You are starting to scare me. I understood every word you said. Further more, that is exactly as I had learned the process to be. Look out 10th grade physics, here I come.
Al
At 01:49 AM 1/3/2003, you wrote:
Hi all,
Let me re-'cast' this into a different perspective and see if we're talking about the same thing. As a simplification lets assume that we have a club head that has zero degrees of loft and is the same thickness as the shaft with the cg in the middle so that centrifugal forces on the club head in a direction parallel to the shaft only bow the shaft toe down. Assume zero loft so there is no confusion when I talk about the face of the club being parallel to the swing plane. Assume the golfer is a 'hitter' so that there is a torque from the hands trying to rotate the club down in the swing plane during the downswing. Let's also assume that the arms and club remain in the swing plane during the swing.
The downswing starts with the club perpendicular to the arms at the beginning of the down swing. The hands apply a torque to the butt of the club trying to rotate the club in the swing plane and an axial pull on the butt of the shaft trying to pull the butt of the club around the arc of the arms. The circular motion of the butt of the club creates a centrifugal force on the whole club (as a rigid body) which causes it to accelerate outward (away from the hands). There is very little reaction force on the hands (in the direction of the axis of the shaft, at least) at this point because the club is free to accelerate outward. As the hands near the bottom of the downswing and the club axis begins to align with the arms the club is no longer able to accelerate outward because the hands (attached to the arms and those to the shoulders and body of the golfer) resist this axial force from the centrifugal acceleration of the club. The club head, however, is still trying to accelerate outward and is being resisted by the shaft. Because the cg of the club head is offset from the axis of the shaft a toe down moment is applied to the end of the shaft, which bows downward, allowing the club head to bow toe down. Because the centrifugal force is only being resisted by the arms at the very last part of the swing and the centrifugal force itself is rapidly peaking (it's proportional to the square of the velocity), 'toe bob', as I understand the meaning of the term, only occurs at the very bottom of the downswing. Because only the tip of the shaft is resisting this bending moment (mostly) it is very stiff and the head bobs down and up at a relatively high frequency (compared to the shaft as a whole). For someone with a very efficient swing (such as a pro) there is probably only time for a half cycle or so, for the rest of us there could easily be time for more than a half but our centrifugal forces aren't as large so there is less effect.
Back up to the top of the downswing, let's talk about the torque that is applied to the butt of the shaft by the 'hitter' that is trying to rotate the club about an axis that is perpendicular to the hands (we'll get to the rotation of the club about the shaft axis in a moment). That torque tries to rotate the shaft and is resisted by the mass of the club head (we'll assume the shaft is mass-less for the sake of argument). This causes the shaft to bow back (up?) in the swing plane. The hands continue to drive the shaft around the swing arc and eventually the stiffness of the shaft stops the bowing of the shaft and starts straightening out the club, which occurs, if the shaft frequency is properly adjusted for the swing tempo, just at impact.
While all of this is going on, of course, the hands are twisting the butt of the club to rotate the face of the head from parallel to the swing plane at the start of the downswing to perpendicular to the swing plane at impact. The really cool thing about this is that the curvature of the shaft, even though the shaft and club head are being twisted from parallel to perpendicular, remains in the swing plane (I just love that, this is so much fun). If you don't believe that I'll post a little experiment you can use to make a couple of bucks off your friends.
This, of course, is a greatly simplified version of a golf swing, but the fundamental mechanics are, I believe, correct. Toe bob occurs at the very bottom of the down swing (you can see it in the TT Shaft Lab charts as the blip in the traces just before impact). The toe-up strain you see in Shaft Lab data at the beginning of the downswing is due to the curvature of the shaft created by the torque on the butt and the inertia of the head. If you plot the 'principle strain', the vector sum of the toe up/down strain and the lead/lag strain you can see the principle strain (the direction of maximum bending) rotate during the downswing from 'toe up' back through 'lag', through 'toe down' (the 'bob' a little before impact) to 'lead' (in my case) at impact. It's really cool, actually. I am sure this is going to have most of you going "What?". If you want a more detailed post on what you can do with the Shaft Lab data let me know and I'll try and put something together with some figures.
Grist, and more grist,
Alan
At 07:00 PM 1/2/03 -0800, you wrote:
Dave Since for most golfers the position of the club at the top of the swing, the toe is pointed down an the clubhead face plain is parallel to the line of flight, turning the club quickly from the back swing to the down swing or pulling down hard from the top will induce a toe up deflection of the shaft out of the hitting plain. Yes, when the player then stats to rotate the club the load is released from the off axis plain and the bob starts. Look at the Shaft Lab data and you can see there is a significant toe up stress in the shaft at the top of the swing. But it dose vary with the player just as determinator accelerations vary with the player ( The way they have you orient the head of the determinator vertical at the top of the swing say the primary acceleration it is reading is at the top of the swing).llhack ----- Original Message ----- From: "Dave Tutelman" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Thursday, January 02, 2003 3:19 PM Subject: Re: ShopTalk: shaft flex v.s. frequency > Let me throw in yet a different explanation. (And yes, I have looked at > ShaftLab data, though it was pre-2000 data.) > > First, about the other two theories I've seen: > > (1) Al, you would not be that far off on the deceleration theory -- if > there were enough deceleration to significantly change the velocity and > thus the centrifugal force. There really isn't, unless the swing is > terrible. The decel of the average middle handicapper probably doesn't > account for even a 5% decrease in clubhead speed from max in the downswing > to impact, not enough for the sort of toe bob we're talking about. > So, while centrifugal force is a major contributor to toe-down > deflection at impact, it probably doesn't explain "toe bob" -- which is > really a dynamic and usually unpredictable component of the toe deflection > that isn't simply explainable by centrifugal force. > > (2) Lloyd, it isn't a reaction to the toe-up deflection. Deflections and > their reactions occur in a single inertial plane. The toe-heel plane is not > an inertial plane; it rotates through the inertial reference during the > downswing. The toe-heel plane rotates from the target plane (an inertial > plane) at the top of the downswing to a plane roughly perpendicular to the > target plane at impact. So any reaction to an initial toe-up deflection > (caused by casting, for instance) would have to be in the target plane and > would not cause toe bob. > > But the argument against #2 does suggest another theory. Toe bob may well > be a reaction to deflections induced by the golfer during the downswing as > Lloyd suggests, but those deflections would have to be in the plane that is > perpendicular to the target plane and through the shaft. Let's remember > that the target plane is, ideally, also the swing plane. In other words, > any off-plane bobbles the golfer introduces during the downswing might > induce a reaction that takes the form of an unpredictable toe-heel > deflection at impact. > > Actually, that makes fair sense to me. One of the things that marks the > better golfer is that the swing is on plane... that from the pull down from > the top the shaft stays in the target plane, with no forces from the hands > pushing it outside the target plane. So if toe bob is a reaction to > outside-the-plane forces in the downswing, one would expect less of it from > the pro than the duffer. > > OK, I think I understand that. Where did I go wrong? > > Cheers! > DaveT > > At 01:16 PM 1/2/03 -0500, Al Taylor wrote: > >Lloyd, > >I hate to argue with an engineer since I am out of my league then, but I > >believe that the TT shaft lab results do show that higher head speeds have > >greater toe down. Along this area, the Pros usually are still > >accelerating into impact and, as a result, have little to nil toe > >bob. The amateur often starts to decelerate prior to impact and the toe > >then starts back up, or bobs. The TT graphs show that somehow there is > >often a series of toe ups and toe downs on the later example. > > > >I know that my irons profile is similar to pro iron profiles (wonder why > >my shot results aren't the same?) but my driver shows some toe bob. > > > >Al > > > >At 09:40 AM 1/2/2003, you wrote: > >>Royce and Alan > >> > >>The centrifugal force is certainly part of the Toe down deflection at > >>impact. Since toe down deflection is dependent on club head speed this > >>would make the better players with the high clubhead speeds have greater toe > >>down deflection ( opposite True Temper results ). What I described earlier > >>is the other component of toe down defection at impact. As can be seen in > >>all of the Shaft Lab data there is initially a toe up deflection at the top > >>of the swing. This deflection along with the time from the start of the down > >>swing to impact gives the shaft time to go through 1/3 to 2/3 cycle of its > >>natural frequency resulting in some degree of toe down deflection. This > >>resulting defection is a function of how much the club is loaded at the top > >>of the swing to produce the initial toe up deflection. Herein lies the > >>difference between the good player and the others.... > >
