Awwww man, and I try soooo hard too.
Al
At 09:09 PM 12/31/2002, you wrote:
Damn right. We finally got somebody around here who speaks English.
Hear, hear.
At 02:53 PM 12/31/02, you wrote:
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
