Understanding Zero-G: Calculating Airplane Acceleration at Different Altitudes

[tahayassen]

I understand that the airplane accelerates at the acceleration due to gravity in the downward direction, making the acceleration of the person relative to the airplane zero. But the acceleration due to gravity isn't constant, so I was wondering if someone could show me how you could calculate the acceleration needed for an airplane at certain altitudes?

 

[tahayassen]

Oh, wait. I'm so dumb...

acceleration due to gravity = Gm/r^2

From that formula, you could calculate the acceleration needed at different altitudes. I still don't understand how would I find the equation to model the airplane's position using sine waves. Any ideas?

 

[D H]

Earth gravity decreases by about 0.3086 mGal per meter of increased altitude near the surface of the Earth. This is the free air correction.

As for your question, this is very tiny, even for a couple of kilometers of altitude change.

 

[rcgldr]

I still don't understand how would I find the equation to model the airplane's position using sine waves. Any ideas?

During the zero g portion of flight, the airplane is following a parabolic path (technically an elliptical path if you don't consider the Earth to be flat), with a downwards acceleration of 1 g and near constant horizontal component of velocity.

 

[PJC01]

I can provide a response to your question about calculating airplane acceleration at different altitudes. The acceleration due to gravity, also known as the gravitational constant, is not constant at all altitudes. It varies depending on the distance from the Earth's center, which is determined by the altitude of the airplane.

To calculate the acceleration due to gravity at a specific altitude, we can use the formula:

a = GM/r^2

Where a is the acceleration due to gravity, G is the universal gravitational constant, M is the mass of the Earth, and r is the distance from the Earth's center.

For example, at sea level, the acceleration due to gravity is approximately 9.8 m/s^2. But at an altitude of 10,000 meters, the acceleration due to gravity decreases to about 9.7 m/s^2.

To calculate the acceleration of an airplane at a certain altitude, we need to take into account not only the acceleration due to gravity, but also the acceleration from the airplane's engines and any external forces acting on the airplane, such as air resistance.

This can be done using the principles of Newton's laws of motion and the equations of motion. By considering all the forces acting on the airplane, we can calculate the net acceleration and determine the speed and direction of the airplane at a specific altitude.

In summary, the acceleration of an airplane at different altitudes can be calculated by considering the acceleration due to gravity and all other forces acting on the airplane. It is important for scientists and engineers to understand these calculations in order to design and operate airplanes safely and efficiently.