Driver Head Weight and Club Length

Variable Club Length

Bernie Baymiller's assertions

• BOM is a component driver clubhead, the Bang-O-Matic 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.)
  

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 45-inch driver with a maximum-length 48-inch 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

• 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 constant-length 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 non-conforming 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.
  

• Baymiller claims 25-30 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 constant-length 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) de-lofted and (b) open. The amount is given by: de-loft  =  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 maximum-length minimum-weight 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 foot-pounds. 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 foot-pound 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

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 re-run 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 multi-curve 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 varied-length 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 25-30 additional yards going from a 45" driver to a 48" driver. The constant-MOI 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 non-conforming.) 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 variable-length drivers does not include the torque-velocity curve. The most important of the studies is the variable-length, constant-MOI 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 weight-length combinations; therefore, accounting for torque-velocity should not make much difference.