Bats, Physics & Aerodynamics (Oh My)

Now, I don’t know how old this kid is, or what level of math you’ve got to, so you can vary this to suit tastes. It might take a lot of wood, though, so perhaps the more theory, the better.

Overall objective – to investigate various bat geometries / wood types to find an “optimal” baseball bat within a given set of parameters.

Task 1: Calculate the force with which a baseball hits a bat. This can be done in one of two ways, depending on whether you want to teach some theory, or practical technique.

1a) Theory – The force with which a ball hits a baseball bat can be calculated using a Newtonian approximation, assuming that in an ideal elastic collision there is no spin, energy is conserved, and there is no physical change in the bat or ball (you might ask the class to comment on these assumptions). You know the mass of a baseball, you know the velocity of a baseball before and after it hits the bat (I’m sure you can find this somewhere, but you can easily calculate / approximate; again, this is good scientific practice), so you’re left with an equation like

F= ma, where F is the force on the bat (and the ball – Newton’s laws teaching point!, m is the mass of the ball, and a is the acceleration. Remember that both force and acceleration are vectors, so DIRECTION IS IMPORTANT).

In addition, as it’s a perfectly elastic collision, energy will be conserved; That is, the kinetic energy of the ball + bat before the collision = the kinetic energy of the ball after the collision (all energy is transfered to the ball!). Anyway, you get an equation like this:

1/2MV^2 + 1/2m(rw)^2 = 1/2MU^2

where M = mass of baseball, V = initial velocity of baseball, m = mass of bat, r = distance of centre of gravity of bat from shoulder (ie, the radius of the swing), w = omega, the angular momentum of the bat (ie, number of radians covered per second), and U = departing velocty of baseball)

You can use this to calculate U, the departing speed of the baseball, and feed it back into the equation above, thus finding the force. Also, if you’ve already taught your class about moments of inertia, then you can use those equations (that’d be super awesome).

1b Practical – You can measure the force of a baseball hitting a bat practically in a number of ways – Seems like the easiest would be to fire, or even throw, a baseball at a pressure pad and measure the force at which it hits. There are issues surrounding modelling real life, here – for instance, how do you get the baseball to travel at a high enough velocity? It’s good to think about, and see if you can quantify, the innacuracies of your data points. This could be a fun experiment, though. You’ll also have to measure the force with which the bat hits the ball, too – you can do this by swinging at a pressure pad.

2. Bat design!

Now that you’ve done the background investigation, we’ll want to investigate various bat designs to see what the ‘ideal’ is. As actually building the experimental apparatus (ie, the bat!) here is quite tough and time consuming, you might want to limit the focus of your investigations. Let’s say you want to investigate something like this:

Assumption: to gain the greatest change in velocity as a baseball hits the bat, the centre of gravity of the bat should be as far from the pivot as is possible – in other words, the mass should be concentrated at the furthest point possible, to maximize the moment of Inertia.

Test: Given that we know the force with which ball and bat meet, how ‘thin’ can we make the rest of the bat, so that its structural integrity remains intact?

In other words, what you’re saying is – it’s better if more ‘bat’ hits the ball, so ideally, we want to concentrate the mass around the sweet spot. The problem is, though, for a given mass, this means that you sacrifice the strength of the rest of the bat (the handle end), and it might result in it splitting.

So, basically – you want to set the bat up so the handle is firmly clamped. You can then apply a force to the bat, and observe the results (this is where it all gets a bit mythbusters, but there’s still some good science in here). Because a bat is round, and the force can be approximated to be non-torsional, it actually doesn’t matter if the force is a ‘pulling’ force or a ‘pushing’ force. Ways of applying it could be to hang weights off the end (or various other parts of the bat).

You can teach about moments, tensile strength and density of materials.

Something else that’d be interesting to think about – can you create a more ‘efficient’ distribution of weight by using a flatter geometry, more like a cricket bat?

This actually seems like a fun experiment overall, and teaches experimental technique and theoretical investigation. And some engineering stuff, too – the whole ‘distribution of mass’ thing applies to most anything that’s built – including bridges between scientists and non-scientists.

Ok, that last bit may not be correct.

Hm, I’m sure there are other things you can teach around this, too. Let me know if you want any help.

Also, other scientists / engineers, please feel free to correct any mistakes I’ve made above.

He should emulate another wooden bat, not aluminum.

Miguel Tejada is set to sign with the Orioles. Makes sense over the A’s - they’re giving him a regular position at 3B; with the A’s he’d be a back-up unless Pennington tanked. Also, Jason Giambi is about the become the Rockie’s designated pinch hitter.

I recently wrote a nontechnical article for The Baseball Analysts entitled “Comparing the Performance of Baseball Bats.” See http://baseballanalysts.com/archives/2010/01/comparing_the_p.php.