How Do Parachute Equations Model Motion and Air Density Changes?

[saud alzaabi]

Hi all,

I have a physics project about parachutes and how they work, everything is fine with me except the task4 which is about its equations. It's really hard to find a good site that can fill in all these equations. And also I have a problem understanding what is needed other than equations.

here is what the task says

Task 4:
Use the given equations to model the motion of the parachutist, before and after the opening of a parachute. Chart the velocity and altitude with time using Microsoft Excel. Use a lookup function to determine the air density at each altitude point.

and can some one explain what do they mean by charting the velocity and altitude with time using excel ?

chech the attached file for all equations and info.


thanks

 

[saud alzaabi]

Anyone ? please ?

 

[andrevdh]

http://www.aeroconsystems.com/chutes/drag_calculator.htm"

You can plot more than one data series on chart. The second series uses a "secondary value axis" , that is the y-axis on the right hand of the graph is scaled with the values of the second series.

One series will contain the speed as a function of time v(t) and the other the altitude as a function of time h(t).

The terminal velocity of the chute changes due to a change in local air density \rho as your document gives (the other quantities are constant and you can insert them as a constant say b in your calculation):

v = \frac{b}{\sqrt{\rho}}

The way to go about the speed calculation for an open chute is therefore:

1. Start out at some altitude (current altitude) with some speed (current speed)
2. Let some time elapse
3. Calculate the new altitude using the current speed and elapsed time
4. Assign the new altitude to the current altitude
5. Calculate the local air density at the current altitude
6. Calculate the new speed at the current altitude
7. Assign the new speed to the current speed
8. Go to step 2 if current altitude > zero

This algorithm differs from the suggested one in the document. In the document a small downwards acceleration is assumed, which is a bit artificial and cannot be justified.