Smash Factor: Myths and Facts
Dave Tutelman - September 14, 2012
If you watch golf on TV or read the golfing magazines, you have heard a
about "smash factor". If you learn about it from those venues, you get
some facts and a lot of half-truths. Let's clear up the confusion about
is the ratio of ball speed to clubhead speed. By definition!
Anything else that is said about it is subordinate to this definition.
is a measure of how well the ball is struck. True, but not
absolute. It is also a measure of the club that was used.
has a maximum theoretical value of 1.5. People who say this fall
into two categories:
really good hitters -- like the best ball strikers on Tour -- can
exceed 1.5, theory or no. Well, no! Not unless they are using
- People who understand that 1.5 is a pretty good approximation
for most drivers, but it isn't exactly 1.5.
- People (like most TV announcers) who think there is some magic
in the number 1.50000.
Typical of the confusion on this subject is an email I got from Justin
Blair this week:
Subject: Re: Smash Factor; is it important?
I wrote back that the email's subject line should have been something
Factor: is it
really 1.5?" or "How
important is 1.5?"
was curious as to your thoughts about smash factor. I was playing
with the Trajectoware software and I noticed for my ball speed numbers
(152mph), the program doesn't give me the theoretical "perfect" smash
factor number of 1.5. At 152mph, the program tells me the swing
speed should be 103.6mph, for a smash factor of 1.47 (rounded
up). I know it's close, but is smash factor really that
Seriously, the smash factor is very
important; do not believe otherwise. But here is what I wrote back to
Justin about keeping it real. (Of course, this isn't the raw email I
sent to him; it has been enhanced to be a stand-alone
What the smash factor really is
Let's start by looking at where the smash factor comes from.
Is that a valid, consistent pair of statements? Approximately, but not
exactly. Let's do the math.
- It is defined
as the ratio of ball speed to clubhead speed.
- It is used as
a measure of the quality of ball striking.
Look at the formula
for ball speed in my tutorial on impact. Read the section, and
understand what it says. While you read it, forget about
smash factor. We'll get there after you are done with the
first read-through and understanding.
OK, done with that? Does it make sense? If so, let's see how the
formula relates to smash factor. Let's start with the ball speed
formula, which we now understand:
|Vball = Vclubhead
|1 + e
1 + m/M
| cos(loft) * (1 - 0.14*miss)
The Smash Factor (SF) is the
ball speed divided by the clubhead speed -- and it is easy to solve the
above equation for SF.
- e = Coefficient of Restitution.
For a modern driver this is pretty much stuck on 0.83, because (a) the
USGA/R&A rules say it can't be more and (b) manufacturers know how
build to 0.83 and even higher.
- m = Ball mass.
46g, for pretty much the same reason as COR is 0.83. The rule says it
can't be more, and less gives poorer performance. A lighter ball may
have more initial ball speed, but its lower inertia gives it less
"punch" through air resistance. Ball manufacturers learned long ago
that heavier balls go farther, and the Rule makers learned almost as
long ago to limit the maximum ball mass. So all balls are just about
- M = Clubhead mass. For
most modern drivers, this is within a couple of grams of 200g. But it
can depart significantly for design reasons. It is an unusual design
that is far from 200g, but they exist. We'll explore this more below.
- loft is a property of the
club. For most Tour drivers (and most drivers in the hands of amateurs)
it is within a degree of 10º. But we will explore what happens when
- miss is the distance, in
inches, that impact misses the sweet spot of the clubhead. It should be
noted that the factor 0.14 dates back to about 1990, when driver heads
were small and made of wood. Today's driver has a much higher clubhead
moment of inertia, so the factor is correspondingly smaller. I haven't
seen any data, but I suspect it is more like 0.07-0.10.
Wouldn't it be a huge coincidence if this worked out to exactly 1.5000?
1 + m/M
| cos(loft) * (1 -
Well it doesn't -- at least not exactly.
And it isn't determined just by how well the ball is struck, but by the
details of the club: like loft, COR, and clubhead mass.
How high can smash factor go?
Let's see how high we can get the smash factor. Is 1.50 the maximum,
the upper limit, or can we go higher? Can we even get it to 1.5? We'll
find out from the equation, using the best possible values for the
parameters to make the smash factor large.
If we plug in these values, we get a smash factor of 1.482.
This is close to 1.5. It is a good engineering approximation, but it
isn't the magic 1.5000 that the media gurus talk about.
- Coefficient of Restitution and ball mass are what they are: 0.83
and 46g respectively. We can't do anything about them.
- The value of loft that maximizes SF is the lowest loft possible.
That means that we want to use a driver. We're looking for a very low
loft, so let's choose a long-drive competitor's driver, with maybe a 5º
loft. (That is unrealistic for anything you -- or even a Tour player --
would use on the golf course. But let's go with it to see how high we
can get the SF.)
- Since we are using a driver, the clubhead mass is about 200g.
Let's go with that.
- Finally, SF is a measure of the quality of ball striking. So
let's not miss the sweet spot. The "miss" is zero for all computations
in this section.
In reality, it isn't really this good even on the Tour, nor will it be
for you. Go ahead
and try to hit a driver with a 5º dynamic loft. You will get slightly
more ball speed (higher smash factor) than your own driver,
but you'll lose a lot of distance because the trajectory will be
horrible. The only guys who can actually hit these drivers for good
distance have clubhead speeds of 130mph and up.
Let's look at how the "free" parameters (the ones we can play with)
affect the smash factor. Actually, the only ones we can play with are
and clubhead mass. Well, we could
play with COR, but the only legal thing we could do would make the SF
lower. And we could play with
ball mass, but you can't buy golf balls with a mass very far from 46
grams, so there's no point.
Here's how smash factor varies as you change the loft. For this table,
we kept the normal driver parameters:
As the loft increases, the smash factor drops. It is worth noting that,
at normal driver lofts (in the vicinity of 10º), the smash factor is
below 1.47. So it is unlikely that you'll see a smash factor
significantly more than this on the PGA tour.
- Clubhead mass = 200 grams
- COR = 0.83
BTW, this variation with loft is actually a confirmation that smash
factor is a reasonable measure of the quality of ball striking. The
reason it drops off with loft is because a strike with a lofted club is
oblique, not square. In an important sense, non-square strikes (even if
due to the loft of the club) can be considered a ball-striking
Increasing the clubhead mass also increases the smash factor, but not
by much at all. A 10% increase in clubhead mass results in only a 1.7%
increase in smash factor. (Again, we are using a driver for the model
club, with a loft of 10º.)
No, it isn't much of an increase, but it is
enough... The smash factor reaches a full 1.5 at a clubhead mass
of about 229g. Now that's way more than you're likely to find on a
driver, but we have shown it is not a mathematical impossibility.
On second thought, there are good reasons you might reasonably find a
driver with a head weight of 210 or even 220 grams. In fact, you will.
Several companies make clubs called "thrivers", which are easier to hit
and more reliable than the conventional driver. One of the
characteristics of a thriver is more clubhead mass; the purpose is so
the club can be made shorter without losing heft (swingweight or moment
of inertia). It is pretty well known that most golfers will not make as
good impact with a 45" or 46" club as they will with a 43" or 44" club.
So a thriver is a driver with a heavy head and a short shaft. Yes it
has a higher smash factor (because of the heavier
head) -- though that is just a side effect and not the primary purpose.
In reality, another usual characteristic of a thriver is a higher loft
than the usual driver, which eats up the smash factor gains and then
some. But that is not a necessary property of a thriver; my current
driver has a heavy head and a shorter shaft than conventional, but a
pretty conventional driver loft. And I have heard of more than one Tour
player that uses this approach, giving up a little clubhead speed for
better control -- and getting a little of that speed back in ball speed because of the higher
The perfect smash factor is really 2.0
Here's another way to look at it. According to physics, the perfect,
idealized smash factor is not 1.5, it's really 2.0. And yes, I mean
2.000 exactly. When we add in reality (loft, COR, finite masses, etc),
it drops down to the general vicinity of 1.5.
Let's look again at the formula for smash factor, and really
1 + m/M
| cos(loft) * (1 -
|What would the absolute ideal
for each of the parameters be? Not the maximum for golf, but the
maximum that physics would possibly allow.
When we do all this, the formula becomes
- The Coefficient of Restitution is 1.0 when there are no
energy losses in the collision. We can't build it to exactly 1.0. Even
if the rules of golf didn't say, "No higher than 0.83," the second law
of thermodynamics would get in the way. (That is, no real physical
process is completely lossless.) But we can get pretty close, certainly
much closer than the 0.83 allowed for golf. Think about a ball bearing
dropped on a heavy steel plate. Almost no loss in the collision, and
the ball bounces almost as high as where it was dropped from.
- If we could swing a club that has way more mass than the
ball (not just 4 or 5 times as much), we could make the ratio m/M
approach zero. Let's assume an infinite clubhead mass.
- With zero loft, we get no loss of speed from oblique
impact. So the cosine of the loft is exactly 1.0.
- As we did before, we will take "miss" to be zero -- that
is, a perfect sweet-spot ball strike.
that is exact!
1 + 0
| * 1 * (1 -
0) = 2
The reason it isn't 2.0 for golf is that golf is real, not ideal. It is
the laws of golf, the laws of thermodynamics, the biomechanical
necessity for a smaller clubhead mass, and the aerodynamic necessity
for a non-zero loft. The fact that reality trims off very close to a
quarter of this (to about 1.5) is convenient for quick calculation, but
is just a coincidence and by no means exact.
Here is a pair of
pictures you can keep in mind to understand the ideal smash factor of
The upper picture shows a ball bouncing off a stationary wall. Think of
it as a ball bearing and a very heavy steel plate, with the steel plate
secured to the earth -- so the wall is essentially infinite mass
compared to the ball bearing. The "reflection" (the bounce) is
completely lossless. If you remember any physics at all, you know that
the ball bearing will rebound with exactly the same speed V that it hit
the plate. Once you are comfortable with this, move on to the lower
In the lower picture, the ball bearing starts out stationary and the
plate is moving with a velocity V. When the
plate strikes the ball, the ball will bounce off and move away from the
plate at a speed of V.
(That's because the physics of the bounce doesn't change just because
the framework -- the plate -- is moving instead of the ball.)
But the plate has not slowed down because of the impact. Just as the
infinite mass plate did not move in the upper picture, it does not slow
down in the lower picture. With infinite mass compared to the ball, the
transfer of a small bit of momentum doesn't affect its own speed. The
plate is still moving at V after impact. Therefore...
In order for the ball to move away
from the plate at a speed of V, it must move
at a total speed of 2V.
Other smash factor tidbits
Clubs other than driver
|We have seen that smash factor
will vary with clubhead mass and loft. We know that clubhead mass and
loft will vary across a set of golf clubs. In fact, as we go from long
clubs to shorter, the loft makes the smash factor go down while mass
makes it go up.
So it is reasonable to ask what happens to the smash factor across a
set of clubs. Here is a table that provides the answer. It uses pretty
standard values for loft and clubhead mass. (I took the values from the
most popular components in the current Hireko catalog.) As for COR, it
necessarily drops as the clubface size decreases, and there is no
spring effect at all in conventional irons. (There are a few iron heads
around made with thin titanium faces that have spring effect, but most
irons do not.)
The smash factor drops off pretty quickly as we get to the shorter
clubs. Loft (and secondarily COR) dominates the small gains due to
clubhead meass. It really isn't close.
The best ball-strikers among the pros do better than 1.5
I know that the TV announcers sometimes point to a measurement at one
of the holes in a tournament they are covering, and say something like,
"That ball was struck so well it even
different. And look at those readings; the smash factor is over 1.5!"
So what is going on here. I can think of two ways this can happen:
None of these explanations says that the apparently huge smash factor
is actually due to really pure ball striking.
- The most likely is measurement
error. Many people assume that the output of digital instruments
is always 100% accurate. It isn't. (See my article on precision and accuracy if you're
interested in the detail.) Every experienced clubfitter and golf
researcher knows that launch monitors give bad readings from time to
time (probably in the vicinity of 5-10% of the time), and you have to
discard those readings. The announcers don't know this, and rhapsodize
about how pure the ball strike was that it even confounded the physics
behind the game.
- Less likely, but still a distinct possibility, is non-conforming
clubs or balls. Remember, the Tour pros are walking
advertisements for the equipment they play, and they are well paid to
be advertisements. So it is likely that they are using selected
"outliers" in terms of spring face (for the driver) and rebound (for
the balls). There are two ways this can happen. Both depend on the
statistical distribution of every parameter of every product that has
ever come off an assembly line. If you build golf clubs to a design
value of 0.83 for COR, some of the drivers will be 0.82 and some 0.84;
how many statistical outliers you find depends on the quality control
in manufacturing and testing. Given this variation, two scenarios will
put the best clubs and balls in the hands of the Touring pros:
Either way, it is likely that the clubs and balls in a Tour
pro's bag are right at -- or even beyond -- the legal limit.
- The manufacturer wants his sponsored players to do well in
public. So the company is motivated to select the best clubs and balls
through quality control testing, and save them for the sponsored
- The sponsored player does not pay anything for the clubs or
balls. So he or she can, and typically does, try a bunch of samples and
pick the ones that perform best to put in the bag.
The best smash factor you can expect with a standard
driver is about 1.47. If you go to a heavier driver clubhead or lower
loft, you can
do a little better -- though you'll still probably fall short of 1.50.
And either of these changes may improve smash factor but will net out
costing you distance.
modified -- Sept 16,