Transcript Air vehicle geometry

Design of UAV Systems
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
c 2002 LM Corporation
Air vehicle geometry
20-1
Design of UAV Systems
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
c 2002 LM Corporation
Air vehicle geometry
20-2
Design of UAV Systems
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
c 2002 LM Corporation
Air vehicle geometry
20-2a
Design of UAV Systems
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)**R^3 and Swet(sphere) = 4**R^2
or
Veff(max theoretical)* = V/Swet = R/3
• Cylinders are reasonably efficient but not at high
fineness ratios. “Flattened” cylinders are inefficient
*Note - Volumetric efficiency(Veff) increases with size regardless of shape
c 2002 LM Corporation
Air vehicle geometry
20-3
Parametric cylinder comparison
Design of UAV Systems
For purposes of comparison we assume cylinders
with hemispherical end domes so that
Side
View
End
View
L
D
Vol = (4/3)(D/2)^3 + [(D/2)^2](L-D)
= (/12)(3L/D-1)D^3 = 100 cuft
Swet = 4(D/2)^2 + D(L-D) = (L/D)D^2
or
Sphere (Lth/D = 1)
Cylinder (Lth/D = 4)
Cylinder (Lth/D = 8)
Cylinder (Lth/D = 16)
D = 5.76 ft; Swet = 104.2 sqft
D = 3.26 ft; Swet = 133.7 sqft
D = 2.55 ft; Swet = 163.6 sqft
D = 2.01 ft; Swet = 203.2 sqft
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
c 2002 LM Corporation
Air vehicle geometry
20-4
Design of UAV Systems
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 < 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 World’s Aircraft
c 2002 LM Corporation
Air vehicle geometry
20-5
Design of UAV Systems
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”
c 2002 LM Corporation
Air vehicle geometry
20-6
Payload volume
Design of UAV Systems
• Varies widely with application
- People + baggage ≈ 5 lbm/ft^3 (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!)
2.5 ppcf
5 ppcf
10 ppcf
Nominal internal area (sqft)
Fuselage cross sectional area
100
70
40
10
10
40
70
100
Nominal external area (sqft)
Raw data sources - Janes All the World’s Aircraft
c 2002 LM Corporation
Air vehicle geometry
20-7
Design of UAV Systems
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 = (Cl^2)*q*S/(*e*AR) = (Cl^2)*q/(*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
c 2002 LM Corporation
Air vehicle geometry
20-8
Wing parametrics
Design of UAV Systems
Reasonable tip t/c
upper limit = 13%
(RosAD.2,pp 156)
(a)
(c)
(b)
(d)
Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources
c 2002 LM Corporation
Air vehicle geometry
20-9
Wing and tail parametrics
Design of UAV Systems
Le (degrees)
See RayAD Fig’s
4.20 for Le vs.
Mmax and 4.24
for wing taper
ratio () vs. .25c
(a)
Tail area parametric
Sht/Sref Svt/Sref
Single engine - prop
0.20
0.14
Multi engine -prop
0.26
0.24
0.25
0.29
0.14
0.16
0.19
0.17
0.23
0.25
0.246
0.13
0.13
0.151
Business Jet
Regional Turbprop
Jet Transport
Military Trainer
Fighter
Average
SE-pro p
Ve rtical
Horizon tal
Biz Jet
Jet Transp
Fi ghte r
Avera ge
0.100
(b)
0.150
0.200
0.250
0.300
Ex pose d area /Sref
Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources
c 2002 LM Corporation
Air vehicle geometry
20-10
Design of UAV Systems
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 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
c 2002 LM Corporation
Air vehicle geometry
20-11
Design of UAV Systems
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
c 2002 LM Corporation
Air vehicle geometry
20-12
Fuselage model
Design of UAV Systems
• 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(1)/ 1, 1 = sqrt(1-(D/L)/(2*K1))^2)
k2 = L2/L, fe2 = arcsin(2)/ 2, 2 = sqrt(1-(D/L)/(2*K2))^2)
Note - arcsin() is expressed in radians
c 2002 LM Corporation
Air vehicle geometry
20-13
Example - TBProp
Design of UAV Systems
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)*Dcyl^3 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
2.29 
c 2002 LM Corporation
9.16
Air vehicle geometry
4.58
2.29 ft
20-14
Example – cont’d
Design of UAV Systems
From the resulting dimensions, we calculate:
k1 = 1/7 = 0.143,
k2 = 2/7 = 0.286
1 = sqrt(1-(0.143/(2*0.143))^2) = 0.866
fe1 = arcsin(0.866)/0.866 = 1.209
2 = 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. 6 cuft is allocated to payload, leaving 13.1 cuft
available for fuel and systems
2.36 
c 2002 LM Corporation
9.43
Air vehicle geometry
4.72
2.36 ft
20-15
Fuselage/nacelle model
Design of UAV Systems
Dnac
Multi-engine prop
Lnac
D
Top
L
Front
Combined Swet  fuselage Swet + nengKswetnacelle Swet
Note - 0.0 < Kswet < 1.0
(20.3)
- Dnac  1.25Deng
- neng = Number of engines
Lnac
Single engine prop
Dnac
D
Side
Front
L
Combined Swet fuselage Swet+Kswet nacelle Swet (20.4)
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Air vehicle geometry
20-16
Design of UAV Systems
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/(*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
c 2002 LM Corporation
Air vehicle geometry
20-17
Design of UAV Systems
Fuselage/nacelle model
Lnac
Multi-engine jet
Dnac
D
Top
Front
L
Combined Swet fuselage Swet+nengKswetDnacLnac
(20.5)
Note - 0.0 < Kswet < 1.0
- Dnac  1.25Deng
- neng = Number of engines
Lnac
Single engine jet
Dnac
D
Kswet0.5
Side
Front
L
Combined Swet fuselage Swet+nengKswetDnacLnac
(20.6)
c 2002 LM Corporation
Air vehicle geometry
20-18
Fuselage/nacelle - cont’d
Design of UAV Systems
Integrated jet
Top
Front
Deng
D
Dnac
L
Combined area  fuselage area + 5*Aeng
Note - Aeng = Engine area at front face
(20.7)
Non-circular cross section
L1
w
Top
Front
L2
h
L
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)
where
De = sqrt(wh)
c 2002 LM Corporation
Air vehicle geometry
20-19
Design of UAV Systems
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
c 2002 LM Corporation
Air vehicle geometry
20-19a
Design of UAV Systems
Pods, stores and multi-fuselages
Model as multiple
ellipse-cylinders per
Eqs. 20.1 and 20.2
……with non-circular cross sections
Front
L1
w
Top
L2
L
c 2002 LM Corporation
Air vehicle geometry
h
Apply Eq. 20.8
as correction
factors
20-20
Data correlation
Design of UAV Systems
• 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%)
Total wetted area
6000
5000
4000
3000
2000
1000
0
0
1000
2000
3000
4000
5000
6000
Swet-fuse from Eq 20.2
Swet-fuse from Eq 20.2
Fuselage wetted area
8000
6000
4000
2000
0
0
2000
4000
6000
8000
10000
Swet – Raymer Fig 7.3
Swet - Roskam (RosAP) Table 5.1
c 2002 LM Corporation
10000
Air vehicle geometry
20-21
Design of UAV Systems
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/(*e*AR) = (Cl^2)*q/(*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
c 2002 LM Corporation
Air vehicle geometry
20-22
Wing model
Design of UAV Systems
Geometry model - Truncated pyramid for fuel volume
- Wing exposed area for Swet
b/2
Kc*Cr
Vpyrmd = A(base)hgt/3
Y1
Cr
Y2
Cr = 2*Sref/b*(1+ )
D/2
Ct
V-fuel = (4/3)*{[(Kc*Pf*(t/c)*Sref^2]/[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 = 2*Y1/b
 = taper ratio (Ct/Cr)
2 = 2*Y2/b
SrefExp = Sref*(1-(D/b)*(2-(D/b)*(1- ))/(1+ ))
c 2002 LM Corporation
Air vehicle geometry
(20.10)
20-23
Design of UAV Systems
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 (Sref*AR) = 40.5 ft
- Cr = 2*Sref/[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)*{[Kc*Pf*(t/c)*Sref^2]/[b*(1-)*(1+ )^2]}*
[(1-1*(1- ))^3 - ((1-2*(1- ))^3] = 4.5 cuft
c 2002 LM Corporation
Air vehicle geometry
20-24
Design of UAV Systems
Tails
• 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)
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Air vehicle geometry
20-25
Design of UAV Systems
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*(75.8+20.5+15.6) = 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:
- 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
c 2002 LM Corporation
Air vehicle geometry
20-26
Design of UAV Systems
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 1927) but it should be more accurate since it captures
geometry features not previously included
c 2002 LM Corporation
Air vehicle geometry
20-27
Design of UAV Systems
New weights and volume
Using on the area based Waf/Sref, the bottoms up
weight spreadsheet will converge to a new set of
weights
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
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)
c 2002 LM Corporation
Air vehicle geometry
20-28
Design of UAV Systems
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 = 2.29*cube(64.4/56.5) = 2.4 ft
At Lf/Df = 7, Lf = 2.4*7 = 16.8
- Engine size would also change
Bhp0 = 0.092*2056 lbm = 189.1 Bhp
Weng = 189.1/2.25 = 84.1 lbm, Vol eng = 84.1/22 =
3.8 cuft, Deng = [4*Vol/(*Lth/Deng)]^1/3 = 1.25 ft
and Dnac = 1.25*1.25 = 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
c 2002 LM Corporation
Air vehicle geometry
20-29
Design of UAV Systems
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 = 2.43*7 = 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, b^2/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
c 2002 LM Corporation
Air vehicle geometry
20-30
Parametric comparison
Design of UAV Systems
Global Hawk
c 2002 LM Corporation
Comparison shows the
airframe weights are
consistent with the
parametric data but that
fuel fraction continues
to be low for a TBProp
Air vehicle geometry
20-31
Design of UAV Systems
Reference
For more information on geometry model
methodology see my paper
- Preliminary Sizing Methodology for
Hypersonic Vehicles, AIAA Journal
of Aircraft, March 1992
c 2002 LM Corporation
Air vehicle geometry
20-32
Design of UAV Systems
Homework
1. 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)
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Air vehicle geometry
2nd
week
20-33
Design of UAV Systems
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Air vehicle geometry
Intermission
20-34