Golf Club Mass Comparison
A while back, a faithful Guisblend reader and commenter requested that I look into the physics of golf clubs. Particularly the claim that a lighter head on a driver will give you greater club speed and thus allow a farther drive. Wouldn't having less mass strike the ball also influence the speed of the ball he wondered (or at least that's how I understood his question)?
The short answer to that question is yes, club speed is not the only factor that influences the speed of a golf ball coming off the club. I can give more details of my calculations in the comments if anyone is interested, but I basically looked up typical values for things like lengths of arms, lengths of clubs, masses of shafts, mass of club head, swing speed, etc. Using these values, I created a baseline for the energy present during a golf swing. From there I varied the mass of the club head, while keeping the energy of the swing constant. This obviously gave faster swing speeds for lighter drivers, but then I calculated the ball speed after a collision with the club...and things got interesting.
The plot below shows that there is an optimal club mass to maximize the speed of the ball, and that a lighter (or heavier) club head will result in inferior performance. So lighter is certainly not always better. Essentially, the lighter club slows down more during the collision, thus counteracting some of the benefit of its greater speed.
If we zoom in on this graph a bit, we see the optimal club head mass is around 187 grams (.187 kg on the graph). This value will be different for each person, so don't read too much into it. The other thing to notice is that the changes in speeds on either side of the optimal mass is really quite small. A 25 gram increase in mass (a sizable increase from a 187 gram club head) only decreases the ball speed by 0.1%. Having a 25 gram decrease is slightly more influential, leading to a 0.4% decrease in speed. It's worth noting that the curve is not symmetric about its max value, but falls off more steeply as you get lighter than as you get heavier (the plot below is horizontally centered on the peak value). So erring on the side of too heavy is safer than too light.
I guess the last question is, does a 0.4% decrease in ball speed translate to much difference in distance travelled...and the answer is not really. Without factoring in air resistance (which would likely just lessen the difference as it would act more strongly on the faster ball), the distance would decrease by about 0.8%. That's about 2.5 yards on a 300 yard drive. For a pro, maybe that's enough to matter.
While real world testing would be far more accurate (but also tricky because consistently replicating a swing is pretty hard for most golfers), my guess is that the only advantage of a lighter driver would be that you feel cooler swinging it faster. And that 25 gram reduction will allow you to swing the club a few mph faster (a respectable 2.7% increase).
Comments
Another question for you. Does being fat help a person drive the ball farther, or is the person's weight irrelevant?
Another thought. With both the golfer and the baseball player, their feet are interacting with the ground. Since the player is typically exerting a force that has upward and horizontal components on the ball, the player is experiencing recoil forces in the opposite directions (down and backwards). The ground will largely limit the player being pushed in those directions, thus making the player's weight even less likely to matter.
Maybe if you were hitting a ball while standing on a frictionless surface or floating in space then the player's weight would matter more. For terrestrial sports, I'm still thinking it's mostly about bat/club speed.