Components Weight Estimating

8/17/2019 Components Weight Estimating

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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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3

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


For extended overwater flights


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

Documents

Components Weight Estimating