In 

Lessons from ShaftLab - 3

Lessons from the data

The previous page presented a few "myth killers" about shaft behavior. Now let's look at a few more assertions and see which ones stand up to the data collected using ShaftLab...


(5) "Kick velocity" exists and can be measured

The last thing we talked about on the previous page was the apparent contradiction between the statements:
  • Changing flex does not change clubhead speed, and
  • Kick velocity increases clubhead speed.
It is possible to deduce the value of kick velocity from the output graph from ShaftLab. Consider:
  • Velocity, by its very definition, is the rate of change of position with time.
  • Lead-lag deflection is a position. The rate at which it changes over time is the component of clubhead velocity due to the shaft flex.
  • And that -- again by definition -- is kick velocity.
We can measure the rate of change of lead-lag deflection from the graph. Let's look again at Peter Jacobsen's swing.



The slope of the deflection curve is its rate of change over time. Let's see how fast the lead deflection is increasing at the moment of impact -- because that is the kick velocity that is transferred to the ball.

I have drawn in red a line that is tangent to the lead-lag curve where impact occurs. Because it is tangent, the slope of that line is equal to the slope of the curve at impact -- which we have said is the kick velocity. We can find the slope of the line by taking any arbitrary segment of the line and finding the ratio of the vertical to the horizontal for that segment. For instance, the line segment shown has a height of 6.3 inches (that's inches of deflection, not necessarily inches on the graph paper) and a width of 188 milliseconds (which is 0.188 seconds).

If we divide 6.3" by .188 seconds, we get 33.5 inches per second. Yes, that's a slope -- but inches per second is also a velocity. You can convert it to miles per hour by multiplying by .0568. Do that and you get 1.9mph.

So Peter Jacobsen's driver kick velocity is 1.9mph. That's not a lot, considering that his clubhead speed is probably something like 115mph. He isn't getting enough kick velocity to have much effect on his overall distance.

But is 1.9mph a typical kick velocity? In Weathers' article, he reported kick velocities as high as 11mph. I guess I can believe that, but I suspect efficient swings have lower kick velocities. Why? Because I went through the calculation for all nine pro swings that TrueTemper included with the 1999 ShaftLab package. Here is the result of those calculations.

The driver kick velocities range from just over 1mph (Corey Pavin) to almost 6mph (Davis Love III). The 5-iron kick velocities were always lower than those of the driver. But they generally tracked; golfers with higher driver kick velocities tended to have higher 5-iron kicks as well.

Yes, the bigger hitters did tend to have higher kick velocities. But even the biggest hitters in the sample (Norman, Palmer, and Love) had kick velocities less than half of the maximum reported in TrueTemper's testing.

So what about the apparent contradiction: changing flex doesn't change clubhead speed, but kick velocity does?

Now we know that kick velocity is just the slope of the lead-lag trace. If changing the flex scales up the graph by 30%, then the slope -- hence the kick velocity -- is increased by 30%. So changing the slope does affect the kick velocity.

Let's go back to the article and see another statement later in the article after the contradictory assertions.
"How can you increase your kick velocity? A change in shafts isn't the answer. Although most of the players we tested had higher kick velocities with whipper shafts, their overall clubhead speed didn't change with whippier shafts."

How can that be? How could kick velocity increase and not add clubhead speed? That was a mystery to me for years. But recent modeling of the swing  has verified it (about 2010), and my improved understanding of the swing suggests a reason for it.

The way this could come about is if kick velocity generates enough force at the grip to slow down the angular velocity of the grip by the right amount to decrease the same amount of clubhead speed. Your 100mph clubhead speed may come from:
  • An honest 100mph swing with a very stiff shaft and no kick velocity, or
  • A 10mph kick velocity, and enough added resistance at the grip so the hands are only moving in a way that would create 90mph of clubhead speed.
This may sound a bit odd. But conservation of energy and momentum frequently does things like that. And it would explain the observations from TrueTemper's test lab. And it agrees with biomechanical studies (both mathematical and measured) in the past 10 years.



For the rest of our lessons, it is more convenient to deal with the X-Y version of the graph, instead of the deflection-time graph that ShaftLab outputs. I have created X-Y plots not only for Peter Jacobsen (we saw that one already), but also Greg Norman and Davis Love III. Here they are. You can click on the image to get a larger view.

Yes they look somewhat different at first glance. And that isn't too surprising, since:
  • Love's swing is a classic double-peak swing.
  • Norman's swing has very little letup in the middle; while technically a double-peak, it is close to a single-peak.
  • Jacobsen's also has almost no letup; but the second peak is so much bigger that it is close to a ramp swing.

But the similarities are also striking.
  • They all start close to the toe-up direction, and stay there from half to two-thirds of the swing.
  • They all experience the maximum bend in the toe-up/lag quadrant, at about 80 milliseconds before impact.
  • They all wander through the toe-down/lag quadrant before finishing the downswing in the toe-down/lead quadrant.
  • Once the downswing is under way, the bend is purely in the lead-lag direction only very briefly -- and not even close in the last 20 milliseconds before impact.
Now let's get back to the "lessons", and see what the X-Y plots teach us about shaft behavior.




(6) At impact, everybody has bend leading and toe-down

Certainly all the pros in the sample did. And I have never seen a ShaftLab trace that showed anything but lead at impact -- and, of course, toe down bend (commonly called "toe droop"). And Weathers' article states that, in the TrueTemper study, "Nearly all players, including pros, contact the ball with the shaft in the lead position."

Most experienced clubfitters and club engineers agree. For instance, see Tom Wishon's take on the subject.


(7) Bend at impact is not just due to CG/centrifugal "pull".

I have seen a number of respected experts argue that the bend at impact is not a rebound from the toe-up bend, but just centrifugal force pulling on the clubhead at its center of gravity (CG). Two of the several places I have seen this assertion are:
  • Tom Wishon's book "Common Sense Clubfitting" (2006).
  • Werner and Greig's book "How Golf Clubs Really Work and How to Optimize Their Designs" (2001).
So is this assertion true? Well, it is true that, if you hold the grip and pull the CG of the clubhead away from the grip, the shaft will bend. Not only that, it will bend into the toe-down/lead quadrant, which is where the bend is at impact. But we need to be more precise if we are to agree that bend at impact is due to centrifugal pull..

Let's ask ourselves what the bend would be at impact it if were. At impact, the X-Y plot would show a leading and toe-down bend, which would be exactly on the line between the hosel and the CG. That is the direction of the CG, so it must also be the direction of the bend. The picture on the left shows that line in yellow. (Note: the driver in the picture is not a ShaftLab driver.) When you lay the shaft on a flat surface and let the clubhead hang, it hangs with the clubhead CG straight down. The angle between the yellow line and the red line of the clubface (the heel-toe line) is the angle of interest here; all bend is on that line. The magnitude of the bend would depend on the golfer's clubhead speed, since centrifugal force varies with the square of clubhead speed.

Since ShaftLab has only one design of driver, all the impact bends should be on the same line. For that driver, the line from hosel to CG is 17 off the toe-down ("droop") axis. (The same is true for the 5-iron, but on a 12 line.)

The graph shows what the scatter plot should look like for all golfers, if it is true that CG-pull accounts for all the bend at impact. The bigger hitters should show up farther from the origin of the graph, but they should all be on the 17 line.

What do we actually see when we plot the impact bend of a bunch of representative golfers? Here are the graphs for the nine pros whose Shaftlab profiles are in the 1999 package.

Not a single point is on the CG line. Every one of the golfers not only has leading bend at impact, the lead is more than can be explained by CG-pull. (If you want to see what you can make of the numbers, here is the raw data.)

So something is going on besides (or instead of) CG-pull. That something might be described as "rebound" from toe-up bend earlier in the swing, because it is leading the CG in every data point we have.

Note on the geometry: Recall that the the club's lead-lag and toe-heel planes rotate 90 with respect to the swing plane during the downswing. The way physics works, the swing plane is the way bend and rebound work; the "inertial framework" does not rotate with the golf club. So toe-up bend at the beginning of the downswing corresponds to lag when you rotate the club to the impact position. Therefore, rebound from that lag would be lead.

Again in this context: I have seen some say that toe droop is "rebound" from (or reaction to) toe-up bend early in the downswing. This would be true if the inertial framework did rotate with the club. But it doesn't.

But there is a more likely explanation than rebound, although harder for many people to swallow. By the time the clubhead nears impact, it has so much momentum (that's velocity times mass) that the hands can't rotate fast enough to keep up. So the clubhead is pulling the hands through impact, and bending the shaft forward in the process. It may be hard to believe, but most serious swing models show it is true; I investigate this in another article, and a computer simulation by Dr Sasho MacKenzie has confirmed that toe droop is due to CG pull but lead bend is more than twice what CG pull can explain.

In summary, the theory that centrifugal pull through the CG accounts for all the bend at impact does not agree with the data. So it must not be true. It probably provides some of the bend, but there is a lot more lead bend than can be explained by CG pull.

(8) Frequency is a proxy for flex, nothing more

Occasionally I see someone argue that the frequency of the shaft represents the behavior of the shaft during some period of the downswing. Of course, a sine-wave free response does not model the entire downswing. Not only are the ShaftLab plots very different from that, but even the frequency isn't right. The closest sine-wave model to the actual data would be a half-cycle of vibration during the downswing. Driver shafts (with frequencies of 200-300cpm) have a half-cycle of 100 to 150 milliseconds, while the downswing is 400 to 600 milliseconds. So that doesn't fly.

But there are more sophisticated theories around. So let's look at the two major competing classes of theory of how shaft behavior changes with the flex of the shaft.

Magnitude scaling holds that the flex changes the magnitude of the bend at every point of the swing. According to this theory, the ShaftLab trace would be essentially the same, except that the change in flex would change the vertical dimension of the trace.

The graph at the right is an example of how flex would affect the ShaftLab trace under magnitude scaling. The solid lines are the lead-lag and the toe-heel traces using the ShaftLab club. The dotted lines are the traces for a more flexible shaft -- assuming magnitude scaling is the way shafts actually behave.

I suspect the TrueTemper engineers have done this experiment. But the rest of us don't have the opportunity without a lot of effort and expense. One cannot get a club instrumented with the proper strain gauges except the ones sold as part of ShaftLab.
Response time scaling holds that stiffer shafts "react faster", whatever that means. Theories of this class say that the higher frequency of a stiffer shaft means that, for at least part of the swing, it is the time that scales rather than the magnitude -- or perhaps along with the magnitude.

Again, let's look at an example of how flex would affect the ShaftLab trace. The most reasonable (to me, at least) of the response time scaling theories is Lloyd Hackman's explanation for the FitChip device he invented. It says that the shaft behaving as a spring with a sine-wave free response from some "release" point to impact.

In the picture to the right, the release point occurs at 500msec. From that point on, the more flexible shaft (the dotted lines) responds slower. The flex chosen has zero lead-lag bend at impact -- the ideal match according to Hackman.

So which theory is correct? I believe the data we have supports magnitude scaling. In other words, frequency of the shaft or the club is a nice, numerical, measurable way to describe the flexibility -- but nothing deeper than that. It doesn't say anything about how fast the shaft responds during a real golf swing, nor the way the shaft bend varies during the downswing. (Note that I said the way the shaft bend varies, not the amount of the bend. The difference is in the graphs above.)

Why do I believe this?

Well, I used to believe in time-response scaling. The Club Design Notes I wrote in the 1990s have some flavor of this in the flex fitting section. (At the time this article was written, the Club Design Notes section was still the 1998 version; I expect to get around to changing it sometime. Actually, the posting of this article is a prerequisite to rewriting the flex chapter.) So, when I heard about the FitChip -- and had an opportunity to spend an afternoon with Lloyd trying it out, I was very excited. It held a lot of appeal.

The FitChip depends upon the shaft behaving as a spring with a sine-wave free response from some "release" point to impact. In that model, choosing the right shaft involves measuring the time between release and impact, and choosing a frequency whose free response gets from the release bend to zero bend in that time. (A slight oversimplification, but nothing that the argument below depends upon.)

It seems pretty obvious that the designers of ShaftLab believe in magnitude scaling rather than time response scaling. The notion that the graph scales as you change the flex assumes that changing the flex (i.e.- changing the frequency) affects only the magnitude of the bend over time. But, since all the ShaftLab traces are made with the same flex shaft, they don't allow us to check this assumption directly.

However, it turns out we do have enough data to show that "partial sine-wave response" doesn't cut it in the real world. Look at the earlier scatter plots entitled Actual Bend at Impact. Note that every single one shows a leading bend. In fact, the lead exceeds what it would be if the bend were due to centrifugal pull. What does that tell us about "free response" theories of shaft behavior?

If shaft "speed" had anything to do with frequency -- as the design of the FitChip assumes -- then the ShaftLab driver is considerably too stiff for any of these touring pros. That's because, if shaft response behaves according to response time scaling, then you could get rid of the lead (and presumable get better impact from a straight shaft) by going to a softer shaft. The lead -- under this theory -- comes from the too-stiff shaft rebounding through straight to a leading position.

Remember that all the ShaftLab traces were taken with the same four clubs (RH driver, LH driver, RH iron, LH iron). So all the driver traces are based on the same shaft design, a TT S-flex steel shaft. (My memory says Dynamic, but it might have been Dynalite. Anyway, doesn't really matter. The important thing is they were all fairly standard, well-understood S-flex shafts.)

Does anybody believe that all these touring pros had a too-stiff shaft in a TT S-flex? I certainly don't. And neither do they. At least half these guys use an even stiffer shaft in their own clubs. And they win tournaments with them. And they depend on them -- so you can bet they have experimented, and know the shafts in their own clubs are very close to optimal for them.

So I will continue to believe that the frequency doesn't say much about the shape of the bend during the downswing, just the overall flex (the magnitude of the bend).



I'd like to qualify the statement that the only thing that happens with a change of flex is magnitude scaling. What I am about to say has no impact on the conclusion stated above; I still think that response-time scaling is not a factor in clubfitting, and probably doesn't occur in any signficant amount except perhaps for grossly too-flexible shafts.

It has been established that a mismatched shaft can cause the golfer to change his swing to compensate for the difference. The better the golfer (or maybe the more sensitive to feeling the club during the swing), the smaller the mismatch required for this, and the quicker the adaptation is made.

This is a potential flaw in the ShaftLab approach. If you try to fit a golfer who is ill-suited to the ShaftLab club, he might adapt his swing before the measurement session is complete -- resulting in enough change in the graph to invalidate the fitting data.

I am guessing that the reason for an S-flex shaft in ShaftLab is... TrueTemper engineers decided that most golfers who would adapt that quickly are golfers who are reasonably suited to that shaft. If this is a correct assumption, that choice would minimize the amount by which the data would be off.

(9) Bend at impact is nowhere near the target line

Several explanations of spine alignment implicitly depend the shaft bend in the vicinity of impact.
  • The most common theory says, "align the shaft so it wants to bend in the target line." Think about it; this statement assumes that the shaft is bending directly toward or away from the target as you are squaring up the clubface. You are squaring up the clubface at impact, and probably for the last few tens of milliseconds before impact. So that is the region where the bend must be in the target line.
  • Another interesting theory says, "the shaft is bending toward the clubhead's CG at impact, so align the shaft so it wants to bend toward the CG."
But does either of these correspond to reality? A quick look at the X-Y and scatter plots above says no. Consider:
  • At impact, the shaft bend is a minimum of 24 and frequently over 45 away from the target line. (The target line would be pure lead bend.)
  • The plots of the three pros where we looked at the complete downswing show that impact is the closest the bend comes to the target line during the last 20msec of the downswing.
  • And even if we compared the bend with the CG line, none of the swings put the bend near there either.
So, while common practice for spine alignment (which is to orient the NBP in the target plane) may or may not be correct, the usual rationale for it makes no sense. (For those not familiar with spine alignment practice, NBP stands for "natural bending plane". NBP is the plane in which bending the shaft takes the least effort.)

Last modified  11/07/2017