Re: How do you calculate the distance you can hit a golf ball or softball, base

How far one can hit a ball can be a very complicated calculation if one wants to duplicate reality. Some similar questions have been answered on the MSN (some by me). I have captured references to many of the answers we have provided in an attempt to indicate some of the effects that need to be considered when calculating "how far a ball can be hit."
Three golden rules of physics will get one pretty far in 99.9% of mechanics problems:

• Conservation of Energy
• Conservation of Momentum
• Balance of Forces

In the simple physics blackboard world of no-friction and no aerodynamic forces the problems are fairly simple and deterministic (if one knows the initial conditions one can solve the problem completely and accurately).

In simplist form your equation might look like:

Total Energy = Energy of Ball_{before hit} + Energy of Bat_{before hit} + Energy of Batter_{before hit}
Total Energy = Energy of Ball_{after hit} + Energy of Bat_{after hit} + Energy of Batter_{after hit} + Energy Losses

where Total Energy is the same for both equations.

Momentum conservation is a bit more complicated, because the batter is applying a force and a torque to the bat, so momentum at the point of contact to just after the hit can be considered to be conserved, but that is about it.
Remember momentum is a vector!

Momentum Ball_{just before hit} + Momentum Bat_{just before hit} = Momentum Ball_{just after hit} + Momentum Bat_{just after hit}

This formulation is completely correct. However, to get something useful out of it, I need to figure out exactly what the various "energies" are in terms of physical quantities like mass, velocity, and heat loss.
This is where the basic physics formulas from class come into the picture.

Kinetic energy = 1/2 * mass * speed².
Momentum = mass * velocity (vector).
Heat loss = just an energy.

Now image throw the effects of inelastic collision, lift, drag, and wind. This problem becomes more difficult and most physicists and engineers would turn to a numerical simulation (computer). The various components of our equations could be modeled in an attempt to duplicate the reality we observe. Let me explain with an example from the above equations.

The term Energy of Batter is not completely understood. So suppose I decide to model it by

Energy Batter = Mass_{batter_in_kg}*(shoe_size_{batter_in_meters})/(neck_circumference_{batter_in_meters})*(wrist_speed² _{batter_in_meter/s})

where the subscript indicates the batter and the units of the parameter. I have a number that comes out in the correct units of energy (kg * meter*meter/(second* second) = Joules). I have decided that shoe size important because I see that all power hitters have big feet, but I decided that if their neck size is too big they will not be able to swing as well. This a perfectly valid model except it seems a bit silly. A real model of Energy Batter, would probably involve mass, bat speed, stride speed, and some sort of efficiency parameter.

One previous response in particular answers a question very similar to yours:

Re: Does the mass of a person transfer energy to a batted ball.
http://www.madsci.org/posts/archives/dec98/912805715.Ph.r.html

Other related responses:

Re: How does a golf club work and what is the effects of different shafts.
http://www.madsci.org/posts/archives/mar99/921608236.Ph.r.html

Re: Why are some golf clubs curved?
http://www.madsci.org/posts/archives/mar97/855190422.Ph.r.html

Re: What is the equation for the lift of a spinning golf ball? Smoothball? http://www.madsci.org/posts/archives/jun99/928944018.Ph.r.html

Re: How does the metal in golf clubs affect your golf game
http://www.madsci.org/posts/archives/mar98/889742387.Ph.r.html

Re: will a smooth surface ball curve when thrown??
http://www.madsci.org/posts/archives/aug97/868462089.Ph.r.html

Re: What % of air resistance is front-half v. rear-half of a smooth ball?
http://www.madsci.org/posts/archives/feb98/884963013.Ph.r.html

Re: How does tennis relate to physics?
http://www.madsci.org/posts/archives/nov99/943209851.Ph.r.html

Re: What can be hit further?
http://www.madsci.org/posts/archives/aug98/896795422.Ph.r.html

Re: Why is low & inside the 'home run' pitch?
http://www.madsci.org/posts/archives/aug98/897010656.Ph.r.html

Sincerely,

Tom "Slow Roller to Third" Cull