HOW TO HIT HOME RUNS. OPTIMUM BASEBALL BAT SWING PARAMETERS FOR MAXIMUM RANGE TRAJECTORIES

American Journal of Physics ^ | November 2003 | George S. Sawicki, Mont Hubbard, and William J. Strong

[MeneMeneTekelUpharsin]

Improved models for the pitch, batting, and post-impact flight phases of a baseball are used in an optimal control context to find bat swing parameters that produce maximum range. The improved batted flight model incorporates experimental lift and drag profiles (including the drag crisis). An improved model for bat–ball impact includes the dependence of the coefficient of restitution on the approach relative velocity and the dependence of the incoming pitched ball angle on speed. The undercut distance and bat swing angle are chosen to maximize the range of the batted ball. The sensitivity of the maximum range is calculated for all model parameters including bat and ball speed, bat and ball spin, and wind speed. Post-impact conditions are found to be independent of the ball–bat coefficient of friction. The lift is enhanced by backspin produced by undercutting the ball during batting. An optimally hit curve ball will travel farther than an optimally hit fastball or knuckleball due to increased lift during flight.

[MeneMeneTekelUpharsin]

The full article costs $$. If someone has the $$, they might be able to get it and post more of it here. I don't have the $$. The article basically says (via a report from National Public Radio) that a curve ball hit at optimum angle will go farther than a fastball hit at optimum angle due to the spin on the ball. The fast ball has backspin and the curve ball has topspin. Fascinating report and excellent research by these gentlemen. Some here might find this to be of interest.

[So Cal Rocket]

I couldn't hit the curveball... that's why I work behind a desk today.

[stylin19a]

see the ball...hit the ball.

[tbeatty]

Last I checked, Barry Bonds has the HR record, not George Sawicki. :)

[MeneMeneTekelUpharsin]

I couldn't hit the curveball... that's why I work behind a desk today.

I remember as a very young boy watching the ball pass between my legs and to the outfield fence. End of my career.

[So Cal Rocket]

I could see it fine... the ball just kept moving to places I didn't expect.

I hit over .400 in HS (3 year varsity), over .375 in my first year in college... then they started throwing the nasty curves & sliders... couldn't do anything but hit weak grounders to second.

Oh well, it's not like professional baseball players make lots of money, now do they?

[Eastbound]

I thought angle of trajectory was just as important if distance was the goal. Forty-five degrees, regardless of spin. Even with top spin, if the ball left the bat at fifty degrees, it would still fall short of one hit at forty-five degrees with the same top spin, wouldn't it?

[MeneMeneTekelUpharsin]

The indication in the feature on NPR (interviewing one of the authors) was that a curve ball hit at optimum angle went farther than a fastball hit at optimum angle. Case closed. I was VERY surprised. The initial experiment was to determine something else and they discovered that information quite by accident.

[supercat]

I thought angle of trajectory was just as important if distance was the goal. Forty-five degrees, regardless of spin. Even with top spin, if the ball left the bat at fifty degrees, it would still fall short of one hit at forty-five degrees with the same top spin, wouldn't it?

An object which is spinning as it flies through the air can convert some of that rotational kinetic energy into translational kinetic energy. This can change the optimal angle of launch.

Further, even if the object in question weren't spinning, air friction would still play a significant role in altering its trajectory. The forty-five degree optimum angle only appies in a vacuum.

[Eastbound]

"The forty-five degree optimum angle only appies in a vacuum."

Thanks for the note, supercat. I helped my grandson construct a catapult for a competitive science project in school years ago. Happy to report the forty-five degree optimum angle also applies in a school gymnasium. :)