How stringy is the shaft at impact?
Dave
Tutelman  January 23, 2022
Since the 1990s, I've been saying, "The shaft is a string at impact!"
to anybody who will listen. I still believe it is
a good rule of thumb. Is it absolutely true? Of course not! Here we
explore the limits of approximating the shaft as a
string during the moment of impact.
Executive summary
We look at the question
from three different points of view:
 Where does the concept come from
anyway? It's pretty silly if you take it literally. What it means
is during
impact
your hands on the grip have no more control over clubhead/ball impact
than if the shaft were a string. We can see from pretty simple physics
that almost all the force the clubhead applies to the ball comes from
the inertia of the clubhead. During impact considerably less than 1% of
that force can be attributed to the hands applying a
combination of force and
torque to the grip at that moment.
Both your effort and the shaft definitely affect ball flight. But not during the instant of impact.
You need to do everything with your hands, body, and the club before impact occurs. From the
start to the end of impact, there is no way your hands can transmit
anything to the clubhead.
 What part of the mass of the shaft
contributes to ball speed at impact? While the classic momentum
transfer assumes all the mass involved is the clubhead, we know that
there is at least a small bit of shaft tip bonded securely into the
hosel. Does that contribute, and how far away from the hosel does shaft
mass continue to matter during impact? It turns out to be less than 2.6
grams, no more than the portion of the shaft tip actually bonded into
the hosel. Usually it is less than a hoselfilling dose.
 So far, we have just talked about creating ball speed with
good center impact. What about things like
gear effect
and smash factor when the impact is not
oncenter?
Does
shaft stiffness have a role to play there? In this case, the shaft
might have more influence than a string. If the strike is
offcenter, the impact point's distance and direction from the center
will cause rotation in some
direction with some speed. Some of that rotation will require the shaft
to twist about its own axis (torsion), and some rotation will require
the shaft to bend along its axis (flex). It turns out that the shaft is
still a string in torsion, but has some effect of limiting rotation in
flex. Because the shaft is at a lie angle of 56°60°, both sidespin and
backspin will have contributions from both torsion (little to none) and
flex (could be noticeable if the shaft is stiff enough).

The basic physics
Yes, I know it is pretty silly to compare the shaft to a string. The
shaft is a rigid rod, right? Well, no. And the harder you look the less
sense that characterization makes. The very notion that fitting
involves shaft "flex" or "stiffness" gives the lie to perfectly rigid.
A much more accurate way to look at a shaft than a rigid rod is as a
spring. It takes a certain amount of force to deflect a shaft a certain
amount. The stiffer the shaft, the more force it takes. In fact, the
ratio of the force to the deflection it produces is what engineers and
physicists call the shaft's "spring constant".The overall spring
constant of the shaft is not the only flex characterization, but it is
the first and most important one.
We measure the spring constant of a shaft with a device called a
"deflection board". Clubfitters and clubmakers have used deflection
boards for well over a century. Here is an almost modern deflection
board sold by by GolfWorks. You clamp the butt of the shaft
horizontally, hang a known weight from the tip, and measure how far the
tip moves. A more modern board may use electronics to measure the
force, rather than hanging a calibrated weight. But they measure the
same thing: a force and a deflection whose ratio is the spring constant
of the shaft.
I just went down to my basement and measured a few fulllength driver
shafts in my NeuFinder 4.1.
(That is a deflection board I codesigned over 15 years ago for shaft
flex trimming and profiling.) The stiffest among them had a spring
constant of less than 1
pound per inch.
(I measured it at 0.90.) Knowing the ranges of stiffness for golf
shafts, the stiffest driver shaft of normal design at this length is
probably less than 1.2 pounds per inch, and it is hard to imagine a
driver shaft as stiff as 2 pounds per inch.
Now we come to the way I think of "string at impact". During impact,
the clubhead is applying force to the ball; this is how ball speed
happens. The question becomes: How much of this force is due to simple
momentum transfer from the mass of the clubhead ("inertial force") and
how much is transmitted from the hands through the shaft to the
clubhead? If the hands represent a negligible portion of the force,
then the shaft is doing no more at impact than if it were a string.
The calculations below were done using a spreadsheet, which you
can download.
The total force
This is simple momentum transfer. The clubhead applies force to the
ball to accelerate it according to F=ma. We know
the mass of the ball. We can compute the acceleration, which is the
change in velocity divided by the time it took to achieve the change.
So:
F = m V_{ball} / t
For this first set of calculations, we will assume a drive struck with
a driver head traveling at 100mph. Everything else is very vanilla for
a golf ball and driver. See the spreadsheet for actual numbers if you
are interested.
When we do this calculation, the force is 1528 pounds. This is an
average force, averaged over the whole duration of impact. It could be
twice this for a peak force.
The shaft force
So how much do you bend the
shaft at impact? That's another way of asking: How much force are your
hands applying to the clubhead via the shaft at impact? In all
likelihood, the answer is: A little less than zero. You read that
correctly: negative force. At least as long ago as the early 1990s, and
probably more, it
was established that just about every golfer has the shaft bent forwards
at impact. This includes tour players. It includes long drive
champions. They all have the clubhead going so fast that, some tens of
milliseconds before impact, the clubhead starts dragging the hands and
wrists along; the hands
simply cannot keep up. Every golfer I have heard of has a lead bend
of up to an inch and a half just before impact.
What I'm saying is that it is
almost impossible to apply a positive
force on the clubhead through the shaft coming into impact. But let's
calculate something still hard and unlikely, but just maybe you stand a
chance. Suppose your hands were able to
keep up with the clubhead coming into impact (very unlikely), and they kept rotating at the same speed through impact
(again, unlikely  but if you can do the first you can probably do the
second). If you can do that, you could impose a positive force on the clubhead during impact  but it would still be miniscule.
Consider the diagram on the right. If the club were to swing through
without any ball, and we
will suppose your hands can turn fast enough to keep the shaft
straight, then it would look like clubhead A in the diagram. But the clubhead does in fact slow down during impact, as
part of transferring its momentum to the ball. If your hands can
maintain that speed as the head slows down, the shaft will start to
bend
backwards  applying some spring force through the shaft.
A driver head slows down during impact by about a third of its initial
speed. That is enough so it has
moved forward during impact by 0.136 inch less that it would have if
the ball had not been in the way. That means your hands are able to
bend the shaft 0.136 inch backwards by the end of impact. Let's assume
that the driver used the Sflex shaft I measured earlier, with a spring
coefficient of 0.9 pounds per inch. That means you are applying
0.136 * 0.9 = 0.122 pounds of
force
to the clubhead through the shaft.
Remember
that the clubhead applies an average of 1528 pounds of force to the
ball during impact. That means that the force applied via the shaft is
less than 1/10,000
of the total force the clubhead applies to the ball. That would
certainly seem to justify the notion of "string at impact". But wait!
It is more of a discrepancy than that! We are comparing the peak force
in the shaft with the average force applied to the ball. So the
fraction applied via the shaft is considerably less than one part in
ten thousand. 
The lack of
force from the shaft should be enough to justify "string at impact".
But wait! There's a little more. It's not just the size of the force,
but the timing as well. When a force is applied to one end of the
shaft, it takes several milliseconds to be felt at the other end. Look
at this video of a shaft right after impact. Note that the flex wave
takes several frames to reach the hands, and the ball is long gone when
it does. (Video
courtesy of Russ Ryden in 2009.)
The same thing is true going the other way, from grip to clubhead.
Assuming you could apply a substantial force at the grip at impact (and
we have just seen that is very unlikely), it could not affect the
head's motion or angles for a while  and by then the ball would be
well on its way. How long? I have seen estimates of 410 milliseconds
for a flex wave to travel the length of a driver shaft. That
corresponds to 38 inches of clubhead motion. And remember that the
lowest estimate there is almost ten times the duration of
clubheadtoball contact.
Before you spend too much effort thinking about how you could
anticipate impact and apply the force early, remember our main argument
that the force will be negligible anyway.
Let me point out that this observation
is by no means recent. It is more than half a century old. In his 1968
book, "Search for the Perfect Swing",
Alastair Cochran states, "Hand reaction to impact can't affect the
shot." He then presents both the force argument and the time argument
to justify the statement. As experimental proof, he built a 2wood with
a hinge in the shaft, just above the hosel. The shaft of this club
actually began to approach a string. Comparisons between shots with
this club and a normallyshafted 2wood showed little difference in
distance.

Tweaking
So far, the shaft seems very stringy indeed! Is there anything we are
justified in changing about this model, that might make force through
the shaft a little more significant? Let's try tweaking it a little.
First off, let's try tweaking things in the spreadsheet. We'll only
tweak things that make sense, not something like the mass of the ball
(every golf ball is within a gram or two of 46g).
 Clubhead speed:
This does nothing for the "stringyness ratio". It stays at the same
value, 12532, for every plausible clubhead speed.
 Coefficient of
Restitution:
Same thing. You can crank it all the way down to 0.7, roughly what it
was 40 years ago with wooden driver heads and balata balls, and the
stringyness ratio stays at 12532.
 Duration of impact:
450 microseconds is the median of the values in the studies I have
seen. But maybe cranking it up to the longest from any of the studies,
500 microseconds, will make a difference. That does move the needle,
all the way to 10151. But the shaft is still providing less than
1/10,000 of the force  still awfully stringy.
 Shaft stiffness:
Let's postulate an XXS shaft (doubleextrastiff). That would be
something like 16% higher spring constant than our Sflex slaft, or a
spring constant of 1.04 pounds per inch of deflection. The ratio in
that case would be 10804. Still less than 1/10,000 of the force, and
still
very stringy.
OK then, how about just making some unreasonable assumptions and seeing
what they do. Let's assume you can apply a 2inch backward bend to the
shaft during
impact. No, I don't believe for a second that you can, and neither
should you. But let's suppose, for argument's sake. Then, let's double
the spring constant of the shaft, to 2 pounds per inch. Again, that is
a completely unrealistic number, but we'll do it for the sake of
argument. A simple calculation gives us a force of 4 pounds applied to
the clubhead through the shaft. But even with that, the force provided
through the shaft is only about 1/400 of the total force. Still a
string!
What's next?
Now we understand why it is reasonable to say, "The shaft is a string
at impact." The forces transmitted to the clubhead via the shaft during
impact are a negligible part of the forces actually involved in impact.
The shaft might just as well be a string, for all the good it does. Of
course, the shaft plays a very important part in getting the clubhead to impact in
the first place. That's why shaft fitting is important. But during
impact itself, it might as well be a string.
But there are still a few interesting related questions.
 We calculate impact based on the mass of the clubhead itself. But
shouldn't some shaft mass also figure in that calculation? At the very
least, the tip of the shaft is epoxied rigidly in the hosel; in
essence, it is part of the clubhead.
Why
doesn't the mass of the tip count, and perhaps more of the shaft as
well?
 We have looked at generating ball speed during a sweet spot
impact. But what about offcenter hits? Does shaft stiffness play any
part in gear effect, either vertical or horizontal? Or is that 100%
stringy as well?
In November 2021, Jay Messner brought to my attention a couple of
papers that contain possible answers to these two questions. The
authors of both studies were Erik Henrikson of Ping and several
researchers
from the University of Waterloo. Here is
what that research tells me.
Mass of the shaft
The usual assumption for the
clubtoball momentum transfer is reflected by the wellknown equation:
V_{b}
= V_{h}

1
+ e
1+ m_{b}/M_{h}

Note that the mass of the shaft is not even considered; only clubhead
mass is considered part of the transferred club momentum. It is hard to
believe this assertion, since there is at least a small portion of
shaft tip inextricably bonded inside the hosel. How could this not act
exactly as the clubhead mass does? And if it is part of the momentum
mass, then how much more of the shaft is involved before there is too
much distance and too much flex to be part of the momentum transfer?
A
2020 paper can give us considerable insight into this question.
(Erik Henrikson, Behzad Danaei, William McNally, John McPhee, "Adjusting a MomentumBased Golf
ClubheadBall Impact Model to Improve Accuracy") The basis of
the paper was to test the accuracy of the classical momentum transfer
model between the clubhead mass and the golf ball. From the
introduction:
Two [simplifying] assumptions that affect the
accuracy of the
momentumbased impact models are neglecting the deformation of the golf
ball during the impact and the influence of
the golf shaft on the impact
dynamics. The purpose of this study
was to account for the
aforementioned factors by making
two simple and physically meaningful
adjustments to the conventional
momentumbased impact model. The first involves making a slight
adjustment to the center of
mass of the golf ball to account for golf ball deformation, while the
second involves adding mass to the
clubhead in proportion to the shaft mass.
The way they did the study was:
 Measure the club and ball extensively, and prepare a
simple momentumtransfer model based on those measurements.
 Do experimental runs using multiple golfers and measuring
launch characteristics with a GCQuad launch monitor. The results for
both spin and ball speed were fairly close to the simple model, but not
exactly the same.
 Tweak a few parameters  OK, we'll use their word,
"adjust"  to make the results come out right on the money. It
turns out that, for ball speed, the parameter to be adjusted was the
clubhead mass, and the adjustment was an added mass. Moreover, the size
of that mass adjustment was a function of the shaft mass.
 The other parameter they adjusted was the position of the
ball's center of mass. This turned out to affect spin considerably, but
ball speed not at all. Why adjust the ball's CoM? Because the ball
compresses on the clubface during impact, so the ball changes shape and
the CoM is not the same distance from the clubface.
The experimental runs included three drivers with identical clubheads
but shafts of different weights. The mass adjustment (Δm) was computed
separately for each shaft. The adjustment was not quite proportional to
the shaft's weight, but it was monotonically related. That is, for each
higher mass shaft, the adjustment Δm was higher.

Here is a graph of Δm,
the dashed blue curve, plotted against the total mass of the shaft.
Even for the almost75g shaft, pretty heavy for a driver, the mass
adjustment to the clubhead was less than 3 grams. That number just begs
for the answer to, "How much shaft mass is firmly inside the hosel?"
Let's try to answer the question.
The red curve shows the length of shaft tip containing Δm grams of mass. It assumes that
there is a uniform mass distribution over the length of the shaft. That
is probably not a terrible assumption, but we'll revisit it in a
moment. Not that the length of shaft that gives Δm grams is less
than an inch for the two lighter shafts and about an inch and a half
for the heaviest shaft.
How does that compare with the hosel insertion depth for a driver? What
we are really asking is, how quickly does the contribution of shaft
mass to impact fall off as we get farther from the hosel. I measured
all the unoccupied driver heads in my basement, and found that
the insertion depth is close to 1.5 inches for most of them. I did find
heads from 1.25" to 1.75", but most were much closer to 1.5" than that.
Therefore, Δm
struggles to even fill the hosel. There seems to be no shaft mass
outside the hosel that is participating in the momentum transfer.
I promised we would get back to the assumption that the mass
distribution is uniform along the length of the shaft. Most driver
shafts have a balance point a fraction of an inch above the geometric
center. That might mean the mass density is a little lower near the
tip. But more than offsetting that is the fact that driver shafts
typically have reinforced tips. The wall thickness inside the hosel is several times more than the average
wall thickness of the shaft. So it is even less likely that any shaft
mass outside the hosel might be part of the mass adjustment.

This paper shows that any shaft mass that is contributing to the
momentum transfer is unlikely to be outside the hosel of the clubhead.
The diagram above might more accurately be drawn as shown here. The
full effect of shaft mass stays inside the hosel, and there is no
momentum provided to the ball by any shaft mass outside the hosel.
Bear in mind that the tiny contribution of the shaft mass is due to the
flexibility of the shaft  its tendency to mimic a string at impact.
In a 2009 paper,
Rod Cross and Alan Nathan estimate the contribution as a quarter of the
shaft mass, a much larger number. But their calculation is based on the
assumption that the shaft is perfectly rigid, so it contribution would
be due only to mass distribution.

Clubhead rotation
So far, we have been talking
about an oncenter impact. The clubhead
remains in a stable orientation through impact, and just applies a
simple deflection to the shaft. But what happens if the impact is
offcenter, either heel, toe, high, or low? Here is a figure that shows
an offcenter impact, in this case toward the toe.
The force applied to the ball by the clubface is offcenter; more
precisely, it does not go through the center of mass (CoM) of the
clubhead. There is a moment of this force, equal to the magnitude of
the force times x
(the distance of the force from the CoM), trying to rotate the clubhead
clockwise around the CoM. The second picture shows the result of this
rotation. The rotation itself is in blue  the radius from the CoM to
the place where clubface meets ball, and a circle representing the
rotation at that radius. The clubface moves tangent to the rotation
circle, in the direction of the red arrow. We have resolved that motion
into two orthogonal motions:
 Parallel to the
clubface (yellow)
 This movement is tangent to the ball's surface, and causes the ball
to spin. The spin is due to what is known as "gear effect".
 Perpendicular
to the clubface (green)
 This movement is away from the ball. This movement subtracts from the
overall clubhead movement toward the target, and thus reduces
ball speed. Another way of putting it is we have lost some "smash
factor".
This combination, giving spin and taking away speed, increases with
distance from the center of mass and decreases with clubhead moment of
inertia, which resists the rotation of the clubhead.
If the impact had been through the CoM, the the clubhead would not
rotate and it would only exert deflection on the shaft. We have seen
that the shaft is close to a string at impact for pure deflection.
Can we treat the shaft as a string for clubhead rotation as well? I
tried to address the problem in my 2009 article on gear effect.
The first several pages treat the shaft as a string, then ask the
question about whether shaft
stiffness can impede gear effect by
limiting clubhead rotation. I dismissed axial twist of the shaft
(usually represented by the shaft's "torque rating") by a similar study
showing that it could not provide a lot of resistance to clubhead
rotation in the moment of impact.
But
it is not nearly as easy for shaft flex. The reason is that impact
creates two opposite deflections fighting against one another.
 On one hand, the force itself wants to push the clubhead
back and deflect the shaft backwards.
 But there is also the rotation created by the moment of the
force. In the picture, the impact is above the center, so the moment of
force wants to rotate the clubhead faceup. That rotation tends to bend
the shaft forward.
With these two bends possible working against one another  large
bending efforts lasting less that half a millisecond  there isn't an
easy way to know what the shaft's influence on head motion might
be. (I tried in 2009, and
never got an answer I was confident in.) A proper analysis would be a
computerintensive Finite Element Analysis (FEA); I do not have access
to software like that.
Fortunately, someone with that sort of resources became interested in
the problem. A 2018 study (Henrikson, McNally, McPhee, "The Golf Shaft’s Influence on
ClubheadBall Impact Dynamics")
was done by pretty much the same team that did the shaft mass
adjustment work discussed in the previous section. What they did was:
 A model of the clubhead and shaft, detailed enough for FEA,
was derived from direct measurement of the components. The model was
calibrated by comparing its kinematics with actual motion capture of
multiple swings from ten elite golfers. The match was good, except for
shaft stiffness. The shaft, nominally a stiff flex, was softer in
calibration than the manufacturer's spec indicated. So the rest of the
study was done with the shaft at 1.5 times the manufacturer's nominal
stiffness. (I'll get back to that in discussion of the results.)
 The calibration had been done using motion capture during
the downswing, especially the last 10 msec before impact. But motion
capture at 723fps is not nearly fast enough to get any detail on impact
itself; the entire duration of impact is only one third of a sampling
interval. So impact was modeled by simulating it with with FEA
software. Two models were used:
 A free body
model, just the clubhead with no shaft. Consider that a 100% "stringy"
shaft.
 A full club
model, including FEA analysis of the shaft firmly attached to the
clubhead.
 The key findings (a set of graphs in figure 5 of the paper)
is the difference between the free body simulation and the full club
simulation. That difference is a
direct measure of how close to a string the shaft is during impact.

Results
Let's start our review of results with the ball speed graph from the
free body impact model.
Here is Fig. 4b from the paper superimposed on an actual driver face,
with a few things I added: a pair of blue centerlines in the center of
the face, and a red circle inscribed in the locus of 255m/s ball speed.
Things to note:
 The maximum ball speed of 260km/h is slightly toward the
toe
from the center of the face. This is pretty well known; it arises from
the fact that point is traveling a bit faster than the center of the
face.
 The curves of constant ball speed fall off in speed as you
get further from the maxspeed curve near the center. This is also
wellknown. As impact moves away from the center, the clubhead rotates
more during impact  meaning the face falls away from the ball more,
so not as much force is applied to the ball.
 The curves of constant ball speed are not perfectly
circular. If you compare the 255 curve with the red circle, it is a
horizontallyaligned ellipse. It isn't too far from a circle, but it is
definitely not a circle. Why? I discuss this in detail in comparing horizontal and vertical gear
effect.
Very simply, the moment of inertia against rotation in the horizontal
plane is greater than that in the vertical plane. So the clubhead
resists horizontal rotation better, and impact can be more offcenter
for the same ball speed.
Now let's do the same thing for the full club impact model. Now the
ellipses of constant ball speed are longer, and they are slanted. Why
should that be? I added a red dashed line where the major axis of the
ellipse is. Note that it is almost parallel to the shaft. That tells us
that the shaft is resisting rotation of the clubface where it flexes,
but not much where it twists.
The red line is not perfectly parallel to the shaft. It may be a
precision problem with my graphing, or it may be real. If it is real,
it is probably due to the fact that the free body model didn't give us
perfect circles either. There was an ellipse due to different moments
of inertia around the two axes, which is probably biasing the full club
ellipses. We should be able to get a better feel for the effect of
shaft itself from the difference
graphs  the difference between behavior with and without the shaft.
Let's look at that.

On this graph, the curves are the differences between the full club
model and the free body model. When you think clearly about it, this
shows the effect of the shaft and golfer. If the shaft were truly a
string at impact, there would be no difference at all, no curves on the
graph, just a blank sheet of graph paper. What can we conclude from
looking at this graph?
 The curves are pretty close to a set of parallel lines. The
space they define is a valley whose floor is a vaue of roughly 2
meters/second; that is the difference in speed at the center of the
clubface between having a shaft and not having one. The valley is long
and narrow, and slanted on the face rather than straight across the
face.
 I drew a red line tangent to the curve nearest the center
of the clubface. A perpendicular to that line is 57° from vertical.
Note that it is extremely close to parallel to the axis of the hosel
and shaft. That tells us that the shaft is offering almost no
resistance to clubhead rotation when twisted about its axis  which
shaft makers specify as "torque". But, since
the difference rises as you move parallel to the shaft, we must
conclude that the shaft is limiting clubhead rotation with its
crossaxis deformation  which we usually refer to as "flex".
 Sanity check time! Here are a couple of tests of gross
ballpark validity of these conclusions.
 The curves of the graph are not all perfectly parallel.
So I tried a nearcenter line (in blue) on the other side of the
center. In order to stay close to the center of the clubface, I
visually bisected the "2m/s" curve at the upper left of the graph. It
was 60° instead of 57°. Still pretty close.
 The paper does not mention the lie angle of the driver
that was used. So I looked in online catalogs for a halfdozen club
manufacturers. Most of their drivers had lie angles of 58°59°, and all
fit in the range of 56°60°. That matches the angle of the curves on
the graph. We can be pretty sure that we are looking at a difference
between shaft twist (pretty much a string) and shaft flex (not so much
a string).
 Finally, just in case you wondered, the picture of the
clubhead (which was not
part of Figures 4 and 5 from the paper; I don't even know what brand
and model of driver was used) is oriented perfectly horizontally. I
performed a measurement that showed the lines on the face are within a
half degree of horizontal.

The
paper's Figure 5 has difference graphs not only for ball speed  which
we have been examining  but also for: launch angle, azimuth (initial
angular direction of the ball), side spin, and back spin.
Here
are
those graphs, together with a centrally measured direction of the
curves. In each case, the direction is pretty close to the lie angle of
a driver. That means that we can continue with our provisional judgment
that the effect of the shaft is very different in flex than
in torsion. Specifically:
 As we move along a direction perpendicular to the shaft
(along the red line), we are moving along a single value of what the
graph is about  for instance, the same amount of side spin. We start
on a curve and we follow it, or perhaps leak off it, but not far from
the same value. Since this is a difference graph between with the shaft
and without one, that tells me that the shaft does not do much during
impact to determine the ball flight.
 As we move along a directon parallel to the shaft
(perpendicular to the red line), the value changes more quickly. So the
shaft does have an effect in this direction. In particular, the
flexural stiffness of the shaft limits the rotation of the clubhead,
even noticeable during impact. So the gear effect in this direction is
reduced.
Let's compare this to my attempts a dozen years ago to analyze the
shaft's ability to limit gear effect.
 I made the mistake of equating horizontal gear effect
(sidespin) to shaft torque, and vertical gear effect (backspin) to
shaft flex. Perhaps that is the "normal" way to think about it, but it
only works for a vertical shaft  that is, a 90° lie angle. Drivers
have a lie angle of 56°60°, so the underlying assumption is not valid.
True, the majority of shaft influence is flex for backspin and torque
for sidespin, but it is a small majority at best  perhaps a bit more
than 3to2.
 I concluded that a rather stiff shaft might have a 14%
reduction of gear effect. This study says it is a lot more, and I am
very prepared to believe that. But... Let's go back to the 50%
adjustment of the shaft's spring constant. The increase in stiffness
from the manufacturer's specs were to make the results agree with the
measurement in the "calibration" phase of the study. That may well have
been a proper adjustment, but 50% is a huge increase in stiffness.
Consider: if you increase the Sflex to XXXflex  tripleX
 that would only be a 30% increase in spring constant. So there is an
off chance this analysis is using an unrealistically high shaft flex.
If that were the case, the influence of the shaft might not be all that
large.
 In support of the idea that shaft stiffness may account for
more than a 14% reduction of gear effect, noted clubfitter Dana Upshaw
cited some anecdotal
experience in 2005. Going to a much more flexible tip shaft helped
two of his clients get lower backspin and hence more distance from their drivers. (Not a study,
no controls, so completely anecdotal.) If true, this might be used in
clubfitting. But Upshaw acknowledges that it only works with a very
consistent swing with an upwards angle of attack and impact above the
center of the clubface; other impacts will be hurt, not helped.

Conclusions
A
shaft is a string at impact!
That means that, during the less than a half millisecond of impact,
there is nothing your hands can do at the grip that would produce a
different ball flight than if the shaft had just been a string. Any
strength you want to exert on the clubhead needs to be done during the
downswing; there is nothing you can do to help during impact. And shaft
fitting is about letting your swing provide the best position and
velocity to the clubhead as it enters impact  and nothing about what
happens during impact.
This article explored the limitations of that statement, and there are
a couple of limitations:
 The statement is mostly true for a center strike. But even there,
the shaft can have a small effect. It is still a string, but a string
with mass. Part of the mass of the shaft tip participates in the
momentum transfer of impact, as part of the clubhead. But it is only
about the amount of shaft that is firmly bonded into the hosel. No big
surprise there, if you have thought about it at all.
 On an offcenter hit, the clubhead wants to rotate as well as
simply slow down. Such rotation adds gear effect to the spin, and
reduces the ball speed compared to a center impact. If the shaft were
truly a string at impact, the only limit to clubhead rotation would be
the moment of inertia of the clubhead itself. The shaft is indeed
stringlike for clubhead rotation that requires the shaft to twist
around its own axis. But that part of the rotation that requires the
shaft to flex along its axis is somewhat limited by the tip stiffness
of the shaft. To that extent, there may be some implications for shaft
fitting  but if so, any use of it requires a golfer who already has
good and very consistent impact.
Acknowledgments
I would like to acknowledge very helpful comments from several
reviewers of the first draft: Erik Henrikson, Jay Messner, Russ Ryden,
and Don Johnson . Thanks for your help.
Last
modified
02/04/2022
