F=ma and Bad Science

[iacas]

A week or two ago, a golf instructor posted this question to fellow instructors on Facebook.

Two golfers, one male, one female, have identical numbers on a launch monitor - launch angle, spin, clubhead speed, etc. Why does the male hit the ball 30 yards farther?

Several people wrote to say what's correct - that if their numbers ( all of their numbers for their impact conditions, including smash factor and ball speed) were identical, the balls would fly identical distances, and that's that. Something was wrong.

We later learned that the numbers were given to us from a range session, but the distances were from play on the course. Clearly the guy must swing harder or otherwise change his launch conditions on the golf course.

The thread was revealing, however. Science has taught us that the only thing that matters during impact is the clubhead and about 3-5 inches of the shaft. The collision between the ball and the clubhead are almost like two free bodies hitting each other. Nothing above the 3-5 inches up the shaft has any influence on impact.

Yet pros were chiming in to say "the male probably weighs more, and F=ma" or "the guy probably has a firmer grip" or some other things I've since forgotten.

Rubbish. We know this to be rubbish, or else Iron Byron wouldn't be able to keep a ball on the range. The simple (slightly over-simplified) reason: impact lasts so short an amount of time that the vibrations and deformations and whatnot that occur to the shaft don't have time to radiate up and back down the shaft very far. That's why only the bottom section of the shaft matters. It doesn't matter if you're squeezing the grip so hard you're cracking your shaft or if you literally let go of the grip at the precise moment of impact - the ball will go the same if the launch conditions are the same.

One of the more common - and frustrating - examples of "bad science" is F=ma. This formula - force = mass * acceleration - is used all the time to explain clubhead and ball interaction. But there are a few problems with this:

1. EVERY clubhead decelerates when it hits the golf ball. It can't help but do so with any kind of golf shaft. Really simple physics there.
2. If we consider the exact instant when impact starts, a clubhead traveling 100 MPH will hit a ball a certain distance. A clubhead accelerating will hit the ball within about an inch of a clubhead decelerating into impact.

Consider this: would you rather be hit by a car going 1 MPH but accelerating or the same car going 100 MPH but slamming on the brakes?

If you want to talk about clubhead/ball collision physics, you're better served (though not fully, of course, as neither the golf ball nor the clubhead are rigid bodies) using E=1/2mv^2. You'll note that only the mass (clubhead, bottom 3-5 inches of the shaft) and the velocity of the clubhead matters - there's no consideration for acceleration.

F=ma does apply to the golf swing, however, but the way it's often used is backwards. It would be more appropriate to see how a clubhead is accelerating and deduce the force required to make it do so. Of course, the problem with that is that F=ma is more of a linear concept, while most of the golf swing involves rotation (where an object that has the same linear speed is always "accelerating" because "acceleration" is a change in the velocity of an object - and velocity is both speed and direction ).

Another? Conservation of angular momentum. The classic example is that a skater goes into a spin. They pull their arms in tight and they spin faster, they put their arms out and they slow down.

COAM is used in the golf swing to describe why the hips slow down and the torso speeds up, then the torso slows down and the hands speed up, then the hands slow down and the clubhead speeds up.

The problem with using COAM is that it too is inaccurate. COAM applies quite nicely to closed systems (given the relatively low amount of friction on ice and due to the air, a skater is a reasonable example of this). The human body is not a closed system - we can use muscles to slow and speed things up.

And the most damning thing may be the very definition of the word "conservation." In science, "conservation" means "to keep the same." What is a golfer's angular momentum at the top of his backswing? Roughly 0. So if we conserved that angular momentum, the golfer would never make a downswing (or the parts swinging down would have to be offset by the parts swinging the other way - THAT's a swing I'd like to see!).

We can make a downswing because our muscles - which are "inside" the system (our bodies) - can continually add forces, change (increase) angular momentum, etc.

The point? There's a lot of junk science out there. Don't fall prey to it.

[jamo]

Every now and then this stuff seems to pop up somewhere; here, the 3Jack forum, Facebook. It's amazing how many places people seem to want apply F=ma to. Anyway, great post. There's a lot of misguided science out there.

[rehmwa]

I think when people toss out "F=ma" they are really just shouting "SCIENCE, we use SCIENCE,,,,somehow,,,,...er,,,,,uh,,,,,SCIENCE"

testify, mr. iacapshysics

((An item moving really fast hits a slightly lighter item sitting still - acceleration?  Force?  not really - 'momentum' both linear and angular?  Sure.  Go conserve those.))

[gwlee7]

Yet another reason why in our conversations about my golf swing I simply ask you what I need to do instead of why.

[colin007]

Originally Posted by iacas

The simple (slightly over-simplified) reason: impact lasts so short an amount of time that the vibrations and deformations and whatnot that occur to the shaft don't have time to radiate up and back down the shaft very far. That's why only the bottom section of the shaft matters.

is this why the Harrison Shaft Insert is still effective?  because its in the bottom of the shaft?

Originally Posted by rehmwa

I think when people toss out "F=ma" they are really just shouting "SCIENCE, we use SCIENCE,,,,somehow,,,,...er,,,,,uh,,,,,SCIENCE"

reminds me of the steve carrell character in Anchorman who at some point screams out "LOUD NOISES" just to chime in and sound indignant...

[iacas]

Originally Posted by colin007

is this why the Harrison Shaft Insert is still effective?  because its in the bottom of the shaft?

I think it can change the way the shaft is shaped (amount of lead deflection, etc.) the shaft has prior to impact, because it's at the top end of that range AFAIK.

[mchepp]

I have never understood why people think F=ma applies to golf. The ball club collision is not a simple phenomenon. One question I wonder about from your post, is a common golfism post impact acceleration. Of course this is speaking more to intent rather than the actual event of hitting the ball. So to put in your car analogy, is it better to be hit by a car going 100MPH but slowing, or 100MPH and accelerating to a point beyond you. I gather from your post that it doesn't matter? Because the ball was hit with 100MPH of speed the ball will go the same distance?

[iacas]

Originally Posted by mchepp

I have never understood why people think F=ma applies to golf. The ball club collision is not a simple phenomenon.

One question I wonder about from your post, is a common golfism post impact acceleration. Of course this is speaking more to intent rather than the actual event of hitting the ball. So to put in your car analogy, is it better to be hit by a car going 100MPH but slowing, or 100MPH and accelerating to a point beyond you. I gather from your post that it doesn't matter? Because the ball was hit with 100MPH of speed the ball will go the same distance?

The ball will go the same distance, yes.

I remember a study done. It was done without a golf ball because the golf ball always slows the clubhead, period.

Anyway, they found:

• Poorest golfers reached maximum clubhead speed before where impact would be.
• Good (low single digit) handicappers often reached max speed after impact.
• PGA Tour level players reached max speed at impact.

Because... why would you want to still be accelerating after where you'd hit the ball?

[rehmwa]

Originally Posted by iacas

Because... why would you want to still be accelerating after where you'd hit the ball?

This is a trick question.

The answer is why we do anything - to attract women.

[Mordan]

F=ma applies to the ball though doesn't it? By taking the mass of the ball, and the acceleration applied to it you can calculate the force applied by the clubface. Not much help to a golfer really as the mass is constant, you're just saying that the more acceleration, the more force which doesn't take a science degree to work out. Nor help the average internet golf improve his 300 yard drive average.

[saevel25]

Striking a golf ball is momentum and kinetic energy. So you have Kinetic energy which is the integral of F = ma, Since m is a constant, your only taking the integral of acceleration which is the the integral of change in velocity over the change in time. So you end up with Kinetic Energy = 1/2mv^2.

People get caught up acceleration, but velocity and acceleration are related. if you look at units, velocity is miles per hour, while acceleration is miles per hour^2. Basically how your velocity changes over time. You go from zero go 60 in 4 seconds, that's an acceleration of 54,000 miles per hour per hour, or 15 mph per second.

So when we say club head speed matter's it does. It should be club head velocity, but that is nit picking. Were not saying, club head accleration, that's wrong. There is no acceleration because the physics says so. Though there is a force applied, its applied in a way were the physics dictate that velocity is what is used.

so if you apply this to hitting a golf ball, you want maximum velocity. Which would mean your accleration at the ball would be ZERO. Shocking i know, but the graph of velocity to acceleration is a parabola, meaning it has a peak and at that peak the velocity is max, and at that peak the acceleration is ZERO. This is because at the peak there is no change in velocity over time, there is just maximum velocity. After the peak we have a negative acceleration or deacceleration, which slows down velocity.

So when you accelerate through the ball, your basically saying, i am accepting that my maximum speed will be way after the ball. So you are not optimizing your distance at all. This is why a flat left wrist at impact is important. If you break your left wrist and flip at the ball, you accelerated early of the ball, and you will have less speed, but if you hold on to long and try to accelerate past the ball, you will not reach max potential.

[rehmwa]

Originally Posted by saevel25

So you have Kinetic energy which is the integral of F = ma,

momentum - mv

d(mv)/dt = v dm/dt + m dv/dt

if you hold mass constant

d(mv)/dt = m dv/dt = ma

so, conversely, the integral of ma (when mass is constant) can also be described as momentum - but it still agrees with you.  if you do a momentum balance on the collision, max V is the best you can give to the ball - and it's a much easier calc than the energy balance which loses out when you try to track all the other energy terms.

[iacas]

Originally Posted by Mordan

F=ma applies to the ball though doesn't it? By taking the mass of the ball, and the acceleration applied to it you can calculate the force applied by the clubface. Not much help to a golfer really as the mass is constant, you're just saying that the more acceleration, the more force which doesn't take a science degree to work out. Nor help the average internet golf improve his 300 yard drive average.

No. The ball deforms and accelerates from 0 MPH to 165 MPH (or whatever) in 400 microseconds. A lot of energy is spent deforming the golf ball, etc. They're not elastic collisions, and the clubhead doesn't stop either. It's a whole lot more complex than applying F=ma.

[uscmatt99]

Erik,

Do you have a source you could refer us to regarding the moment of impact?  I'd be interested to read more about it.  Well-written post up top by the way, and thanks for responding to my PMs.

[rehmwa]

Originally Posted by iacas

accelerates from 0 MPH to 165 MPH (or whatever) in 400 microseconds.

It's very nearly better modeled as an 'impulse' calc than just force.  But again, Force and energy balances seem to be way too cumbersome when a simple momentum balance does the trick.

I think people use "energy" and "force" generically just to discuss all sorts of interactions.  It makes it a bit confusing

(nice posts, BTW)

[boogielicious]

The average person only remembers a few equations from High School physics, which is why they rely on "F=ma".  What they don't remember is how to apply the equations.  This falls under "a little knowledge is dangerous."  They have mistaken mass as the mass of the golfer and not the club head.

Now if you threw both the male and female golfers off of, let's say, Niagara Falls, they would apply a different force at impact on the rocks below.  As long as the had different mass, of course.

[rehmwa]

Originally Posted by boogielicious

The average person only remembers a few equations from High School physics, which is why they rely on "F=ma".

and then use phrases such as "nuff said"

[Mulligan Jeff]

I read an article several months back written by a golf pro, he said take for example you're hitting demo clubs on the range at a local golf shop. You're hitting a particular driver extremely well, you simply can't believe how well you're hitting this driver but you notice that it has a small dent in the head - what do you do, should you go back to the rack and find the exact match - no way, buy the driver with the dent in the head. The point is - it is difficult for a major OEM to get the exacting characteristics for each club i.e. club fitting trailors on pro circuit have a difficult time exacting their golf club characteristics, so getting one to match in a local pro shop is even more impossible.