David,
You're
welcome to follow both Dave T and Lloyd, both of whom 'know' so much about the
golf swing.... The folks on tour have been measuring acceleration for many
years, but according to Dave T (and hid 'bible' on the golf swing that many
modern experts on this game threw in the trash years ago), acceleration has
nothing to do with ball speed. Last I checked, basic physics says
force = mass x acceleration, but I'm sure we'll see many reasons why this
doesn't apply to golf.
I
guess I'd forgotten why I don't post here - the 'expert' (who
has apparently never earned a dime in the golf business) is not woth my
breath.....
Good
luck in your fact finding - you seem both intelligent and open minded, both of
which will allow you to make progress.
Pat
K
-----Original Message-----In a message dated 10/13/2004 2:28:28 PM Pacific Daylight Time, [EMAIL PROTECTED] writes:
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On Behalf Of [EMAIL PROTECTED]
Sent: Thursday, October 14, 2004 2:19 AM
To: [EMAIL PROTECTED]
Subject: Re: ShopTalk: long drive
At 07:50 AM 10/12/04 -0400, The Kelley's wrote:
>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
Thanks,
Dave and all that responded,
Im sure that we are all a hold of a piece of the grail, there is no doubt a point of diminishing return and finding it is easier for some than most.
For the acceleration data I believe Pat may be on to something.
If you can imagine the acceleration curve as an upside down v and pick a clubhead speed such as 100 mph and imagine it at the peak of the V, and if you can further imagine that at just before the peak and just after the peak you have a clubhead speed of 99 mph I would expect that you would achieve a higher ball speed at 99 prior to the peak than you would after it.
