initial sizing

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Wing model

Geometry model - Truncated pyramid for fuel volume - Wing exposed area for Swet

V-fuel = (4/3)*{[(Kc*Pf*(t/c)*Sref^2]/[b*(1-λ)*(1+ λ)^2]}* [(1-ζ1*(1- λ))^3 - ((1-ζ2*(1- λ))^3] (20.9) Where Kc = Tank chord ratio Pf = packing factor (≈ 0.8) ζ1 = 2*Y1/b λ = taper ratio (Ct/Cr) ζ2 = 2*Y2/b

SrefExp = Sref*(1-(D/b)*(2-(D/b)*(1- λ))/(1+ λ)) (20.10)

Cr

Ct

Y1

D/2

Y2

b/2 Kc*Cr

Cr = 2*Sref/b*(1+ λ)

Vpyrmd = A(base)hgt/3

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Example

1. Calculate SwetExp for the example TBProp UAV - We select a nominal taper ratio (λ = 0.5) and use starting values of t/c = 0.13, AR = 20 and Sref = 82.1 sqft (2463/30)

- Fuselage diameter is 2.29 ft (chart 20-14) - We calculate wing basic wing geometry

- b = sqrt (Sref*AR) = 40.5 ft - Cr = 2∗Sref/[b∗(1+ λ)] = 2∗(82.1)/[40.5∗(1.5)] = 2.7 ft - Ct = λ∗Cr = 1.35 ft

- From equation 20.10, we calculate SrefExp = 76 sqft 2. Calculate wing fuel volume - Assume the tank extends from centerline to 80% span

(ζ1 = Df/b = 0, ζ2 =0.8) and nominal packing factor (Pf = 0.8) and tank chord ratios (Kc = 0.5)

- From equation 20.10, Volume available for wing fuel = (4/3)∗{[Kc∗Pf∗(t/c)∗Sref^2]/[b∗(1-λ)∗(1+ λ)^2]}∗

[(1-ζ1∗(1- λ))^3 - ((1-ζ2∗(1- λ))^3] = 10.05 cuft∗Pf

Vs. calculated value of AR = 14.75 in 16-14

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• Tails - Horizontal and vertical tail areas can be expressed as nominal fractions of Sref

Sht = Kht*Sref (20.11) Svt = Kvt*Sref (20.12)

Where for an average air vehicle (chart 20-10) Kht ≈ .25 Kvt ≈ .15 • Tail wetted area ≈ 2*planform area • For V-tails - Use projected areas or

KV-tail = 2*sqrt(Kht/2^2+Kvt^2) (20.13)

Tails

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Final example – areas & aero

Using typical air vehicle horizontal and vertical tail area ratios (Kht = 0.25 and Kvt = 0.15) we can estimate tail areas for the example UAV:

- Sht = 0.25(82.1) =20.5 sqft, Svt = 0.15(82.1) =12.3 sqft We can also calculate total wetted area (fuselage and nacelle plus 2 times the exposed wing and tail areas)

Swet = 106.3+38.6+2*(76+20.5+12.3) = 362.6 sqft With these areas and assuming nominal values of Cfe = 0.0035 (RayAD Table 12.3) and e = 0.8 (chart 16-6) we can make basic aero performance estimates:

- b^2/Swet = 4.53, Swet/Sref = 4.42 and … - (L/D)max = 28.5 (Eq 16.8)

We can also use calculated component areas and wing-body-tail unit weights to estimate airframe weight

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Example – airframe weights

Unfortunately, we have no data on UAV unit weights: - All we have are RayAD Table 15.2 unit weights for

fighters, transports/bombers and general aviation where from chart 19-31, for an aircraft at our estimated wing loading (W0/Sref = 30), Waf/Sref should be ≈ 30% greater than typical general aviation aircraft

- From this we can extrapolate from RayAD Table 15.2 unit weights: - Wing: UWW ≈ 1.3*2.5 = 3.25 psf - Tails: Uwht = Uwvt ≈ 1.3*2.0 = 2.6 psf - Fuselage (+nacelle) ≈ 1.3*1.4 = 1.8 psf

Using these values we can estimate from geometry: - Waf = (106.3+38.6)*1.8+75.8*3.25+32.8*2.6 = 593 lbm

or Waf/Sref = 7.23 psf This value is 80% of the previous estimate (chart 19-27) but it should be more accurate since it captures geometry features not previously included

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New weights and volume

Using on the area based Waf/Sref, the bottoms up weight spreadsheet will converge to a new set of weights

Using typical densities for fuel (50 pcf) and 25 pcf for remaining systems, fuselage volume required (Vreqd) for payload, fuel (less wing fuel volume) and systems is: Vreqd = [26.55 + 400/(50∗.8) -10.0 + 419/25] = 43.3 cuft Which compares to fuselage useable volume available of 39.7 cuft (chart 20-15)

Converged TBP weights (lbm) Waf 594 Wpay 720 Weng (instl) 131 WF 400 Wlg 123 Wmisc 23 Wspa 296 W0 2286 We 1143 EWF = 0.52

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Since the volume available exceeds volume required, we need to resize the fuselage (and the rest of the air vehicle) to eliminate the excess - Since fuselage volume scales with the cube root of

diameter (Eq 20.1), new fuselage geometry would be Df = 2.29∗(43.3/39.7)^1/3 = 2.36 ft At Lf/Df = 7, Lf = 16.5

- Engine size would also change Bhp0 = 0.092∗2286 lbm = 210.3 Bhp Weng = 210.3/2.25 = 93.5 lbm, Vol eng = 93.5/22 = 4.3 cuft, Deng = [4∗Vol/(π∗Lth/Deng)]^1/3 = 1.29 ft and Dnac = 1.29∗1.25 = 1.62 ft

- Which then changes the geometry model, the calculated areas and weight and aero calculations …..

And the cycle continues until weight, aero, propulsion and geometry converge

New size and airframe weights

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After a number of iterations, the weight, volume and size calculations will converge to a consistent set of values - Volume available = Volume required = 50.6 cuft Df = 2.34 ft, Lf = 2.34*7 = 16.4 ft - Engine size = 198 Bhp, Weng(uninstalled) = 87.7 lbm Vol eng = 4.0 cuft, Dnac = 1.6 ft - Sref = 71.7 sqft, Swet = 336 sqft, b = 37.9 ft, Swet/Sref =

4.68, b^2/Swet = 4.27; LoDmax = 27.7, Waf/Sref = 7.71

Converged weight/volume/size

Converged TBP weights (lbm) Waf 553 Wpay 720 Weng (instl) 114 WF 377 Wlg 108 Wmisc 22 Wspa 258 W0 2152 We 1033 EWF = 0.48

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Parametric comparison

Airframe Weight Comparisons - Manned Aircraft (data from Roskam)

0

10

20

30

40

0 50 100 150

GTOW/Sref (psf)

Biz JetSE Piston PropME Piston PropReg TurboJet TransJet f ightersMil Train

UAV Fuel Fractions

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 8 16 24 32 40 48

Max Endurance (hrs)

Piston TurbopropJetJetPiston

Global Hawk

Comparison shows the airframe weights are consistent with the parametric data but that fuel fraction continues to be low for a TBProp

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Reference

For more information on geometry model methodology see my paper

- Preliminary Sizing Methodology for Hypersonic Vehicles, AIAA Journal of Aircraft, March 1992

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3. Fuselage Design

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Fuselage design factors •Optimal aerodynamics, reducing aerodynamic drag •Suppression of aerodynamic instability

•Comfortable and attractive seat design, placement, and storage space •Safety features to deal with emergencies such as fires, cabin depressurization, etc.; proper placement of emergency exits, oxygen systems, etc.

•Easy handling for cargo loading and unloading, safe and robust cargo hatches and doors

•Structural support for wing and tail forces acting in flight, as well as for landing and ground operation forces

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•Structurally optimized, saving weight while incorporating protection against corrosion and fatigue

•Optimized flight deck, reducing pilot workload and protecting against crew fatigue and intrusion by passengers

•Convenient size and placement of galleys, lavatories, and coat racks

•Suppressed noise and vibration, providing a comfortable, secure environment

•Control of cabin climate including air conditioning, heating, and ventilation

•Providing housing for different sub-systems, including auxiliary power units, hydraulic system, air conditioning, etc.

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LNC

L

LC LTC

θTC

Major components of fuselage

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•A circle has the greatest cross-sectional area per unit perimeter. The drag of a typical fuselage, which has a rather large fineness ratio (l/d), is dominated by skin friction

•A circle is strongest under internal pressure. At stratospheric cruising altitudes the outside pressure is 0.2 to 0.3 atmospheres, while the internal pressure is maintained at that at 8,000 feet, or about 0.7 atmospheres. Pressure difference across the thin skin of the cabin ranges from 0.4 to 0.5 atmospheres, or 6 to 7 psi (40 to 50 kPa)

•A circle more easily accommodates growth in Np in terms of manufacturing since cylindrical sections, called plugs, can be reasonably easily added to so-called stretched versions of a given aircraft.

Circular fuselage cross-section

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•Limited space outside the passenger compartment for auxiliary systems and cargo. The passenger compartment must be located around a diameter of the circle for the greatest width for seats and aisles.

•Awkward circular sectors above and below the passenger compartment to house other items.

•Modern designs have expanded the lower portion of the circular cabin into a more rectangular cross-section in the vicinity of the wing root chord to accommodate more internal carriage.

•Cabin forward and aft of the wing root is maintained as a circular cross-section, and stretching will require plugs to be added in these regions.

Circular cross-section limitations

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a’ a

Cargo containers

Passenger seats Passenger compartment floor

Pressure shell Passenger aisle

d

Overhead storage bins

Layout of the cabin cross-section

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Cabin cross-section

a’ a

Cargo containers

Passenger seats Passenger compartment floor

Pressure shell Passenger aisle

d

Overhead storage bins

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Cabin floor plan

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L/d = 0.9(LC /d) + 5

(LTC+LNC)/d = 5 – 0.1(LC / d)

0 2 4 6 8 10 12 LC /d

10 5 0

Correlation of fineness ratio and fuselage dimensions

L/d=0.9(Lc/d+5)

(LTC+LNC)/d=5-0.1(LC/d)

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4 3 2 1 0

LNC /d LTC /d

Tail cones

Nose cones

0 2 4 6 8 10 LC /d

Nose and tail cone correlations

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LNC

L

LC LTC

τw p p

p

d

τw

τw

Fuselage drag breakdown

, , , , , ,p NC f NC p C f C p TC f TCD D D D D D D= + + + + +

D

0 Base drag

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Nose cone pressure drag is approximately zero

Cp

1.0

0 S

Underpressure

Overpressure S

The overpressure is just about balanced by the underpressure so that the pressure drag on the nose cone is approximately zero, Dp,NC~0

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( )

, , , ,

.Re,

f NC f C f TC p BASE

p BASEwettedD f

D D D D DDSDc c M

qS S qS

= + + +

= = +

General equation for fuselage drag

( ), 3 / 2 3

1.5 74 Re, 1D fuselage Fc kc M FF F

= + +

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Variation of fuselage drag with fineness ratio

0

0.02

0.04

0.06

0.08

0.1

0.12

0 5 10 15 20

Fineness ratio

Cd

base

d on

fro

ntal

are

a

M=0.85 at 35,000ft altitudeRe~3x10 8̂

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Optimal fineness ratio The minimum drag coefficient occurs for F~3 but this would not be a practical fuselage design for safely and efficiently packing passengers

For compressible flows where M~1 the slimmer fuselages would have reduced wave drag due to compressibility and they have the advantage of efficient use of space

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Group Discussion Problem Sets

1. Describe what you think is the best air vehicle type to meet team requirements (make a sketch if needed) • Explain why you think it is a good starting point for your first

design cycle 2. Provide rationale for key configuration features (wing,

fuselage and tail type, engine location and installation type, payload and landing gear location, etc.)

3. Make a copy of the geometry worksheet from your AE261 spreadsheet program and generate a list of inputs required to calculate overall and component areas and volumes for your proposed configuration

4. Verify by hand that fuselage and nacelle wetted area and exposed wing area are correct. Sum all wetted areas and check against spreadsheet Swet (row 109)

5. Select (and provide rationale for) representative airframe unit weights for your concept and calculate the resulting airframe weights. Compare your answers with the spreadsheet result

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3-View Drawing of the Preliminary Design

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Recommended reading

Raymer - Aircraft Design - A Conceptual Approach • Chapter 6 : Initial Sizing

6.4 – Geometry sizing 6.5 – Control Surface Sizing

• Chapter 7 : Configuration Layout and Loft 7.8 – Wing-Tail layout 7.9 – Wetted area

• Chapter 9 : Crew Station, Passengers and Payload 9.1 – Introduction 9.5 – Weapons Carriage

• Chapter 11 : Landing Gear and Subsystems 11.1 - Introduction 11.2 - Landing Gear Arrangements

2013 Chapter 7.Wing and Tail Aerodynamic Design

Documents

Transcript of 2013 Chapter 7.Wing and Tail Aerodynamic Design