Driver Head Weight and Club Length
Dave Tutelman  October 28, 2012
Variable Club Length
In
the constantlength studies above, the club's feel  its "heft" 
varied considerably as we changed the head weight. One of the problems
this produced is that the gains are limited by the torquevelocity
curve. But suppose we could use a lighter head, but still preserve the
"heft" of the club, the load it presents to the golfer. (Heft is
normally measured by swingweight or moment of inertia of the club.) If
we can do this, we might be able to keep the angular velocity profile
the same from club to club, and not incur additional losses to
torquevelocity.
There are
other
ways to use a lighter head to get more clubhead speed, while not losing
heft. An obvious one is, lengthen
the
club itself as the head gets lighter.
This not only utilizes the light head, but provides a longer radius. If
we can keep the angular velocity up, the longer radius itself should
give higher clubhead speed. And indeed it works that way.
Bernie Baymiller's assertions
Bernie Baymiller, a clubfitter in a retirement community, has often
held forth on how older golfers can regain lost distance by using a
longer driver. His assertion is that a longer driver, together with a
lighter head and shaft so the swingweight doesn't overwhelm the golfer,
gives a substantial increase in distance. His estimate is 2530 yards
for himself, at age 75 when he wrote about it.
Posted to ShopTalk, March 22, 2009:
Why mess around with the short clubs when you can go to 48" club
length? A 193 gram BOM plugged to 1½" bore depth with a 58 gram Pure
Energy A (about 55 trimmed) and 43 gram Winn Excel midsize comes in at
about 296 grams and D9. If I can swing that at 75, so can you. It's
worth 25 to 30 yards beyond what I get with a 45" driver and I seldom
miss a fairway with it. (Of course, I'm seldom over 260 yards with it
anymore.)
Bernie is writing to clubmakers here. For those of you who are not:
 BOM
is a component driver clubhead, the BangOMatic
from Bang Golf.
 Pure
Energy A is the Pure
Energy shaft from SK Fiber shafts, in an "A" flex.
 Winn
Excel midsize is a grip.
 D9
is a swingweight. (It is a much
heavier swingweight than the driver I built.)
This is a huge gain! It works out to 810 yards per inch. Bernie has
cited a number like
that recently, but I am unable to find the post at the moment. If I run
across it, I will add the quote to this article.
The rest of the article will be spent in trying to quantify the gain,
to test Baymiller's assertion.
Simplistic first cut
Before we get down to serious studies, let's take
a very simplistic
first cut at the maximum yardage that might be gained by extra length.
As with most
of this article, we are comparing a typical 45inch driver with a
maximumlength 48inch driver, in the hands of someone who can swing
the 45" driver at 100mph clubhead speed.
Let's assume that golfer can swing some ideal
48" driver with the
same angular velocity as his best 45" driver. That is really the best
we could expect from a longer driver, and it is easy to estimate the
extra distance this might generate. Physics tells us (actually not even
physics,
but geometry) that the clubhead speed due to angular velocity
is:
clubhead speed
= angular velocity * club length
So if we change the length, the clubhead speed due to the same angular
velocity should change in exact proportion to the length. Increase the
length 5%, and the clubhead speed increases 5%.
But wait! The hands are also moving forward, adding to clubhead speed.
Studies have shown that, with a good swing and centrifugal release, the
hands are moving at impact at about a fifth of the total clubhead
speed. We have no reason to expect the hands to speed up with a longer
driver. In fact, they will probably slow down. But, since we're doing
an optimistic estimate of the maximum gain, let's assume the same hand
speed for the 45" driver and the 48" driver.
With the 45" driver at 100mph, the hand speed is 20mph and the speed
due to angular velocity is 80mph. Let's see what increasing that
80mph proportional to the length would give us.
80 * 48/45 + 20
= 105.3mph
That's an extra 5.3mph, which gives us an extra 16 yards.
So
the most our golfer could expect from an extra 3" of driver length is
16 yards,
using some very optimistic assumptions. We assumed no loss of either
angular velocity nor hand speed from the longer driver. It is very hard
to believe that gains in excess of this number can be due to physics.
Now let's see
what experience and a more exact model give us.

Another computer study
Let's
repeat the computer study, using a longer shaft as well as lighter head
weight. We will use the same 45" club with a 200g head and swing
it with the same SwingPerfect model, but
adjust the length as the head weight changes. We will change length and
weight so
that we keep the same wholeclub moment of inertia (MOI) the same.^{[3]}
The table below has the results of the computer study. A few points
about the table:
 Obviously, we added a 'length' column. The length is computed to
keep the club MOI constant as the head weight changes. We use the same
65g shaft weight for all the rows of the table.
 The clubhead loft is computed as follows:
 Start with the dynamic loft that TrajectoWare Drive says you
need for maximum carry distance, at the clubhead speed computed in
SwingPerfect.
 Subtract 2º, assuming we get an additional 2º of loft from
shaft bend. (We made this same assumption in the constantlength study.)
 If this one does not make sense to you, look below where we
discuss wrist angle. Add 82% of the wrist
angle, which contributes to the loft.
(Positive wrist angle subtracts loft from the club.) Wrist angle occurs
in the swing plane, which is about 55º for a driver. Because the plane
is not vertical, the wrist angle contributes to both loft and clubface
closure, in the proportion of the sine to the cosine of the swing
plane. Sin(55º) is about 82%, so we want to add 0.82 of the wrist angle
to the club loft. Cosine(55º) is about 57%, which represents the angle
the face is open at impact.
 The
upper rows are shaded in red because they represent
nonconforming clubs. The USGA and R&A rules limit the club length
to 48". This corresponds to a clubhead weight of 173 grams. I included
the extra rows to get a better picture of the trend, but you can't
build those drivers. Even if they were not illegal clubs, it would be
hard to find shafts long enough to build them over 50 inches.
Head
weight 
Length 
Clubhead
speed 
Ball
speed 
Carry
distance

Wrist
angle 
Clubhead
loft

100

60.74

134.0

166

270

20

23.4

110

58.39

128.8

164

267

17.8

22.3

120

56.29

124.1

162

263

15.9

20.4

130

54.40

120.1

160

260

13.1

18.8

140

52.69

116.4

158

256

10.8

17.2

150

51.14

112.9

155

252

9.0

16.2

160 
49.71

109.8

153

248

6.7

14.5

170 
48.39

106.9

151

243

5.4

13.9

180 
47.18

104.4

149

240

3.2

13.3

190 
46.05

102.0

147

236

1.0

10.5

200 
45.00

99.6

145

232

0.1

10.2

210 
44.02

97.6

143

229

2.0

8.9

Given

Computed
to give
constant MOI

From
SwingPerfect

From
TrajectoWare
Drive

From
TrajectoWare
Drive 
From
SwingPerfect 
Optimum
loft
 shaft bend
+ .8*wrist angle

The result is a somewhat greater increase of distance than if the club
length were held constant, but not as great as Baymiller claims.
 Baymiller claims 2530 yards in going from a 45" driver to a 48"
driver.
 The table above shows a gain of about 10 yards going from 45" to
48". (This is less than the simplistic/optimistic calculation we did
earlier: 10yd vs 16yd.)
 As a side comment we will get back to later, a constantlength
driver shows a gain of 5 yards with just the
change of head weight
required to go from 45" to 48". (That is, a 45" driver where all we do
is change the head weight from 200g to 173g. We know this from the first computer study
above.)
Tuning Out Wrist Angle
The base swing for our computer models was tuned
for a perfectly flat
wrist at impact (zero degrees). When we go to a longer or shorter
club, the same swing gives a substantial wrist angle at impact: almost
5º for a 48" driver with the same MOI as our 45" driver. What this
means to the clubface is shown in the figure to the right.
 A flat wrist (the yellow shaft line) has the clubface
pointing at the target.
 If the wrists are bowed, the hands are leading the club
(the red shaft line). That corresponds to a positive wrist angle in our
model. Because the swing plane is not vertical, the consequence is that
the clubface is pointing down and to the right. The more the wrist
angle, the more the clubface points down and right.
 Conversely, a cupped wrist with the clubhead leading the
hands (the green shaft line) leaves the clubface pointing up and to the
left.
In other words, the longer driver with the positive wrist angle has the
club (a) delofted and (b) open. The amount is given by:
deloft =
wrist angle * sine (swing plane angle)
open =
wrist angle * cosine (swing plane angle)
A driver typically has a swing plane angle of about 55º at impact, so
(checking the sine and cosine of 55º) each degree of wrist angle
delofts the club about 0.82º and opens the face about 0.57º.
Example: with
the maximumlength minimumweight driver (173g at 48"), there is a 4º
wrist angle still left at impact. The result is a loft
reduction of 3.3º and an open
face of 2.3º.
So
how can we hit drives at the target and with the right trajectory?
Baymiller has said
that you have to learn to time the release  specifically, start the
release earlier (e.g., add wrist torque)  to
square up the club.^{[4]}
I looked at what that would involve, using two
different approaches:
 Add a constant
wrist
torque to the torque we use at the end.
The constant wrist torque to remove the wrist angle is 0.7 footpounds.
This is, in essence, is what Baymiller has recommended.
When you do that, the clubhead speed drops from 106.2mph to 104.3mph.
 Start the 3.9
footpound torque earlier than 200msec.
You have to start the wrist torque at 160msec to remove the wrist
angle. When you do that, the clubhead speed drops from 106.2mph to
104.2mph, a similar loss of distance.
Either way, using the wrists to force the release costs clubhead speed.
But there is a better approach. Accept the wrist angle, and do what is
necessary to live with it. In other words, build the driver with
increased loft and strengthen
your grip, so your normal swing hits the ball with the proper clubface
position. Not only does this solve the problem with no loss of clubhead
speed, it also doesn't require learning a new swing. All you have to
learn is how much you need to strengthen your grip. That is a static
(positional) change rather than a dynamic (swing) change, and therefore
easier to learn. 
A few more computer studies
One question that immediately comes to mind is how distance varies with
head weight at the longest allowable
driver length, 48 inches. If a longer driver gives more
distance, then what is the most distance we could possibly get from a
longer driver?
We already did
this at 45",
the conventional driver length. Let's run through it again, at 48
inches, just for fun. For this study, we're not
going to bother keeping track of wrist angle or loft; we just want to
see how much of the distance gain is due to the longer club and how
much to the lighter clubhead.
Head
weight 
Length 
Clubhead
speed 
Ball
speed 
Carry
distance

100

48"

124.5

154

247

110

48" 
121.4

154

248

120

48" 
118.8

155

249

130

48" 
116.1

154

249

140

48" 
113.6

154

248

150

48" 
111.2

153

247

160

48" 
108.9

152

245

170

48" 
106.8

151

243

180

48" 
104.9

150

242

190

48" 
102.8

148

239

200 
48" 
100.9 
147

236

210 
48" 
99.1

146

233

Given

Maximum
legal
length

From
SwingPerfect

From
TrajectoWare
Drive

From
TrajectoWare
Drive 
The maximumlength driver shows a maximum distance at a head weight of
125g. That is remarkably similar to the 45" constantlength driver,
with a maximum at 130g. The maximum distance here is a longer distance:
248yd rather than 243yd
at 45". The extra 3 inches is worth 5 yards. Not a lot but worth going
after, all other things being equal. (However, try to find a driver
head weighing 125 or 130 grams. They are not made.)
Just for completeness, let's see what happens when you change club
length and leave the head weight the same. Again, we are ignoring wrist
angle and loft, to be solved the same way we did above. And again, we
have marked in red the nonconforming driver lengths.
Head
weight 
Length 
Clubhead
speed 
Ball
speed 
Carry
distance

200

60.74

104.7

153

247

200

58.39

104.1

152

246

200

56.29

103.5

151

244

200

54.40

103.2

150

243

200

52.69

102.6

149

241

200

51.14

102.2

149

240

200 
49.71

101.6

148

238

200 
48.39

101.2

147

237

200 
47.18

100.6

146

235

200 
46.05

100.2

146

234

200 
45.00 
99.6 
145 
232

200 
44.02

99.2

144 
231

Given

Lengths
are
the constant
MOI lengths

From
SwingPerfect

From
TrajectoWare
Drive

From
TrajectoWare
Drive 
Comparison
At the
right is a graph of several studies. They are:
 Bernie
Baymiller's claim for a long driver. Actually, that is an
overstatement on a number of counts.^{[5]}
But it is the best representation I can come up with for Baymiller's
assertions, for purposes of comparing them with the other studies.
 The computer simulation above, where the club gets longer
as the head gets
lighter, to keep a constant moment of
inertia.
 A rerun of the previous study, where the club length was kept
constant at 45" as the head weight was varied.
 The study where the club length was
varied
while the clubhead weight was kept at a constant 200g. (The horizontal
axis here is not the actual weight, but the weight a club that length would have been at constant MOI.
The point is to separate out the effect of length alone, on this
multicurve graph.)
 The dotted red curve is the sum of the gains from varying just the head weight (the green
curve) and varying just the
length (the blue curve).
The
shaded red area called the "Forbidden Zone" is the area where the
club length would be over 48", and thus forbidden under the Rules of
Golf. I extended the curves well into this zone to see if there were
any apparent maxima: there was for constant length at 130 grams, but
all the variedlength curves show no sign of flattening out.
Here are some things we learn from this graph:
 None of the models comes close to Bernie Baymiller's claim
of 2530 additional yards going from a 45" driver to a 48" driver. The
constantMOI comes closest at 10 yards, less than half
the gain Bernie
reports.
 Look at the gain from varying both length and head weight
to maintain constant MOI (the red curve). For conforming drivers
(outside the forbidden zone), it is almost the same as the composite of
the constant head weight (blue) and constant length (green) curves (the
composite is the dotted red
curve). The difference between them is only a yard, and we rounded
carry
distance to the nearest yard. So the gains appear to be
additive;
add
the gain from lengthening the club to the gain from lightening the
head, and you get the gain from doing both at the same time. (They get
further apart below 160g, but those drivers are distinctly
nonconforming.)
 When
viewed that way (additive gains), it is interesting to
note that lightening the head (the green curve) contributes slightly
more gain than lengthening the club (the blue curve). That is not what
I
would have expected, and certainly not what Baymiller would have
expected. He believes that the longer club is the secret; this curve
says that lightening the head to keep the longer club at the same heft
is even more important.
It
is worth noting that the computer studies of variablelength drivers
does not include the torquevelocity curve. The most important of the
studies is the variablelength, constantMOI curve, and in that one the
extra length balances out the lighter head so they have the same heft.
The result is that the angular velocity is fairly similar for the
different weightlength combinations; therefore, accounting for
torquevelocity should not make much difference.

Last updated
Jan 16, 2013
