# 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 lot 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 smash factor.
1. It is the ratio of ball speed to clubhead speed. By definition! Anything else that is said about it is subordinate to this definition.
2. It 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.
3. It has a maximum theoretical value of 1.5. People who say this fall into two categories:
• 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.
4. The really good hitters -- like the best ball strikers on Tour -- can exceed 1.5, theory or no. Well, no! Not unless they are using non-conforming equipment.
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 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 "smashing"?
I wrote back that the email's subject line should have been something like "Smash Factor: is it really 1.5?" or "How important is 1.5?"

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 article.)

## What the smash factor really is

Let's start by looking at where the smash factor comes from.
• It is defined as the ratio of ball speed to clubhead speed.
• It is used as a measure of the quality of ball striking.
Is that a valid, consistent pair of statements? Approximately, but not exactly. Let's do the math.

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)
where:
• 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 to build to 0.83 and even higher.
• m = Ball mass. This is 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 46g.
• 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 this varies.
• 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.
The Smash Factor (SF) is the ball speed divided by the clubhead speed -- and it is easy to solve the above equation for SF.
 SF = Vball Vclubhead = 1 + e 1 + m/M cos(loft) * (1 - 0.14*miss)
Wouldn't it be a huge coincidence if this worked out to exactly 1.5000?
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.
• 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.
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.

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 loft 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.

Loft

Here's how smash factor varies as you change the loft. For this table, we kept the normal driver parameters:
• Clubhead mass = 200 grams
• COR = 0.83
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.

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 deficiency.
 Loft Smash Factor 0 1.488 5 1.482 10 1.465 15 1.437 20 1.398 25 1.348 30 1.288

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 smash factor.

 Clubhead Mass Smash Factor 180 1.435 190 1.451 200 1.465 210 1.478 220 1.491 230 1.502 240 1.512

## 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 idealize everything.
 SF = Vball Vclubhead = 1 + e 1 + m/M cos(loft) * (1 - 0.14*miss)

What would the absolute ideal for each of the parameters be? Not the maximum for golf, but the maximum that physics would possibly allow.
• 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.
When we do all this, the formula becomes
 SF = Vball Vclubhead = 1 + 1 1 + 0 * 1 * (1 - 0)  =   2
And that is exact!

The reason it isn't 2.0 for golf is that golf is real, not ideal. It is limited by 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 2.0.

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 picture.

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.
 Club Loft Clubhead Mass COR Smash Factor Driver 10 200 0.83 1.465 3-wood 15 210 0.80 1.426 3-hybrid 20 242 0.79 1.413 5-iron 26 256 0.77 1.349 8-iron 37 277 0.77 1.212 Pitching wedge 46 291 0.77 1.062

### 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 sounded different. And look at those readings; the smash factor is over 1.5!" So what is going on here. I can think of several ways this can happen -- apart from the assertion that something supernatural is happening:
1. 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% of the time), and you have to recognize and 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.
2. Let's look at a possible special case of measurement error. I have seen assertions that the clubhead speed reading for TrackMan does not necessarily represent (a) the center of mass of the clubhead nor (b) the part of the clubhead striking the ball. Those assertions are undoubtedly true to some extent. To a large enough extent to report a smash factor over 1.5? Perhaps. I don't know, but I would certainly consider the possibility.
3. 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:
• The manufacturer wants his sponsored players to do well in public. So the company is motivated to select the best clubs and balls that come through quality control testing, and save them for the sponsored players.
• 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.
Either way, it is entirely possible that the clubs and balls in a Tour pro's bag are right at -- or even beyond -- the legal limit.
None of these explanations says that the apparently huge smash factor is actually due solely to really pure ball striking.

## Conclusion

Bottom line: 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 probably net out costing you distance.