Lesson objective to discuss

1

• 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
20-1
2
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 dont 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
20-2
3
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
• D(geom) typically is an equivalent, not a true
  diameter
• It is calculated from cross sectional area (Ac)
  where
• D Deq 2?sqrt(Ac/?)
• 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

20-2a
4
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)?R3 and Swet(sphere)
  4?R2
• 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
20-3
5
Parametric cylinder comparison
For purposes of comparison we assume cylinders
with hemispherical end domes so that Vol
(4??/3)?(D/2)3 ??(D/2)2?(L-D)
(?/12)?(3?L/D-1)?D3 100 cuft Swet
4???(D/2)2 ??D?(L-D) (??L/D)?D2 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

• 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

20-4
6
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

• - Minimize Swet, keep forward and aft facing
  slopes lt 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

Raw data sources - Roskam and Janes All the
Worlds Aircraft
20-5
7
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
20-6
8
Payload volume

• Varies widely with application
• - People baggage 5 lbm/ft3 (ppcf)
• - Typical cargo 10 ppcf
• - Typical cargo area / fuselage cross section
  0.67
• UAV payloads vary with type
• - Density typically ? 25 ppcf (as is almost
  everything else!)

10 ppcf
Raw data sources - Janes All the Worlds Aircraft
20-7
9
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 - 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 (Cl2)qS/(?eAR)
(Cl2)q/(?eb2) Horizontal and
vertical tail geometry is another consideration
- For pre-concept design, we only need to know
tail type (conventional, Vor tailless) and area
Parametrics provide inputs for initial sizing
20-8
10
Wing parametrics
Reasonable tip t/c upper limit 13 (RosAD.2,pp
156)
(a)
(b)
(d)
(c)
Raw data sources - Roskam, Janes All the Worlds
Aircraft and unbublished sources
20-9
11
Wing and tail parametrics
See RayAD Figs 4.20 for ?Le vs. Mmax and 4.24
for wing taper ratio (?) vs. ?.25c
?Le (degrees)
(a)
(b)
Raw data sources - Roskam, Janes All the Worlds
Aircraft and unbublished sources
20-10
12
Geometry models why?
From Chart 20-2
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 dont 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
20-11
13
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
(?) - 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
20-12
14
Fuselage model

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

V-fuse (p/4)(L/D)D31-(k1k2)/3
(20.1) Swet-fuse (p/2)D21(L/D)k1
(fe1-2) k2(fe2-2)2 Where (20.2)
k1 L1/L, fe1 arcsin(?1)/ ?1, ?1
sqrt(1-(D/L)/(2K1))2) k2 L2/L, fe2
arcsin(?2)/ ?2, ?2 sqrt(1-(D/L)/(2K2))2) Note
- arcsin(?) is expressed in radians
20-13
15
Example - TBProp
Calculate Vfuse and Swet for example TBProp UAV -
We assume payload goes in a constant area payload
section and previously caluclated required volume
26.55 cuft (720 lbm at 27.1 lbm/cuft). We
assume a cargo section packing efficiency (Pf) of
70 (30 not useable) - Center section volume
required, therefore, is 37.7 cuft - We assume a
minimum center section Lth/Diam 4 and calculate
diameter (Dcyl) of the cylindrical section
Vcyl (?/4)(Lcyl/Dcyl)Dcyl3 or Dcyl 2.29
ft - We assume the fuselage forebody transitions
to maximum diameter over a length of one diameter
and that the aftbody transitions in 2 fuselage
diameters or Lth 16.1 ft
20-14
16
Example contd
From the resulting dimensions, we calculate k1
1/7 0.143, k2 2/7 0.286 ?1
sqrt(1-(0.143/(20.143))2) 0.866 fe1
arcsin(0.866)/0.866 1.209 ?2
sqrt(1-(0.143/(20.286))2) 0.968 fe2
arcsin(0.968)/0.968 1.361 Swet
((p/2)2.292)(1(0.143)(0.143(1.209-2)
0.286(1.361-2)2) 106.3 ft2 Vol
(p/4)(7)D31-(.143.286)/3 56.5 cuft Of
the total fuselage volume available of 39.7
cuft - 26. 6 cuft is allocated to payload,
leaving 13.1 cuft available for fuel and systems
20-15
17
Fuselage/nacelle model
Combined Swet? fuselage SwetKswet ?nacelle Swet
(20.4)
20-16
18
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 4Vol/(?Lth/Deng)1/3 1.33
• - Dnac, therefore, 1.331.25 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

20-17
19
Fuselage/nacelle model
Multi-engine jet
Combined Swet? fuselage Swetneng?Kswet???Dnac?Lna
c Note - 0.0 lt Kswet lt 1.0 - Dnac ?
1.25?Deng - neng Number of engines
(20.5)
Single engine jet
Kswet?0.5
L
Combined Swet? fuselage Swetneng?Kswet???Dnac?Lna
c (20.6)
20-18
20
Fuselage/nacelle - contd
Integrated jet
Combined area ? fuselage area 5Aeng Note -
Aeng Engine area at front face (20.7)
Non-circular cross section
Swet-fuse (p/2)De21(L/De)k1(fe1-2)k2
(fe2-2)2 sqrth/ww/h/sqrt(2)
(20.8) De sqrt(w?h)
where
20-19
21
Example nacelle (jet)

• Jet engine nacelle diameters are also estimated
  from engine size required but use engine airflow
  (WdotA) to calculate diameter using Raymers
  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

20-19a
22
Pods, stores and multi-fuselages
Model as multiple ellipse-cylinders per Eqs. 20.1
and 20.2
with non-circular cross sections
Apply Eq. 20.8 as correction factors
20-20
23
Data correlation

• Fuselage volume and area data not widely
  published
• - RosAP Table 5.1 has Swet-fuse data for some
  general aviation (GA) aircraft and jet transports
• - Data correlates reasonably well with Eqn 20.2
  (/- 10)
• - Eq 20.1 predicts Raymer Fig 7.3 fuselage volume
  (/- 10)

Fuselage wetted area
Total wetted area
6000
10000
5000
8000
4000
6000
Swet-fuse from Eq 20.2
3000
Swet-fuse from Eq 20.2
4000
2000
2000
1000
0
0
0
2000
4000
6000
8000
10000
0
1000
2000
3000
4000
5000
6000
Swet Raymer Fig 7.3
Swet - Roskam (RosAP) Table 5.1
20-21
24
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
(Cl2)qS/(?eAR) (Cl2)q/(?eb2)
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
20-22
25
Wing model
Geometry model - Truncated pyramid for fuel
volume - Wing exposed area for Swet
Vpyrmd A(base)hgt/3
Cr 2Sref/b(1 ?)
V-fuel (4/3)(KcPf(t/c)Sref2/b(1-?)(1
?)2 (1-?1(1- ?))3 - ((1-?2(1- ?))3
(20.9) Where Kc Tank chord
ratio Pf packing factor ( 0.8) ?1
2Y1/b ? taper ratio (Ct/Cr) ?2
2Y2/b SrefExp Sref(1-(D/b)(2-(D/b)(1-
?))/(1 ?)) (20.10)
20-23
26
Example
1. Calculate SwetExp for the example TBProp UAV
- We select a nominal taper ratio (? 0.5) and
use starting values of t/c 0.13, AR 20 and
Sref 82.1 sqft - Fuselage diameter is 2.29 ft
(chart 20-14) - We calculate wing basic wing
geometry - b sqrt (SrefAR) 40.5 ft - Cr
2Sref/b(1 ?) 2(82.1)/40.5(1.5) 2.7
ft - Ct ?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 (?1 Df/b 0, ?2 0.8)
and nominal packing factor (Pf 0.8) and tank
chord ratios (Kc 0.5) - From equation 20.10,
Vwing-fuel (2/3)KcPf(t/c)Sref2/b(1-?)
(1 ?)2 (1-?1(1- ?))3 - ((1-?2(1- ?))3
4.5 cuft
20-24
27
Tails

• Tails - Horizontal and vertical tail areas can be
  expressed as nominal fractions of Sref
• Sht KhtSref (20.11)
• Svt KvtSref (20.12)
• Where for an average air vehicle (chart 20-10)
• Kht .25
• Kvt .15
• Tail wetted area 2planform area
• For V-tails - Use projected areas or
• KV-tail 2sqrt(Kht/22Kvt2) (20.13)

20-25
28
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 106.338.62(75.820.515.6) 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
• b2/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

20-26
29
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 ? 1.32.5 3.25 psf
• Tails Uwht Uwvt ? 1.32.0 2.6 psf
• Fuselage (nacelle) ? 1.31.4 1.8 psf
• Using these values we can estimate from geometry
  
• Waf (106.338.6)1.875.83.2532.82.6 593
  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

20-27
30
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
  payload and remaining systems (25 pcf), fuselage
  volume required for payload, fuel (less 4 cuft in
  the wing) and systems is
• Vr pfs 26.55(360/40)350/25-4.5/0.7 64.4
  cuft
• Which compares to total fuselage volume available
  of 56.5 cuft (chart 20-15)

Converged TBP weights (lbm) Waf 496
Wpay 720 Weng (instl) 109 WF
360 Wlg 103 Wmisc 22 Wspa
247 W0 2056 We 954 EWF
0.46
20-28
31
New size and airframe weights

• 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 2.29cube(64.4/56.5) 2.4 ft
• At Lf/Df 7, Lf 2.47 16.8
• Engine size would also change
• Bhp0 0.0922056 lbm 189.1 Bhp
• Weng 189.1/2.25 84.1 lbm, Vol eng 84.1/22
  3.8 cuft, Deng 4Vol/(?Lth/Deng)1/3 1.25
  ft and Dnac 1.251.25 1.56 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
20-29
32
Converged weight/volume/size

• After a number of iterations, the weight, volume
  and size calculations will converge to a
  consistent set of values
• Volume available Volume required/0.7 67.4
  cuft
• Df 2.44 ft, Lf 2.437 17 ft
• Engine size 201 Bhp, Weng(uninstalled) 89.3
  lbm
• Vol eng 4.0s cuft, Dnac 1.6 ft
• Sref 72.9 sqft, Swet 348 sqft, b 38.2 ft,
  Swet/Sref 4.78, b2/Swet 4.19 LoDmax 27.4,
  Waf/Sref 7.88

Converged TBP weights (lbm) Waf 572
Wpay 720 Weng (instl) 116 WF
382 Wlg 109 Wmisc 22 Wspa
262 W0 2184 We 1160 EWF
0.49
20-30
33
Parametric comparison
Comparison shows the airframe weights are
consistent with the parametric data but that fuel
fraction continues to be low for a TBProp
Global Hawk
20-31
34
Reference
For more information on geometry model
methodology see my paper - Preliminary Sizing
Methodology for Hypersonic Vehicles, AIAA
Journal of Aircraft, March 1992
20-32
35
Homework

• Work your way through the example problems in
  this lesson and check/document the area, volume
  available, volume required, LoDmax and weight
  calculations. Compare your results using
  ASE261.Geometry.xls and identify any differences
  (team grade)
• 2. Use spreadsheet ASE261.Geometry.xls to
  calculate first and second pass values for your
  proposed air vehicle using the example problem
  inputs for Cfe, e and component unit weights
  (individual grade)
• 3. Discuss ABET issues 3 and 4 and document
  your conclusions (one paragraph each team
  grade)

2nd week
20-33
36
Intermission
20-34