Analytical Solution to the Falling Parachutist Problem

Problem Statement. A parachutist of mass 68.1 kg jumps out of a stationary hot air balloon. Use Eq. (1.10) to compute velocity prior to opening the chute. The drag coefficient is equal to 12.5 kg/s

The downward pull of gravity FD and the upward force of air resistance FU.

therefore

(It is a differential equation)

The exact solution as shown as follow,

Refer to the exact solution , we can write the Fortran code as follow,

program AS ! AS is program name

IMPLICIT NONE ! 關閉內定型態的功能, 每個變數必需事先宣告,位置在PROGRAM指令的下一行

REAL*8 m,g,c,v ! 宣告m,g,c,v為浮點數, REAL*4-浮點數單精度, REAL*8-雙精度浮點數

Integer*4 t ! 宣告t為長整數 – 使用4位元組（4 bytes, 32 bits）

m=68.1

g=9.8

c=12.5

OPEN(66, FILE=’AS.TXT’, STATUS=’UNKNOWN’)

Do t=0, 50, 1

v=((g*m)/c)*(1-exp((-c/m)*(t)))

WRITE(66 ,*) t, v

END Do

pause

stop

end

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We can copy the results form AS.TXT to Excel, and present them to graphic diagram.

Reference:

Numerical Methods for Engineers 6th P12-P15, Steven C. Chapra Raymond P. Canale