The effect of spin on golf ball flight

C H A P T E R 5
Projectiles
Basic Concepts

Figure 5-1. <strong>The</strong> projectile trajectory frame
<strong>of</strong> reference

<strong>The</strong> Gravity-Only Model
Figure 5-2. Force diagram for the gravity-only
model

Figure 5-3. A typical trajectory under
the gravity-only model

Figure 5-4. A sample Golf Game
screen shot

Figure 5-5. A bird’s-eye view <strong>of</strong> the Golf
Game

Table 5-1 Summary <strong>of</strong> Equations <strong>of</strong> Motion
Table 5 1. Summary <strong>of</strong> Equations <strong>of</strong> Motion
for the Gravity-Only Projectile Model

Aerodynamic Drag

Figure 5-6. <strong>The</strong> drag coefficient <strong>of</strong> a sphere
as a function <strong>of</strong> Reynolds number

Table 5-3. Drag Coefficients <strong>of</strong> Three-
Dimensional Shapes (Re = 1.0e+5)

Table 5-4. Values <strong>of</strong> Air Density As a y
Function <strong>of</strong> Altitude

Table 5-5 Laminar and Turbulent
Table 5-5. Laminar and Turbulent
Drag Coefficients

Figure 5-7. <strong>The</strong> force diagram with gravity
and drag <strong>effect</strong>s

Figure 5-8. A typical Golf Game version 2
display

Figure 5-9. <strong>The</strong> <strong>effect</strong> <strong>of</strong> drag on
the flight <strong>of</strong> a golf ball

Wind Effects

Figure 5-10. Apparent velocity is the vector sum
<strong>of</strong> the projectile velocity and wind velocity.

Figure 5-11. A typical Golf Game version 3
screen shot

Figure 5-12. <strong>The</strong> <strong>effect</strong>s <strong>of</strong> headwind or
tailwind on a golf ball trajectory

Figure 5-13. <strong>The</strong> <strong>effect</strong> <strong>of</strong> crosswind on
golf ball flight

Spin Effects

Figure 5-14. A <strong>spin</strong>ning object generates lift.

Figure 5-15. <strong>The</strong> projectile force diagram
including gravity, drag, and Magnus force

Figure 5-16. A typical Golf Game version 4
screen shot

Figure 5-17. <strong>The</strong> <strong>effect</strong> <strong>of</strong> <strong>spin</strong> on golf ball flight

Figure 5-18. A tilt in the <strong>spin</strong> axis causes
the ball to curve.

Figure 5-19. Bullets usually have a yaw
angle during flight.

Answers to Exercises