You need to have acceleration information for each combination to evaluate the data - I'd expect that the longer shaft is allowing the player to accelerate the clubhead a bit more as impact approaches than the other drivers, thereby imparting a bit more force to the ball. I'll offer that the 5g difference in clubheads in your test is not significant with respect to the force imparted on the ball, as seen in the #2 and #4 test data.
Sorry, but I have to disagree with both assertions.
The formula for ball velocity (ignoring centeredness of the hit and loft) is
Vb = Vc*(1 + COR) / (1 + Mb/Mc)
Ref: Cochran & Stobbs "Search for the Perfect Swing", but most of it is derivable from basic freshman physics.
Note that there is no component of acceleration at impact involved, and there shouldn't be.
But the clubhead mass does make a difference, small but not completely negligible. The difference between 195g and 200g should be worth about 1/2%, or 1mph at the ball speeds involved.
(BTW, those who look will notice that my numbers are very different from those that Lloyd just posted. We agree completely that mass matters and acceleration at impact doesn't, but disagree considerably on just how much mass matters.)
Let's try out this formula for each of the drivers, to see whether something else is going on...
driver 1 2 3 4
avg chs 142 148 148 150 avg bs 206 198 198 202 club length 50" 48" 48" 48" spin rate 2100 2100 2200 2400 hd wt 200gr 195gr 195gr 200gr launch a 11.5 12 12.5 12.5 hd vol 455cc 444cc 450cc 400cc my smash # 1.45 1.33 1.33 1.34
Let's assume that, for all four drivers: * The COR for the hit is 0.83, the legal limit. * The hit is in the center of the clubface. * The balls are all the same mass; we'll use 46g.
Driver #1:
Vb = 142(1.83) / (1 + 46/200) = 211mph (actual 206)
Driver #2:
Vb = 148(1.83) / (1 + 46/195) = 219mph (actual 198)
Driver #3:
Vb = 148(1.83) / (1 + 46/195) = 219mph (actual 198)
Driver #4:
Vb = 150(1.83) / (1 + 46/200) = 223mph (actual 202)So only driver #1 is anywhere near what the theory says it should be able to get. #1 is off by 2.5%, which is a pretty significant difference for a long driver -- it corresponds to ten yards or more for those guys. The other three drivers are only achieving about 90% of what the theory says they should. Something is wrong here, and something serious.
Let's look at a few possibilities:
(1) Are the assumptions correct? In particular, did somebody use impact tape to verify that all measurements were on centered hits?
(2) Did somebody measure the COR of each driver using the type of ball used in the range tests? (I doubt it; the drivers were undoubtedly tested using the USGA pendulum test.) I know I disagree with Lloyd on lots of things, but his comment about a clubhead/ball match is a real possibility. In 1998, Dick Helmstetter said in my presence -- and Alastair Cochran's as well -- that they were looking at the opportunities for extra distance by matching balls to clubheads. Most of their effort was based on matching resonant frequencies, as Lloyd mentioned. Not at all an outrageous consideration.
(3) Somebody mentioned a difference in loft or launch angle. That might make a substantial difference in distance, but the difference in ball speed would be small but measurable. The difference between 11.5 and 12.5 degrees would be under 1/2%, or less than 1mph. So that isn't the problem.
Any ideas on what can be concluded from this data?
My conclusion is that there is some VERY significant difference from test to test. I don't know if it's something about the club itself or how it is being swung (and impacting the ball), but this is not apples and apples.
David, I know we've discussed this before (via private email) with other drivers. But those tests were a lot closer to the theory. Yes, they confounded the direction the theory says they should go, but they were closer. This is WAY off.
DaveT
