NOTE 4: I was always puzzled about the 4cpm or so slope on most fitting charts. Why is the 9 iron stiffer, cpm wise, than the 2 iron? Did somebody just dream this up? I know some clubmakers that swear by flatlining a set of clubs. When I looked at the equation of a cantilever beam (Tech Note 1) with its variables in the denominator and a cube term and square roots etc., it sure didn't appear to be a straight-line function by any stretch of the imagination. I decided to do a little paper exercise (spread sheets are the second best thing since sliced bread) and plotted the equation knowing that each club in the set gets shorter while the head gets heavier and the shaft gets a bit lighter. The material didn't change and the cross sectional shape remains the same throughout the set. I assumed the term EI therefore was constant throughout the set. I computed the term EI from a given frequency of the first club in the set (292cpm for a 40" 225 gram 1 iron with a 125 gram shaft). The frequency of each club was then computed using the equation in Tech Note 1. The following assumptions were made: Each successive club is ½ inch shorter, each head is 7 grams heavier and each shaft is 1.6 grams lighter. The length used in the equation is the club length minus the 5 inch clamping length. I then plotted this derived frequency of each club to see what the curve looked like. I was happy to get a fairly straight like with a slope gradually increasing from 2.5 cpm/club to 4.4 cpm/club. I guess the fitting charts do have some mathematical heritage. This also indicates, that at least theoretically, the fitting charts should have a slope of about 3 cpm per club. Contact me if you want more details.
(First cpm selected, approx. R flex)
Using this approach I then worked backwards into the woods starting with a 41" 5 wood and continuing on to a 44" driver. Unfortunately there's significant discontinuity between the 5 wood and the 1 iron, about 10 cpm. I'm still scratching my head trying to figure out what this means in terms of club fitting. I'll put the plot in a future Tech Note.
...some time later...
Oops! Well I thought about it some more and realized that I must be senile in my old age. In the above interesting yet seriously flawed exercise I assumed the term I in the equation was a constant. The term, I, is dependent on the cross-sectional shape of the shaft. Since the shaft is tapered or stepped its value must change as you butt or tip trim the shaft. If I was constant throughout it would be impossible to flatline a set of clubs.
Just to check I took an AP50 shaft and attached a test weight to the tip whose weight I could change very accurately. Using the same weight club heads as I did in my flawed exercise I butt trimmed the "set" and got essentially a flat line frequency result. I then repeated the process, this time tip trimming in ½" steps. I got roughly a 4cpm per club slope.
As Gilda used to say on Laugh-In "...never mind"