## Sunday 18 October 2015

### Modelling Skydiving with Tracker Software

Following my last post explaining the skydiving, here it comes the Skydiving Modelling using TRACKER Software.

Notes for teachers and learners who would like to use this TRZ file.

The fy is parameterize for the ease of modelling.
m = mass of human body
A_h = surface area of human body
A_p = surface area of parachute
g at 2000 m height
d = density of air
Cd = drag coefficient of human body
Cd2 = drag coefficient of parachute
g2 = g near surface of Earth
T – duration for parachute opening in Model A

Model A(Red):  Parachute opens slowly over T seconds

Fy function:

if(t<35,m*g-A_h*0.5*d*Cd*vy^2,if(t<35+T,m*g-0.5*d*Cd2*(A_h+(t-35)/T*A_p)*vy^2,if(t<55,m*g-0.5*d*Cd2*(A_h+A_p)*vy^2,if(vy>0,-m*g,0))))

Model B(Blue): Parachute opens fully immediately

Fy function:

if(t<35,m*g-A_h*0.5*d*Cd*vy^2,if(t<55,m*g-0.5*d*Cd2*A_p*vy^2,if(vy>0,-m*g,0)))

Velocity-time graph for Model A:

Velocity-time graph for Model B:

Comparison of Velocity-time graph for Model A & B:

Acceleration-time graph - Model B compared to Model A

Model B has a deceleration of 17g, while Model A’s deceleration is 3.1g.

I think it is a bad idea to open the parachute immediate while the parachutist is falling at 40 m/s. In real life, according to a Discovery Education Channel video (https://www.youtube.com/watch?v=ur40O6nQHsw), the parachute takes about 2-3 seconds to open fully.

Ideas for teaching and demonstration:

Adjust the parameters and compare the velocity-time graph and acceleration-time graph.