Question

I am working on building a little game program like this one for a sky diving sim and I have got a lot of the equations down but my terminal velocity is way too high for the given alt for any of this. I have been looking at this and gone over it the only thing I can think of is that I have one of the measurements wrong or something. Any help will be appreciated with this.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace GasLaws
 {
   class Program
{


    static void Main(string[] args)
    {

           double temperature;
           double airPressure;
           double airDensity;
           double tV;

           double alt;

           //constants
           const double gasCont = 287.05;
           const double startTemp = 15; //this is C ground level
           const double aidRate = 0.0065; //adiobatic rate for temperature by elevation

        //Human Constannts
           const double drag = 0.7; //in meters
           const double area = 7.5; //ft^2
           const double wieght = 175;



        Console.WriteLine("Enter the alt in feet");
        int tempint = Int32.Parse(Console.ReadLine());
        alt = (double)tempint * 0.3048; //convert feet to meters
        Console.WriteLine("Alt = " + alt + " m");

        //calculate air pressur
        airPressure = AirPressure(alt);
        temperature = CalTemp(startTemp, alt, aidRate);
        airDensity = AirDensity(airPressure, gasCont, temperature);
        tV = TerminalVelocity(wieght, drag, airDensity, area);

        //pasue screen for a second
        Console.ReadLine();

    }

    //p = 101325(1-2.25577 * 10^-5 * alt) ^5
    //this calculates correctly
    private static double  AirPressure(double al) 
    {
        double tempAlt = 1 - 2.25577 * 0.00001 * al;
        Console.WriteLine("Inside eq = " + tempAlt);
        tempAlt = Math.Pow(tempAlt, 5 );
        Console.WriteLine("Power of 5 = " + tempAlt);
        tempAlt = 101325 * tempAlt;
        Console.WriteLine("Pressure is = " + tempAlt + " Pascal");
        return tempAlt;
    }

    //temperature calculation
    // use adiobatic rate to calculate this
    //this is right
    private static double CalTemp(double t, double al, double rate) //start temperature and altitude 
    {

        double nTemp = t;
        for (int i = 0; i < al; i++)
            {
                nTemp -= rate;
            }
        Console.WriteLine("Temperature in for loop = " + nTemp);
        return nTemp;
    }

    //claculate like this
    //D  Pressure / gas constant * temperature
    //this works fine
    private static double AirDensity(double pres, double gas, double temp) 
    {
        temp = temp + 273.15; //convert temperautre to Kelvans
        double dens = pres / (gas * temp);
        dens = dens / 1000;
        Console.WriteLine("PResure = " + pres);
        Console.WriteLine("Gas cont = " + gas);
        Console.WriteLine("Temperture = " + temp);
        Console.WriteLine("Air Density is: " + dens);
        return dens;

    }

    private static double TerminalVelocity(double w, double cd, double p, double a)
    {
        double v = (2 * w) / (cd * p * a) ;
        v = Math.Sqrt(v);
        Console.WriteLine("Terminal Velocity = " + v);
        return v;

    }
}

}

Answer 1

Your formula doesn’t seem to include gravitational acceleration, and you are also mixing SI and US/imperial units. What unit will your calculated velocity have? It would probably be easier if you stay with SI units only. Another thing that looks a little strange is this line:

const double drag = 0.7; //in meters

The drag coefficient is a dimensionless number. It shouldn’t have a physical unit (like meter).

The correct formula is:

v = sqrt((2 * m * g) / (d * A * C))

The variables, with corresponding SI units, are:

m [kg] – Mass of falling body.

g [m/s^2] – Gravitational acceleration.

d [kg/m^3] – Air density.

A [m^2] – Projected area.

C [-] – Drag coefficient.

If you use these units, the formula will yield the velocity in [m/s]. As an example. let’s try the following values with units as above: m=80, g=9.8, d=1, A=0.7, C=0.7

This gives the terminal velocity v = 57 m/s which seems reasonable.