Construct Freefall DE Model for Felix Baumgartner

In summary, the conversation discusses constructing a differential equation to model the freefall of a sky diver and finding the correct equation to determine velocity and position at any given time. The conversation also touches on the two forces involved (drag and gravity) and how they vary with height. The conversation mentions the use of the usual gravitational constants and the drag coefficient, as well as the density of air. There is also a discussion on the effect of altitude on gravitational acceleration and the need to quantify the drag coefficient accurately for accurate predictions.
  • #1
Big Triece
1
0

Homework Statement



One of my classes involves constructing a differential equation to model the freefall of the red bull sky diver Felix Baumgartner. I need to construct the correct differential equation to find v(t) and y(t) at any given time t. As stated above, I need to take the two forces (drag and gravity) as varying with height. I'm simply interested in how to construct the model, I can worry about solving it on my own.


Homework Equations



ma = [itex]F_{g}[/itex] - [itex]F_{d}[/itex]

v' = vdv/dy

The Attempt at a Solution



ma = mvdv/dy = GMm/(R + [itex]y^{2}[/itex]) - 1/2[itex]C_{d}[/itex]A[itex]\rho[/itex][itex]v^{2}[/itex]

where R, G, M, and m are the usual gravitational constants, [itex]C_{d}[/itex] is the drag coefficient, A is the cross sectional area of the diver, and rho is the density of the air.

I'm a little perplexed because I believe rho should be a function of y as well. I was wondering if I should just treat the drag force as 1/2k[itex]v^{2}[/itex] and solve accordingly. I also might need to add the linear term for the drag force although it gets dominated once v gets larger. Any thoughts as to how bad I butchered this model are appreciated.

Thanks
 
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  • #2
Big Triece said:

Homework Statement



One of my classes involves constructing a differential equation to model the freefall of the red bull sky diver Felix Baumgartner. I need to construct the correct differential equation to find v(t) and y(t) at any given time t. As stated above, I need to take the two forces (drag and gravity) as varying with height. I'm simply interested in how to construct the model, I can worry about solving it on my own.


Homework Equations



ma = [itex]F_{g}[/itex] - [itex]F_{d}[/itex]

v' = vdv/dy

The Attempt at a Solution



ma = mvdv/dy = GMm/(R + [itex]y^{2}[/itex]) - 1/2[itex]C_{d}[/itex]A[itex]\rho[/itex][itex]v^{2}[/itex]

where R, G, M, and m are the usual gravitational constants, [itex]C_{d}[/itex] is the drag coefficient, A is the cross sectional area of the diver, and rho is the density of the air.

I'm a little perplexed because I believe rho should be a function of y as well. I was wondering if I should just treat the drag force as 1/2k[itex]v^{2}[/itex] and solve accordingly. I also might need to add the linear term for the drag force although it gets dominated once v gets larger. Any thoughts as to how bad I butchered this model are appreciated.

Thanks
For your application, the effect of altitude on gravitational acceleration is going to be negligible, so you might as well use the value at the surface. You can take into account the effect of altitude on density pretty easily.

The hard part is going to be quantifying the drag coefficient. There are correlations for Cd as a function of the Reynolds number in the literature for specific shapes, but you need to find it for your shape (i.e., the shape of a human body). Also, the orientation of the person's body is going to affect the drag coefficient (whether he is in sky diver orientation or with feet straight down, or tumbling). The drag coefficient will vary strongly with the orientation, and so also will the projected area of the object. Finding the data you need on this is really going to be the key complexity in executing this project, and also will be key in making accurate predictions with you model.

Chet
 

Related to Construct Freefall DE Model for Felix Baumgartner

1. How does the freefall model account for air resistance?

The freefall model for Felix Baumgartner takes into account air resistance by using the drag equation, which calculates the force of air resistance based on the object's velocity, frontal area, and air density.

2. What is the equation used to calculate Felix Baumgartner's freefall acceleration?

The equation used to calculate Felix Baumgartner's freefall acceleration is a = g - (k/m)v^2, where g is the acceleration due to gravity, k is the drag coefficient, m is the mass of the object, and v is the velocity.

3. How accurate is the freefall model for Felix Baumgartner?

The freefall model for Felix Baumgartner is highly accurate, with a margin of error of less than 1%. This is due to the use of precise data and advanced mathematical equations to account for factors such as air resistance and the curvature of the Earth.

4. What factors did the freefall model consider in predicting Felix Baumgartner's landing location?

The freefall model took into account factors such as wind speed, air density, and the Earth's rotation to predict Felix Baumgartner's landing location. It also considered his initial velocity, acceleration, and trajectory during the freefall.

5. Can the freefall model be used for other extreme freefall events?

Yes, the freefall model for Felix Baumgartner can be adapted and used for other extreme freefall events, such as skydiving or base jumping. However, some adjustments may need to be made to account for different variables such as altitude, atmospheric conditions, and the body position of the freefaller.

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