The Trampoline Effect

1. The Trampoline Effect Amilcah Gomes February 2, 2005 PHY3091 - 01

2. The Trampoline Effect • Introduction • The Trampoline Effect in Baseball • The Trampoline Effect in Tennis • The Trampoline Effect in Golf

3. Introduction • The trampoline effect refers to pronounced elasticity in the impacting object (baseball bat, tennis racquet, golf club, etc.) such that it acts like a trampoline. • It is also referred to as the spring-like effect because of the degree to which the object depresses, then springs back into shape when striking a ball.

4. The Trampoline Effect in Baseball • The trampoline effect in baseball refers to the elasticity of a bat upon impact with a baseball. • When a ball hits a wood bat, it compresses to nearly half its original diameter, losing up to 75% of its initial energy to internal friction forces. • However, in a hollow bat such as an aluminum bat, the bat barrel compresses somewhat like a spring. This means that the ball is not compressed as much and loses less energy to internal friction forces. • Furthermore, most of the energy temporarily stored in the bat is returned to the ball in a metal bat. The energy which is lost in the bat compression is much smaller than that lost without compression. Figure 1. Velocity diagram describing the swing of a baseball bat before impact, upon contact, and after impact with a pitched ball.

5. Wood or Metal Bats? • The Crisco-Greenwald study compares batted ball speeds for balls hit with a wood bat and the highest performing metal bat used in their study. • Figure 2 shows that for a given swing speed, the aluminum bat can potentially hit the ball 5-7 mph faster than the wood bat. • This can be explained if the metal bat has a trampoline effect which returns more of the energy to the ball. • Thus, the study offers some evidence of an enhancement in performance for metal bats due to an elastic property of the bat . Figure 2. A comparison between batted ball speeds for balls hit with a wooden bat (orange) and an aluminum bat (blue). The horizontal axis represents the bat’s swing speed. Plotting the data as such normalizes the results, removing the effect of different moments-of-inertia.

6. The Trampoline Effect in Tennis • The trampoline effect in tennis refers to the elasticity of a tennis racquet upon impact with a tennis ball. • In science, power is the rate of doing work. The player/racquet system has power, with the player providing the effort and the racquet providing the interface with the ball to deliver that player effort.  • So if, consistent with this scientific meaning, we consider a powerful racquet to be one can achieve a certain ball speed with the least player effort per unit time, and we limit the time of the stroke, what power then becomes is the inverse of Work: low Work means high power. This concept can be best understood as efficiency.   

7. The Trampoline Effect in Tennis • The strings of the racquet are the major component in racquet bounce. The strings act as a medium that absorbs much of the ball's kinetic energy and returns some of that energy back to the ball. Anecdotally, stiff frames with large heads are known to be bouncy, with a pronounced trampoline effect.  • In the ball-racket interaction, it is good to have most of the energy stored in the strings, which can give back 95% of it. Tighter strings produce lower ball speeds because of energy loss when the strings start to move and rub within the string frame. If the strings are looser rather than tighter, it will lead to slightly higher rebound velocities (more efficiency). The elasticity of the strings is a very important factor for storing energy. • Control, however, suffers as bounce increases, particularly with large heads.  Expert players tend to prefer lower efficiency racquets in order to maintain control during a match.

8. The Trampoline Effect in Tennis Figure 3. Typical force at the base of index finger (IF) and onlittle finger side (G) of the hand in an off-center impactof a tennis forehand with an eastern grip. Note that the forces of frame vibrations are smaller than the pattern of impulsive loading and are damped out in less than 1/10th of a second.

9. The Trampoline Effect in Golf • The trampoline effect in golf refers to the elasticity of a golf club face upon impact with a golf ball. • Similar to the player/racquet system in tennis, the player/club relationship in golf also has power, with the player providing the effort and the golf club providing the interface with the ball to deliver that player effort. 

10. The Trampoline Effect in Golf • Over the years of golf, driving distance has improved. This has changed from 255.0 yards (the average on the Tour in 1968) to 278.5 yards in 2001, which is a 23.5-yard increase in 33 years. 14.3 of these yards (60.8% of the increase) within the last six years. The average driving distance has increased at a rate of only 1.0 foot per year from 1968 to 1995. Using this as a base rate, the sudden jump to 7.2 feet per year, from 1995 to 2001 is quite interesting. (See Figure 4) • It was over this period of time that Titanium drivers with enhanced rebound velocity "Spring Like Effect" (SLE) were introduced. Test data indicates that this type of club (at the USGA limits) will significantly increase the ball velocity and this may be sufficient to increase distance from 10 to 15 yards over clubs without SLE. • The scoring average has only changed from 71.9 strokes per round in 1968 to 70.88 in 2001. This change is 1.12 strokes per round in more than thirty years. But in the last ten years the average score has changed almost 0.4 of a stroke. (See Figure 5)

11. The Trampoline Effect in Golf Figure 4. PGA Average Driving Distance (1968-2001). Note the sudden increase from 1.0 foot per year from 1968 to 1995 to 7.2 feet per year from 1995 to 2001.

12. The Trampoline Effect in Golf Figure 5. Actual vs. Adjusted Scores: PGA Tour (1968-2001). Note the major decrease from 1995 to 2001.

13. The Trampoline Effect in Golf • In 1998, the US Golf Association (USGA) announced a test that would determine if the face thickness (or other properties of the face) in some manner launched the ball too quickly, thus producing a noticeable distance advantage to players. The USGA concluded that as the face thickness decreases, the resultant trampoline effect increases. • What most players don’t realize is that although a ball hit longer that goes straight is a distinct advantage; one that goes longer in the wrong direction (i.e., hooked or sliced) becomes a greater disadvantage.