Added air drag to kalman filter ball tracking.

baseball.py

@@ -0,0 +1,83 @@
+# -*- coding: utf-8 -*-
+"""
+Spyder Editor
+
+This temporary script file is located here:
+/home/rlabbe/.spyder2/.temp.py
+"""
+
+
+""" 
+
+Computes the trajectory of a stitched baseball with air drag.
+Takes altitude into account (higher altitude means further travel) and the
+stitching on the baseball influencing drag. 
+
+This is based on the book Computational Physics by N. Giordano.
+
+The takeaway point is that the drag coefficient on a stitched baseball is 
+LOWER the higher its velocity, which is somewhat counterintuitive.
+"""
+
+
+
+import math
+import matplotlib.pyplot as plt
+
+def a_drag (vel, altitude):
+    """ returns the drag coefficient of a baseball at a given velocity (m/s)
+    and altitude (m).
+    """
+    
+    v_d = 35
+    delta = 5
+    y_0 = 1.0e4
+    
+    val = 0.0039 + 0.0058 / (1 + math.exp((vel - v_d)/delta))
+    val *= math.exp(-altitude / y_0)
+    
+    return val
+
+
+
+def compute_trajectory(v_0_mph, theta, v_wind_mph=0, alt_ft = 0.0, dt = 0.01):
+    ### comput
+    theta = math.radians(theta)
+    
+    v_0 = v_0_mph * 0.447 # mph to m/s
+    v_x = v_0 * math.cos(theta)
+    v_y = v_0 * math.sin(theta)
+   
+    v_wind = v_wind_mph * 0.447 # mph to m/s
+    altitude = alt_ft / 3.28   # to m/s
+    
+    ground_level = altitude
+    
+    x = [0.0]
+    y = [altitude]
+    
+    i = 0
+    while y[i] >= ground_level:
+        g = 9.8
+        
+        v = math.sqrt((v_x - v_wind) **2+ v_y**2)
+        
+        x.append(x[i] + v_x * dt)
+        y.append(y[i] + v_y * dt)
+        
+        v_x = v_x - a_drag(v, altitude) * v * (v_x - v_wind) * dt
+        v_y = v_y - a_drag(v, altitude) * v * v_y * dt - g * dt
+        i += 1
+        
+    return (x,y)
+ 
+if __name__ == "__main__":
+    x,y = compute_trajectory(v_0_mph = 110., theta=35., v_wind_mph = 0., alt_ft=5000.)
+    
+    plt.plot (x, y)
+    plt.show()
+    
+
+    
+
+