You're correct, if you assume that the force applied to the ball is not changing. There are many tour pros whose smash factors don't fit the equations - pundits will say their clubs fail COR, but the data for many pros is similar to David D.'s. The equations don't work, and we know that they hit the ball on the center of the face.
Baseball and golf are very similar in this respect - the force applied to the club (or bat) changes through the swing, and resulting ball speeds ARE different when clubhead (or bat) speeds are equal. It's not the same as the 'balls suspended by strings' collision, or the 'billard ball' collision - the force applied to the club is changing (increasing for a good player) as impact approaches. Answer this: If the impact velocity for 2 players is equal and 1 has accelerated from the top and is coasting through impact while the other starts slowly and accererated through the ball, which one hits it further???? Or.... If a moving car hits a stopped car at 35mph, will the collision be different if the moving car is accelerating to 35mph, coasting at 35mph, or decelerating from a higher speed?? Again, I'm prolly wasting my breath with the 'expert' here. Pat K > > From: "Childers, Tedd A" <[EMAIL PROTECTED]> > Date: 2004/10/14 Thu AM 09:45:44 EDT > To: [EMAIL PROTECTED] > Subject: RE: ShopTalk: long drive > > Pat, > > I'm no physics expert, but I believe that the collision between a golf ball > and a clubhead is represented by the conservation of momentum equation > (M1V1=M2V2, in a perfect collision with no loss of energy), which is based > on mass and velocity, not acceleration. Of course the collision between a > golf ball and a clubhead is not a perfect collision, as there are other > factors involved (COR of clubhead for example), which makes the equation a > bit more complicated (see equation below). Clubhead acceleration probably > is a very important factor to measure to determine proper shaft stiffness > (i.e shaft lab), but I believe that Dave T. is correct when he says that > acceleration at impact has nothing to do with ball velocity. > > Tedd > > > > > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] > Behalf Of The Kelley's > Sent: Thursday, October 14, 2004 7:43 AM > To: [EMAIL PROTECTED] > Subject: RE: ShopTalk: long drive > > > > 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----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] > Behalf Of [EMAIL PROTECTED] > Sent: Thursday, October 14, 2004 2:19 AM > To: [EMAIL PROTECTED] > Subject: Re: ShopTalk: long drive > > > In a message dated 10/13/2004 2:28:28 PM Pacific Daylight Time, > [EMAIL PROTECTED] writes: > > > > > 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. > > >
