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Weight - Level 3

The weight of an airplane is the force, which acts vertically downward toward the center of the earth and is the result of gravity on the airplane.

Just as the lift of an airplane acts through the center of pressure, the weight of an airplane acts through the center of gravity (C.G.). This is the point through which the resultant of the weights of all the various parts of the airplane passes, in every attitude that the airplane can assume.

The weight of the body (such as that of an aircraft) is dependent upon the mass of the body and the acceleration of gravity and comes from the attractive force between two bodies, in this case the earth and the aircraft.

The law of attraction is given by

F = G m₁m₂ / r²

where G is the universal gravitational constant equal to 66.73 x 10^-12 m³/(kg - s²);
m₁ is the mass of the earth;
m₂ is the mass of the aircraft; and,
r is the radial distance between the centers of both masses.

If the mass m₂ is on the earth's surface, the combination G m₁ / r² turns out to be close to 9.81 m/s²(or 32.2 ft / s² ) almost everywhere and we designate this value as the acceleration of gravity, g. And so, the law of attraction reduces to the familiar

F = m g = weight

Actually, the earth is an oblate spheroid (like a football but less pointy and fatter) and so the variation in g depends upon location on the earth. For simplicity's sake we assume that the earth can be approximated by a sphere whose radius R is about 4000 miles. We also note that g depends inversely upon the square of the distance from the aircraft to the earth's center. Therefore, at altitude, the value of g will be different and will be given by g times (R/(R+h))²where h is the height above the surface of the earth (measured radially from the earth's center); and, R is the distance from the center of the earth to the surface of the earth directly below the aircraft. Therefore, as h increases, the acceleration of gravity, g, will decrease.

The other factor that we have not spoken about is the mass. In general, the mass is a constant, whether here on earth or on the Moon, Venus or anywhere else, as long as the mass does not move at speeds close to the speed of light or as long as we do not lose mass. For aircraft in flight, the speeds are slow compared to the speed of light, BUT, the weight will decrease with time due to changes in its mass (fuel carried aloft in fuel tanks is burned up to create thrust).

The information in this section has been extracted from several sources. Those sources have been contacted and permission to use their material on our site is pending. However, the format in which this material has been presented is copyrighted by the ALLSTAR network.

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Updated: February 23, 1999