components weight estimating
TRANSCRIPT
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Components Weight Estimating
General Aviation Airplanes
Note: These equations are only valid for the British Units System.
Wing Weight
Cessna method
The following equations should be applied only to small, relatively low performance type airplanes withmaximum speeds below 200 knots. The equations apply to wings of two types: cantilever wings and strut
braced wings. Both equations include, weight of wing tip fairing wing control surfaces both equationsexclude: Fuel tanks wing/fuselage spar carry-through structure effect of sweep angle for cantilever wings,the wing weight is determined from:
7121360039703970046740
.
w
.
ult
.
w
.
TOw ARnS W .W Cessan Eqn-1
WhereW TO Takeoff Weight
S w Wing Areanult Ultimate Load Factor
ARw Wing Aspect RatioThe wing weight for strut braced wings is found from:
4732611001810029330 .w.
ult .
ww ARnS .W Cessan Eqn- 2
Note: The equation for the strut braced wing does not account for take-off weight and should therefore beused with caution.
USAF method
The following equation applies to light utility type airplanes with performance up to about 300 knots.
The wing weight is solved from:
9930360
610570
4
650
5500
12
1
1001094896
.
H
.
r ct
w
.
w
.
/ c
w
.
ult TO
w EAS
ww
USAF
V S
cos
ARnW .W
Eqn- 3
WhereWTO Takeoff WeightSw Wing Area
nult Ultimate Load FactorAR w Wing Aspect Ratio
c/4w
Wing Sweep Angle @1/4 Chord
w Wing taper ratio(t/c)W Wing thickness ratioVH
EAS Equivalent Maximum Level Speed
Torenbeek method
The equation below applies to light transport airplanes with take-off weight below 12,500 lbs (55,603 N).
The wing weight is determined from:30
2
50
2
750
2
550 256
1001250
.
/ cTOr
ww
.
w
/ c
.
/ c
w.
ult TOw
ww
w
w
Torenb cosW t
S b
b
cos.
cos
bnW .W
Eqn- 4
For WTO >12500 Ib30
2
051
2
550 256
100170
.
Zf r
w
w
/ c
.
/ c
w.
ult zf wW t
S
b
cos.
cos
bnW .W
w
w
w
g
Eqn- 5
Where
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W TO Takeoff Weight
W zf maximum zero fuel weight = F TO Zf W W W
S w Wing Areanult Ultimate Load Factor
c/2w
Wing Sweep Angle @ 1/2 Chord
w Wing taper ratio(t/c)W Wing thickness ratiot r
w
The maximum thickness of the wing root chord
The wing span is calculated from: www ARS b
The maximum thickness of the wing root chord for straight tapered wings is found from:
ww
w
r
r b
S
c
t t
w
w1
2 Eqn- 6
NotesEqn - 5 include weight of normal HLD and aileron
Spoiler and speed brake +2%2 wing mounted engine -5%4 wing mounted engine -10%Landing gear mounted -5%Braced wing -30% and for strut +10%
For fowler flaps +2%
Horizontal Tail Weight:
Cessna method
The following equations should be applied only to small, relatively low performance type airplanes withmaximum speeds below 200 knots. The horizontal tail weight is found from:
2230
138010108870
04174
1843
.
r
.
h
.
h
.
TO
h
h
Cessna t .
ARS W .W Eqn- 7
S h Horizontal Tail Area ARh Horizontal Tail Aspect Ratio
t r h The horizontal tail root maximum thickness is found from:
hw
h
r
r b
S
c
t t
h
h1
2 Eqn- 8
(t/c)r h Horizontal Tail thickness ratio
bh Horizontal Tail spanS h Horizontal Tail Area
h Horizontal Tail taper ratio
The horizontal tail span is given by: hhh ARS b
USAF method
The following equation applies to light and utility type airplanes with performance up to about 300 knots.The horizontal tail weight is solved from:4580
483021870
510
289010010
127
.
r
h
.
h
.
h
.
ult TO
h
h
USAF t
bl .
S nW W
Eqn- 9
bh horizontal tail span(t/c)r
h Horizontal Tail thickness ratio
The X-distance between the horizontal tail and wing mean geometric chord quarter chord points isdetermined from:
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44w
mgcapexh
mgcapexh c x X c x X l wwhh
Where:
X a pexh is the X-coordinate of the horizontal tail apex.
xmgch is the X-location of the horizontal tail mean geometric chord leading edge relative
to the horizontal tail apex.
hC is the horizontal tail mean geometric chord.
X a pexw is the X-coordinate of the wing apex.
xmgcw is the X-location of the wing mean geometric chord leading edge relative to the wing
apex.
wC is the wing mean geometric chord.
The X-location of lifting surface mean geometric chord leading edge relative to the lifting surface apex is
given by:
lslsls LE mgcmgc tan y x
where:l. s. Stands for 'lifting surface'
ymgcl. s is the Y-distance between the lifting surface apex and the lifting
surface mean geometric chord.
LEl s
is the lifting surface leading edge sweep angle.
The Y-distance between the lifting surface apex and the lifting surface mean geometric chord is given by:
ls
lslsmgc
b y
ls
16
21
where:
l.s. stands for "lifting surface".bl
s is the lifting surface span.
l s is the lifting surface taper ratio.
The lifting surface leading edge sweep angle is computed from:
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lsls
ls / c LE
ARtantan
lsls1
14
1
where:
C/4 is the lifting surface quarter chord sweep angle.
is the lifting surface taper ratio.
AR is the lifting surface aspect ratio.The lifting surface mean geometric chord is given by:
lsls
ls
lslsls AR
S c 2
2
13
14
It denotes either 'w' for wing, 'h' for horizontal tail or 'c' for canard.
The lifting surface span is given by: lslsls ARS b
Torenbeek method
2870
1000813
2
20
.cos
V S .S K W
h
EAS
lTorenb
/ c
D
.
h
hhh Eqn- 10
where
K h =1.0 for fixed incidence stabilizers K h = 1.1 for Variable incidence stabilizers
where:k h is a horizontal tail weight constant.Sh is the horizontal tail area.
VD EAS
is the equivalent flight design dive speed.
C/2h is the horizontal tail half chord sweep angle.
Vertical Tail Weight:
Cessna methodThe following equations should be applied only to small, relatively low performance type airplanes withmaximum speeds below 200 knots.
The vertical tail weight is determined from:
vv
Cessna
/ c
.
r
.v
.v
.TO
vcost .
ARS W .W
4
7470
482024915670
04174
681
Eqn- 11
where:Sv is the vertical tail area.
AR v is the vertical tail aspect ratio.tr
v is the vertical tail root maximum thickness.
c/4v is the vertical tail quarter chord sweep angle.
USAF method
The following equation applies to light and utility type airplanes with performance up to about 300 knots.The vertical tail weight is calculated from:
45805021870
5 289010010
598
..
v
.
v
.
ult TOv
vr
USAF t
b.
S nW .W
Eqn- 12
where:nult is the airplane ultimate load factor.
S v is the vertical tail area.bv is the vertical tail span.t r
v is the vertical tail maximum root thickness.
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Torenbeek method
2870
1000813
2
20
.cos
V S .S K W
v
EAS
Torenb
/ c
D
.
v
vvv Eqn- 13
where K v =1.0 for fuselage mounted horizontal tails
vv
hhv
bS
z S . K 1501 for fin mounted horizontal tails
where: K v is a vertical tail weight constant.S v is the vertical tail area.
V D EAS
is the equivalent flight design dive speed.
C/2h is the horizontal tail half chord sweep angle.
Fuselage Weight:
Cessna method
The following equations should be applied only to small, relatively low performance type airplanes with
maximum speeds below 200 knots. The equation does not account for pressurized fuselages. The
fuselage weight is computed from:
24
f
fcC
f
f f
f f
z Z Z
z
W W W W
ww / r
lowhigh
lowcessna
Eqn- 14
where:W f
low is the fuselage weight for a low-wing airplane according to Cessna method.
W f high
is the fuselage weight for a high-wing airplane according to Cessna method.
Z f is the fuselage height at wing root. Z cr/4
w is the Z-coordinate of wing root quarter chord point.
Z fcw
is the Z-coordinate of fuselage centerline in region of wing.
The fuselage weight for a low-wing airplane is found from:590037406920
046820 .
f
.
max
.
TO f L P W .W low Eqn- 15
where:
P max is the maximum fuselage perimeter. L f is the fuselage length.The fuselage weight for a high-wing airplane is determined from:
455038307780
14408614
.
crew pax
.
f
.
max
f .
TO f N N L P
LW .W
high
Eqn- 16
where: N pax is the number of passengers. N crew is the number of crew.
The maximum perimeter is calculated from:wmax
f max D P Eqn- 17
where:
D fmaxw is the fuselage maximum diameter.
Torenbeek
For cylindrical cabin sections of fuselages with high fineness ratio, L/d >5, the gross area may beestimated with the following equation:
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2
32
21
21
d / Ld / LdLS
/
g Eqn- 18
The fuselage weight may then be approximated by
d
l V S .W t E , D
.
g f Toreen
210210 Eqn- 19
S g fuselage gross shell area in ft2
In this equation the lengths are in feet, the weight is in pounds, and the design dive speed, V D,E , is in
knots. The length l t is the distance between the root quarter-chord points of the tail and the wing, and, fora first approximation, it may be taken to be the estimated value for l h . To this basic weight, 8% should be
added to account for a pressurized cabin and 7% added if the engines are mounted on the aft fuselage.
USAF method
The following equation applies to light and utility type airplanes with performance up to about 300 knots.The fuselage weight is calculated from:
11338085702860
1001010100200
..
c f f
.
f
.
ult TO f
EAS maxmax
USAF
V hw LnW W
Eqn- 20
where:
L f is the fuselage length.
w f max is the maximum fuselage width.h f
max is the maximum fuselage height.
V c EAS
is the equivalent design cruise speed.
Landing Gear Weight
Cessna method
The following equations should be applied only to small, relatively low performance type airplanes withmaximum speeds below 200 knots. Also, the method is not suitable for airplanes with tail gear(s). Thegear weight is determined from:
cessnacessnacessna mg ng g W W W Eqn- 21
The main gear weight is found from:183095004170
3
236200130
.
ss
.
ult
.
LTOretract TOmg mg cessna LnW .W K W .W Eqn- 22
The nose gear weight is calculated from:78807490
3
10071500013026
.
ssult
.
LTOretract TOng ng cessna LnW .W K W ..W Eqn- 23
where:
L ss mg is the shock strut length for the main gear. L ss ng is the shock strut length for the nose gear. W L is the design landing weight.
K retract = 0.0 for non-retractable gears.K retract = 0.012 - .016 for retractable gears.
Torenbeek method
The landing gear weight for General Aviation airplanes is calculated using the Torenbeek equations forCommercial Transport Airplanes. The following method applies to transport airplanes and business jets
with the main gear mounted on the wing and the nose gear mounted on the fuselage. Each gear group isevaluated separately using the following equation and the appropriate constants for the gear configuration.The gear weight is computed from:
TorenbTorenbTorenbTorenb tg ng mg g W W W W Eqn- 24
The gear weight is given by:51750 .
TO xgTorenbTO xgTorenb
.
TO xgTorenb xgTorenb gr xg W DW C W B Ak W Torenb Eqn- 25
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where,xg = mg for main gear,xg = ng for nose gear,xg = tg for tail gear.
Note: B xgToren and D xgTorenb are zero for the tail gear. The landing gear weight wing location correction factor is determined from:
f
/ cr fc f
gr z
z z z ..k ww
450
0801 Eqn- 26
The above equation yields:
K gr = 1.0 for low wing airplanes. K gr = 1.08 for high wing airplanes.
A/c Type Gear Type Gear Comp A g B g C g D g
Jet TrainerBusiness Jet
retract Main 33.0 0.04 .021 0.0
Nose 12.0 0.06 0.0 0.0
Other civil
Aircraft
Fixed Main 20.0 0.10 .019 0.0
Nose 25.0 0.0 0.0024 0.0
Tail 9.0 0.0 0.0024 0.0
retract Main 40.0 0.16 0.019 1.5x10-5
Nose 20.0 0.10 0.0 2.0x10-5
Tail 5.0 0.0 0.0031 0.0
USAF method
The following equation applies to light and utility type airplanes with performance up to about 300 knots.
The gear weight is solved from:
684050100540 .ult L. ssmg g LUSAF nW L.W Eqn- 27where:
L ss mg is the shock strut length for the main gear. Note: This equation includes nose gear weight. The ultimate load factor for landing may be taken as 5.7.
Powerplant WeightThe aircraft powerplant weight, weight ,W pwr will consist of the following
1. Engine W e (engine, exhaust, cooling, supercharger and lubrication system)2. Air induction system W ai ( inlet ducts, ramps, spikes and associated controls)3. Propellers4. Fuel System5. Propulsion system( engine controls, starting system, propeller controls)
p fs propaie Pwr W W W W W W Eqn- 28
Obtain actual weight data from engine manufacturers is highly recommended
EngineCessna method
The following equations should be applied only to small, relatively low performance type airplanes withmaximum speeds below 200 knots. The total engine weight is found from:
TOeng eng SHP k W Cessnacessna Eqn- 29
Where:SHP TO takeoff shaft horse power
K engCessna =1.1 to 1.8 for piston engines.
K engCessna =0.35 to 0.55 for turboprop and propfan engines.
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Note: These weights represent the so-called dry weight. Normal engine accessories are included in thisweight and engine oil.
USAF method
e
.
eng p propaieng N W .W W W W USAF 9220
5752 Eqn- 30
Use engine manufactures data to obtain W eng or use ( Cessna method engine weight)W eng Weight per engine in Ibs
N e Number of engine
Torenbeek method
For piston engine airplanes, the total engine weight is determined from:
65820314864 . / cyl cyl geared inject seng eng N V K K K N .W Torenb Eqn- 31where:
K inject piston engines with fuel injection ( correction factor)
1.00 for carburated engines 1.08 for engines with fuel injection K geaed = 1.00 for direct drive engines 1.12 For piston engine gearing correction factor
K s is factor for supercharged and turbocharged piston engines=
V cyl is the total swept cylinder volume per engine N cyl is the number of cylinders N eng is the number of engine
K s = f (Pmani/Pair ) from figure
For jet engine airplanes, the total engine weight is found from:
50
2
3
7501
11120
1
17432010
.TO FanType
t
t aeng
eng BPR.
T K . BPR
P
P m. N .
W Torenb
Eqn- 32
where: K FanType =1 for conventional turbofans K FanType =1.2 for geared turbofans
K FanType =1.2 for variable pitch fans K FanType =1.4 for geared and variable pitch fans
Propulsion System Weight
Torenbeek method
eng OilSys
.
eng ai
.
TO
.
eng P W K W .W SHP N .W Torenb 94307030
4550031 Eqn- 33
N eng Number of engine
SHP TO the takeoff powerW eng engine weight
K oilSystem Engine Type Correction Factor for Oil System and Oil Cooler WeightTypical value:Engine Type
Jet Engines(Included in Engine Weight) 0.0
Turboprop Engines 0.07Radial Piston Engines 0.08Horizontally Opposed Piston Engines 0.03
Air induction system
Cessna method
Wai is included in the propulsion system weight W p USAF method
Wai is included in the propulsion system weight W p
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Torenbeek method
7030
1
031 .TO
.
eng
ais
aisToren _ ai SHP N
K
K .W
Eqn- 34
Propeller weight Estimation
Its recommended to use propeller manufacturer data where ever possible
GD method
7820
3910
1
1000
.
e
TO p
.
bl p propGD _ prop
N P D
N N K W
Eqn- 35
The Constant K propl take on the following values: K prop1 24 for turboprops above 1500shp
31.92 for piston engines and turboprops below 1500 shp N p is the number of propellers N bl is the number of blades per propeller
D p is the propeller diameter in ft P TO is the required take off power in hp
N e is the number of enginesTorenbeek method
78205021802
..
bl TO p
.
p propToren _ prop N P D N K W Eqn- 36
K prop1 0.108 for turboprops0.144 for piston engines
Fuel System Weight
Cessna method
For aircraft with internal fuel system no tip tanks
fsp
f
_ fs K
W .W 400Cessna
Eqn- 37
With external fuel system ( tip tanks)
fsp
F _ fs
K
W .W
700
Cessna Eqn- 38
K fsp 5.87 Ibs/gal for aviation gasoline
6.55 Ibs/gal for JP-4
W F mission fuel includes reservesUSAF method
211
13020
3060
11492
.
.e
.t
..
fsp
f USAF _ fs N N
int K W .W
Eqn- 39
K fsp 5.87 Ibs/gal for aviation gasoline6.55 Ibs/gal for JP-4
int fraction of fuel tanks which are integral
N t number of separated fuel tanks N e number of engines
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Torenbeek method
For single piston engine installation60
8752
.
f
sp _ Toren _ fs.
W W
Eqn- 40
For aircraft equipped with non self sealing bladder tanks7270
23
.
fsp
f
ssb _ Toren _ fs
K
W .W
Eqn- 41
For aircraft equipped with integral fuel tanks wet wing
3330
5015180
.
fsp
f .
t t eit _ Toren _ fs K
W N N N W
Eqn- 42
Propulsion System Weight
Depending on aircraft type, the propulsion system weight Wp is either given as function of total engineweight and /or mission fuel or by
osc pcesses p W W W W W Eqn- 43
WhereW ec weight of engine controls W ess weight of engine starting systemW pc weight of propeller controls in IbsW osc weight of oil system and oil cooler in Ibs.
Cessna method
Use actual dataUSAF method
W p is included in Eqn-30
Torenbeek method
W p is included in Eqn-31
Fixed Equipment Weight
The list of fixed equipment carried on board aircraft varies significantly with aircraft type and aircraft
mission it will be assumed that the following items are to be included in the fixes equipment cateqory:1. Flight control system , W fc 2. Hydraulic system, W hps 3. Electrical system , W els 4. Instrumentation, avionics and electronics, W iae 5. Air-conditioning, pressurization, anti- and de-icing system W api 6. Oxygen system, W ox 7. Auxiliary power unit (APU) , W apu 8. Furnishings, W fur
9. Baggage and cargo handling equipments, W bc 10. Operational items, W ops 11. Auxiliary gear, W aux 12. Ballast, W bal 13. Paint, W pt 14. W etc
etc pt bal auxopbc fur
apuoxapiiaeelshps fc feq
W W W W W W W
W W W W W W W W
Eqn- 44
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Flight control system
Cessna method
TOcessna _ fc W .W 0160 Eqn- 45
W TO take off in Ibs
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M D is design dive mach number
Torenbeek method
For single engine, unpressurized aircreaft
paxToren _ api N .W 52 Eqn- 55
For multi – engine
E Toren _ api W .W 018 Eqn- 56
Oxygen systemCessna method
70207 . paxcr GD _ ox N N W Eqn- 57Torenbeek method
For flight below 25,000ft
paxToren _ ox N .W 5020 Eqn- 58
For short flight above 25,000 ft
paxToren _ ox N .W 2130 Eqn- 59
For extended overwater flights
paxToren _ ox N .W 4240 Eqn- 60
Auxiliary Power unit
Auxiliary power units are often used in transport or patrol type aircraft, commercial as well as military.
The weight ranges are typical of these weight fractions:W apu=0.004-0.013 W TO Eqn- 61
Furnishings weight
The furnishings category includes the following items:1. Seats insulation, trim panels, sound proofing, instrument panels, control stand Light and wiring.2. Galley (pantry ) structure and provisions.3. Lavatory (toilet) and associated system
4. Overhead luggage containers, hattracks, wardrobes5. Escape provisions, fire fighting6. Food, Potable water, Drinks, Lavatory supplies
Cessna method48901451
4120 .
TO
.
paxCessna _ fur W N .W Eqn- 62
Torenbeek method
For single engine aircraft
row paxToren _ fur N N W 25135 Eqn- 63
For short flight above 25,000 ft
oarg c pax paxToren _ fur V . N W 0115 Eqn- 64
Where V pax+cargo is volume of the passenger cabin plus the cargo volume in ft3
Baggage and Cargo Handling Equipments 4561.
paxbcGD _ bc N K W Eqn- 65
K bc 0.0646 without preload provisions0.316 with preload provisions
Torenbeek method
ff Toren _ bc S W 3 Eqn- 66
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Where S ff is the freight floor area in ft2
For baggage and cargo containers, the following weight may be used
Freight pallets including nets Weight
88x108 in 225Ibs
88x125 in 262 Ibs
96x125 in 285Ibs
Containers 1.6 Ibs/ft3 (for container dimensions)
Ballast weight
When looking over the weight statements for various airplanes carry amount of ballast. This can havedetrimental effects on speed , pay load and rang performance.
The following reasons can be given for the need to include ballast in the aircraft:1. The designer goofed in weight and balance calculation.2. To achieve certain aerodynamic advantages it was judged necessary to locate the wing or to size
the empennage so that the static margin became insufficient. This problem can be solved with ballast. In this case, carrying ballast may in fact turn out to be advantageous.
3. To achieve flutter stability within the flight envelope ballast weights are sometimes attached tothe wing and/or to the empennage.
Note: balance weights associated with flight control surfaces are not counted as ballast weight.The amount of ballast weight required is determined with the help of the X-plot. It is can be helpful in
determining the amount of ballast weight required to achieve a certain amount of static margin.
Paint
Transport jets and camouflaged military airplanes carry a considerable amount of paint. The amount of paint weight is obviously a function of the extent of surface coverage. For a well painted airplane a
reasonable estimate for the weight of paint is:
0060 to0030 TOTO pt W .W .W Eqn- 67
Estimation of W etc
This weight item has been included to cover any items which do not normally fit in any of the previousweight categories.
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Empty Weight
Structure Weight Powerplant Weight Fixed Equipment
Weight
Wing
Horizontal Tail
Vertical Tail
V- Tail
Canard
Fuslage
Landing Gear
Nacelles
Tailboom
Propellers
Engines
Air induction
Fuel system
Flight Control
Hydraulic &
Pneumatic
Instrumentation
Avionics &
Electronics
Electrical
Auxiliary Power
Furnishings
Baggage & Cargo
Handling
Operational Items
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Wing Group Center of Gravity
The center of gravity (CG) of the wing group may be estimated according to the suggestions provided inTable 8-15 of Torenbeek. We may examine this case more closely by consulting the schematic diagram ofthe wing shown in Fig 1.
Figure 1 Schematic diagram of wing layout for estimating thelocation of the wing CG
Fuselage Group Center of Gravity The fuselage center of gravity (CG) may be taken from the estimates given by Torenbeek (Table 8-15)and illustrated in Figs. 2 and 3.
Figure 2 Approximate location of CG of fuselage group alonefor wing-mounted engines
0.35b/2
YMAC
b/2
mean aerodynamic chord (MAC)
wing group CG at 0.7(Xrs-Xfs)
centerline fuselage skin
0.42 to 0.45 L
L
front spar at 0.25C
rear spar at 0.55C to 0.6C
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Figure 3Approximate location of CG of fuselage group alonefor fuselage-mounted engines
Landing Gear Group Center of Gravity The nose gear is placed near the nose of the aircraft and the main landing gear must be placed aft of the
overall CG of the complete aircraft. A first approximation would place the nose and main landing gear at
the approximate locations , depending upon the engine mounting configuration. Using the estimatedweights of the nose and main landing gear and the fuselage length one may approximate the location ofthe CG of the complete landing gear system.
Figure 4 Approximate locations of landing gear components as functions of fuselagelength for different engine mounting configurations
Tail Group Center of Gravity
The CG of the tail group is dependent on the nature of the tail configuration. Torenbeek (Table 8-15) provides some estimates of the CG location for conventional and T-tail arrangements, as shown in Figs.5
and 6.
0.47L
L
0.6L
0.55L
0.17L
0.14L
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(a) (b)Figure 5 Approximate location of the CG location of the horizontal tailfor (a) wing-mounted engines and (b) fuselage-mounted engines
Figure 6 Approximate location of the CG location of the vertical tailfor (a) wing-mounted engines and (b) fuselage-mounted engines
These approximate locations may be used along with the estimated weights of the tail surfaces to developthe location of the CG of the entire aircraft.
Propulsion Group Center of Gravity
The engine CG should be obtained from the engine manufacturer, or from and estimate based upon the
general configuration of the engine using actual dimensions. The nacelle housing the engines may beassumed to have a CG located 40% of the length of the nacelle, as measured from the lip of the nacelle.
Figure 7 Composite sketch of wing group, fuel tank, wing-mounted engine, and landing
0.35b/2
0.45b/2
b/2
f ront spar at 0.25C
rear spar at 0.55C to0.6C
fuel tank
wing group CG at 0.7(Xrs-Xfs)
centerline
fuselage
main landing gear CG at rear sparand Y=0.22(b/2)
0.42c
hv0.55hv
0.42c
0.38hvhv
0.42c
0.38bh /2
0.42c
0.38bh /2
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gear from which a collective CG may be determined
Aircraft Center of Gravity
The center of gravity (CG) of the aircraft is of great importance with respect to stability and control. Thisaspect of the design process follows directly after the weight estimation process and is described in some
detail in Section 8.5 of Torenbeek. Table 8-16 of Torenbeek gives CG limits for a number of differentaircraft and Section 8.5.4 outlines a design procedure to obtain a balanced aircraft. As pointed out in
previous sections of this chapter, Table 8-15 gives the CG locations of various aircraft components. Inaddition, information on nacelle placement is given on p. 211 and on wing spar locations on p. 261.
One method for proceeding with the determination of the center of gravity of the complete airplaneinvolves dividing the airplane into two groups: the fuselage group that includes the fuselage and the tailsurfaces, and the wing group that includes the wing engines, and landing gear. Side and plan views ofthese two groups with appropriate dimensions are shown in Figs. 8 and 9.
Figure8 Schematic diagram of the two mass groups used in determining the center of gravity of thecomplete airplane
Taking moments about the nose of the aircraft yields
W OE X OE = W FG X FG + W WG( X LEMAC + X WG)
Setting X*= X OE – X LEMAC and solving for X LEMAC leads to the following result:
X LEMAC = X FG + (W WG /W FG) X WG – (1 + W WG /W FG) X *
The displacement of the center of gravity of the airplane ahead of its Center of pressure determines thedegree of the airplane’s longitudinal static stability. If the two points coincide the stability is neutral,
while if the center of gravity falls aft of the center of pressure the airplane will be unstable. It is desirablein a commercial passenger transport to have sufficient static stability for comfort and robustness of safetymargins while maintaining a level of maneuvering agility suitable to its mission.
XFG
XOE
XLEMAC
cMAC
XW
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Figure 9 Plan view of the two mass groups for determining the center of gravity of the complete airplane
Presentation of Weight and Balance Results The results of this chapter are to be presented in a table of group weights as suggested by Table 1, thediagram of CG locations and travel, and the three-view of the design aircraft showing pertinentdimensions.
Table 1 Table of aircraft weight breakdown by groups
Group Weight (lbs) XCG(in.)
Wing group
Tail groupBody group
Landing gear group
Surface controls group
Nacelle group
Propulsion group
Airframe services and equipment
Empty weight (WE)
Operational items
Operational empty weight (WOE)
Payload weight (WPL)
Fuel Weight (WF)Take-off Weight
XFG
XOE
XLEMAC
cMAC
XWG