centre of gravity estimate

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CENTER OF GRAVITY LOCATION

Chapter 8


8.1 Introduction

An airplane in flight can be maneuvered using the aerodynamic control

surfaces; the elevator, rudder, or ailerons. As the control surfaces change the

amount offorce that each surface generates, the aircraft rotates about a point

called the center of gravity. The center of gravity is the average location ofthe weight of the aircraft. The weight is actually distributed throughout the

airplane, and for some problems it is important to know the distribution. But

for total aircraft maneuvering, we need to be concerned with only the total

weight and the location of the center of gravity.

8.2 Methodology used for calculating center of Gravity

An airplane is a combination of many parts; the wings, engines, fuselage,

and tail, plus the payload and the fuel. Each part has a weight associated withit which the engineer can estimate, or calculate, using Newton's weight

equation:

w = m * g

where w is the weight, m is the mass, and g is the gravitational constant To

determine the center of gravity cg, we choose a reference location,

or reference line. The cg is determined relative to this reference location. The

total weight of the aircraft is simply the sum of all the individual weights of thecomponents. Since the center of gravity is an average location of the weight,

we can say that the weight of the entire aircraft W times the location cg of the

center of gravity is equal to the sum of the weight w of each component times

the distance d of that component from the reference location:

W * cg = [w * d](fuselage) + [w * d](wing) + [w * d](engines) + ...

The center of gravity is the mass-weighted average of the component

locations.
http://www.grc.nasa.gov/WWW/k-12/airplane/elv.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/rud.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/alr.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/forces.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/rotations.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/cg.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/weight1.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/geom.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/turbine.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/fuselage.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/elv.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/wteq.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/wteq.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/cg.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/weight2.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/weight2.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/cg.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/wteq.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/wteq.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/elv.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/fuselage.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/turbine.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/geom.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/weight1.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/cg.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/rotations.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/forces.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/alr.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/rud.htmlhttp://www.grc.nasa.gov/WWW/k-12/airplane/elv.html


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We can generalize the technique discussed above. If we had a total of

"n" discrete components, the center of gravity cg of the aircraft times the

weight W of the aircraft would be the sum of the individual i component

weight times the distance d from the reference line (w * d) with the index

Igoing from 1 to n.

W * cg = SUM(i=1 to i=n) [w * d]i

This equation says that the center of gravity times the sum of "n" parts'

weight is equal to the sum of "n" parts' weight times their distance. The

discrete equation works for "n" discrete parts.

In general the procedure adopted for calculating center of gravity of the

entire aircraft is as follows:-

Estimate the weights of individual masses

Determine the distances(arm) of the above masses from the particular

reference point in the aircraft

Calculate moments by multiplying weights with distances of the

masses

Add the moments of all the masses together

Divide the total moment by the total weight of the aircraft to give an

overall arm

8.3 The arm that results from this calculation must be within the arm limits

for the center of gravity that are dictated by stability conditions. If it is

not, weight in the aircraft must be removed, added (rarely), or

redistributed until the center of gravity falls within the prescribed limits.

Formulae Used:-


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Xcg =

Zcg =

8.4 Fuselage

Fuselage cross section is of rectangular shape. Its variation is as per the

3D view shown in the following figure.

8.4.1 Fuselage nose


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Mass of the section = 69.5 gm

Location of C.G:-

Xi from nose of fuselage = 187.438 mm

Zi from bottom of fuselage = 37.253 mm

Y from the reference point = 0 mm


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8.4.2Fuselage mid section

Mass of the section= 92.7 gm

Location of C.G:-

Xi from nose of fuselage = 475 .99 mm

Zi from bottom of fuselage = 50 mm



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8.4.3 Fuselage rear section

Mass of the section=112.27 gm

Location of C.G:-





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8.4.4 Fuselage tail

Fuselage tail

Mass of the section=14.3 gm

Location of C.G:-

Xi from nose of fuselage = 1256 mm




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For complete fuselage

Hence, Total mass of the fuselage, Mfuselage = 289 gm

Location of C.G:-




8.5 Wing

Wing was designed with 1 spars and 20 ribs. Centre of gravity of aerofoil

is calculated using CATIA software. The co-ordinates of centre of gravity

were obtained in terms of chord length. For ribs, the c.g. is calculated by

multiplying with chord length. Hence total mass of the main wing,


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Mw = g.

Centre of gravity of entire wing was calculated by taking into account

c.g. of individual components.

8.5.1 wing ribs

Mass of the wing ribs = 124.7 gm

Location of C.G.:-

X from nose of fuselage = 437.921 mm

Z from base of fuselage = 76.491 mm

Y from reference point = 0 mm


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8.5.2 wing spar

Mass of the wing spar = 59.49 gm

Location of C.G.:-





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8.5.3 wing skin

Mass of the wing skin = gm

Location of C.G.:-





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For complete wing

Mass of the wing = 209 gm

Location of C.G.:-



Y from reference point = 28.179 mm


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8.6 Horizontal tail

8.6.1 horizontal tail ribs

Mass of the Horizontal Tail ribs= 70 gm

Location of C.G.:-


Z from base of fuselage =82.441mm



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8.6.2 horizontal tail spar

Mass of the horizontal tail spar. = 11 gm

Location of C.G.:-





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8.6.2 horizontal tail skin

Mass of the horizontal tail skin. = 12 gm

Location of C.G.:-





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For complete horizontal tail

Mass of the horizontal tail = 93 gm

Location of C.G.:-





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8.7 Vertical Tail

8.7.1 vertical tail ribs


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Mass of the Vertical Tail ribs. = 5.57 gm

Location of C.G.:-




8.7.2 vertical tail spar


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Mass of the Vertical Tail spar = 5 gm

Location of C.G.:-


Z from base of fuselage = 283 mm



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For complete vertical tail

Mass of the Vertical Tail = 14.6 gm

Location of C.G.:-





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8.8 propeller

Mass of the propeller = gm

Location of C.G.:-

X from nose of fuselage = -43.971 mm


Y from the reference point = 1.415 mm


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8.9 Landing gear


Z from base of fuselage = -89.804 mm

Y from the reference point = .487 mm


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8.10 Complete Aircraft

Mass of the aircraft =



Y from the reference point = 73.804 mm


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Table-8.1: Tabulated Data For All Components

Component Mass (g)

X(mm) from

nose of

fuselage

Z(mm) from

Base of

fuselage

Y(mm) from

the reference

point

Fuselage 289 593.628 53.759 0

Wing 209 435.925 76.488 28.179

Propeller 22 -43.971 1.415 20.36

Landing Gear 50 652.693 89.804 -0.487

Horizontal Tail 93 1257.897 82.442 7.645

Vertical Tail 14.6 1250.113 263.8630.006

Payload 200 568.506 16.067 73.804

Motor 25 568.506 16.067 73.804

Battery 428 568.506 16.067 73.804

8.9 Motor, battery and payload is placed such that its c.g. coincides with the

c.g. of the aircraft. Whereas servos are arranged symmetrically about the c.g.

of aircraft so that they dont affect position of c.g.

Xc.g = 568.506 mm from nose of fuselage.

Zc.g = 73.804mm from bottom of fuselage.

Yc.g = 16.067mm from the reference point.

8.10 Conclusion:

The location of c.g. is obtained with the help of CATIA software (for

aerofoil) and considering other components separately.


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References:

1. Daniel P. Raymer Aircaft design: A conceptual approachAmerican Institute of Aeronautics and Astronautics, Inc. 370 LEnfant

Promenade, S.W., Washington, D.C., 20024

2. Dr. S. Kamle Aircraft Design lecture notes Department ofAerospace, IIT Kanpur.

3. Dr. E.G. Tulapurkara Introduction to airplane design(Aerodynamic- lecture notes) IIT Madras August 2008

4. Lloyd Jenkinson and Jim Marchman III Aircraft Design Projects forEngineering Students Butterworth-Heinemann Limited, 2003.

5.

http://www.grc.nasa.gov/WWW/k-12/airplane/acg.html

centre of gravity estimate

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