Brian Manzella
Administrator
My comments will be in the large, serif, typeface. Like this. —Brian
Focus: Smash Factor
Trackman Newsletter • May 2008
In the analysis of a golf shot, “smash factor” is referred to increasingly in the golfing community. This in-depth interview with Fredrik Tuxen – CTO at ISG and the inventor of TrackMan™ – touches upon the relevance, measurement, and maximization of smash factor.
What is the smash factor?
The smash factor is the ratio between ball speed and club head speed.
What does smash factor tell a golfer about a shot?
As a parameter, it is an expression of the player's ability to generate ball speed based on a given club speed. Technically, the smash factor says a lot about the centeredness of impact and the solidity of the shot - there is a strong correlation between the degree of centeredness at impact and the obtained smash factor.
How important is smash factor as a launch parameter?
It is very important – and to be honest, it is much more important than many think. Especially for those amateurs that try to swing too hard at the ball. By trying to achieve a high club speed, they lose control and don't obtain a solid, centered impact, resulting in a relatively low smash factor, far from what is optimal. When working with TrackMan™, the amateur and the pro should focus a lot more on ball speed and the smash factor in order to improve their ball striking. This is the reason why we have deliberately taken club speed away from the first page on the TrackMan™ screen and moved it down to page 3. We want players to focus on what is really significant to improve in their swing.
Let me give you an example. With a club speed of 100 mph and a smash factor of 1.40, the ball speed is 140 mph. But if the golfer could obtain a smash factor of 1.48 with a more controlled swing having a lower club speed of 98 mph, the ball speed would be increased to 145 mph – i.e. an additional 5 mph ball speed by swinging slower. Since 1 more mph ball speed (all other things equal) will generate 2 more yards carry, an extra 10 yards is added to the drive in this case by swinging with more control! Further, the more controlled swing will most likely have a very positive effect on dispersion.
What is the highest smash factor you can obtain?
The laws of physics do put some limitations on what is possible. Even though you may impact the ball dead-center on the club face, so the ball departs on a line that goes directly through the Center of Gravity (CoG) of the club head, there are 3 more factors that determine the maximum obtainable smash factor:
For the coefficient of restitution, USGA and The R&A have limited golf clubs and balls to a maximum COR of 0.83.
While the spin loft could theoretically be 0 deg, it is impractical since this would mean something like a 0 deg lofted driver with a zero flex shaft producing 0 rpm of spin! The lowest realistic spin loft for a driver is around 8 deg.
A word of caution, before you start putting lead tape on your driver to make it heavier, that the heavier the club head the harder it is to generate club head speed. Maximum ball speed for a 45 inch driver is obtained for most people with a club head weight around 200 g. See “Search for The Perfect Swing” by Cochran and Stobbs for a study on how the club head speed varies with club head weight.
What is a good smash factor?
This depends highly on what club you are looking at and what ball type you are playing. For a driver with a premium ball, as an amateur, your smash factor should be above 1.42 and if you have elite ambitions, you should not be below 1.47. Tour pros should aim for nothing less than 1.48 as a minimum. But do note that if you are hitting the very common high durability range balls the effective COR can easily be as low as 0.73 which will limit the smash factor realistically to about 1.41!
How much does the smash factor vary from club to club in a bag?
By using the equation above and assuming standard loft as being the SPIN LOFT and average male club head weights, the theoretical optimal smash factor throughout the set is shown in Table 1. For illustration the corresponding club head speed and ball speed are shown where the club head speed has been scaled to match the average for the PGA TOUR.
The results in Table 1 agree very well with our observations of male and female tour pros for longer irons and woods. Some examples are presented in Table 2.
In general, both the PGA and LPGA players seem to be right at the optimal smash factor - and sometimes actually slightly above. In particular on the shorter irons, the pros are achieving a higher smash factor than what is reasonably expected from the club loft. The likely explanation for these high smash factors is that the spin loft is actually lower than the club loft which will be the case if the ball is impacted with the hands leading the club head.
Another interesting observation in Table 2 is that LPGA players seem to generate higher smash factors for the longer irons in particular. A possible explanation for this is that there is a small increase in club/ball COR at lower club head speeds.
Also the ladies tend to use more cavity back type of clubs which has slightly higher COR and slightly lower loft than corresponding blade type which is preferred by most PGA Tour players.
Have you come across any smash factors on the pro scene that stand out, positive or negative?
One thing I have found very remarkable is how consistently the tour pros are able to produce smash factors of 1.48 and above with their drivers.
One of the biggest concrete surprises I have had was when we had the Danish European Tour player Mads Vibe-Hastrup in front of TrackMan™ with his driver. Mads initially had a smash factor of 1.42 (110 mph club head speed, 156 mph ball speed)! Interestingly enough, he was launching the ball at 14 degrees with a spin rate of 2500 rpm, so if you only looked at the ball speed, launch angle and spin rate, the data would look very close to optimal. But by measuring club head speed and ball speed independently, thus having a fully measured smash factor result, we could immediately see that something was very far from optimal.
It turned out that Mads was hitting significantly down on the ball and impacted the ball high on the club face, slightly towards the heel. As you can read elsewhere in this newsletter, Mads achieved the 1.48-1.49 smash factor with a significant distance increase in return for his hard work on TrackMan™.
Another surprise was LPGA player Natalie Gulbis during Wendy’s 3-Tour Challenge in 2007 (see also newsletter #2). She was consistently getting smash factors around 1.42. So despite her very nice positive attack angle, she was at this event losing about 12 yards carry compared to her potential.
How does TrackMan™ actually measure smash factor?
While the calculation of smash factor is simply the ratio between ball speed and club head speed, there are some details that are worth noticing. The ball speed is very well defined, and TrackMan™ measures the ball speed directly within 0.1 mph.
However, with the club head speed things are not quite as simple. It might be a surprise to many golfers, but the club head speed actually varies significantly depending on where on the club face you are looking. On average there is a 14% difference between heel and toe speed. This means that if you have 100 mph club head speed in the center of the club face, the speed of the heel will be around 93 mph and the toe 107 mph. This is primarily due to two things: 1) the further distance from grip to the toe of the club compared to the grip to heel 2) the rotation of the club head during the downswing. Likewise, the club head speed low on the club face is higher than high on the club face.
TrackMan™ always refers to the club head speed at the center of the club face, but because of around a ⅜ inch uncertainty of the location of the radar reflection point on the back of the club face, this leads to an accuracy of the club head speed measurement of the TrackMan™ of ±1 mph with reference to the center of the club face.
Let me give you an example of how this affects your smash factor measurement: Let us assume a club head speed of 100 mph (in the center of the club face) with a dead center ball impact producing 148 mph ball speed. This should theoretically give a smash factor of 1.48. However, due to the uncertainty of the exact location of the club head speed reading of the TrackMan™, the smash factor might be measured somewhere between 148/101 and 148/99 (1.465 to 1.495).
Let us then take the other case where the ball is impacted at the 5 different locations indicated on the club face above but having the club delivered with the same speed and spin loft to the ball (Figure 1). The club head measured by the TrackMan™ is independent on where on the club face the ball is impacted, so this will be 100 mph for all the 5 different impact locations. In the table below, an example of a realistic variation of the COR variation across the club face has been used. Maximum ball speed is obtained with impact ¾ of an inch towards the toe despite the lower COR of 0.81 at this point on the club face.
If the smash factor was calculated from straight theory (last column in table 3): ball speed divided with the club head speed at point of impact, the smash factor producing the highest 150.3 mph ball speed would come out as 1.463.
Since ball speed (together with launch angle and spin rate) is what matters for the ball flight, by using the center of the club face as reference for the club head speed measurement, maximizing your TrackMan™ smash factor means also maximizing your ball speed for a given physical strength.
This means that in the case the ball is impacted towards the toe (higher club head speed) but still with a high COR and no loss of energy due to twisting of the club head during impact, the theoretical maximum smash factor might be 1.48, but the TrackMan™ smash factor could come out higher.
Are there more smash factor discoveries left to make?
We have so far spent most of our time looking at smash factors for drivers. We have now started looking at smash factors for irons. The tour pros seem to generate a slightly higher smash factor with their irons, especially the shorter ones, than what you would expect from the loft of the club. So we are currently analyzing the tour pros’ club delivery – in particular attack angle and dynamic loft to understand more precisely what the world’s best ball strikers are doing. The results of this will be very valuable for both fitting and instruction.
Focus: Smash Factor
Trackman Newsletter • May 2008
In the analysis of a golf shot, “smash factor” is referred to increasingly in the golfing community. This in-depth interview with Fredrik Tuxen – CTO at ISG and the inventor of TrackMan™ – touches upon the relevance, measurement, and maximization of smash factor.
What is the smash factor?
The smash factor is the ratio between ball speed and club head speed.
What does smash factor tell a golfer about a shot?
As a parameter, it is an expression of the player's ability to generate ball speed based on a given club speed. Technically, the smash factor says a lot about the centeredness of impact and the solidity of the shot - there is a strong correlation between the degree of centeredness at impact and the obtained smash factor.
How important is smash factor as a launch parameter?
It is very important – and to be honest, it is much more important than many think. Especially for those amateurs that try to swing too hard at the ball. By trying to achieve a high club speed, they lose control and don't obtain a solid, centered impact, resulting in a relatively low smash factor, far from what is optimal. When working with TrackMan™, the amateur and the pro should focus a lot more on ball speed and the smash factor in order to improve their ball striking. This is the reason why we have deliberately taken club speed away from the first page on the TrackMan™ screen and moved it down to page 3. We want players to focus on what is really significant to improve in their swing.
Let me give you an example. With a club speed of 100 mph and a smash factor of 1.40, the ball speed is 140 mph. But if the golfer could obtain a smash factor of 1.48 with a more controlled swing having a lower club speed of 98 mph, the ball speed would be increased to 145 mph – i.e. an additional 5 mph ball speed by swinging slower. Since 1 more mph ball speed (all other things equal) will generate 2 more yards carry, an extra 10 yards is added to the drive in this case by swinging with more control! Further, the more controlled swing will most likely have a very positive effect on dispersion.
OK.
Here how Homer Kelley and many others got to thinking there was something that we would come to call a "Heavy Hit."
Because you could swing slower and hit the ball further. Just not because you were resisting deceleration, which you can not do.
If the strike was more in the center of the club, verses not in the center, that would do it.
But, there are other ways as well, which we will see below. These would add to the incorrect conclusion.
Here how Homer Kelley and many others got to thinking there was something that we would come to call a "Heavy Hit."
Because you could swing slower and hit the ball further. Just not because you were resisting deceleration, which you can not do.
If the strike was more in the center of the club, verses not in the center, that would do it.
But, there are other ways as well, which we will see below. These would add to the incorrect conclusion.
What is the highest smash factor you can obtain?
The laws of physics do put some limitations on what is possible. Even though you may impact the ball dead-center on the club face, so the ball departs on a line that goes directly through the Center of Gravity (CoG) of the club head, there are 3 more factors that determine the maximum obtainable smash factor:
• coefficient of restitution between club and ball (COR),
• the SPIN LOFT – the angle between club face orientation and club head direction
• the SPIN LOFT – the angle between club face orientation and club head direction
SPIN LOFT = Dynamic ("delivered") Loft —(minus) Attack Angle
and
• the mass ratio between ball weight and club head weight.
Ahh....
The "Mass Ratio."
Homer Kelley knew this from simple physics. He thought that the golfer was part of this "Mass Ratio," or could beome part of it with precise positioning, and through extensor action.
Thanks to Mandrin and Zick, we know better. A heavier clubhead will make the ball go further if the speed is the same.
But before you go run out and get heavy heads, you will lose speed with weight, and you might lose control. Worth trying with one club though if you are a tinkerer.
The equation below shows the maximum obtainable smash factor assuming a dead-center hit:
• the mass ratio between ball weight and club head weight.
Ahh....
The "Mass Ratio."
Homer Kelley knew this from simple physics. He thought that the golfer was part of this "Mass Ratio," or could beome part of it with precise positioning, and through extensor action.
Thanks to Mandrin and Zick, we know better. A heavier clubhead will make the ball go further if the speed is the same.
But before you go run out and get heavy heads, you will lose speed with weight, and you might lose control. Worth trying with one club though if you are a tinkerer.
The equation below shows the maximum obtainable smash factor assuming a dead-center hit:
For the coefficient of restitution, USGA and The R&A have limited golf clubs and balls to a maximum COR of 0.83.
While the spin loft could theoretically be 0 deg, it is impractical since this would mean something like a 0 deg lofted driver with a zero flex shaft producing 0 rpm of spin! The lowest realistic spin loft for a driver is around 8 deg.
But, how do you do that?
OK.
We have a driver with 10° of loft.
If we have a level strike, with a delivered loft of 10° (no forward or backward lean), the spin loft will be 10°.
If we have a forward leaning shaft of 2°, and a delivered loft of 8° (because in this example, we are delofting the 10° head), and a downward strike of 2°, we have the same damn spin loft of 10°.
Rats!
But...
If we can accomplish a forward lean of 2°, and a upward strike of 1°, and a delivered loft of 8°, we get a SPIN LOFT of 7° and more ball speed, thus a higher smash factor.
How 'bout them apples!
Now, I am not saying the above is optimum, but, trust me, the long drive guys are doing something like this, and so are the LPGA gals who have good numbers.
As for the ball, the maximum allowed mass is 45.93 g, with no lower limit. However, it turns out that almost all golf balls have a mass above 45 g since the heavier weight makes the ball slow down less during flight (due to air resistance). For the club head mass, there are small variations among drivers. They typically range from 197 to 201 g, with tour pros using 202-207 g. The heaviest driver head I have heard about is 212 g. By inserting realistic numbers in the equation above for maximizing the smash factor (COR 0.83, SPIN LOFT 8 deg, mass ratio 45/212), the highest realistic smash factor is 1.494.OK.
We have a driver with 10° of loft.
If we have a level strike, with a delivered loft of 10° (no forward or backward lean), the spin loft will be 10°.
If we have a forward leaning shaft of 2°, and a delivered loft of 8° (because in this example, we are delofting the 10° head), and a downward strike of 2°, we have the same damn spin loft of 10°.
Rats!
But...
If we can accomplish a forward lean of 2°, and a upward strike of 1°, and a delivered loft of 8°, we get a SPIN LOFT of 7° and more ball speed, thus a higher smash factor.
How 'bout them apples!
Now, I am not saying the above is optimum, but, trust me, the long drive guys are doing something like this, and so are the LPGA gals who have good numbers.
A word of caution, before you start putting lead tape on your driver to make it heavier, that the heavier the club head the harder it is to generate club head speed. Maximum ball speed for a 45 inch driver is obtained for most people with a club head weight around 200 g. See “Search for The Perfect Swing” by Cochran and Stobbs for a study on how the club head speed varies with club head weight.
What is a good smash factor?
This depends highly on what club you are looking at and what ball type you are playing. For a driver with a premium ball, as an amateur, your smash factor should be above 1.42 and if you have elite ambitions, you should not be below 1.47. Tour pros should aim for nothing less than 1.48 as a minimum. But do note that if you are hitting the very common high durability range balls the effective COR can easily be as low as 0.73 which will limit the smash factor realistically to about 1.41!
How much does the smash factor vary from club to club in a bag?
By using the equation above and assuming standard loft as being the SPIN LOFT and average male club head weights, the theoretical optimal smash factor throughout the set is shown in Table 1. For illustration the corresponding club head speed and ball speed are shown where the club head speed has been scaled to match the average for the PGA TOUR.
The results in Table 1 agree very well with our observations of male and female tour pros for longer irons and woods. Some examples are presented in Table 2.
In general, both the PGA and LPGA players seem to be right at the optimal smash factor - and sometimes actually slightly above. In particular on the shorter irons, the pros are achieving a higher smash factor than what is reasonably expected from the club loft. The likely explanation for these high smash factors is that the spin loft is actually lower than the club loft which will be the case if the ball is impacted with the hands leading the club head.
Another interesting observation in Table 2 is that LPGA players seem to generate higher smash factors for the longer irons in particular. A possible explanation for this is that there is a small increase in club/ball COR at lower club head speeds.
Also the ladies tend to use more cavity back type of clubs which has slightly higher COR and slightly lower loft than corresponding blade type which is preferred by most PGA Tour players.
Have you come across any smash factors on the pro scene that stand out, positive or negative?
One thing I have found very remarkable is how consistently the tour pros are able to produce smash factors of 1.48 and above with their drivers.
One of the biggest concrete surprises I have had was when we had the Danish European Tour player Mads Vibe-Hastrup in front of TrackMan™ with his driver. Mads initially had a smash factor of 1.42 (110 mph club head speed, 156 mph ball speed)! Interestingly enough, he was launching the ball at 14 degrees with a spin rate of 2500 rpm, so if you only looked at the ball speed, launch angle and spin rate, the data would look very close to optimal. But by measuring club head speed and ball speed independently, thus having a fully measured smash factor result, we could immediately see that something was very far from optimal.
It turned out that Mads was hitting significantly down on the ball and impacted the ball high on the club face, slightly towards the heel. As you can read elsewhere in this newsletter, Mads achieved the 1.48-1.49 smash factor with a significant distance increase in return for his hard work on TrackMan™.
Another surprise was LPGA player Natalie Gulbis during Wendy’s 3-Tour Challenge in 2007 (see also newsletter #2). She was consistently getting smash factors around 1.42. So despite her very nice positive attack angle, she was at this event losing about 12 yards carry compared to her potential.
How does TrackMan™ actually measure smash factor?
While the calculation of smash factor is simply the ratio between ball speed and club head speed, there are some details that are worth noticing. The ball speed is very well defined, and TrackMan™ measures the ball speed directly within 0.1 mph.
However, with the club head speed things are not quite as simple. It might be a surprise to many golfers, but the club head speed actually varies significantly depending on where on the club face you are looking. On average there is a 14% difference between heel and toe speed. This means that if you have 100 mph club head speed in the center of the club face, the speed of the heel will be around 93 mph and the toe 107 mph. This is primarily due to two things: 1) the further distance from grip to the toe of the club compared to the grip to heel 2) the rotation of the club head during the downswing. Likewise, the club head speed low on the club face is higher than high on the club face.
TrackMan™ always refers to the club head speed at the center of the club face, but because of around a ⅜ inch uncertainty of the location of the radar reflection point on the back of the club face, this leads to an accuracy of the club head speed measurement of the TrackMan™ of ±1 mph with reference to the center of the club face.
Let me give you an example of how this affects your smash factor measurement: Let us assume a club head speed of 100 mph (in the center of the club face) with a dead center ball impact producing 148 mph ball speed. This should theoretically give a smash factor of 1.48. However, due to the uncertainty of the exact location of the club head speed reading of the TrackMan™, the smash factor might be measured somewhere between 148/101 and 148/99 (1.465 to 1.495).
Let us then take the other case where the ball is impacted at the 5 different locations indicated on the club face above but having the club delivered with the same speed and spin loft to the ball (Figure 1). The club head measured by the TrackMan™ is independent on where on the club face the ball is impacted, so this will be 100 mph for all the 5 different impact locations. In the table below, an example of a realistic variation of the COR variation across the club face has been used. Maximum ball speed is obtained with impact ¾ of an inch towards the toe despite the lower COR of 0.81 at this point on the club face.
If the smash factor was calculated from straight theory (last column in table 3): ball speed divided with the club head speed at point of impact, the smash factor producing the highest 150.3 mph ball speed would come out as 1.463.
Since ball speed (together with launch angle and spin rate) is what matters for the ball flight, by using the center of the club face as reference for the club head speed measurement, maximizing your TrackMan™ smash factor means also maximizing your ball speed for a given physical strength.
This means that in the case the ball is impacted towards the toe (higher club head speed) but still with a high COR and no loss of energy due to twisting of the club head during impact, the theoretical maximum smash factor might be 1.48, but the TrackMan™ smash factor could come out higher.
Are there more smash factor discoveries left to make?
We have so far spent most of our time looking at smash factors for drivers. We have now started looking at smash factors for irons. The tour pros seem to generate a slightly higher smash factor with their irons, especially the shorter ones, than what you would expect from the loft of the club. So we are currently analyzing the tour pros’ club delivery – in particular attack angle and dynamic loft to understand more precisely what the world’s best ball strikers are doing. The results of this will be very valuable for both fitting and instruction.
