Computation of Drag Coefficients

Assuming the free-fall terminal velocity is known, the free-fall drag coefficient is found by setting the RHS of the EOM to zero and solving for . The rate of descent for the T-10 parachute is given as 16 ft/sec [ebk, p. 86]. This suffices to compute the drag coefficient when the parachute is fully deployed. A second method for finding the drag coefficient when the parachute is fully deployed is to use the characterization of the impact force as being equivalent to jumping from a five-foot high wall. To find this impact velocity it is necessary to solve each model with an initial height of 5 ft (1.52m), find the time when the height is zero, then determine the velocity at that time.

It would not be unreasonable to make these computations into a function of the values in param2 .

>

> i := 'i':

> k := 'k':

> for i in [lin,quad] do

>

> if i=lin then printf("\n\nLINEAR MODEL\n============\n")

> elif i=quad then printf("\n\nQUADRATIC MODEL\n===============\n")

> fi;

>

> PARAM[FF,i] := solve(subs( v(t)=VtermFF, paramFF, Vterm[i] ), {k});

> PARAM[D ,i] := solve(subs( v(t)=VtermD , paramFF, Vterm[i] ), {k});

>

> fsolve( subs( paramFF, PARAM[FF,i], X[i] )=0, t, 0..2 ); # time of impact for jump from 5-foot wall

> evalf( subs( t=%, paramFF, PARAM[FF,i], V[i] ) ); # corresponding impact velocity

> subs( v(t)=%, paramFF, Vterm[i] );

> PARAM[D,i,5] := solve(%, {k});

>

> printf("\nDrag Coefficients\n" );

> print( k[FF]=subs( PARAM[FF,i], k ) );

> print( k[D]=subs( PARAM[D,i], k ) );

> print( k[D,5]=subs( PARAM[D,i,5], k) );

> od:

LINEAR MODEL

============

Drag Coefficients

QUADRATIC MODEL

===============

Drag Coefficients

>