This document discusses the physics behind fastpitch softball pitching. It covers the pitching motion, drag force, empirical calculation of drag using terminal velocity, the Magnus force, and the net acceleration due to drag and Magnus forces. It shows that the net acceleration is proportional to velocity squared and inversely proportional to the square of terminal velocity, allowing calculation without knowing values like mass or cross-sectional area.

1. The Physics of Fastpitch
Emily Johnson

2. Pitching Motion
 Windup
 Stride
 Arm Motion
 Hip Rotation
 Release
 Follow Through

3. Drag Force
 The coefficient of the drag force (FD) is often
calculated using
FD = ½ρCDA·V2 = kD·V2
ρ = density of air
V = velocity
CD = coefficient of drag (about 0.5 for a
smooth ball)
A = cross sectional area
kD = net drag coefficient

4. Empirical Calculation of Drag
 The net drag coefficient (kD) was calculated
using the terminal velocity (VT) of a softball from
mg = kDVT2
giving
kD = mg/VT2
 Empirically measured terminal velocity of a
softball is 80 mi/hr (≈35.8 m/s)

5. The Magnus Force
 The coefficient of the Magnus force (FM) has
a similar form to the drag force:
FM= ½ρCLA·V2 = kM·V2
ρ = density of air
V = velocity
CL = lift coefficient
A = cross sectional area
kM = net Magnus coefficient

6. Net Acceleration due to Drag and Magnus Forces
 aD = -FD/m (points opposite the direction of motion)
 aM = FM/m (points perpendicular to the direction of motion)
 kD = ½ρCDA and kM = ½ρCLA = kD·kspin
where kspin is a relative spin constant where
+1 produces a strong up-spin force
-1 produces a strong down-spin force
0 produces no Magnus Force
 aD + aM = ( FD+ FM )/m = kD( 1 + kspin )V2/m
 Since kD = mg/VT2,
 aD + aM = g ( 1 + kspin )V2/VT2 which does not require
information about the softball’s mass or cross sectional area or the
density of the air