How to calculate force of air resistance in 2D projectile motion - Computational Science in C#
<p>I am writing a program that will output a table of various stats on a 100th of a second interval of throwing a ball at a specific angle with a specific initial speed. I am having trouble calculating the air resistance. I have my Code below. Level 1 is solved, witch is modeling the 2D projectile motion without air resistance. I am stuck on level 2 witch is the same thing, but I need to factor in air resistance.</p>

<pre><code>using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Homework2ProjectileMotion
{
class Program
{
    private const double interval = 0.001;
    private const int mass = 5;
    private const double initialSpeed = 10;
    private const double angle = Math.PI / 4;
    private const double startTime = 0;

    private void CalcAll(StreamWriter sw, double drag)
    {
        double speed = initialSpeed;
        double xPos = 0;
        double pXPos = 0;
        double yPos = 0;
        double pYPos = 0;
        double zPos = 0;
        double pZPos = 0;
        double distance = 0;
        double xVel = 10 * Math.Cos(angle);
        double yVel = 0;
        double zVel = 10 * Math.Sin(angle);
        double xAcc = 0;
        double yAcc = 0;
        double zAcc = -9.8;
        double mAcc = 9.8;
        double xAir = 0;
        double yAir = 0;
        double zAir = 0;
        double air = 0;
        double slope = 0;
        double vector = 0;
        sw.WriteLine("Time\tx\ty\tz\tDistance\tvx\tvy\tvz\tSpeed\tax\tay\taz\tm_Acc\n" + startTime + "\t" + xPos + "\t" + yPos + "\t" + zPos + "\t" + distance + "\t" + xVel + "\t" + yVel + "\t" + zVel + "\t" + speed + "\t" + xAcc + "\t" + yAcc + "\t" + zAcc + "\t" + mAcc);
        for (double i=startTime+interval;zPos&gt;=0;i+=interval)
        {
            air = drag * speed * speed;
            if (xPos == 0)
            {
                slope = 1;
            }
            else
            {
                slope = (zPos - pZPos) / (xPos - pXPos);

            }
            vector = Math.Atan(slope);
            xAir = air * Math.Cos(vector);
            zAir = air * Math.Sin(vector);
            xAcc = ((xAcc * mass) - xAir) / mass;
            yAcc = ((yAcc * mass) - yAir) / mass;
            zAcc = ((zAcc * mass) - zAir) / mass;
            mAcc = Math.Sqrt(xAcc * xAcc + zAcc * zAcc);
            xVel = xVel + (xAcc * interval);
            yVel = yVel + (yAcc * interval);
            zVel = zVel + (zAcc * interval);
            speed = Math.Sqrt(xVel * xVel + zVel * zVel);
            pXPos = xPos;
            pYPos = yPos;
            pZPos = zPos;
            xPos = xPos + xVel * interval;
            yPos = yPos + yVel * interval;
            zPos = zPos + zVel * interval;
            distance = Math.Sqrt(xPos * xPos + zPos * zPos);
            sw.WriteLine(i + "\t" + xPos + "\t" + yPos + "\t" + zPos + "\t" + distance + "\t" + xVel + "\t" + yVel + "\t" + zVel + "\t" + speed + "\t" + xAcc + "\t" + yAcc + "\t" + zAcc + "\t" + mAcc);
        }
        sw.Close();
    }

    private void Level1()
    {
        StreamWriter writer = File.CreateText("Level1.txt");
        CalcAll(writer, 0);
        writer.Close();
    }
    private void Level2(double dragCoe)
    {
        StreamWriter writer = File.CreateText("Level2.txt");
        CalcAll(writer, dragCoe);
        writer.Close();
    }
    static void Main(string[] args)
    {
        Program run = new Program();
        //run.Level1();
        run.Level2(0.3);
    }
}
</code></pre>

<p>}</p>

<p>Here is an image of the first few outputs and a graph of the horizontal vs the vertical:</p>

<p><img src="https://i.stack.imgur.com/HClN3.png" alt=""></p>