Well said, Dave....absolutely right on the issue of E*I, I had forgotten about that. As you stated, for different shafts by the same manufacturer, there will be slight differences, and for different manufacturers' designs, the differences could be significant. The problem I have with Braly's results is that they are subjective in that flex was **perceived** constant if the frequency changes by 8.5 cpm for each inch of length change. I wonder if we've been conditioned to the Brunswick curves, so we think something that falls on the line is "matched".
Thanks! Royce -----Original Message----- From: [EMAIL PROTECTED] [mailto:owner-shoptalk@;mail.msen.com]On Behalf Of Dave Tutelman Sent: Thursday, October 17, 2002 8:35 PM To: [EMAIL PROTECTED] Subject: Re: ShopTalk: Shaft flex ----- Original Message ----- From: Royce Engler <[EMAIL PROTECTED]> Sent: Thursday, October 17, 2002 9:16 PM > Yep. You're right. I mixed terms up. If we define "flex" as a combination > of spring constant, length, and clubhead weight that results in a given > frequency, I think that makes more sense. You can vary the three > parameters, but as long as they result in the same frequency, the "flex" is > the same. A few researchers (e.g., Cook) would agree. Most (e.g., Braly, Wishon & Summitt, etc) would not. Braly's original research resulted in the "Brunswick" slope (now, I guess, "FM Precision" slope). He did extensive subjective testing to see how frequency related to perceived flex. His conclusion was that flex was perceived as constant if the frequency decreases by 8.5cpm for each inch that the length is increased, assuming constant swingweight. Others (including TrueTemper and Dynacraft) agree. Cook's research was also subjective testing, and he concluded that a flat line (zero slope) was the best for most golfers. I disagree with some of his testing, if that is the conclusion he wishes to draw from it, but there is is anyway. How does this relate back to Pat's original question? Royce, I think you had it right when you first answered it. Let me try to paraphrase it. As you lengthen the club, the frequency WILL DROP. According to Braly's conclusion: * If it drops by more than 8.5cpm per inch of added length, then it will play softer. * If it drops by less than 8.5cpm per inch of added length, then it will play stiffer. In my experience, when you butt-lengthen a club, it tends to soften by 8-10cpm per inch. That's pretty close to "plays the same flex" if you're only lengthening an inch or two. I have one nit to pick with the rest of what you and Al agreed to... > For a given > shaft, the frequency that it vibrates when you clamp one end and twang the > other is a function of the spring constant (a material property of the > shaft), the length of the shaft, and the mass of the weight on the end of > the shaft (i.e. the clubhead). Close. The spring constant is a property of both the material and the cross-section geometry of the shaft. When you look at the formula for frequency (conveniently in the Appendix of Cochran & Stobbs), there is a factor of E time I. E is the elastic modulus of the shaft material. I is the moment of inertia of the cross-sectional area of the shaft. Multiply them together and you have the spring constant (or something proportional to it at least). Hope this helps. DaveT
