Finally, Some Actual Science

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leon

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Well, its maths really (and yeah, math is plural this side of the pond - as it should be!). In amongst all this sh!t was Zick's nugget:

"Although the club face's direction at separation doesn't determine the direction of the ball's flight, I didn't exactly say that the ball leaves the club face in the direction of the force at the ball's greatest deformation. I said that that direction would be a fairly good approximation of the ball's direction (much better than the face's direction at separation, anyway).

The ball is influenced by the club only between the time of first contact (let's call that tc) and the time of separation (ts). The velocity vector at separation (Vs) will equal the integral of its acceleration vector over time, from tc to ts. The acceleration vector equals the vector of net force on the ball (F) divided by the ball's mass (m). F is actually a function of time, expressed as F(t). It changes in both magnitude and direction during the impact interval. It is zero at tc and ts, climbs to a maximum magnitude of several thousand pounds at the time of maximum ball compression, and must average about 1400 pounds to accelerate the ball from 0 to 150 mph within half a millisecond (the approximate difference between ts and tc). Mathematically, then,

Vs = Integral from tc to ts of F(t)/m dt.

The direction of F(t) will be dominated by the club face's normal vector at time t. There might be a smaller contribution from frictional shear forces if the club head's velocity vector doesn't align with the club face's normal vector at any given time. This will, of course, be true if the club has a nonzero loft, but we're not interested in the vertical components of the forces and velocities here. Let's define a right-handed coordinate system with x in the direction that our assumed right-handed golfer would face at set-up, y in the direction of his target, and z in the vertical direction. From this point on, we will ignore the z direction, treating F(t) and Vs as two-dimensional vectors with x and y components only (as though the club had zero loft).

Let's first consider Homer Kelley's "angled hinging", during which the club head's x-y velocity vector will always align with the club face's x-y normal vector. Assuming the club head doesn't twist from an off-center hit during impact, there will theoretically be no shearing forces on the ball (imparting no side-spin, contrary to Kelley's assertions about angled hinging), so F(t) will always align with the face's normal vector (technically, the dynamics of ball compression and decompression might affect the direction of F slightly, but we will ignore any such potential complications).

If the swing is designed to have the club face's normal vector aligned with the y direction (i.e., pointing at the target) at separation, then the normal vector will have a zero x component at ts, but it will have a positive x component for all previous times (since the club face is continually closing as its normal vector follows the club head's path). As a result, F(t), which aligns with the normal vector, and which is zero at tc and ts, will have a positive x component for all times in between. Therefore, from the integral above, Vs is guaranteed to have a positive x component. In other words, the ball will be pushed somewhat to the right of the target.

Similarly, if the club face is squared to the target line at tc, then its normal vector, hence F(t), will have a negative component for all subsequent times, guaranteeing that Vs will have a negative x component. In other words, the ball will be pulled somewhat to the left of the target.

For the ball to fly directly at the target, Vs must have a zero x component. The only way that can happen is for F(t), and therefore the club face's normal vector, to have negative x components during the later portions of the impact interval to offset the positive x components from the earlier portions. Therefore, the club face must be square to the target line about midway between tc and ts. The exact time (let's call it tm) would be very difficult to calculate, but a good approximation would be the time of maximum compression. That would also make sense, intuitively, since that is when the club will exert most of its influence on the ball.

The situation is a little more complicated with "horizontal hinging", during which the club face is square to the club head's path only when it is square to the target line. Before that time, the club face will be slightly open to the target line (creating a normal force with a positive x component) and to the club head path (adding a clockwise shearing force to the ball). After that time, the club face will be slightly closed to the target line (creating a normal force with a negative x component) and to the club head path (adding a counter-clockwise shearing force). For this type of swing, it is even more important to have the club face square to the target line about midway between tc and ts. Prior to the club face becoming square to the target line (and to the club head path), F(t) will still have a positive x component, but now, because of the shearing contribution, F(t) will be directed slightly to the left of the ball's center. That will induce a clockwise torque on the ball, giving it a slicing side-spin. If the club face doesn't become square until ts, the ball will be guaranteed to have a positive x component for Vs and a non-zero clockwise angular velocity. In other words, the ball will be both pushed and sliced somewhat to the right of the target. Similarly, if the club face is squared at tc, the normal vector, and hence F(t), will have a negative x component for all subsequent times. In addition, because of the shearing contribution, F(t) will be directed slightly to the right of the ball's center, inducing a counter-clockwise torque throughout the impact interval. The ball will therefore be guaranteed to have a negative x component for Vs and a non-zero counter-clockwise side-spin. In other words, the ball will be both pulled and hooked to the left of the target.

For the ball to fly directly at the target, with little or no side-spin, the horizontal hinging must be performed in a way that squares the club face to the target line (and the club head path) about midway between tc and ts, say at tm. Between tc and tm, F(t) will have a positive x component and will cause a clockwise torque (and hence, angular acceleration) on the ball. Between tm and ts, F(t) will have a negative x component and will cause a counter-clockwise torque (and hence, angular acceleration) on the ball. A judicious choice of tm will cause the x components of F(t) and the opposing directions of angular acceleration to integrate to nearly zero (it might not be possible to exactly zero both simultaneously, however), giving a ball flight straight at the target with little or no side-spin. The exact value of tm would again be very difficult to calculate, but a good approximation would again be the time of maximum compression, which is again when the club exerts most of its influence on the ball.

Got it?

Now that's some good stuff. Pretty obvious really, but good stuff none-the-less. See its o.k. to say 'we have the science to prove it' but unless you publish for peer review then its just your opinion. I'd love to see a lot more of this kind of stuff here.
 

leon

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Getting interested now

They can where Dr. Wood works, and they have. They have a camera that takes HD quality pics at 50,000 fps.

Been there done that.

We went to Ping with 100 questions last year.

Brian, have you ever spoken to any guys from Callaway? Their VP of Innovation and Advanced Design is a really smart guy called Alan Hocknel. He did his PhD on golf ball impacts at Loughborough University here in the UK (the same place I did mine - he got the better job though!) They use finite element analysis (FEA) to model club to ball impacts and you can basically model anything with this in great detail, if you have enough money for a huge computer (which I'm sure they do). FEA could tell you exactly what a ball would do given any club path/orientation through impact that you could think of. I don't know Zick of Wood's backgrounds, but they may already have experience of this.
 
Leon, Dr. Wood visited Loughborough three weeks ago - he said they have published some info and are soon to publish more. We will definitely be trying to track it down - maybe you can help us, too.

Thanks,
Michael
 

Brian Manzella

Administrator
Maybe we'll get along better the second time around...

Surely the "average" golfer would chuckle to know that there is such a feisty debate raging over at what part of the half of a millisecond that ball is on the clubface, should the clubface be square. Surely it matters to the ball, but the player can only hope that what he done by the time the clubhead gets a few feet from the ball will result in the desired conditions during collision.

Well, it matters.

Basically, in plain old english, with the milliseconds taken out, in the real world, the golfer needs to pretty much try to hit the back of the ball to make the ball fly straight.

Not the "inside-aft" quadrant, even the stack & Tilters know that STRAIGHT PLANE LINE + INSIDE-AFT QUADRANT ON THE WAT DOWN means a push draw.

Eons of man hours wasted by goers trying for "straightaway ball flight" with push draw mechanics.

Really Todd, I'd rather spend an hour on the phone with Dr. Zick, or another golf scientist talking swing, and learning from each other, than fight a fight I and everyone else with a brain knows I am going to win.

But if not me, who? If not now, when?


Cochran and Stobbs showed that during collision, the clubhead acts as a "free body" and as such, may as well not be connected to the player at all....a year before Homer's book.

It sure did.

Paul Wood confirmed at the symposium.

when is the bottom of the D Plane formed? At seperation or before, like the top of the D Plane?

Great question!

The ball receives all of the club data that creates ball flight (more accurately—ball behavior), very near the point of maximum deformation.

So the sweetspot travel at that time is when the bottom of the D-Plane will be formed. It is, of course, WAY more complex than that, and Dr. Zick will provided this for us at some point.

Interestingly, here is a NEW finding:

The Top of the D-Plane, the vector from the "Clubface Normal" is not just "Face Angle" but "Dynamic Loft" as well.

So now we have four term:

1. Static Loft (what the club measures in a loft-lie gauge)

2. Delivered Loft (loft at impact)

3. Dynamic Loft (loft near the point of max deformation)

4. Separation Loft (loft when the ball leaves he face)​

Here is an example:

Tiger hits a 30° lofted iron dead flush off of a level lie at Augusta National.

Static Loft (30°).​

He leans the hosel forward 5 degrees for his intended ball-flight, and he will NOT contact the ball high enough to find the exact sweetspot, so this and one of Newton's laws make the club de-loft during the impact interval.

Delivered Loft (25°).​

The face wraps around the ball and de-lofts itself all the way to separation, but the ball only gets close to the maximum deformation loft.

Dynamic Loft (20°).​

The face "hooded" even more after that point and the ball is gone.

Separation Loft Loft (16°).​

Thanks.


The Top of the D-Plane Vector from loft comes at the same time it does for face (they are the part of the same "clubface normal" lie a lie angle tool point in 3D space.
 
Well, it matters.

Basically, in plain old english, with the milliseconds taken out, in the real world, the golfer needs to pretty much try to hit the back of the ball to make the ball fly straight.

Not the "inside-aft" quadrant, even the stack & Tilters know that STRAIGHT PLANE LINE + INSIDE-AFT QUADRANT ON THE WAT DOWN means a push draw.

Eons of man hours wasted by goers trying for "straightaway ball flight" with push draw mechanics.

Really Todd, I'd rather spend an hour on the phone with Dr. Zick, or another golf scientist talking swing, and learning from each other, than fight a fight I and everyone else with a brain knows I am going to win.

But if not me, who? If not now, when?




It sure did.

Paul Wood confirmed at the symposium.



Great question!

The ball receives all of the club data that creates ball flight (more accurately—ball behavior), very near the point of maximum deformation.

So the sweetspot travel at that time is when the bottom of the D-Plane will be formed. It is, of course, WAY more complex than that, and Dr. Zick will provided this for us at some point.

Interestingly, here is a NEW finding:

The Top of the D-Plane, the vector from the "Clubface Normal" is not just "Face Angle" but "Dynamic Loft" as well.

So now we have four term:

1. Static Loft (what the club measures in a loft-lie gauge)

2. Delivered Loft (loft at impact)

3. Dynamic Loft (loft near the point of max deformation)

4. Separation Loft (loft when the ball leaves he face)​

Here is an example:

Tiger hits a 30° lofted iron dead flush off of a level lie at Augusta National.

Static Loft (30°).​

He leans the hosel forward 5 degrees for his intended ball-flight, and he will NOT contact the ball high enough to find the exact sweetspot, so this and one of Newton's laws make the club de-loft during the impact interval.

Delivered Loft (25°).​

The face wraps around the ball and de-lofts itself all the way to separation, but the ball only gets close to the maximum deformation loft.

Dynamic Loft (20°).​

The face "hooded" even more after that point and the ball is gone.

Separation Loft Loft (16°).​

Thanks.


The Top of the D-Plane Vector from loft comes at the same time it does for face (they are the part of the same "clubface normal" lie a lie angle tool point in 3D space.

Thanks, Brian. But, respecting TrackMan definitions, if the vertical dimension of the top of the D Plane is formed at max compression, shouldn't that angled vector be called Spinloft? And then the angle between the Spinloft and the vertical dimesion of the bottom of the D Plane, or Attack Angle, be the Dynamic Loft?
 
Dugan. He's reversing the definitions of Dynamic Loft and Spin Loft.

Trackman defines Spin Loft as:

SL = DL - AoA
 
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leon

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Leon, Dr. Wood visited Loughborough three weeks ago - he said they have published some info and are soon to publish more. We will definitely be trying to track it down - maybe you can help us, too.

Thanks,
Michael

Cool. Its a small world! I've been out of sports tech for a while (and feel like I need to do a LOT of reading to get back up to speed) but I do still have a few contacts at Loughborough, if its any use to you guys.
 
Thanks, I will stay in touch - Dr. Wood was going to try to help us out - but we may need your contacts as well. Thanks for the offer.
 
Who got it backwards??

I realized after I posted, while driving down the road, that it is INDEED Dynamic Loft that is responsible for the vertical "height" of the top of the D Plane. The Spinloft is the vertical height of the "normal" to the clubface, relative to the Attack Angle. Obviously, the top of the D Plane will be the vertical height of the normal to the clubface, relative to the horizon. My bad :(
 
did we get this info

Hey I was digging through some old threads ( finally some real science 10 20 2010 )

""Dr. paul wood Wood visited Loughborough three weeks ago""

there was talk about getting some information on some of the latest science...

Any new news on this??
 
Aha, sounds as if it is indeed a bit less simple than the wheel analogy.

http://www.brianmanzella.com/forum/newreply.php?do=newreply&p=178962
My point is this: that simple geometric equation working out degrees relative to a wheel analogy does not tell the whole story. Its an over simplification. "Keep it simple, but not simpler than it actually is".

But it's great that we're getting closer to golf's holy grail: what truly determines ball flight. My only worry is that its influenced by so many variables that it will remain intangible to those who don't hit it good because its not in their genes to hit it good. It will however hopefully put an end to the misinformation and bull turd spouted out on TV by guys who sell themselves well or used to play on the tour because it was in their genes to play on tour, not becuase they knew how it actually works. Maybe, as a by-product more hobby golfers will want to hear the truth - TV show may well be on the horizon.
 
Given that the whole impact interval forces (and therfore alignments) are dependent on time (t) then the optimal D-plane is dependent on speed, or in plain English, how hard you hit it. That means Player A with 6-iron clubhead speed of 85mph needs a different D-plane to Player B whose clubhead speed is 95mph, right?
 
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