My Room is now spinning##!#@%(^():-O ----- Original Message ----- From: "Alan Brooks" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Tuesday, December 31, 2002 3:53 PM Subject: Re: ShopTalk: shaft flex v.s. frequency
> Hi Lloyd, > > We're talking about the same phenomena so I suspect our differences are a > question of semantics. If you clamp the butt of the club and displace the > head and then release it, the club will return to straight (that's a > quarter cycle), pass through straight to displaced an equal (nearly) amount > in the opposite direction (half cycle), return to straight (3/4 cycle), and > pass through straight to its original position (full cycle) and repeat. At > the start of the downswing a golf shaft is nearly straight, flexes back > during the downswing due to the forces applied to it by the hands, and > returns to straight at impact. I consider that a half cycle, although > because it is a forced oscillator instead of a free oscillator the analogy > is certainly not exact. With the shaft as a clamped free oscillator it > begins displaced with zero velocity, a quarter cycle later is has zero > displacement but the velocity is a maximum, at the half cycle point the > displacement is again maximum (but in the opposite direction) and the > velocity is zero. With a swung golf club it starts with zero displacement > and zero velocity (in a reference frame that rotates with the shaft and > positive is towards the ball/target), as the shaft is driven forward in the > swing plane by the hands the club head is driven back by its inertia and > acquires both negative displacement and velocity, at some point the force > on the club head from the shaft (driven by the hands) determined by the > shaft stiffness and it's displacement stops its backwards movement (in our > reference frame) and starts it moving forward. At impact the shaft is > again straight (its gone from straight to negative displacement to straight > again) and the head has velocity in the forward direction (its gone from > zero velocity to negative velocity to positive velocity, in a reference > frame moving with the shaft). Is this a quarter cycle or a half > cycle? Your choice. > > This is a very dynamic problem and I have completely ignored centrifugal > forces on the club. The rate that the shaft tries to recover from a > displaced position is that of the free oscillation frequency and is > independent (nearly) of the magnitude of displacement. This shaft > stiffness (oscillation frequency) must be tuned so that it recovers from > the time history of its forced displacement (which is determined by the > individual golfer and their swing characteristics) and is again straight > (maximum velocity) at impact. Is this simple description complete? Of > course not. There are many other things going on during the average > golfers swing that effect the dynamics of the club, but this is, I believe, > the fundamental response. You are right, of course, that swing > characteristics are what you want to match with shaft frequency, not final > velocity. > > As far as 'toe bob' goes I am not sure that I know what you mean by > this. I think it is probably the toe down deflection of the club head > caused by the centrifugal force on the offset cg of the club head. This > force increases very rapidly near impact (it's proportional to the square > of the head velocity) and is resisted mostly by a relatively short section > of the shaft near the tip. The oscillation frequency of this 'sub-system' > on the shaft is going to be much higher than of the entire shaft so the > timing problem here is different. The forcing function is of much shorter > duration and the response much more rapid. It basically effects the lie of > the club head at impact and occurs easily in the last 100-ms before impact > (at least it does on my Shaft Lab plots). > > Are we getting close to the same page? > > Regards, > > Alan > > > > At 12:11 PM 12/31/02 -0800, you wrote: > >Alan > > > > First we need to get the 1/2 cycle thought straightened out. The club flex > >normal to the club face that affects hitting the ball by adding club head > >speed, preferably returns to impact though only 1/4 cycle of its natural > >frequency. The deflection during the loading process is controlled by the > >swing rates or loading rates of the player not the natural frequency of the > >club. This club release or natural frequency controlled 1/4 cycle seems to > >occur in all the data I have seen, including Shaft Lab, in the last 100 > >milli seconds of the swing. This 1/4 cycle time is the most important timing > >factor in selecting club stiffness not club head speed. > > > >Now toe bob is a different problem. The loading that causes toe bob occurs > >much earlier in the swing and can go through a 1/2 cycle + or - according to > >the stiffness of the club. The major cause of toe bob is the failure to > >pause at the top of the swing or a strong casting from the top of the swing. > >Because of the toe down position of the club at the top of the swing the > >loading imparted by casting causes a toe up deflection of the shaft. As the > >club begins to rotate into the position for impact the loading is now more > >normal to the club face and the toe up deflection is released and now > >controlled by the natural frequency in the toe bob plain. If the stiffness > >of the club is such that the club has returned though the 1/2 cycle the head > >is in a toe down position at impact. > > > >I hope this helps clarify your thoughts about the affect of natural > >frequency on the golf club as related to the swing. > > > >llhack > > > > >
