# How Do Parachute Equations Model Motion and Air Density Changes?

• saud alzaabi
In summary: The suggested algorithm is: 1. Start out at some altitude (current altitude) with some speed (current speed)2. Let some time elapse3. Calculate the new speed at the current altitude by doing the following: 3.a. Take the new altitude and subtract the previous altitude3.b. Take the new speed and multiply it by the density of air at the new altitude
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

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

#### Attachments

• Physics project.doc
76.5 KB · Views: 388

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.

Last edited by a moderator:

## 1. What are the equations used to calculate the descent of a parachute?

The two main equations used to calculate the descent of a parachute are the drag equation and the motion equation.

## 2. How does air resistance affect the descent of a parachute?

Air resistance, also known as drag, is the force that opposes the motion of an object through the air. It increases as the speed of the object increases. In the case of a parachute, air resistance slows down the descent of the parachute, allowing for a slower and safer landing.

## 3. What factors affect the descent of a parachute?

The descent of a parachute is affected by several factors, including the weight and shape of the parachute, the air density, and the velocity of the parachute.

## 4. How does the size of the parachute affect its descent?

The size of the parachute directly affects its descent. A larger parachute will have a larger surface area, which means more air resistance and a slower descent. A smaller parachute will have less air resistance and a faster descent.

## 5. Can the equations for parachute descent be used for any object?

The equations for parachute descent can be applied to any object that experiences air resistance during its descent. However, the equations may need to be modified for different shapes and sizes of objects.

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