# Fitting Graphite & Steel

NOTE 18: When a clubmaker builds a set of clubs is he or she trying to match the clubs in frequency or stiffness to the players swing? It seems to me there is a slight difference. I've swung steel shafted and graphite shafted drivers that frequencied ( is there such a word, Microsoft Word doesn't think so) exactly the same but the graphite felt weaker. I used to wonder if it was my imagination or what. I got to thinking about this and it occurred to me there actually was a difference. (This is a perfect example of one having too much time on one's hands and the weather being too crummy to play golf.)

If you go back to Tech Note 1 the equation defining the frequency of a shaft is described. It basically says that frequency is proportional to the square root of the stiffness of the shaft and inversely proportional to the square root of length (actually length cubed) and weight. This is fairly intuitive. If the shaft were stiffer its frequency would go up. If the shaft were made longer or its weight heavier its frequency would go down. Weight (or mass) is a combination of the weight of the club head (or test weight) and the weight of the shaft itself. The actual expression being: M + .23m. In this expression M is the weight on the end of the shaft and m is the weight of the shaft itself. In the past shaft weights have generally been consistent but light weight graphites are a different story. Let's try a little numbers experiment. Static stiffness is basically the numerator in the Tech Note 1 equation, or the 3EI term. Assume we have two shafts that have identical stiffness as determined statically say on a flex board. The first is a 125 gram Dynamic Gold the second is a 45 gram Ultralite. Assume the steel shaft tests at 260 cpm. What will the Ultrlaite test at? Remember its static stiffness is identical to the steel shaft. If the shaft is 45" long and 5" of the butt is in the clamp its effective shaft weight is 8/9th of its total weight (40/45) or 40 grams. Using a 205 gram head the term M + .23m becomes 230.53 for the Dynamic Gold and 214.2 for the Ultralite. The square root of the ratio of these is 1.04. Since the Dynamic Gold was 260 cpm the Ultralite frequency will be 260 times 1.04 or 270 cpm. This makes sense (I hope) since the overall weight of the Ultraite is less its frequency should go up. Ten cpm is a pretty big difference.

If you were trying to build a 260 cpm club using an Ultralite you'd have to find a one flex weaker shaft to match the Dynamic Gold's 260 frequency. Maybe this is why the graphite shaft of the same frequency feels weaker than its steel counterpart. Since the graphite shaft invariably has a higher torque maybe it all comes out in the wash when it comes to playability.

Here's a table of the frequencies as the shaft gets progressively lighter.

 Shaft wt 125 grams 100 grams 75 grams 50 grams Frequency 260 cpm 263 cpm 266 cpm 269 cpm

Just food for thought.