Club Ruler  New vs Old
Dave
Tutelman 
December 6, 2011
As of 2004, the USGA and R&A introduced a rule specifying how
the
length of a golf club is to be measured. They did this in order to be
able to impose a maximum length to a club. When it comes
right down to it, they wanted to limit the length of drivers, as part
of their effort to control the distance that the best players hit the
ball.
This had an interesting effect on the design of shop equipment,
specifically the club ruler. There was already in place a traditional
method for measuring club length, and every clubmaking shop had a club
ruler designed to implement the traditional method. With the new method
called for in the Rules of Golf, manufacturers of clubmaking
instruments put new club rulers in their catalogs, designed to
implement the USGA/R&A rule.
The question arises: "How
different
are the measurements of the old
ruler and the new ruler?" This article answers that
question.
The short form of the answer is: generally less than 1/12" (2mm). For
more information
than that, you'll have to read the article.
The Old Way
Let's
start
with the old method of measurement. Here is a picture from an article
by Jeff Summitt at the Hireko web site
showing the traditional way. The length was measured along the
shaft, from the floor to the butt of the grip, with the head level.
That meant that the angle of the shaft (and the angle of the ruler) was
the lie angle of the club.
Instrument makers built their club rulers to this method. The example
shown
below is from GolfMechanix,
and is typical of a pre2004 club ruler. The shaft of the club lies
along the ruler, and the sole of the clubhead presses against a hinged
stop. The angle of the stop is adjusted so that it equals the lie
angle. With the sole resting against a stop set at the lie angle, the
geometry is exactly the same as the diagram to the left. The length
measured
along the ruler is the length of the club.


The New Way
Now
along come the rulemakers, who want to put a limit on the maximum
length of a driver. Being experienced rulemakers, they don't want any
loopholes, any way to "game" the rules. And one way to game
the
rules is to lie about the lie  that is, to assure that the lie angle as
measured
is very different from the lie angle as
played.
This is easy to do for a driver. Consider:
 Lie measurement is usually taken assuming that the
scorelines on the face are perfectly horizontal at address. And that is
the case, if the clubhead was made without any ulterior motives. But...
 Grooves do nothing for a driver. Launch conditions
are not influenced at all by a smooth
face, horizontal grooves, vertical grooves, or grooves at any angle you
want.
So the way to "game" the length measurement is to put seriously slanted
scorelines on the face. If lie angle is measured (as it usually is)
with scorelines level, you can make the measurement occur at a very
flat lie angle, with no compulsion to actually play the club that way.
The result is that the club measures maybe an inch shorter than it
plays  and it beats the length limit by an inch.
In order to head off such gaming, the rule makers said the angle of the
sole stop had to be 60º  as opposed to hinged and matched to the lie
angle. 60º is well within the range of lie angles
across the bag, and closer to the driver end of the bag. Sounds like a
reasonable way to measure, if the goal is to control maximum driver
length.
So
a lot of clubmakers and instrument makers said, "OK, there's a new way
to measure club length. Let's redesign the club ruler to this new
method." Certainly worthwhile if you need to be sure you are building a
legal driver. Here is a picture of GolfMechanix' product to meet that
need. It has a
nonhinged solid sole stop, cut at a 60º angle. This actually has a
number of advantages over the old way:
 Inexpensive.
Certainly less expensive than a good hinged stop.
 Easy
to use.
No need to adjust the stop to align it with the scorelines, in order to
get the lie angle right.
 Harder
to misuse.
You can't accidentally bump the stop to a flatter angle as you are
setting the club in the ruler. (Don't laugh; that has been done, and
not infrequently.)
But you will notice that the photos show an iron being measured, not a
driver. So it
is being used as the
primary
club ruler,
not just a check on legality. When you use it for your
club ruler, you
should want to know if it gives you the same reading as the traditional
club ruler.
Of course it doesn't! The different angle of the stop will give a
different measured length. The real question is "how
different?"
That is what this article is about.

What's the Difference?
No, really! What is
the
difference between the length measured by an old ruler and a new one?
Here is a graph of the difference for typical clubs. The assumptions
made in producing the graph include:
 Drivers have lie angles between 56º and 60º, with the
majority at 58º. (The graph shows the whole range, but we should
probably use 58º for most purposes.)
 The highest lie in the set is 64º, the specification
for
most wedges.
 The sole curvature is about 4 degrees per inch.
(Below, we test sensitivity to this assumption, over the range of 3 to
6 degrees
per inch.)
 The distance along the stop where the sole hits is
1.7",
when the stop is set to the lie angle. (I measured a bunch of clubs,
and they were between 1.5" and 1.8". 1.7" is toward the upper end of
the range. Below, we test sensitivity to this assumption.)
 The graph assumes the traditional method gives the
correct answer, and we
want to find the difference due to the new method. If we want to view
it the
other way around, just change the sign of the difference.
(The equations to draw this graph come from the analysis in the
Appendix. The equations were implemented in Excel to produce the graph,
and to run the sensitivity analysis below.)
The immediate conclusion to be drawn from the graph is that the error
is less than 1/8" (.125"), and usually much less. If we limit the lie
to the usual driver lie of 58º, the error is barely above 1/16"
(.063"). A sixteenth of an inch is tighter than I control club length
in my shop, so it is plenty good enough for me. I suspect that is true
for the vast majority of shops.
(Side note:
I know
clubmakers who are completely analretentive about getting every
measurement to the last decimal place. The usual justification, when
you dig down, is "because I can". Feel free to do your thing, guys. But
now you have a decision to make: which method is the right
measurement of length. I can't help you there.)

"I'm a pioneer"
In the late 1990s, I did a backoftheenvelope calculation that told
me the error due to a fixed stop could be limited to about 1/8". It was
not nearly as careful an analysis as this one, but I knew it was not
too far off. I could see the advantages as being easy to make and
maintain, easy to use, and not very errorprone.
Based on that, I built the club ruler shown in the photo for my own shop, with a stop of
sheet aluminum bent to 60º. I have been using it to measure club
length ever since.

Sensitivity analysis
Our conclusion is that, over the lie range from 58º to 64º, the
difference between the two rulers is less than .075"  just over 1/16"
and just under 2mm  maximum. But there are two assumptions that may
be driving the answer, so we should see how the answer changes when we
change the assumptions. The assumptions we are going to test are:
 Curvature of the sole: we will test using 3 to 6
degrees
per inch.
 Effective length of the stop: we will test using 1.5
to 1.9
inches.
Differences:
Sensitivity to assumptions

Curvature
(degrees
per
inch)

Length
of stop
(inches)

Driver
(lie = 58º) 
Wedge
(lie = 64º) 
1.5

1.7

1.9

1.5

1.7

1.9

3

.055 
.061

.067

.052

.064

.076

4

.052

.058

.064

.062

.074

.086

5

.051

.057

.063

.068

.080

.093

6

.050 
.056 
.062

.072

.084

.097

The results are in the table at right. The table shows the extremes of
the curve, the driver at 58º and the
wedge at 64º. The difference are smaller for all the other clubs. Of
course, the
difference is always zero at 60º lie; the stops are at identical angles.
Observations:
 In every case, the difference was less than 0.1", a
tenth of an inch.
 The differences are larger for larger stop lengths
and more
curvature. In my measuring, I found that highcurvature clubs tended to have smaller
stop lengths, so the high end of the differences would not have been
encountered with real clubs. Therefore a more realistic estimate of the
maximum difference you would encounter is about 0.08", about a twelfth
of an inch.

Conclusion
The length measured by the new rule is not very different from the old.
The difference in every realistic case for normal clubheads is less
than 0.08" (or 2.0mm). The new method is a simpler and more foolproof
operation, lower cost, and with greater potential to build it yourself.
And it comes at very little accuracy penalty, if the old method is
considered "correct".
Appendix: Analysis
of the difference
(Feel free to skip this if you
aren't interested in where the numerical results came from.)
Here is the
geometry of the problem we are trying to
solve. The elements are:
 The ruler body, represented by the black horizontal
line.
 The sole of the club, represented by the black arc.
 The 60º stop is a blue line tangent to the sole, at a
60º
angle (naturally) to the ruler body.
 The lieangle stop is a green line tangent to the
sole.
Its angle to the ruler body is equal to the lie angle.
Each of these elements has some measure associated with it:
 The sole
of the club
has a curvature, denoted as C.
The curvature
of the sole is expressed in degrees per inch; that is,
how many degrees does the direction change for each inch moved from
heel to toe along the sole? Most clubfitters are familiar with bending
lie angle based on scuff marks on the sole; the usual rule of thumb is
one degree per quarter inch off center. That implies a curvature of one
degree per quarter inch, or C=4.
Much to my
surprise, the number was fairly similar with the drivers I measured. So
we'll use C=4,
and check the sensitivity to C
when we're
done.
 The distance
along
the stop, from the ruler to contact with the sole, is L1
for the 60º
stop and L2
for the true lie angle. I measured a bunch of clubs and found L2
to be in the
range of 1.5" to 1.8".
 What we want to find is the difference,
or
error, between the two measurements. That is the distance
along
the ruler from the green line to the blue line, shown as E
on the diagram.

Let's look at
the problem in more detail. We'll complete
the green and blue right triangles, and see what we can deduce. Let's
label distances along the ruler (or even just parallel to the ruler) as
X
distances. So:
 The blue distance, corresponding to L1,
is X1.
 The green distance, corresponding to L2,
is X2.
 The horizontal component of the distance between the
tangent points is X3,
shown in red. (We'll
identify another right triangle later, that will enable us to compute X3.)
A quick inspection of this diagram gives us an equation for the error:
or
The rest of this analysis consists of finding the values of X1,
X2,
and X3
so we can
calculate E.
Another observation about the diagram: the distance between the blue
and green tangent points subtends an angle along the arc which we will
call d.
A
few interesting points from that observation:
 d
is equal to the difference between 60º and the actual lie angle.
 The distance along the arc can be computed, since we
know
the curvature in degrees per inch. That distance is d/C.
For purposes of the work that follows, let's keep the blue angle more
general than 60º. We'll call it a.
We can always
set a=60º
when we need a numerical value.
We will call the lie angle b,
and remember
that b=a+d.
On to
finding the Xs...
From basic trigonometry:
X1 = L1 cos(a)
X2
= L2
cos(b)
The difference between L1
and L2
is very close
to the length of the arc between the tangents. We already identified
the arc length as equal to d/C
and angle b
as a+d.
So we can
closely approximate:
L1 = L2  d/C
Therefore:
X1 = (L2 
d/C) cos(a)
X2 = L2 cos(a+d)

All
we need now is X3. To find it, we will take a closer look at the area
where the stops are tangent to the sole curve. We can draw another
right triangle, this one shown in red. If we knew L3
and the
angle between X3
and L3,
we
could compute X3
easily. So let's try to find L3
and the angle.
First L3.
It is the chord between the tangents. Since the arc covers very few
degrees, the chord and the arc are almost the same length, which we
know to be d/C.
Now, what do we know about that angle? Just from inspection, it must be
larger than a
and smaller than b.
It looks to be about halfway between them. Actually, it is not hard to
prove that it is exactly
halfway between a
and b,
which is (a+d/2).
Therefore:
We now have expressions for X1,
X2,
and X3
that we can
plug into the expression for E.
E

=
X1  X2 + X3


=
(L2  d/C) cos(a)  L2 cos(a+d)
+ (d/C)
cos(a+d/2)

A
word about the sign (direction) of the error. As it stands, this
equation treats measurement at 60º as the correct way, and measurement
with a stop
at the lie angle to be in error. But we came at this with a
traditionalist view: "What
sort of
error does the new club ruler introduce, assuming we were measuring
things correctly before." So, when we plot the graphs, we
will
plot E,
which is the error introduced by the new ruler.

Last modified  Feb 6, 2015
