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Aside from golf ball speed which is primarily a function of clubhead speed, ball

launch angle and spin rate are the only other two factors under the control of the golfer

that can affect driving distance. For a perfectly impacted golf ball, no side spin is

imparted to the ball and the flight of the ball does not deviate from a path directly above

the target line. Under these conditions, launch angle refers to the angle between the

velocity vector of the ball and the horizontal immediately after impact, while spin rate

refers to the amount of angular velocity (back spin) imparted to the ball. With respect to

the execution of a golf drive, spin rate is primarily a function of clubhead loft (including

dynamic loft), while launch angle is a function of both clubhead loft and clubhead path

(Winfield & Tan, 1994). If a golfer has a consistent swing, then the path of the clubhead

relative to the ball will not change from swing to swing. Therefore, by adjusting the

amount of clubhead loft relative to the ball, an optimal ball launch angle and ball spin

rate can be found for achieving maximum driving distance. Results from the computer

simulations demonstrated that clubhead loft can change by as much as 0.65° depending on shaft stiffness for a golfer with a swing speed of approximately 45 m/s (101 mph)

(Table 3.1.2.1). For example, the Golfer-Medium\Club-Stiff simulation resulted in

4.82° of dynamic loft at impact, while the Golfer-Medium\Club-Flexible simulation resulted in 5.47° of dynamic loft. The results from the optimization study conducted by Winfield and Tan suggest that a loft change of this magnitude may be enough to have a

meaningful influence on driving distance. However a golfer must swing very

loft could be expected when comparing the non-optimized swings of many amateur

golfers.

It should also be pointed out that the loft increases brought about as a result of

shaft flexibility could also be made simply by changing the static loft of the club. For

example, clubhead loft dynamically increased by 0.65° when Golfer-Regular was matched with Club-Flexible (5.47°) in comparison to the Golfer-Regular\Club-Stiff (4.82°) combination (Table 3.1.2.1). These two simulations would theoretically produce different ball flight conditions because of the discrepancy in clubhead loft at impact. If

the face angle of Club-Stiff was geometrically changed to increase the static loft of the

club by 0.65°, both conditions would then produce the same theoretical ball flight. This would be the case because the clubhead paths between conditions were already not

meaningful different (not previously reported), and the clubhead speeds were already

very similar (44.96 m/s vs. 45.04 m/s). The effect of statically changing the loft of

clubface was confirmed using the model. Statically increasing the loft from 10° to 10.65° resulted in the loft at impact increasing by 0.6496°. Physically altering the loft of the clubface will not change the position of the center of mass of the clubhead and

therefore, will have no influence on shaft deflections during the swing.

In summary, clubhead path, loft and speed influence ball flight. As a variable,

only shaft stiffness was found to have a meaningful effect on clubhead loft which can

also be changed by altering the physical geometry of the club. Therefore, it seems that

shaft stiffness is not a necessary variable to consider when fitting a driver to a golfer’s

However, there are two other factors to consider before defining the role of shaft

stiffness. First, perhaps solely manufacturing a more complete spectrum of clubhead

geometries with a single shaft stiffness is not practical. It may be more economically

feasible for club manufacturers to provide a range of both clubhead geometries and shaft

stiffness that produce the desired impact conditions. Second, the influence of feel

cannot be easily dismissed. Certainly, the feel of the driver is linked to the golfer’s

confidence in executing the shot which will inevitably weigh heavy on the final outcome

of the swing.

4.3 The Mechanisms Behind Shaft Bending

Both radial and tangential forces, relative to the circular path traced by the

longitudinal axis of the shaft, played important roles in shaft deflection during the

downswing and in the resulting clubhead orientation at impact. The possible

mechanisms behind shaft bending were previously discussed in the introduction. It was

argued that using a conceptual frame work that described forces that were either radial

or tangential to the longitudinal axis of the shaft would help understand the cause of

shaft deflection during the downswing. The same conceptual frame work will be used

in this discussion.

The largest magnitude of shaft deflection during the downswing was in the toe-

up direction. For the computer simulation swings of Golfer-Medium, the maximum toe-

up deflections were approximately 10 cm in magnitude and occurred during the initial

part of the downswing. Tangential forces acting along the x axis were the primary cause

clubhead speed and little influence on the final orientation of the clubface at impact.

Initial bending in the toe-up direction may superficially appear to be storing energy

which could later be released to increase clubhead speed. However, due to the 90° rotation of the club about the lead arm during the final stage of the downswing, none of

the energy stored in the initial part of the swing could ever be returned to the clubhead

along the intended direction of ball flight. Further, any residual effects of this deflection

present at impact will only have a small effect on the dynamic loft of the club. Based on

the results of this thesis, it would appear that the initial bending in the toe-up direction

would only serve to increase the variability in a golf swing. This information supports

the view of those golf instructors that advocate a ‘smooth’ transition into the

downswing, as opposed to a rushed transition that would lead to larger shaft deflections

early in the downswing.

The next important period of shaft deflection occurred in the lag direction over

the final half of the downswing. For the computer simulation swings of Golfer-

Medium, the maximum lag deflections were approximately 3.5 cm in magnitude.

Tangential forces, acting along the y axis were the primary cause of deflections in the

lag direction. Shaft deflection in this direction resulted in the storage of strain energy

that had the potential to be released near impact and result in a faster clubhead speed.

This period of shaft deflection cannot be predicted from a 2D model and is essentially

why a 3D simulation was needed to sufficiently model the downswing.

The final phase of shaft deflection was the most important since it described

clubhead orientation at impact. It was also the most complex because both tangential

time period (0.03 s). Over the final few hundredths of a second of the downswing, the

clubhead rapidly moved from its maximum lagging position into its maximum leading

position at impact. For the computer simulation swings of Golfer-Medium, the lead

deflections at impact were approximately 6.0 to 6.5 cm in magnitude. The complete

removal of radial force during the downswing only reduced lead deflection to 4.72 cm

(Fig. 3.2.3.1). Therefore, when acting in isolation, the tangential forces were

responsible for a considerable portion of the lead deflection at impact. The complete

isolation of radial force demonstrated that while acting alone, radial force could only

result in 1.22 cm of lead deflection at impact (Fig. 3.2.3.2). Summing the lead

deflection that occurred from the isolation of the two sets of forces results in a lead

deflection of 5.94 cm, which is 0.31 cm less than when radial and tangential forces acted

simultaneously. This finding suggests that there is an interaction effect between the

force components in terms of lead deflection.

Toe-down deflection at impact was also affected by both radial and tangential

force components. Both radial and tangential force components contributed

approximately equally to the magnitude of toe-down deflection at impact. When acting

in isolation, radial force was shown to deflect Club-Regular by -1.33 cm in the toe-down

direction. For the optimized swing of Golfer-Medium with Club-Regular, toe-down

deflection was -2.26 cm at impact; therefore, just over half of that deflection was the

direct result of radial force action. The additional deflection was the result of the club