Conference rusure::math

1858.0. "Maximizing Clubhead Speed in Golf" by NOVA::FINNERTY (Sell high, buy low) Wed Mar 16 1994 15:39

    
    I was thinking about my golf swing yesterday (after watching 
    John Daly hit many amazing drives on the weekend), and I started
    wondering how to characterize clubhead speed in terms of the geometry
    of the club, arms, etc.
    
    Since I have no training in physiology, this is very tentative, and
    possibly entirely wrong.  With that in mind, I have included a maple
    script below that attempts to characterize clubhead speed, and with
    some assumptions about the angular velocities involved, derives the
    the angle of the forearms that must be present at the point of impact
    to maximize clubhead speed.
    
    ...no guarantees that this is correct, and comments are welcome!
    
#; 
#; The velocity of a golf clubhead is determined by the angular velocities
#; and the radiuses involved in the golf swing:
#;
#; 	1.  The left shoulder.  The radius is equal to the distance between
#; 	    the left shoulder and the ball in three dimensions. 
#; 
#; 	2.  The left wrist.  The radius is equal to the club length.  Action
#;	    of the right forearm (about the right elbow) and the right wrist 
#;	    rotates the club around this axis.  Since the right wrists moves
#;	    directly away from the right forearm, it follows that maximum
#;	    leverage is obtained when the right forearm is aligned directly
#;	    at the ball at the point of impact.
#;
#;	3.  A point that is in line with the left arm, but at a distance
#;	    club_length * cos(theta) from the left wrist, where theta is 
#;	    the angle formed between the left arm and the shaft.  Rotation 
#;	    of the left forearm accelerates the clubhead by this radius.  
#;	    Rotation of the right forearm around the left forearm provides 
#;	    leverage relative to this axis.
#;
#;	    theta is the complement of the angle formed between the left arm 
#;	    and the shaft, but since the right forearm is also in line with
#;	    the shaft, theta is also the angle that is formed between the
#;	    left arm and the right forearm.  This angle can be increased by
#;	    lifting the left shoulder and dropping the right shoulder, thereby
#;	    increasing the radius club_length * sin(theta).
#; 
#;
radius_wrist		:=	club_length;
radius_theta            :=      club_length * sin(theta);
radius_shoulder         :=      sqrt(radius_theta^2 + 
				     (arm_length + club_length * cos(theta))^2
				    );
clubhead_speed          :=      ang_velocity_arm * radius_shoulder 	+
                                ang_velocity_axial * radius_theta	+
				ang_velocity_wrist * radius_wrist;
dSpeed_dTheta           :=      diff(clubhead_speed,theta);

ang_velocity_wrist	:=	ang_velocity_arm * 2;	#; approximation
ang_velocity_axial	:=	ang_velocity_arm;	#; approximation

opt_theta		:= 	solve(dSpeed_dTheta, theta);

    
    re: .-1	
    
    	The assumption that the shaft is an extension of the right forearm
    	at the point of impact is false.  This would be true if the right
    	wrist was cocked downward and fully straightened at the point of
    	impact, but this is not the position that professional golfers
    	assume.
    
    	The angle between the left and right forearms is still related to
    	theta, though, under the assumption that there is a preferred
    	or natural orientation of the hands.  For example, Ben Hogan talked
    	about 'supinating' the left wrist (toward the right wrist) at the 
    	point of impact, which according to some has the effect of maintaining
    	club alignment, thereby reducing the tendancy to 'hook' the ball.