Low point and such

[mandrin]

Modern video, even swing vision video, will not allow readily to infer the precise trajectory of the club head through the impact zone. Using graphics driven by mathematics it is more convenient to look at impact trajectories. A possible golf swing, using a three segment golf model, consisting of shoulders (half shown), lead arm, and golf club, is shown in Fig1.

Blue dot - taken to be the stable physical center of the model. Is the also the center of the swing for the first part of the downswing.
Red dot - effective instantaneous center of clubhead trajectory during the bottom part of the swing.
Green dot - ball position

Looking at Fig1 one would be very much inclined to think that to take a large pro like divot there has to be also a downward movement of the physical center during the down swing. The angle of attack as shown is not really resulting in much of a divot with the trajectory almost level. Yet the swing bottom is quite ahead of the ball position (14.5 cm).

It is interesting to note that whilst the shoulder joint moves away from the ball and the club strives towards the inline condition that the trajectory of the clubhead is nevertheless still moving quite closely along a circular path with a stable center given by the placement of the red dot. However, its location can vary greaty. For instance for a "fipper" it might be located close to the wrists but it can also move out to infinity, depending on the relative angular motion of the three segments.

 

[Martee]

I have read it several times, I am not sure I am getting your actual point.

I believe one point if I understand what you have here, proves that a lot of the modeling done, the theory, may not be accounting for the true motion in some of golf strokes we observe.

Of course I am still trying to isolate a center point that doesn't move, so far no luck, at least not with the ground as a reference.

Actually when I was first introduce to Low Point, it was explained as the clubhead being the furthest from the center point and was referenced to the ground. That one really was confusing, in fact just trying to recall and write it seem confusing.

 

[Cope]

questions

Mandrin,

For a steeper angle of descent the green dot would have to move back or the blue dot more forward. Is this correct.

2nd-- The diagram shows the shoulder, left arm, and club reaching a in-line condition much later than I think top players do. Most seem to be in-line at or just after impact. Am I seeing this right?

 

[jmessner]

Angle of Attack Estimation

Mandrin,

Minor threadjack but in a clubmaking forum I frequent, we had quite a discussion on angle of attack vs effective loft for the purposes of driver fitting. Your model could address those questions I think.

The basic question was centered around the assumption that at any given angle of attack the effective loft (relative to the clubhead path) would be basically constant (equal to the actual clubhead loft at the impact point on the face - ignoring any shaft bending for the moment) and that the apparent loft (relative to the ground) would be the loft plus the angle of attack. That sounds confusing after rereading, but basically the question centers around this - does the clubhead move generally perpendicular to the shaft angle at impact?

For example if the shaft at impact is say 2 degrees forward leaning (grip of shaft closer to target than clubhead), does the clubhead basically have a 2 deg downward angle of attack or is it possible to have an upward angle of attack with this shaft condition?

Without doing any calculations, I was of the opinion that since the shaft is moving faster than the rest of the components (hands, arms, torso, etc) that it would primarily dictate the angle of clubhead movement through the ball, but I'd be interesting in your thoughts on this based on your model.

Jay

 

[mandrin]

Mandrin,

For a steeper angle of descent the green dot would have to move back or the blue dot more forward. Is this correct.

2nd-- The diagram shows the shoulder, left arm, and club reaching a in-line condition much later than I think top players do. Most seem to be in-line at or just after impact. Am I seeing this right?

Cope, imo, obtaining a steeper angle is basically a question of getting the hands a bit more ahead of the clubhead at impact and/or positioning the ball (green dot) more towards the trail foot.

The intention is to show clearly some geometric relations. There is still a fair amount of confusion circulating in various quarters. For instance, some strongly believe that low point is always below the lead shoulder. This is not correct. Also hands can move upwards while the club head goes downwards, another possible source for confusion.

I would suggest that you look at Bobby Clampett’s swing vision derived pictures as shown in his book. There is for example Vijay Singh clearly having a forward leaning shaft, using his driver, at impact. Similarly for Phil Mickelson, also using his driver. Cope, how are pros unearthing those large pieces of sod, past the ball, when you feel that in general there lead arm and club are aligned at impact?

 

[Cope]

low point

Mandin,

I'm asking for my own clarification. I don't have the answers. In describing the in-line condition of shoulder, left arm, and clubhead, I did not mean vertical. I clearly see shaft lean and whole-heartly agree that even the driver should have forward lean. Degree of shaft lean with an in-line condition would depend on motion and location of left shoulder relative to ball position. I'm thinking that the left shoulder is moving on an arc (plane), and I would think that where it is on that arc relative to ball postion at impact would control angle of descent and depth of divot. I would think that a more open and higher left shoulder (farther along arc) would tend towards shallower, and a more square and lower left shoulder would tend toward steeper and deeper.

Without considering leg action, axis tilt, etc and how these affect shoulder motion.

 

[mandrin]

Mandrin,

Minor threadjack but in a clubmaking forum I frequent, we had quite a discussion on angle of attack vs effective loft for the purposes of driver fitting. Your model could address those questions I think.

The basic question was centered around the assumption that at any given angle of attack the effective loft (relative to the clubhead path) would be basically constant (equal to the actual clubhead loft at the impact point on the face - ignoring any shaft bending for the moment) and that the apparent loft (relative to the ground) would be the loft plus the angle of attack. That sounds confusing after rereading, but basically the question centers around this - does the clubhead move generally perpendicular to the shaft angle at impact?

For example if the shaft at impact is say 2 degrees forward leaning (grip of shaft closer to target than clubhead), does the clubhead basically have a 2 deg downward angle of attack or is it possible to have an upward angle of attack with this shaft condition?

Without doing any calculations, I was of the opinion that since the shaft is moving faster than the rest of the components (hands, arms, torso, etc) that it would primarily dictate the angle of clubhead movement through the ball, but I'd be interesting in your thoughts on this based on your model.

Jay

Jay,

The answer to your question can be estimated visually directly from inspection of Fig1. Tonight I will try to put up a more detailed answer.

 

[mandrin]

Mandin,

I'm asking for my own clarification. I don't have the answers. In describing the in-line condition of shoulder, left arm, and clubhead, I did not mean vertical. I clearly see shaft lean and whole-heartly agree that even the driver should have forward lean. Degree of shaft lean with an in-line condition would depend on motion and location of left shoulder relative to ball position. I'm thinking that the left shoulder is moving on an arc (plane), and I would think that where it is on that arc relative to ball postion at impact would control angle of descent and depth of divot. I would think that a more open and higher left shoulder (farther along arc) would tend towards shallower, and a more square and lower left shoulder would tend toward steeper and deeper.

Without considering leg action, axis tilt, etc and how these affect shoulder motion.

Cope,

The prime factor determining angle of attack at impact is the position of the hands relative to the clubhead at impact. You are correct with regard to the lead shoulder position but it has less influence on steepness of approach than the position of the hands since angular velocity around wrists is greater than angular velocity around lead shoulder joint.

 

[Jim Kobylinski]

For example if the shaft at impact is say 2 degrees forward leaning (grip of shaft closer to target than clubhead), does the clubhead basically have a 2 deg downward angle of attack or is it possible to have an upward angle of attack with this shaft condition?

Jay

Yes, because even though your hands are in front of the clubhead (even just 2*) the shaft can be "kicking" the head "foward and up" creating an upward angle of attack on the launch monitor.

This is what i try to achieve with students as it is the longest way to hit a driver CONSISTENTLY in my opinion.

 

[puttmad]

....

Yes, because even though your hands are in front of the clubhead (even just 2*) the shaft can be "kicking" the head "foward and up" creating an upward angle of attack on the launch monitor.
.

So for the $64,000 question....what do you physically do to make the shaft kick at the right time, or is it all down to the shaft?...

 

[Jim Kobylinski]

So for the $64,000 question....what do you physically do to make the shaft kick at the right time, or is it all down to the shaft?...

Shaft, flex, and how you swing all influence when that shaft kicks and what it does to the face.

 

[jmessner]

Yes, because even though your hands are in front of the clubhead (even just 2*) the shaft can be "kicking" the head "foward and up" creating an upward angle of attack on the launch monitor.

This is what i try to achieve with students as it is the longest way to hit a driver CONSISTENTLY in my opinion.

Jim- I was trying to neglect the action of the bending shaft since that gets into a whole new topic which has got me into quite a discussion on a TGM forum I used to frequent. But since you brought it up...

Yes, I agree in general for a well timed swing the clubhead will bend the shaft forward prior to impact(this is the supposition that created the stir - the TGM purists believe in all lag all the time). The speed of the kick, however, from what I have read is between negligible or maybe 6% or so of the total clubhead speed. Based on that, I have the mindset that while the shaft bending increases the effective and apparent loft, I'm not sure that it can really affect the angle of attack to any significant degree - but it certainly can achieve a slightly higher launch angle albeit probably with a bit more spin due to the higher loft.

 

[mandrin]

Mandrin,

Minor threadjack but in a clubmaking forum I frequent, we had quite a discussion on angle of attack vs effective loft for the purposes of driver fitting. Your model could address those questions I think.

The basic question was centered around the assumption that at any given angle of attack the effective loft (relative to the clubhead path) would be basically constant (equal to the actual clubhead loft at the impact point on the face - ignoring any shaft bending for the moment) and that the apparent loft (relative to the ground) would be the loft plus the angle of attack. That sounds confusing after rereading, but basically the question centers around this - does the clubhead move generally perpendicular to the shaft angle at impact?

For example if the shaft at impact is say 2 degrees forward leaning (grip of shaft closer to target than clubhead), does the clubhead basically have a 2 deg downward angle of attack or is it possible to have an upward angle of attack with this shaft condition?

Without doing any calculations, I was of the opinion that since the shaft is moving faster than the rest of the components (hands, arms, torso, etc) that it would primarily dictate the angle of clubhead movement through the ball, but I'd be interesting in your thoughts on this based on your model.

Jay

Jay,

I have tried to compress in Fig2 useful information pertaining to your question re to the angle of attack. at impact. I have shown 3 cases in Fig2.

-1- The arms slow considerably at impact, i.e., the hands are really ‘pinned’ momentarily into one stationary position during impact. As a result point A (wrists) is the instantaneous center of rotation.

-2- Imagine a golfer who manages to swing lead arm and club with the same angular velocity during impact with momentarily a stationary lead shoulder joint. Now point B (lead shoulder) is the instantaneous center of rotation.

-3- The third case is a more realistic case where the relative angular velocities of club, lead arm and shoulders are such that during impact the instantaneous center of rotation is at C.

The 3 arrows drawn perpendicular to the instantaneous radii of rotation are kind of self explanatory. The instantaneous center of rotation C can be really all over the place as a function of the time history of the angular velocities of the club, lead arm and shoulders.

As you can see the angle of attack can either increase or decrease depending on the position of the instantaneous center of rotation C. Hence I feel that there is no clean simple answer. As suggested I have ignored the effect of flexing of shaft.

 

[jmessner]

​

Jay,

I have tried to compress in Fig2 useful information pertaining to your question re to the angle of attack. at impact. I have shown 3 cases in Fig2.

-1- The arms slow considerably at impact, i.e., the hands are really ‘pinned’ momentarily into one stationary position during impact. As a result point A (wrists) is the instantaneous center of rotation.

-2- Imagine a golfer who manages to swing lead arm and club with the same angular velocity during impact with momentarily a stationary lead shoulder joint. Now point B (lead shoulder) is the instantaneous center of rotation.

-3- The third case is a more realistic case where the relative angular velocities of club, lead arm and shoulders are such that during impact the instantaneous center of rotation is at C.

The 3 arrows drawn perpendicular to the instantaneous radii of rotation are kind of self explanatory. The instantaneous center of rotation C can be really all over the place as a function of the time history of the angular velocities of the club, lead arm and shoulders.

As you can see the angle of attack can either increase or decrease depending on the position of the instantaneous center of rotation C. Hence I feel that there is no clean simple answer. As suggested I have ignored the effect of flexing of shaft.

Mandrin,

Interesting way to look at the problem. In the past, I've looked at video and tried to estimate center of rotation by tracing the clubshaft in three successive video frames (60fps), but I now see that method is flawed and I should have been looking at the clubhead path and estimating the location of the center of rotation - although at that coarse frame rate it's likely not accurate either.

It looks like only in case 1 (which I wouldn't consider a typical good swing) would the angle of attack be basically perpendicular to the shaft angle.

So, with the three different centers you used in your example, can you estimate the difference between them in terms of angle of attack?

Jay

 

[mandrin]

Mandrin,

Interesting way to look at the problem. In the past, I've looked at video and tried to estimate center of rotation by tracing the clubshaft in three successive video frames (60fps), but I now see that method is flawed and I should have been looking at the clubhead path and estimating the location of the center of rotation - although at that coarse frame rate it's likely not accurate either.

It looks like only in case 1 (which I wouldn't consider a typical good swing) would the angle of attack be basically perpendicular to the shaft angle.

So, with the three different centers you used in your example, can you estimate the difference between them in terms of angle of attack?

Jay

Jay,

I have derived the mathematical expression for the angle alpha which either adds or detracts form the club loft. It depends if the instantaneous center of rotation is on the left or right side of the club shaft line. For the particular conditions shown there is less effective loft.

An interesting conclusion can be immediately drawn from inspection of Fig3. If the instantaneous center of rotation lies anywhere on the club shaft line than the angle alpha is zero and the club has its natural loft.

 

[jmessner]

Good stuff

​

Jay,

I have derived the mathematical expression for the angle alpha which either adds or detracts form the club loft. It depends if the instantaneous center of rotation is on the left or right side of the club shaft line. For the particular conditions shown there is less effective loft.

An interesting conclusion can be immediately drawn from inspection of Fig3. If the instantaneous center of rotation lies anywhere on the club shaft line than the angle alpha is zero and the club has its natural loft.

Mandrin,

Great - thanks for doing the geometry and posting the equation. I'll have to play around with this a bit using some dimensions with various centers and see what happens.

Jay

 

[jmessner]

Example

Mandrin,

Finally got around to looking at this with some actual swings. Here's an example of David Toms with points marked as per your drawing. In this case, his hands are clearly ahead of the ball at impact yet he seems to be achieving an upward angle of attack. Interesting that the center of rotation is fairly close to what you used in your example. Flattening it out to 2 dimensions, I calculate that the deviation angle is around 4 degrees.

As an aside, Tom Wishon has recently mentioned that in recent testing he has done he has found that many players have a 2-3 degree upward angle of attack even with the hands ahead of the ball at impact with the Driver so I guess this effect is greater than I would have thought.

Jay

 

[mpro]

Mandrin,
About the divot with irons. From the collision of club against ball, does not the club head get pushed downward as an "opposite reaction from the ballistics of impact?" The quotes are there because I'm no math wiz, but it seems sensible to me that there must be some kind of resultant force just from contact. This would explain shallower divots with longer irons and deeper divots with shorter irons. What do you think?

John Dunigan

 

[mpro]

Check out this clip of Ernie Els. I think it does a good job showing what I'm talking about. http://www.youtube.com/watch?v=4TbFragrJDo

JD

 

[Jim Kobylinski]

Mandrin,

Finally got around to looking at this with some actual swings. Here's an example of David Toms with points marked as per your drawing. In this case, his hands are clearly ahead of the ball at impact yet he seems to be achieving an upward angle of attack. Interesting that the center of rotation is fairly close to what you used in your example. Flattening it out to 2 dimensions, I calculate that the deviation angle is around 4 degrees.

As an aside, Tom Wishon has recently mentioned that in recent testing he has done he has found that many players have a 2-3 degree upward angle of attack even with the hands ahead of the ball at impact with the Driver so I guess this effect is greater than I would have thought.

Jay

See...hands ahead yet clubhead "kicking" upward.