ShaftLab - 3
from the data
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...
"Kick velocity" exists and can be
The last thing we talked about on the previous page
was the apparent contradiction between the statements:
It is possible
to deduce the value of kick velocity from the output graph
from ShaftLab. Consider:
flex does not change clubhead speed, and
velocity increases clubhead speed.
can measure the rate of change of lead-lag deflection from the graph.
Let's look again at Peter Jacobsen's swing.
- Velocity, by its
very definition, is the rate of change of position with time.
deflection is a position. The rate at which it changes over time is the
component of clubhead velocity due to the shaft flex.
that -- again by definition -- is kick velocity.
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.
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
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
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.
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
what about the apparent contradiction: changing flex doesn't change
clubhead speed, but kick velocity does?
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.
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.
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
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
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."
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:
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.
honest 100mph swing with a very stiff shaft and no kick velocity, or
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.
(6) At impact,
bend leading and toe-down
all the pros in the sample did. And I have never seen a ShaftLab trace
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.
at impact is not
just due to CG/centrifugal "pull".
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).
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
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 17º off the toe-down
("droop") axis. (The same is true for the 5-iron, but on a 12º
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 17º line.
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.
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
in every data point we have.
Note on the geometry
Recall that the the club's lead-lag and toe-heel planes rotate 90º 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.
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.
is a proxy for flex, nothing more
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.
holds that the flex changes the magnitude of the bend at every point of
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
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
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
magnitude -- or perhaps along with the magnitude.
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.
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.
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.)
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
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?
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.
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.
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
of the bend).
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
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.
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.
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.
at impact is nowhere near the target line
explanations of spine alignment implicitly depend the shaft bend
in the vicinity of impact.
But does either of these correspond to reality? A quick look at the X-Y and scatter plots above
- 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."
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.)
impact, the shaft bend is a minimum of 24º and frequently over
45º 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
- And even if we compared the bend with the CG line, none of the swings put the bend near there either.