Shaftuner

We match your driver to your favorite club

    My theory is that a narrow bandwidth club can be hit further than a wide bandwidth club, but needs to be swung at just the right tempo. Conversely, a wider bandwidth club  is more forgiving of off-speed swings.  

   Before we consider how bandwidth affects club fitting, it should be mentioned that  it can be shown mathematically that  in order to perfectly duplicate a club, both the original and the duplicate would need to have the same frequency response curve when shaken across the entire frequency spectrum. In other words, they are not deemed equal just because their natural flexes are the same, as measured on the popular frequency meters found in most golf club shops, but would need to also have the same bandwidth around its natural frequency. To be mathematically correct, the second, third and higher harmonics would also have to match but we will ignore them for now.

    Most golfers can detect a difference in the feel, direction control or shot distance  or all of these factors when hitting clubs with the same flex but different bandwidths. This is an important consideration if one tries to use a favorite club as a template for assembling a driver that will perform as well. As shaft length increases from  wedges to drivers, f0 decreases and so does BW which adds to the risk of tempo errors.  Today’s retail driven world features 46 inches drivers, out of the range of repeatable swings for most golfers and PGA Tour players whose drivers average 44.75 inches. Most favorite clubs  reside in the shorter clubs  for good reason. If your driver is not your favorite, either its flex is off or its bandwidth is too narrow or most likely, both are wrong. I can fix that.

   The  motions of at least two thousand body parts moving during a golf swing vary from swing to swing.  It is difficult to characterize each body part or to measure their motions to gain a good understanding of swing consistency.  I am continually amazed at computer models of a golfer swinging a club   simplifying all the moving body parts into only one or two pivot points. Not only are thousands of parts involved, but each part plays a different role at each phase of the swing, an almost impossibly complex simulation.  

    For a prospective customer to aid in fine tuning the bandwidth of his soon-to-be re-shafted driver, he might take a few minutes to record  the speeds of 15 or 20 swings and forward the raw data to us along with his favorite club. From the record of these swings, a picture of his swing consistency emerges. This data can be added to flex and bandwidth data extracted from his favorite club, and a measure of  each player’s tolerance to bandwidth narrowing swims into focus.

   

     The easiest way to explain why bandwidth is important and to understand why we need the raw data of sucessive swings, we can compare the swing data of two players to form a probability distribution of their swing speeds and use the measure of consistency called the standard deviation, a measure of the width of the curve, to characterize each player. This measure can be matched to the bandwidth of a prospective driver that would give each player the best chance that most of his swings wil fit within the boundary  of swings accepted by his new driver to provide good shot results.  

    Statistical analysis formulas dictate that 68% of  player  A ‘s swings are contained within  2x (std dev). Also, a figure of merit for these swings can be defined as Z=average speed divided by  2 times the  standard deviation, StdDev.


                         Player A                                                                                Player B                             

                     Swing Statistics                                                                 Swing Statistics















        

 


                           Player A                                                                         Player B

                          Ave swing speed    = 89.33                                         Ave. Swing speed = 95.87                

                   Z=89.33/2(1.312)   =  34                                 Z= 95.87/2(2.147   =  22.3

    .  

   Next we can look at the driver bandwidth figure of merit called Q and try to match it to the swing speed statistics of both players. For this task, we will define Q as the ratio of each player’s best flex, fo , divided by  the driver bandwidth, BW.  This ratio is  then matched to the value of the Z  scores for both players.  (The best flex, fo, for each player was determined by extrapolating the flex of their favorite clubs to the driver length of 45 inches).

    











                         



  




                      Player A                                                                                Player B

                          Best flex = 255 CPM                                                         Best Flex = 265 CPM        

                     Bandwidth =   7.5                                                              Bandwidth = 11.9

               Q=255/ 7.7    =   34                                                     Q=265/12.8  =  22.3

                     

    Notice that by making each layer’s Z value that characterizes his swing consistency to equal the Q value of his driver, which is a measure of the driver’s ability to accept off-speed swings, we are presenting each player with the best chance of hitting the longest drives tempered with the highest probability of being in the fairway. The bandwidth figures in the above examples are well within the boundaries of today’s club designs, the range of driver bandwidths I have measured being 6 to 22.

     While these calculations may not be rigorously defensible, one might understand why the player on the right would have difficulty with consistency trying to hit the driver the player on the left might choose. The root cause of the difficulty would arise from the low or high swing speed events that often happen to player B. These off-speed swings would most probably result in miss-hits. If you don’t agree with this theory, why don’t you try swinging your own driver at a slower or faster speed than your normal tempo dictates and see what happens.

    Player A could play with the wide bandwidth club on the right, but he would give up distance unnecessarily by using the wide bandwidth driver.  This happens because wider bandwidth clubs deliver slower swing speeds  by dint of the factors that determine bandwidth; head and shaft weight, shaft length and grip hardness.

    The optimum relationship between bandwidth and swing speed statistics is in the evolutionary stage of development and may never be known with perfect accuracy. This notion may be no more than a cautionary  tale  used to halt the progression of lighter and longer driver shafts  that narrow the bandwidth beyond most player’s swing control. Many PGA pros play with drivers in the 44 to 45 inch range for that reason, avoiding the errant shots that accompany the 46 inch driver length favored by club manufacturers in 2018. Of course, many week-end golfers will opt for narrow bandwidth drivers to impress their playing partners with the one monster driver of the day willingly giving up on consistency. But most players strive for low scores overall and should choose bandwidths that match the repeatability of their swings. That is the benefit of bandwidth matching to swing speed consistency; more fairways hit and lower scores.

   My book Match Your Driver to Your Favorite Club goes into detail on the subject of swing speed statistics relating to shaft choices. The swing speed data analysis of 15 to 20 swings could be analyzed for the deviation from the average in order to assign a figure of merit for tempo consistency. Believe it or not, that provides an approximation of how consistent one can play with different shaft bandwidths.

    To demonstrate the two elements of the  bandwidth theory: narrow bandwidth drivers hit further but have more shot dispersion. Two drivers with the same head, flex and swing weight but different bandwidths were presented to a 9 handicap volunteer and the following chart illustrates the results of several shots hit with each driver.























  

 The 7 CPM,  bandwidth  driver hits about 2 yards longer on average (see circles) than the wider bandwidth driver at 14 CPM, illustrating the higher gain of a narrow bandwidth club. But it had a wider spread of shot distance than the wide bandwidth driver, as the chart shows.  The difference reflects the increased risk entailed with playing narrow bandwidth drivers. While shot distance variation of driver shots may not be a concern, remember that cross track or side-to-side variations are proportional to distance variations. I apologize for not collecting cross track data to substantiate this claim, but in my defense I should mention that accurate measurements of cross track need to be made with a tape measure on a range because  launch monitors estimate cross track from side spin data, since they cannot measure side-to-side ball flight deviations directly. So linking shot distance spread to cross track spread is probably  as good as we can do until better launch monitors come along.

   I prefer 15 to 20 swing speed data points from customers to determine their best driver bandwidth. Lacking such data, the favorite club probably has the right degree of tempo forgiveness (bandwidth) and so your driver needs to be close to it to feel and hit with the same dependability.

    By letting  your favorite club serve as the model for building you a driver and matching your driver bandwidth (and flex) to it, your driver will have the same feel and tempo forgiveness since these factors play a major role in making your favorite what it is.  We need to measure these characteristics of  your favorite club and we are the only ones who know how to do it using our patent pending technique.

How golf club bandwidth is measured

      Your Driver Needs the Same Bandwidth as Your Favorite Club

  You have probably never heard this phrase, except when it was applied to communication transmission networks. But it is an engineering term that also describes mechanical energy transmission systems, and a golf club is such a system. To assemble a driver that is an accurate “copy of a favorite club” and have the same feel and act like the favorite, the bandwidth, or damping factor, should be matched to it. In engineering terms, a golf club is a highly tuned power transfer system. Since you have never heard of bandwidth for golf clubs, here is the explanation.

     We can measure the frequency response of a golf club by shaking the club, clamped by its grip, over a band of frequencies which yields a spectral response curve similar to those of  sophisticated instruments used in physics and medicine. The output is measured in inches of side-to-side excursion of the head for different frequencies of the oscillating motor used to drive the grip clamp. I am sorry to be introducing another spectrum added to the one used to fit flex described on the Shaft Flex page, but I hope this concept will help us understand why clubs hit and feel differently even though their flexes are exactly the same as measured on a frequency meter which detects only its natural flex shown below as f0.

    Our frequency analyzer measures both the natural  frequency, f0, its bandwidth, BW, and the maximum excursion at f0, shown as h in the diagram below.  As the height of the curve, h,  increases, the width, BW,  decreases due to the factors that affect the shape of the curve. So there is a trade-off of  h and BW that needs to be made at the time the club is constructed.




































                    






Wide swing speed dispersion Plyer with well congtrolled swing speed dispersion Matched narrow bandwidth for narrow swing speed dispersion Example of wide bandwidth club matched to wide swing dispersion