OT: A Puzzle Concerning the Physics of Sports

[JoePgh]

This question pertains to the sports of tennis and baseball, not basketball, which is why it is OT.

In tennis, when top players serve, the velocity of the serve is typically measured at around 120 mph for men and 105 mph for the most powerful women such as Serena Williams.

In baseball, the fastest major league pitch speeds are around 100 mph, and the fastest exit velocities on batted balls are in the 105-110 mph range.

Obviously, tennis balls are different from baseballs, and I'm sure that accounts for some of the difference. There is also a big difference insofar as the batter in baseball is hitting an object that is moving at a high velocity in the opposite direction to his hit, whereas the tennis player (when he or she serves) is hitting a ball with a minor upward or downward velocity but essentially zero horizontal velocity.

Question: Does the speed of the pitch help or hurt the velocity of the batted ball in baseball when the batter makes solid contact? In other words, if a batter applies the same swing and hits the ball equally solidly, will the exit velocity be higher or lower when the pitch is 80 mph vs. when it is 100 mph? I can see intuitive arguments for either conclusion. On the one hand, one could argue that the speed of the pitch functions like a headwind on an airplane, such that a plane's ground speed will be slowed by a headwind. That would imply that the same swing and the same contact on a fast pitch would result in a lower exit velocity if the pitch is fast than if it is slow. On the other hand, one could analogize to throwing a baseball against a cement wall. In that case, the ball will bounce back faster and further if it is thrown hard than if it is thrown slowly against the wall. That would suggest that the energy of the pitch (higher on a fast pitch than a slow pitch) would add to the energy generated by contact with the bat and lead to a higher exit velocity.

Does anyone know the "right" answer as a matter of physical mechanics? If so, could you explain (hopefully simply) the physics behind your answer?

 

[eebmg]

If you have 2 objects colliding, the energy imparted in the collision is larger if the net collision velocity is larger and that energy has to go somewherr. Into the ball. Of course, all other factors being equal.

This principle is the heart of particle colliders in high energy physics as well as car collisions

 

[oldude]

If you have 2 objects colliding, the energy imparted in the collision is larger if the net collision velocity is larger and that energy has to go somewherr. Into the ball. Of course, all other factors being equal.

This principle is the heart of particle colliders in high energy physics as well as car collisions

Thank you professor...

 

[rvwsleep]

The speed of the pitch helps a batted ball go farther, but not that much of a difference.
According to "The Physics of Baseball" the difference in distance of a battered ball of a pitch thrown 90mph and one thrown 95mph is less than 10 ft. I believe the example given was if a home run went 400ft off a 90mph pitch, then it would have traveled 408ft if the pitch was 95mph.
(I read this book years ago and this is to the best of my memory. I'll try to find it and confirm) .

 

[rvwsleep]

I found the book !!
On a 400 ft homerun to centerfield, an increase of 5 mph in pitch velocity would amount to an increase in distance of only 3.5 ft. (Table 5.1).
Interestingly, every...
1,000 ft in elevation results in a 7 ft increase in distance.
1 mph tail wind would add 3 ft on distance traveled.

 

[JordyG]

If you have 2 objects colliding, the energy imparted in the collision is larger if the net collision velocity is larger and that energy has to go somewherr. Into the ball. Of course, all other factors being equal.

This principle is the heart of particle colliders in high energy physics as well as car collisions

This is also one of the major arguments used when people discuss the difference between impacts in American football and rugby, and the necessity of helmets and pads in American football. That and of course, the difference in tackling rules, off ball hitting, tackling techniques, and some other things.

 

[eebmg]

I found the book !!
On a 400 ft homerun to centerfield, an increase of 5 mph in pitch velocity would amount to an increase in distance of only 3.5 ft. (Table 5.1).
Interestingly, every...
1,000 ft in elevation results in a 7 ft increase in distance.
1 mph tail wind would add 3 ft on distance traveled.

The way the question was asked, the OP wanted a yes / no answer. In the real world, the degree in which the batted ball velocity increases and overall travel distance increases with higher pitch velocity clearly changes with input factors such as higher spin rates , lower probability of on- center contact, higher air friction etc so experiments themselves will undoubtedly have different 'less pure' results.

I am sure there is a wide literature in which this question is addressed in a theoretical manner in an attempt to isolate the effects of different factors but I don;t have the courage to dig in.

 

[Ozimoto]

Just remember, everything can be derived from F=MA or Force equals mass times acceleration.

 

[eebmg]

Just remember, everything can be derived from F=MA or Force equals mass times acceleration.

partial credit.

 

[SVCBeercats]

Does anyone know the "right" answer as a matter of physical mechanics? If so, could you explain (hopefully simply) the physics behind your answer?

For your reading pleasure:
The BESR (Ball Exit Speed Ratio)
https://www.acs.psu.edu/drussell/bats/besr/BESRWhitePaper.pdf

What does a 100mph swing speed mean?

 

[Bama fan]

I found an article addressing the math /physics of this problem. There are many other issues such as spin, angle of contact, wind direction, humidity ,etc. But this presents the equations involved in a theoretical format.

Exit Velocity vs. Pitch Speed

This week we find ourselves in the middle of the Major League Baseball (MLB) Post Season. In the flurry of excitement we hear commentators spouting off different stats. Since everyone "digs the long...

www.localmathhelp.com

 

[oldude]

Professor Judge conducting a physics experiment with a baseball last night at 116 mph.

https://www.mlb.com/video/statcast-judge-s-467-ft-homer

 

[Bigboote]

I found the book !!
On a 400 ft homerun to centerfield, an increase of 5 mph in pitch velocity would amount to an increase in distance of only 3.5 ft. (Table 5.1).
Interestingly, every...
1,000 ft in elevation results in a 7 ft increase in distance.
1 mph tail wind would add 3 ft on distance traveled.

For your reading pleasure:
The BESR (Ball Exit Speed Ratio)
https://www.acs.psu.edu/drussell/bats/besr/BESRWhitePaper.pdf

What does a 100mph swing speed mean?

I would have expected the result from the site that SVC linked. If you use a Newton's Cradle (the little thing with five metal balls), the recoil of one ball is proportional to the velocity of the other ball.

But I solved an ideal case, and got something closer to what RVW cited. Basically, if you assume that the bat acts as something with a much greater mass than the ball (a valid assumption), the bat velocity is the main determinant of the exit speed. The pitch velocity comes in as a much smaller component, and a faster pitch leads to a slightly higher exit velocity for the batted ball.

I try to learn something new every day, and this is what I learned today. (I'd add that I learned a new level of incompetence of the IT people at work, but that's only degree, nothing new.)

 

[Triad]

The way the question was asked, the OP wanted a yes / no answer. In the real world, the degree in which the batted ball velocity increases and overall travel distance increases with higher pitch velocity clearly changes with input factors such as higher spin rates , lower probability of on- center contact, higher air friction etc so experiments themselves will undoubtedly have different 'less pure' results.

I am sure there is a wide literature in which this question is addressed in a theoretical manner in an attempt to isolate the effects of different factors but I don;t have the courage to dig in.

Courage you have! I suspect it is the inclination to answer a question in physics and physical attributes whose multiple inputs provide answers that take more effort than the question is worth. No disrespect to the originator of the question . We are after all spinning our wheels towards Novemeber

 

[JoePgh]

I found an article addressing the math /physics of this problem. There are many other issues such as spin, angle of contact, wind direction, humidity ,etc. But this presents the equations involved in a theoretical format.

Exit Velocity vs. Pitch Speed

This week we find ourselves in the middle of the Major League Baseball (MLB) Post Season. In the flurry of excitement we hear commentators spouting off different stats. Since everyone "digs the long...

www.localmathhelp.com

I'm glad that so many people were sufficiently interested in this conundrum that they were motivated to respond. I would simply point out that the article cited by Bama Fan clearly reaches a conclusion which is opposite to that of most people who responded to this thread. The article says that if all else is equal (force of bat, squareness of contact, friction generated by the ball against the air), then the exit velocity of a hit against a faster pitch will be LESS than the exit velocity of the same hit against a slower pitch. The key (as I understand the article) is that the energy of the pitch is opposite to the energy of the bat, so it reduces the net velocity rather than increasing it.

As I said, I can think of intuitive arguments that support either conclusion, but the article claims to resolve the hypothetical question definitively.

 

[Bigboote]

I'm glad that so many people were sufficiently interested in this conundrum that they were motivated to respond. I would simply point out that the article cited by Bama Fan clearly reaches a conclusion which is opposite to that of most people who responded to this thread. The article says that if all else is equal (force of bat, squareness of contact, friction generated by the ball against the air), then the exit velocity of a hit against a faster pitch will be LESS than the exit velocity of the same hit against a slower pitch. The key (as I understand the article) is that the energy of the pitch is opposite to the energy of the bat, so it reduces the net velocity rather than increasing it.

As I said, I can think of intuitive arguments that support either conclusion, but the article claims to resolve the hypothetical question definitively.

That article wasn’t written by a physicist, at least not a respectable one. It assumes the impulse (change in momentum) is independent of anything. It solves a problem requiring two equations with one equation. The impulse is greater for a higher-speed pitch. You can’t conserve momentum for two bodies if you don’t account for one of them.

As I said above, I did a simplification, but I did solve the two-variable problem. The simplifications: I approximated the bat by assuming that it’s a more massive object. I assumed an elastic collision (kinetic energy is conserved). The first assumption is robust. The second will change the magnitude of the effect but not the sign. My solution indicates that the exit speed of the ball is higher for a faster pitch, but the effect is really small.

 

[eebmg]

That article wasn’t written by a physicist, at least not a respectable one. It assumes the impulse (change in momentum) is independent of anything. It solves a problem requiring two equations with one equation. The impulse is greater for a higher-speed pitch. You can’t conserve momentum for two bodies if you don’t account for one of them.

As I said above, I did a simplification, but I did solve the two-variable problem. The simplifications: I approximated the bat by assuming that it’s a more massive object. I assumed an elastic collision (kinetic energy is conserved). The first assumption is robust. The second will change the magnitude of the effect but not the sign. My solution indicates that the exit speed of the ball is higher for a faster pitch, but the effect is really small.

Here is a solution which I think is slightly more general than @Bigboote which can be found at

Collisions and the Conservation of Momentum

X Bats - The Players' Choice. The Worldwide Leader in Custom Baseball Bats

www.xbats.com

Here, the energy conservation is not strictly satisfied and the loss of energy into heat is empirically approximated by a coefficient of restitution (e) taking into account a 'compressability or elasticity ' of the ball which connects the change in ball velocities to a change in bat velocity and gives the 'second' equation for the 2 variable problem.

In fact elastic collisions (energy conservation) is satisfied in the case e=1

see Coefficient of restitution - Wikipedia


The formula they get (verified) is

This equation says the batted ball velocity (v1a) depends on the mass of the ball (m1) and bat (m2), the elasticity of the ball (e), the pitched ball speed (v1b) and the bat swing speed (v2b). However, keep in mind that v1b is negative since it is directed opposite the other velocities.

What is interesting about this solution is that only if (m1-e*m2) <0 ; will the affect of increasing the pitched ball speed acts to increase the batted ball velocity. In the article, they say for a baseball, e ~ .55 so as long as m1 < m2*e or m2 > 2*m1 , increased pitch velocity gives increased exit velocity. This condition is clearly satisfied in real life. See next post

 

[eebmg]

Just a follow up. Using the following parameters

m2=1; % baseball bat 1 kg

m1=.15; % baseball 150 gms
v2b=70; % max baseball swing 70 mph

Maximum possible exit velocity as function of pitch velocity assuming perfect impact for different elasticity parameters. Higher elasticity means more recoil which maximizes the ball exit velocity.

clearly, the exit velocity % change is significantly smaller than the pitch % velocity increase.

 

[Ozimoto]

Well l am now having flashbacks to college physics!

That is both good and bad...

 

[eebmg]

Well l am now having flashbacks to college physics!

That is both good and bad...

It's good because you are not being graded.

 

[Ozimoto]

Thank goodness!

 

[Bama fan]

It's good because you are not being graded.

I think everyone is always being graded here on the BY. Perhaps the results are not always published, but we are all being graded!

 

[eebmg]

I think everyone is always being graded here on the BY. Perhaps the results are not always published, but we are all being graded!

Just hope Geno does not get a hold of it.