Understanding Zero-G: Calculating Airplane Acceleration at Different Altitudes

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Discussion Overview

The discussion revolves around calculating the acceleration of an airplane at different altitudes, particularly in the context of zero-gravity conditions experienced during flight. Participants explore the implications of varying gravitational acceleration and seek to model the airplane's position using mathematical functions.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that the airplane accelerates at the acceleration due to gravity, making the acceleration of a person inside the airplane relative to the airplane zero.
  • Another participant references the formula for gravitational acceleration, suggesting it can be used to calculate the acceleration needed at different altitudes.
  • A third participant mentions that Earth's gravity decreases by approximately 0.3086 mGal per meter of altitude increase, introducing the concept of the free air correction.
  • There is a repeated inquiry about modeling the airplane's position using sine waves, indicating a lack of clarity on how to approach this aspect.
  • A participant describes the airplane's trajectory during the zero-g portion of flight as following a parabolic path with a downward acceleration of 1 g and a near-constant horizontal velocity.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the modeling of the airplane's position and the implications of varying gravitational acceleration. No consensus is reached on the best approach to these calculations or modeling techniques.

Contextual Notes

Participants acknowledge the small effect of gravitational changes at typical flight altitudes, but the implications of these changes on calculations remain unresolved. There is also an ongoing exploration of the mathematical modeling of the airplane's motion.

Who May Find This Useful

Individuals interested in aviation physics, gravitational effects on flight, and mathematical modeling of motion may find this discussion relevant.

tahayassen
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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?
 
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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?
 
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.
 
tahayassen said:
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.
 

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