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Swing plane restoring torque




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Fig 1


In Fig1 is shown a golf swing using a simple 3D model utilizing two segments.  The blue plane represents the dynamic swing plane.  There are two in-plane angles, θ1[t] and θ3[t], and the out-of-plane angle, θ2[t].  The latter is the angle between distal segment 2 and its projection onto the swing plane - the dashed white line segments.   As shown, θ2[t] is kept constant at an arbitrary chosen angle of  5 deg during the swing.  

This 3D model can be used to find conveniently the magnitude of the restoring torque operating on segment 2 trying to bring it down to the swing plane - blue surface - during the down swing.  The larger this restoring torque the more the dynamic swing plane imposes itself on the gofler.  It is somewhat complicated to derive but the torque derived is as shown in relation (1) :

<br />Torque = .12 L2 (3 L1 (M2 + 2 M3) Cos[θ2[t]] Cos[θ1[t] - θ3[t]] θ1 ...                 

For the swing as shown in Fig1 with an impact speed of 115 m/h, and appropriate values substituted for the various parameters, leads to the curve shown in Fig 2.

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One notices from Fig2 that the restoring torque from the top of the swing initially is very small and than increases rapidly to quite large values towards impact.  A torque of  35 lbft is indeed quite respectable.  

For small angles the torque is virtually proportional with the angle.  For θ2 quite small, for instance 1/2 deg, there is still a respectable restoring torque of  3.5 lbft operating on the shaft.  The restoring torque at impact as a function of the angle  θ2  is shown in Fig3. Notice that the restoring torque can get quite substantial.

It explains why most golfers have club shaft and lead arm much more in line than at address. It is very difficult to resist such large torques.

The very small  restoring torque at the top of the swing corresponds to the fact that we can initially very readily manipulate the clubhead such as for instance to flatten the swing plane.  However we better establish the correct down swing plane quickly since  the restoring torque rapidly increases in value.

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To put the information of Figs 1 and 2 in a more visually attractive way I have combined the information in Fig4.   The restoring force vector - magnitude and direction - as it is operating through the clubhead,  is shown with the multicolor line segments.   

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Fig 4

mandrin