What is Weight?
Weight is the force generated by the gravitational attraction of the earth on the airplane. We are more familiar with weight than with the other forces acting on an airplane, because each of us have our own weight which we can measure every morning on the bathroom scale. We know when one thing is heavy and when another thing is light. But weight, the gravitational force, is fundamentally different from the aerodynamic forces, lift and drag. Aerodynamic forces are mechanical forces and the airplane has to be in physical contact with the the air which generates the force. The gravitational force is a field force; the source of the force does not have to be in physical contact with the object to generate a pull on the object.
Weight is a force, and a force is a vector quantity having both a magnitude and a direction associated with it. For an airplane, weight is always directed towards the center of the earth. The magnitude of this force depends on the mass of all of the parts of the airplane itself, plus the amount of fuel, plus any payload on board (people, baggage, freight, ...). The weight is distributed throughout the airplane, but we can often think of it as collected and acting through a single point called the center of gravity. In flight, the airplane rotates about the center of gravity, but the direction of the weight force always remains toward the center of the earth. During a flight the aircraft burns up its fuel, so the weight of the airplane constantly changes. Also, the distribution of the weight and the center of gravity can change, so the pilot must constantly adjust the controls to keep the airplane balanced.
Flying involves two major problems; overcoming the weight of an object by some opposing force, and controlling the object in flight. Both of these problems are related to the object's weight and the location of the center of gravity. The dream remains that, if we could really understand gravity, we could create anti-gravity devices which would revolutionize travel through the sky. Unfortunately, anti-gravity devices only exist in science fiction. Machines like airplanes, or magnetic levitation devices, create forces opposed to the gravitational force, but they do not block out or eliminate the gravitational force.
The weight W, or gravitational force, is then just the mass of an object times the gravitational acceleration.
Scientists have combined the universal gravitational constant, the mass of the earth, and the square of the radius of the earth to form the gravitational acceleration, g . On the surface of the earth, its value is 9.8 meters per square second or 32.2 feet per square second.
g = G * m earth / (d earth)^2
The weight W, or gravitational force, is then just the mass of an object times the gravitational acceleration.
W = m * g
Since the gravitational constant (g) depends on the square of the distance from the center of the earth, the weight of an object decreases with altitude.
Let's do a test problem to see how much the weight of an airplane changes with altitude. If an airplane is flying at 35000 feet (about 7 miles) the distance to the center of the earth is about 4007 miles. We can calculate the ratio of the gravitational constant to the value at the surface of the earth as the square of (4000/4007) which equals .9983*.9983 = .9965. If the airplane weighs 10000 pounds on the surface of the earth, it weighs 9965 pounds at 35000 feet; it has lost 35 pounds, a very small amount compared to 10000 pounds.
Let's do another problem and compute the weight of the Space Shuttle in low earth orbit. On the ground, the orbiter weighs about 250,000 pounds. In orbit, the shuttle is about 200 miles above the surface of the earth. As before, the gravitational constant ratio is the square of (4000/4200) which equals .9523*.9523 = .907. On orbit, the shuttle weighs 250,000 * .907 = 226,757 pounds. Notice: the weight is not zero. The shuttle is not weightless in orbit.
"Weightlessness" is caused by the speed of the shuttle in orbit. The shuttle is pulled towards the earth because of gravity. But the high orbital speed, tangent to the surface of the earth, causes the fall towards the surface to be exactly matched by the curvature of the earth away from the shuttle. In essence, the shuttle is constantly falling all around the earth.