Be Wary of Phony Science - AJ Bonar and Be Better Golf

[iacas]

I debated putting this here, but I thought it deserved its own topic. (There's another AJ Bonar topic here, too, if you care.)

Golfers aren't often scientists. Same goes for golf instructors. I don't call myself a scientist, either, despite having studied the sciences for a looooong time.

At 8:00, the "science" talk starts (both videos are timestamped to take you to the correct parts):

AJ says that the moment of inertia is an object's resistance to changes in angular momentum. And he gets that part right.

Then he says "a moment arm has an object attached to it" and things start to go downhill from there.

AJ talks about a 16-pound bowling ball on a 1-foot length of rope, and says that will have the same moment of inertia as a 1-pound bowling ball on a four-foot long rope, because you multiply the weight by the length of the moment arm squared. I mean, okay, but where are you going with this…

At 10:45, things start to go off the rails:

(Assuming a 1-pound head for the sake of the math is fine). 1 x 3.5^2 = 12.25, so he's not wrong there. But I think some of you will begin to see how wrong this is about to get…

Basically, AJ is saying that the MOI of the left wrist to the clubhead is 12.25 units, but if you don't break the left wrist down at impact, the radius is the length of the shaft plus your left arm, which lengthens the moment arm all the way up his arm, or seven feet long. Let's leave aside how he added 3.5' just by going from his wrist to his… "neck?" for now, but then he does the math and gets 1 x 7^2 = 49 units, and concludes that is where true power comes from in the golf swing. Not from the speed at which the clubhead is moving, but… how much it resists changes to its angular momentum?

No.

Just no.

The issues here, primarily, are:

• The "moment arm" is almost never actually a physical thing (let alone a literal "arm"), and the point on which a force acts is often not a physical thing either (or if it is, it's a point along a stretch of space filled by physical things). You have a moment arm when you direct force just above the centerpoint of a cue ball, for example: there's no physical "arm" and the area just inside or outside the end of the moment arm is just the same as the point on that moment arm.
• If you swing a 1 pound bowling ball back 1mm I don't care how long the rope is - it's not going to knock the cinder block off the table. He should have used 1/2mv^2 or something, not moment arm formulas.
• The clubhead and the bottom 4 or 5" of the shaft are all that matter in the clubhead-ball collision. Your neck, your elbow, your wrist… has nothing to do with it. Nada.
• CLUBHEAD SPEED is the primary determinant of distance here, not the freaking moment arm.
• He says that you hit a good shot when the ball felt really "light" coming off the clubhead, and that's when you had the long moment arm? No. It's when you finally hit the sweet spot and the club didn't twist.

There's probably more, but those are the big ones.

I've seen a few of these BBG videos, now (and admittedly these are older, from 2018), but the host never really seems to question anything. I understand not wanting to upset the guests, but… yeesh.

[Pretzel]

So right off the bat, ignoring everything wrong with how he's defining the moment arm for calculating MOI and the fact that your wrist and elbow will never be stiff enough to count your arm and shaft as one continuous member, he's very confused about the fundamental physics behind what he is saying. The moment of inertia of the clubhead about the axis of rotation created by your spine/shoulder (what he's referring to here) is entirely irrelevant to the collision between ball and clubhead. 

Moment of inertia is the resistance to change in angular momentum, he got that correct. If you have a higher moment of inertia about your spine's axis of rotation it means the angular momentum of your swing will experience less change than it would if the axis of rotation was on the same angle and plane but smaller diameter (such as locating the axis of rotation at your wrists). The thing is, a smaller change in angular momentum still equates to the same change in linear momentum because angular momentum is also proportionate to the radius of the rotation.

Let's assume, for the sake of easy math, that the clubhead is 1kg, the short radius is 1m, and the long radius is 2m. This means that I1 = m * r^2 = 1, and I2 = m * r^2 = 4. Now we're going to assume equal clubhead speed in both cases, which is a linear speed rather than angular velocity, of 45 m/s or about 100mph which can be converted with the formula V = r * w. For the short radius w = 45, and for the long radius w = 22.5. The kinetic energy of the clubhead in both scenarios is the same, because it is the same mass traveling at the same speed, which is KE = 1/2 * m * v^2 = 1,012.5 Joules in this case. The angular momentum of the short radius clubhead is L = I * w = 45 and the angular momentum of the long radius clubhead is L = I * w = 90. 

From here we have three options for determining what happens when we hit a golf ball.  We can calculate the club-ball interaction using linear momentum which makes the angular momentum crowd unhappy because they think we should be talking about angular momentum. We could also calculate the club-ball interaction using angular momentum in which case we already screwed the pooch because we didn't include the motionless golf ball's mass or lack of velocity in our earlier inertia and angular momentum calculations and it also involves some nasty cross products because the ball's launch angle is not perfectly orthogonal to the axis of rotation. Finally we can calculate the club-ball interaction using kinetic energy, which makes everybody unhappy because I'm ignoring stupid momentum pedants entirely since kinetic energy readily converts between rotational and linear frames of motion. Naturally we're going to choose the kinetic energy route, both to piss everybody off and because we happen to know the exact coefficient of restitution of this particular ball-club interaction.

The USGA specifies a maximum coefficient of restitution of 0.822 for the collision between ball and clubhead following the equation below (the epsilon is your coefficient of restitution):

We also know that the initial and final total kinetic energy of the system (ball plus club) is equal to the following equations:

And finally we know the impulse (dp, delta-p, whatever you want to call it) for both the club and the ball will be equal and opposite to one another, because they are both experiencing an equal force (in opposing directions) for the same duration per Newton's Second Law.

From 4 equations, you can derive the loss of the system's overall kinetic energy based on initial velocities and the coefficient of restitution as shown in the equation below:

For our system m1 - the clubhead - is 1kg, m2 - the ball - is 0.04593kg, and v1i = 45 m/s while v2i = 0. This leaves us with a total kinetic energy loss of 0.782%

Thus the amount of kinetic energy lost from our original system total of 1,012.5 Joules is 7.91775 Joules for a final total kinetic energy of 1004.582. Due to the COR limitations the golf ball, if struck perfectly, will have an initial velocity of 67.5 m/s (~150mph) and will thus have a kinetic energy of 104.634 J, leaving a total kinetic energy of 899.948 J for the clubhead. That equates to a final clubhead speed of 42.425 m/s. 

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The astute among you may have noticed by now that the angular momentum or moment of inertia of the clubhead about the axis of rotation is not mentioned anywhere in these equations for calculating the final clubhead speed or the final speed of the ball. That's because it doesn't actually matter - we know the COR of the collision, we know the initial speed of the club and ball, and that's all we need. The only thing that matter is how fast your clubhead is moving. Both clubhead and ball experience the same amount of force regardless of lever length, but the torque applied by that force to the system with a longer lever length is larger because torque is also proportionate to momentum. So what you gain in increased resistance to change of angular momentum is later lost because the longer lever means an equal force will create a larger change in momentum.

In conclusion, everybody is unhappy now because we all had to deal with systems of equations and I ignored momentum entirely in the process of proving that talking about momentum in the golf swing is stupid.

[saevel25]

2 hours ago, iacas said:

He should have used 1/2mv^2 or something, not moment arm formulas.

Yep. In the case of bowling, that assumes the person isn't applying force with their body to increase the speed of the bowling ball outside of gravity dropping it. 

2 hours ago, iacas said:

The "moment arm" is almost never actually a physical thing (let alone a literal "arm"), and the point on which a force acts is often not a physical thing either (or if it is, it's a point along a stretch of space filled by physical things). You have a moment arm when you direct force just above the centerpoint of a cue ball, for example: there's no physical "arm" and the area just inside or outside the end of the moment arm is just the same as the point on that moment arm.

Yep. I did way to much of this math in my engineering statics course in college. 

The cue ball is a good example. The force applied to the cue ball, assuming the cue is perpendicular to the table, centered horizontally, but not vertically. So we strike the cue like 1/2 inch above the center of mass of a cue ball. It will create top spin and forward movement. If the cue hits the center of the cue ball, it will most likely slide for x amount of inches, before friction kicks in and cause the ball to start rotating end over end. Even friction can cause a moment on an object. 

Also, it isn't like we keep the club shaft inline with the shoulder the entire swing. The wrist hinge and unhinge. 

[iacas]

But… you didn’t talk about acceleration either, and everyone knows F = ma.

[Warlock]

Is this video about applying positive alpha torque into impact phony science? Many golfers could be tempted to buy the book ''Science of the Golf Swing' which seems very expensive?

I looked at Dave Tutelman's analysis of this claim (link below) which makes me think it could be wrong but not 100% sure because Dr Steven Nesbit seems a well-regarded scientist.

Nesbit or Kwon or MacKenzie?

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My favorite swing modeling pioneers, Young-Hoo Kwon, Sasho MacKenzie, and Steven Nesbit, seem to come out on different sides of an important...

Edited September 5, 2022 by Warlock

[Denny Bang Bang]

On 8/31/2022 at 10:49 AM, iacas said:

but the host never really seems to question anything. I understand not wanting to upset the guests, but… yeesh.

The host could very well have been thinking the same thing as myself… “it’s better to remain silent and be thought a fool, than to speak out and remove all doubt.”  That, or… “my high school physics teacher would be disappointed in me for not knowing what this guy is talking about.”

[iacas]

12 hours ago, Warlock said:

Is this video about applying positive alpha torque into impact phony science?

This is probably better served in a topic related to this specifically.

I will make some general statements:

• If an object is moving in one direction, it can continue to move in that direction even if forces pushing it in that direction cease to exist or reverse. In the case of the former, it will maintain, and in the latter, decelerate.
• A torque can operate on either side of the axis. You can push the left side of a propeller blade down, or the right side up, to produce the same torque.
• I'm not a big fan of studies that have only four subjects. They've done more since then, but still.
• I believe the hand speed in almost every good player is slowing the last half of the downswing. (This isn't as big a point as you may think, as the club's CG isn't in the hands.)
• Because your arms and hands and wrists have muscles, your arms can be moving at one speed (and accelerating or decelerating), and you can be making the club do something else, the same thing, or the opposite. It's not a closed system - we can add forces and torques via our muscles.

I think the whole alpha torque stuff is… a whole bunch of nothing. I've never really waded into the discussions, because I find it doesn't really help golfers hit the ball better, and we don't have a super easy way to measure it or check it or anything like that anyway. I've taught some golfers to feel like they're throwing it, some to feel like they're accelerating through impact (they aren't and won't, but they may have to feel that they do), and everything in between.

So… while I'm interested in these things, I'm also generally practical about them, too. While it's cool to know, for example, that the shaft is in lead deflection on most good golf shots (or swings), you can't really "apply" that to teaching people, so… it's usefulness is limited. Same here. Feel ain't real.

12 hours ago, Warlock said:

I looked at Dave Tutelman's analysis of this claim (link below) which makes me think it could be wrong but not 100% sure because Dr Steven Nesbit seems a well-regarded scientist.

I think the most damning bit is… (and the ellipsis is added by me to indicate some unrelated parts are clipped):

Quote

I have heard at least a few people dismiss this paper as, "Oh that's just two-dimensional." (The people I have in mind are Jacobs and Manzella, who apparently want to limit all discussion of Nesbit to "Work and Power".) What's wrong with 2D, if it's appropriate to the problem? The two dimensions are clearly intended (and even stated) to be the swing plane. Not vertical and not horizontal. If it were just a vertical plane, I'd also question its value, but a swing plane model is not to be easily dismissed.

[…]

Clearly Nesbit didn't think there was a problem with 2D models, even several years after he did the 3D "Work and Power" study. He and McGinnis did a follow-up, featuring optimization of the hand path, in 2014 -- long after the 3D "Work and Power" paper. See Kinetic Constrained Optimization of the Golf Swing Hub Path, Dec 2014. It sets up the same, identical equations of motion in two dimensions. Think about it; he did several 3D papers (not just "Work and Power") in 2005, then several 2D papers in 2009 and 2014.

Where do I come out on this? I agree with Tutelman's conclusions. But also… I don't really care too much to have done more than about five or six hours of reading on this stuff and another two hours or so talking about it with people (like Dr. MacKenzie). And while I do read quickly… that's not a ton of time.