Mike's questions  Part 2:
How Much Distance are You Leaving Out There?
Dave Tutelman  December 27, 2014
This work was instigated by a couple
of
questions asked by Mike Stachura. He wanted to know how many yards of
driving distance you get for every mile per hour of clubhead speed, and
also how many extra yards of driving distance could a golfer pick up
without increasing clubhead speed.
Mike's second question is, How
much driving distance does the average golfer "leave on
the table", assuming his/her clubhead speed is what it is and won't
increase?
Here is a bit of further explanation of what is behind his questions,
excerpted from another email.
The search to define human potential may be the ultimate
fool's errand (especially for golfers), but I think if I can get there
(or close to an answer), I'm going to educate golfers and put them in a
position to succeed in dramatic new ways. I think your work is helping
me take a big step in that direction. I'm sure I'll have more
questions, so I hope you won't mind me pressing you further as things
come up.
Assumptions and
approach
Answering the second question requires flipping the whole approach from
the
first question on its head. For the first question, we
assumed away or
defined away everything except the clubhead speed, and saw what
clubhead speed does for driving distance. Now we have to do just the
opposite: define the clubhead speed as constant, and see the effect we
get from everything else.
In discussions with Mike, we clarified the ground rules of the
question. Remember, the spirit of the question is, "I can't change my
clubhead speed, but anything else within the Rule of Golf is fair game.
 Changing parameters of the club within the rules is
allowed. Your driver may may fit you poorly, or it may just
not have all the technological improvements up to date.
 Learning to do things better with your swing is allowed,
though we will rule clubhead speed improvements to be out of
bounds. Yes, that's arbitrary, but not necessarily a bad idea.
We will find some things to work on that could help more than a couple
of MPH of clubhead speed. And sometimes working on speed distracts us
from these other distanceimportant skills.
We will assume a few things, but not nearly as many as for question #1.
 We have a relatively modern driver and ball. They combine
for a coefficient of restitution (COR) of 0.83.
 The same plain vanilla ambient conditions as for question
#1: temperature 80ºF, sea
level, no wind, flat fairway, no elevation of tee box, etc.
Here are the things we will investigate:
 Better contact on the clubface. (Learning and Equipment)
 Proper clubhead loft (Equipment)
 Raise the angle of attack. (Learning)
 Lower the center of gravity of the clubhead. (Equipment)
 Hit the ball above the center of the face. (Learning)
For each, we will see how much distance we stand to gain.
Unfortunately, the tool that I use for most of this study only computes
carry distance. So we will see how much carry distance we might gain,
but not total distance. At the end, I will give some qualitative feel
for total distance, but I'm afraid I don't know enough to quantify it
right now. If and when I know more, I will update the article.
This is an investigation of things
we can do to improve distance without increasing clubhead speed. So we
will have to pick a clubhead speed. Since I have computed the graph for
a launch space at an 86mph clubhead speed, that is what we will use. I
would expect the gains at different clubhead speeds to be sort of
proportional to the ones we find, but that is just a guess. We would
have to construct the launch space for that speed and go through the
drill to really know.
Let's go through the five areas of improvement described above, and see
how much yardage we leave on the table.
1  Better
contact on the clubface
One of Mike's emails said:
Through our own research and input from dozens of fitters, we have the
launch conditions of 150 random golfers (we didn't ask if they had been
through a fitting on their driver). I think the vast majority of
average golfers hit it shorter than optimal, and that is in fact the
theme of an article I'm trying to write and hoping to prove with this
experiment.
Unfortunately, I'm having a hard time finding a way to explicitly
quantify just how short we might be. Maybe most telling in that data is
that the average smash factor is only 1.41.
The average spin rate was only
about
3000, but the high was 6,000 and the low was 1,100. More than half were
over 3,000, a number most equipment companies are advising all golfers
stay under (Practical? Possible? I don¹t know). Average launch angle
was
12, but a third were under 11 and only 30 were over 15.
None of these
subsets of data is particularly indicative of a key area of failure,
although the weak Smash Factor could be nifty catchall for poor
instruction and illfitting drivers.
We will start with smash
factor.
As Mike notes, this could be due to poor instruction or an illfitting
driver  or both. First let's quantify the damage, then we'll think
about the cause.
If our 86mph golfer has the average golfer's smash factor of 1.41, that
means that they are leaving
12 yards on
the table.
How did I come up with that number? Remember the answer to
question #1 included the fact that you get 2 yards of
increased carry distance for every MPH of increased ball speed. Let's
do the
calculations:
BallSpeed =
ClubheadSpeed * SmashFactor
So let's figure ball speed for the ideal smash factor of 1.48, and
again for our golfer's smash factor of 1.41.
BallSpeed =
86 * 1.48 = 127.28
BallSpeed
= 86 * 1.41 = 121.26
That
is 6mph we are losing because of imperfect ball contact. At 2 yards for
each MPH, a loss of 6mph is a loss of 12 yards of carry distance.
(Notice how easy it is if we are just looking at gains and losses. We
don't even have to worry about the yintercept, just the slope.)
Let
me take a moment to discuss Mike's survey result of a 1.41 smash
factor. Here are some clubfaces showing impact marks, reported by Tom
Stickney II in a January 2014 GolfWRX article "Impact
location by handicap" .
From
experience, I would guess that the Tour Pro has close to a 1.48 smash
factor, and the 7 handicap somewhere in the mid to low 1.4 range. I
would be surprised if the 15 handicap is over 1.30. At a 1.30 smash
factor, the yardage loss is more like 30 yards. That is a lot!
Causes and cures
A poor smash factor comes from imperfect contact between ball and
clubface. This could be a combination of an offcenter strike or the
clubface not being square with the clubhead path. Either way, you will
lose ball speed and distance. And either way, it might be your swing or
your driver. In fact, a poorly fit club can even be the root cause of a
poor swing  a swing that compensates for the club's deficiencies.
So
the first step to finding these 12 lost yards is to get a driver that
fits you. Not necessarily the latest in technology (we'll get to that
later), but one that you can swing well enough to repeat your swing
consistently and square the clubface to the path.
Once you have
that, you can learn to make that consistent contact on the sweet spot
so you don't lose distance. Consistency has to come first, then learn where to apply the
clubface. I have stories about that sequence, one about learning and
one about clubs.
Learning
to hit the sweet spot: John Ford of The Golf Institute in
Lady Lake FL is a friend whose business is
clubfitting, but who gives lessons along with the fitting. (Many good
clubfitters measure for the best the golfer can do, and that involves
instruction during the fitting.) His specialty is not changing the
swing, but rather encouraging whatever swing that golfer can repeat,
then teaching him/her how to hit the sweet spot consistently with that
swing. He tells me, "Dave, I do it every day." I use a variant of his
approach, and
it works for me.
How does John teach golfers to hit the sweet spot consistently? There
are three requirements: a consistent swing, a setup that leaves you a
consistent distance from the ball, and a finetuning of that distance
so that your
swing gets the sweet spot. John's approach to each requirement:
 Consistent
swing: John doesn't try to tinker with your swing.
Instead, he custombuilds clubs to you that fit the swing you have and
are comfortable making. No compensations in the swing to allow for
clubs that don't quite fit it. That means it is easy to make the same
swing every time. It may not be the most powerful nor efficient swing,
but it is consistent enough to begin the search for a high smash factor.
 Repeatable
impact: If you have a consistent swing, you should make
consistent impact, right? Well, almost right. If you always set up the
same distance from the ball and always make the same swing, the impact
should be consistent. During the final fitting and testing of the
clubs, John teaches a preshot routine, a setup technique, that assures
you are the the same distance from the ball every time. (This is
subject, of course, to the length of the club; the routine accounts for
different club lengths.) Then he checks the consistency using impact
tape, making sure the impacts are at the same spot on the clubface.
 Centered impact:
We're still not there, but the hard part is done. Not everybody has a
swing where the clubhead at impact is in the same position it was at
address. In fact, such swings are relatively rare among golfers in
general. Suppose you set up with the ball perfectly centered at
address, but always hit the ball a half inch toward the toe. (That
happens to be the most common pattern among mid and highhandicap
golfers.) John has found you can fix this by setting up consistently,
but with the ball a half inch toward the heel, to allow for the
towardthetoe impact. The result is a centerface strike.
John has a
patent (No. 6,471,599, Oct 2002) on a clubhead to aid this process. His
custom clubs have a head with a row of recessed dots in
the topline, shown in the illustration. If the impact tape
in step #2 shows that impact is N dots in one direction on the
clubface, John puts a drop of red paint in the recess N dots in the
other
direction. For instance, if you are hitting 2 dots toward the toe, he
will put paint
2 dots toward the heel, and teach you to set up with the ball opposite
the dot (instead of centered in the clubface). It works very well.

Clubs
that make it hard to hit the sweet spot: I did a study
a few years ago focused on how much extra distance is available by
using a longer driver. I started with a survey of papers in the
field, and did some computer modeling myself. I looked at anecdotes
from clubfitters, and even interviewed a couple of longdrive
competitors. There was a considerable
disparity in the results of these studies, almost as much disagreement
as
agreement.
In the interest of bringing some unity to the conclusions, I experimented with long
drivers myself.
I needed to in order to decide which conflicting data and anecdotes to
believe. I concluded that a common and important theme is that extra
length (which has become the
norm in commercial drivers these days) plays havoc with smash factor.
You will probably hit the occasional big drive, as much as 1012 yards
further than you are used to. But unless you are wellfit to a long
club, or practice a lot to learn to hit the sweet spot, you will lose
distance on average because of lousy smash factor. Here is some
representative data from FlightScope tests I did with my own clubs and
swing.
This
scatter plot shows clubhead speed vs ball speed for a number of swings.
As all studies predicted, the longer driver develops more clubhead
speed than the shorter one. In spite of the increased clubhead speed, I
got lower ball speed  which means less distance. 
If
anybody wonders about the reason for the drop in ball speed, here are
the
impact tapes from the faces of the drivers. Any questions?

I was
having a bad swing day when we did the tests. None of the drives, with
either club, equaled Mike's average smash factor of 1.41. But even on a
good swing day, I only get a few
drives from the longer driver with noticeably more distance than the
shorter driver. And I lose distance on average.
In fact, I have found that the long driver is a better training aid
than golf club. If I play a round with the long driver, the following round
(with the shorter driver) is usually a very good driving day, both more
consistent and longer than usual. 
Potential gain
By all means, the most
productive thing most golfers can do to gain distance is to improve
their impact between ball and clubface. If you have the average random
golfer's smash factor of 1.41 with your driver, you can pick up 12
yards from smash factor alone. If your smash factor is worse, you can
pick up more.
What
we did 
Carry distance 
Improvement 
Baseline 
 
0 
Improve
impact 
 
+12
yd 

Launch space
The rest of the improvements we will
work on require improving the launch angle and spin. To evaluate that,
we need to become familiar with a
graph I call "launch space". We will use this tool for most of the
distance gain evaluations. I am borrowing here a tutorial on launch
space from another
of my articles.
Launch
space is the threedimensional graph of distance vs both launch
angle and spin.
A launch space is a graph for a specific ball speed. But it
could also be for a specific clubhead speed if we assume a smash
factor.^{[1]}
For this study, we will be working with a clubhead speed of 86mph with
a nearly
ideal smash factor of 1.47. Why? Because launch space graphs are a lot
of work to construct, and I had one lying around for 86mph.
The launch space graph (shown here) is threedimensional, with launch
angle and spin being the horizontal axes and distance the vertical
axis. We need it to answer Mike's question because  except for very
fundamental stuff like hitting the ball with the clubface  any
distance gain we hope to make will happen by changing launch angle and
spin. The launch space
graph tells us what any change of launch angle and spin will do to
distance, which is exactly what we need for this work.
So let's explore what a typical launch space looks like.
As conventional wisdom leads us to expect, the highest point on
the graph is where the launch angle is highest and the spin is lowest.
But the converse is not true; the low point of the graph is not the
opposite corner, of low
launch and high spin. Rather, it is the "off corners", at high launch
and spin, and low
launch and spin. There is a diagonal "ridge" of fairly high distance,
and falling off the ridge on either side loses distance much faster
than simply climbing down along the ridge. This is perhaps better seen
in a
twodimensional colorcoded map of the graph, so let's look at that. 
The colors denote classes of distance as they move through the rainbow:
red for long distance and purple for short drives. we can see the ridge
 the black dotted line  that goes from highlaunch/lowspin down to
lowlaunch/highspin. The distance changes rather slowly as you move
along the ridge, but falls off rapidly on either side. That is why it
is called a ridge.
As we look for ways to get
more distance, we will become very familiar with this launch space.

2  Proper clubhead loft
This
typical golfer of ours... what kind of driver does he use? It's
probably a brand name driver bought offtheshelf, with the most common
loft of 10.5º. Is this the right loft, the best loft for distance? We
can use the launch space graph to find out.
Let's start by mapping a driver onto the launch space? We
start by mapping just the dynamic loft at the given clubhead speed of
86mph,
keeping everything else neutral. Using
TrajectoWare Drive, we get the following points on the line:
Dynamic
loft 
Launch
angle 
Backspin 
8º 
7.2º 
1915 
10º 
8.9º 
2389 
12º 
10.5º 
2861 
14º 
12.0º 
3329 
16º 
13.5º 
3793 
18º 
15º 
4252 
20º 
16.4º 
4706 
22º 
17.7º 
5155 
The
result is a line, the locus of the lofts in launch space. In the launch
space graph below, the red balls
are labeled with the loft they represent, from 8º to 22º. Each loft is
placed at the launch angle and spin produced by the driver. You can
read the distance from the nearby cells in the launch space map. For
instance, 14º gives a carry distance of 188 yards, and 18º about 185
yards.
The
important thing to note here is that varying the loft
changes both launch angle and spin in
the same direction.
An increase in loft increases both launch angle and spin. Therefore,
the line of possible lofts crosses
the ridge almost at a right angle.
It isn't anything like parallel to the ridge; just the opposite, in
fact. There is no opportunity here to move along the ridge  to
increase distance by playing
with increased launch and decreased spin.
If
we were to use loft alone to optimize the driver, we would choose the
point where the locus of lofts intersects the ridge of maximum
distance. For this golfer  who swings at 86mph, remember  we would
use a loft of 15º, giving a carry distance of 189 yards.
Details of the cure
A
lot of optimization
efforts stop here, and it's not a bad place to stop. Already, it
probably suggests more loft than the player is using; that has been my
experience, and it will tack on a few yards. But we won't stop here; we
want to see how
much distance we can wring out of proper club choice and a bit of
fiddling with the swing.
Before we go any further, we need to know what the golfer is
actually
doing at impact. We assume a zero angle of attack (so far, anyway). But
there are other factors that go into dynamic loft, which is the loft
the ball sees at impact. Remember, the ball doesn't know what club you
used, or how good a swing you made. All it knows is what the clubhead
is doing at impact. So let's list the things that could affect the
dynamic loft:
 The
loft of the clubhead. That may or may not be the actual loft stamped on
the sole; there is such a thing as a "vanity loft", a loft labeled
stronger than it really is so the owner can feel macho and still hit a
decent drive. The loft we need to optimize distance is the real loft.
 The angle of attack, of course. But (so far) we are
assuming it is zero.
 Shaft
bend. This might add a few degrees to the dynamic loft, depending on
the swing and the shaft flex. In most cases, it adds about 2º.
 Wrist position. A cupped or bowed wrist at impact usually
has more effect on AoA than on loft, but it can have some effect on
loft.
So our average golfer is using a 10.5º driver. Let's
assume that the shaft bend adds 2º to the dynamic loft, and the other
effects are negligible. So the effective loft of the driver at impact
is 12.5º.
The launch space tells us we need a loft of
15º, and that includes the 2º bend of the shaft. So we need a 13º
driver head.
Potential gain
We are going from a dynamic
loft of 12.5º to 15º. Find where 12.5º would be on the launch space
graph; it is 1/4 of the way from the 12º circle to the 14º circle. That
would correspond to a carry distance of about 183 yards. And we already
know that the optimum loft of 15º gives a carry distance of 189 yards.
So we have gained another 6 yards.
Here are the gains so far.
What
we did 
Carry distance
(yards) 
Improvement
(yards) 
Cumulative
improvement 
Baseline 
171 
0 
0 
Improve
impact 
183 
+12 
+12 
Fit
the right loft 
189 
+6 
+18 
Let's keep going with our improvement
program. The gains will be smaller and harder to come by, but they are
there.
3  Raise the
angle of attack
It is generally known that a
higher angle of attack can be used to lower spin and/or raise the
launch angle  which is exactly what we want to do to increase
distance. At this point in the optimization, we need both increased
launch and decreased spin; fiddling with the loft can only give us one
at the expense of the other. So let's try for a modest gain.
Suppose I could improve my AoA by 2º, from 0º to +2º, with no loss of
speed nor reliability. With enough instruction and practice, that might
be achievable by our typical golfer. I know teaching pros who can vary
AoA at will from 5º to +5º. But we're talking about the typical golfer
here; an additional 2º is enough of a challenge.
Let's
see what this would mean in launch
space. Adding
2º to AoA increases the launch angle by 2º with no change in spin. So
it moves us to the right in launch space by 2º. Let's show this in
launch space; we will move the driver dots 2º to the right.
In the launch space diagram, I have moved the driver lofts 2º to
the right. I left in the old lofts as pink "ghosts", so we can see
where we were before.
Now the maximum distace occurs at a 14º
dynamic loft, down 1º from before. The distance achieved is 193 yards,
a gain of 4 yards.
Here is something worth noting. The additional angle of attack can be
used either of two ways, or a combination:
 Increase the launch angle by the angle of attack, with no
spin penalty.
 Decrease the loft, and get the same launch angle with a
lower spin.
 A combination, splitting the difference between a small
increase of launch angle and a small decrease in spin.
In
this case, the best choice was a combination. We increased the AoA by
2º and decreased the loft by only one of those degrees. We know it was
the best choice not because we tried both; we looked at the launch
space and the optimum was visually apparent.
Potential gain
The
increase of 2º in Attack Angle was split between increasing the launch
angle and lowering spin. The result was a 4yard gain in carry distance.
Here are the gains so far.
What
we did 
Carry distance
(yards) 
Improvement
(yards) 
Cumulative
improvement 
Baseline 
171 
 
0 
Improve
impact 
183 
+12 
+12 
Fit
the right loft 
189 
+6 
+18 
Increase
attack angle 2º 
193 
+4 
+22 
Gear effect
There
is one more thing to play with here, and that is vertical gear
effect. Here's a quick primer, in case you don't know what that is.
When
the clubhead strikes the ball, the clubhead and ball exert large forces
on one another; the force could easily be 2000 pounds. If the impact
force goes through the center of gravity (CG) of the clubhead, then the
clubhead glides through impact without being thrown off course.
But
suppose the force is above the CG, as the picture shows? That applies a
torque to the clubhead, wanting to rotate the head around the CG to a
face up
position. And it does
rotate
the head (the purple arrow), because the forces are briefly so much
greater than the shaft's ability to resist them.
With the ball compressed on the clubface, the
clubhead and ball are like two gears engaged together. So
the counterclockwise (in the diagram) rotation of the
clubhead
will cause
a clockwise rotation of the ball. That is topspin. There is not enough
topspin from gear effect to completely overcome the backspin due to the
loft of the clubhead. But the backspin can be considerably reduced by
the gear effect topspin.
Conversely, if impact is low on the
clubface, the ball will start its flight with even more backspin than
the loft supplies. Again, there is gear effect, but the clubhead
rotates face down and the gear effect applies
additional backspin.
The amount of the gear effect depends
mostly on where the impact force is compared to the center of gravity.
The more above the CG the force is, the more the gear effect topspin 
thus the smaller the net backspin the ball has. Other things that
figure into the gear effect spin are:
 Exact position of the CG.
 Moment of inertia of the clubhead.
 Clubhead speed at impact.
If you want more detail on gear effect, including the math involved,
see my article
on the subject.
So what?
How does gear
effect get me more distance?
Now we know that it can reduce backspin. And we know from the launch
space that reducing backspin without reducing launch angle can be used
to move along the ridge of maximum distance. So let's explore two ways
we can get gear effect topspin, and see what they do for us:
 Build more gear effect into the driver 
specifically, lower the center of gravity of the clubhead.
 Use more gear effect in your swing  specifically,
strike the ball high on the clubface.
One is equipment, the other is learned technique. We'll look at both.

4  Lower the center of
gravity of the clubhead
In early 2012, Jeff
Summitt asked me some
questions about the effect of CG placement. That led to a multipage
article that characterizes how the position of the CG
manipulates the gear effect spin. There is even an Excel spreadsheet
that you can download to calculate spin from the CG position. Let's go
through that exercise now, to see what a 0.1" lowering of the CG can do
to help us increase distance. (Jeff assures me that lowering the CG a
tenth of an inch is a real design challenge, so I'm reluctant to
evaluate a more dramatic change.)
I used the Excel spreadsheet
to quantify the gear effect spin due to moving the center of
gravity downward. No matter where on the clubface the ball was struck,
it reduced the backspin by between 410 and 430rpm. In the center of the
clubface, it reduced backspin by 427rpm.
To see how this affects
distance, we turn again to the launch space graph. This time, we move
downward in spin by 427rpm from each of the feasible loft "balls".
If
we look at the 14º loft that was best for us in the attack angle
exercise, moving the CG down actually loses a bit of distance. We were
right on the ridge of maximum distance, at 193 yards. Reducing the spin
drops us below 192 yards. But we can still use this to improve
distance; we just have to increase loft, so the decreased spin moves us
back to the ridge.
If we loft up to 15.5º or even 16º, we will get the distance up to 195
yards. That's a small gain, but still a gain.
This finding agrees with the "loft up" campaign that TaylorMade
launched to promote the SLDR driver. The SLDR lowered the center of
gravity of the clubhead. (Don't worry right now about "down and
forward" vs "down and back"; the forwardback does not produce nearly
as much spin change as just plain "down" does.) I know
people who tried the SLDR and said, "I don't know what's wrong, but I
lost distance with it. I got rid of it." When I quizzed them further,
they said, "The crazy salesman wanted me to get a 14 degree loft. I
know the right loft for me is 10.5, so I got a 10.5 SLDR." Well of course
you lost
distance. At a 10.5º loft, you're in the part of the
launch space where reduced spin hurts rather than helps. You're already
well below the ridge; moving down another 427rpm will just make matters
worse.
Potential gain
Lowering
the center of gravity by 0.1" reduced spin by over 400rpm. But that
does not help distance by itself. We had to bump up the loft to
increase the launch angle; otherwise, the decreased spin actually hurt
distance. When we combined the decreased spin with increased loft, the
result was a
2yard gain in carry distance.
Here are the gains so far.
What
we did 
Carry distance
(yards) 
Improvement
(yards) 
Cumulative
improvement 
Baseline 
171 
 
0 
Improve
impact 
183 
+12 
+12 
Fit
the right loft 
189 
+6 
+18 
Increase
attack angle 2º 
193 
+4 
+22 
Lower
CG by 0.1" 
195 
+2 
+24 
5  Hit the ball
above the center of the face
The
spin reduction we get from gear effect is proportional to how far
the impact force is above the center of gravity. There are two ways to
make this bigger: lower the center of gravity or raise the impact
point. Our improvement #4 was a club improvement, lower the CG. Now
let's look at the other side, raising the impact point.
This is
dependent on the golfer's skill, not on technologically advanced
equipment. If the golfer was able to learn to hit the center of the
face consistently, then hitting a half inch above the center of the
face should be a similar challenge, and similarly mastered. In fact, it
can be accomplished with the same swing and the ball teed a half inch
higher.
Hitting higher on the clubface gives both a spin
reduction and a launch angle increase. Here's why.
 The
spin reduction should not be surprising. We're putting more vertical
distance between the impact force and the CG, so we should get more
gear effect topspin to work against the backspin.
 The
launch angle increase is due to the fact that the clubface is
curved. The typical commercial driver has bulge (horizontal curvature)
and roll (vertical curvature). If we hit higher on the face, then we
encounter a higher loft  hence a higher launch angle.
The
diagram shows how face curvature affects loft, depending on where on
the face you hit the ball. It is clear just by looking that the lower
ball strike (the red lines) occurs at a lower loft than the higher
strike (the green lines). It may not look like much, but it is. Most
drivers are built with face roll at a 1012" radius. At an 11" radius,
a half inch of height is worth two and a half degrees of loft. The full
face height of two
inchs spans a loft difference of ten degrees of loft.
That is a lot.
As before, we will quantify the improvement by using the launch space
graph. And we will use the Excel spreadsheet
to tell us where to move in launch space. We are going to move the
impact point from the center of the clubface (the point of nominal loft
and no gear effect) to a point a half inch above it. According to the
spreadsheet, that moves us in launch space:
 2º higher launch angle. That is motion to the right
on the launch space graph.
 1100rpm less spin. That is motion downward on the
launch space graph.
Let's see what the launch space looks like. 
The
green arrows were sized and angled to move 2º right and 1100rpm down.
The tips of those arrows are what we can achieve by hitting a half inch
above center. (I am assuming that the COR of the clubface is maintained
at least ½" away from the center of the clubface. That is a reasonable
assumption with today's drivers.) Look at the arrowhead on the ridge.
It shows a carry distance of 201 yards. That is a substantial
improvement over our previous best distance. And it requires increasing
the loft at least 2º to 18º  even though we get another 2º of launch
angle just from face curvature. We need the additional loft to keep us
on the ridge.
Let's remember that this is not really an 18º
driver. It's a 16º driver head, with another 2º of dynamic loft coming
from shaft bend. But still, how many 16º driver heads do you see out
there? If we are going to "loft up", we need more clubheads available
with the necessary loft. But remember, this is carry distance.
I
believe that, once I understand total distance quantitatively,
maximizing total distance will require a somewhat lower loft. So the
optimum driver will not be quite as extreme. 
Potential gain
Raising
the impact point on the clubface by 1/2" gave us a substantial increase
in carry distance. It increased the launch angle by 2º, at the same
time it reduced spin by 1100rpm. That is huge. And the result was a
6yd gain.
Here are the gains we have managed to achieve. This is what the typical
golfer with an 86mph clubhead speed leaves on the table.
Discussion and
additional topics
If you were looking for the answer to
Mike's question, now you know. The typical golfer we chose (86mph
clubhead speed, 10.5º driver, 1.41 smash factor) is leaving 30 yards
"out there". That's 15% of his/her potential distance.
But there
are things still to be said that I find interesting, and you might
too. You can skip this part or read what grabs your attention.
Here's another version of our results table.
What
we did 
Carry
distance
(yards) 
Improvement
(percentage
of total) 
Type
of
effort 
Baseline 
171 
 
 
Improve
impact 
183 
40% 
Learning,
club fitting 
Fit
the right loft 
189 
20% 
Club
fitting 
Increase
attack angle 2º 
193 
13% 
Learning 
Lower
CG by 0.1" 
195 
7% 
Club
design 
Raise
impact on the face by 1/2" 
201 
20% 
Learning 
We
can see that the relative contributions of learning and equipment can
be anywhere from 3:1 to 1:2, depending
on their relative contributions in improving the smash factor. If
the lowerthanoptimum smash factor was due to ill fitting
clubs,
then equipment accounted for 2/3 of the improvement (40+20+7=67%). If,
on the other hand, the clubs fit reasonably and the improved smash
factor was
from learning and practice, then learning accounted for almost 3/4 of
the improvement (40+13+20=73%).
Smash
factor
Let me make a further guess 
but only a guess  that if both equipment and technique were the cause
of the poor smash factor, then the starting smash factor was lower than
1.41. The split may be closer to 50:50, but the total gain was
significantly larger. For instance, starting with a 1.30 smash factor
means that there is 30 yards to be reclaimed from smash factor alone!
In fact, let's see what the tradeoff is between clubhead speed and
smash factor. If going for more clubhead speed prevents us from getting
consistent, good impact, which is more valuable? Here's a table that
gives us the answer in plain numbers.
Clubhead
speed 
Gain
in smash factor 
0.05 
0.10 
0.15 
0.20 
0.25 
0.30 
70 
2.2 
4.4 
6.6 
8.9 
11.1 
13.3 
80 
2.5 
5.1 
7.6 
10.1 
12.7 
15.2 
90 
2.8 
5.7 
8.5 
11.4 
14.2 
17.1 
100 
3.2 
6.3 
9.5 
12.7 
15.8 
19.0 
110 
3.5 
7.0 
10.4 
13.9 
17.4 
20.9 
120 
3.8 
7.6 
11.4 
15.2 
19.0 
22.8 
This requires a little explanation, so here it is.
 The yellow numbers are your current clubhead speed in MPH.
 The blue numbers are the amount in smash factor that you
gained or lost. For instance, if you improved from 1.35 to 1.45, that
would be a gain of 0.10.
 The white numbers are MPH of clubhead speed you would need
to gain in order to get the same distance as that gain in smash factor.
Let's look at an example:
Suppose you have a clubhead speed of 100mph and a smash factor of 1.35.
(This is fairly common. In fact, it probably described me a decade
younger.) Improving your smash factor from 1.35 to 1.45 (a gain of
0.10) will
give you the same distance as if you improved your clubhead speed by
6.3mph, to more than 106mph. 6.3 is the entry in the table for clubhead speed = 100mph
and gain in smash factor
= 0.10.
A 6.3mph gain of clubhead speed is significant! It requires a lot of
work, practice, conditioning, etc. And it won't get you any more
distance than a 0.10 improvement in your smash factor!
For those interested in how we compute this, see note [3] below.
Spin,
launch angle, and loft
Here's
an observation about the last three improvements, the ones made after
we got a good smash factor and decent first approximation to the
correct loft.
 When our improvement caused an increase in
launch angle, that did not necessarily increase the distance. We had to
decrease the loft to get back to the ridge.
 When our
improvement caused a reduction in spin, that did not necessarily
increase the distance. We had to increase the loft to get back to the
ridge.
 Even our combined launch angle/spin improvement required a
loft adjustment to consolidate the maximum improvement.
The takeaway is that all these distance tweaks require getting to the ridge and staying on the ridge to maximize the gains.
Another
comment on spin and launch angle. Except for smash factor, our
improvements consisted of finding higher launch angles and/or lower
spin. But, as noted above, we had to adjust the loft to stay on the
ridge. In describing the launch tests of 150 random golfers, Mike said:
The average spin rate was only
about
3000, but the high was 6,000 and the low was 1,100. More than half were
over 3,000, a number most equipment companies are advising all golfers
stay under (Practical? Possible? I don't know). Average launch angle
was
12, but a third were under 11 and only 30 were over 15.
If you have a low launch, you
better have a high spin.
This is a case of two wrongs making a right. You'll need the spin to
stay on the ridge. Let's take an extreme example using our 86mph
golfer. By the time all
the improvements were made, the good drives launched at 19º and had
2700rpm of backspin. But if the same headspeed launched a ball at an
angle of only 10º, that same "proper" spin would not be proper at all.
The ideal spin  given that you screwed up the launch angle  would
be 3700rpm, a full 1000rpm higher, and well above the common wisdom's
rule of thumb. Here's a table of a few points, along with the launch
space
we've been working with. The purple arrows show the movement in launch
space.
What? 
Launch
angle 
Backspin 
Distance 
Best
drive for
86mph clubhead speed 
19º 
2700rpm 
201yd 
Drop
the launch to 10º,
same spin 
10º 
2700rpm 
175yd 
Fix
the spin to
optimum at 10º 
10º 
3700rpm 
183yd 
Fix
the spin instead
by changing the loft 
12º 
3400rpm 
188yd 
No,
we don't get back most of the distance we lost. But, in this case, the
very high spin helps rather than hurts. We do get back some of our lost
distance.
When someone hits some good drives, and some low drives
with much higher spin using the same club, it is almost always due to a
lowface impact. The face curvature reduces the launch angle low on the
face. Fortunately, there is gear effect. The low strike will generate
more backspin, and things won't be
quite as bad as if all you changed was launch angle.
There is
even a nice, intuitive explanation for why you want high spin if you
launch too low. A low drive wants to fall to earth fairly fast. The
spin provides lift that keeps the ball in the air as a "frozen rope",
not just a stupid low duff.
Carry vs total
yards
Mike asked his question about total distance, not carry distance. I
answered in terms of carry distance. As I said, my tools
don't give total yards, but I do have a sense of what improves the
rollout after landing. We want to decrease the angle of descent, and we
want to decrease the backspin at the point of landing. A lower loft
will help both. Here is my
heuristic. I haven't done scientific tests on it  and I probably
should  but it has produced pretty good results in practice.
When I have the driver designed for the golfer based on carry
distance, I back off to one or two degrees lower loft. That drops the
angle of descent and the final backspin, which will increase the
runout. Let's look at an example; we'll take the final optimization we
have done here for the 86mph golfer. The final loft is 18º. Let's look
at what happens there, and also at 17º and 16º.

Launch 
Landing 

Dynamic
Loft 
Launch
angle 
Spin 
Descent
angle 
Spin 
Carry
distance 
18º 
19º 
2700 
40.2º 
2000 
201 
17º 
18.2º 
2500 
37.9º 
1850 
200 
16º 
17.4º 
2250 
35.2º 
1700 
199 
So
each degree of reduced loft cuts angle of descent by two and a half
degrees and final spin by 150rpm. But we only give up a yard of carry
for each degree of reduced loft, at least this close to the optimum. That is probably a good tradeoff; we
will probably get back more than that in improved runout.
I
compared this strategy with the TrackMan data. They have separate
optimizers for total distance and carry distance^{[2]},
and I looked at how
the lofts differed between optimized carry and optimized total
distance. After looking at their data, it looks like the same strategy
would work, but be even more agressive. Back off 2º of loft at the high
speeds and as much as 4º at the low speeds. By doing that, you might
get another
1719 yards total distance, above and beyond what carry distance
optimization gives. You give up some carry distance, but gain a lot
more in runout.
Since
the TrackMan data is based on PGA Tour fairways, it includes more
runout than the fairways you probably play. I haven't worked the
problem in detail, but my intuition is that most golfers will optimize
total distance a little closer to the optimum carry conditions than the
TrackMan chart suggests. So maybe backing off from maximum carry by 12
degrees is the best strategy for most of us.
I wish I could quantify it better for you, but I can't for now. That's
on the agenda, starting with a more thorough analysis of the TrackMan
data.
Notes
 In
fact, the launch space is valid for a ball speed. In claiming we have a
launch space for a clubhead speed, we are ignoring 1 or 2 mph of change
in ball speed, due to reduction of smash factor as the loft increases.
The changes
in distance, and the movement in launch space to achieve the change, is
almost unaffected by this detail.
 TrackMan
has in the past published an optimization table for driving distance.
Two tables in fact: one for optimizing carry distance and one for total
distance. The tables, created by TrackMan's Justin Padjen, used to be
on the TrackMan
web site.
It is no longer there; the optimization function is included in the
product itself. Nevertheless, it is still available on lots of sites.
For instance, a Tom Wishon article at GolfWRX
includes both charts.

Here is how we computed the tradeoff between clubhead speed and smash
factor. Let's start by looking at the change in distance due to smash
factor. We know that smash factor affects ball speed, and now we know
how a change in ball speed affects distance (from the answer to Mike's first question).
In the algebra below "deltasomething" (shown as Δsomething) refers to the size
of a change in that something. That is common notation in algebra,
calculus, and science.
ΔVb
= (Smash1 * Vc)  (Smash2 * Vc) = ΔSmash * Vc
ΔDist
= 2 * ΔVb
Thus:
ΔDist
= 2 * ΔSmash * Vc
Similarly, the answer to Mike's
first question told us how changes in clubhead
speed affects distance
ΔDist
= 3.16 * ΔVc
In order to have a tradeoff, the ΔDist due
to ball speed must be set equal to the ΔDist
due to clubhead speed. Therefore:
2
* ΔSmash * Vc = 3.16 * ΔVc
Solving this for the change in clubhead speed, we get:
This is the formula we used for computing the cells in the table.
Last
updated  Jan 12, 2015
