Numerical Method Terminal Velocity

Parachutist of mass(m) = 68.1 kg

drag coefficient(c) = 12.5 kg/s

g= gravitational acceleration = 9.81

ti=0

vi=0

ti+1 - ti = 0.1

here is the eqn

v(ti+1)=v(ti)+(g-(c/m)*v(ti))*(ti+1 - ti)

I just want to plot within such a point that v(ti+1)-v(t)<0.001

thanks

[James Tursa]

What have you done so far? What specific problems are you having with your code?

[Torsten]

If you set the initial condition for v to be zero, the solution is v=0 for all times. I guess this is not what you want.

Best wishes

Torsten.

[Jan]

@Torsten: Why?

v(2) = v(1) + (g - (c/m)*v(1)) * 0.1 =
     = 0    + (g - 0) * 0.1

This is an acceleration.

@Ali Enes Yildirim: What have you tried so far? The only pitfall if not to confuse the index of the times and the value.

Answer 1

[Jan]

The terminal velocity is reached, when there is no further acceleration. This means that g-(c/m)*v(ti) must be 0.0 and you can calculate the result without any iterations or rough limits.

If you really want to calculate this by a loop:

v(1)  = 0;
ti    = 1;
tStep = 0.1;
vStep = inf;  % Arbitrary large value to allow entering the loop
while vStep > 0.001
  ... increase ti by 1 (not by 0.1)
  ... calculate new speed and store it in v(ti) using tStep (not ti)
  ... calculate the step in the velocity vStep
end

Answer 2

[Ali Enes Yildirim]

this is about falling parachutist problem. I solved it with EXCEL by using a lots of rows and columns. ı just wanted make sure whether there is a simple way to solve Numerical Methods with MATLAB. Thank you MS Excel and you guys trying to help me :)

[Jan]

As said already: you can solve it manually: v(final) = g*m/c