Potential improvement in deflection from narrowing shaft diameter

D

Dead Crab

AzB Silver Member
Silver Member
I offer the following, based largely on Ron Shepard's work:
http://billiards.colostate.edu/physics/Shepard_squirt.pdf


Based on the data in table I, my own McDermott cue which has a pivot point of about 10.5" and a 13mm diameter probably has a cueball mass:endmass ratio of about 20/1.
I calculate that the contribution of endmass of the cue is limited to the last 2.67cm of your typical 1.3cm maple shaft. The assumptions used in this computation are a cue ball mass of 170g, density of maple wood of 0.6 g/cc, and pro taper. Ratio of ball mass to cue endmass of 20:1. the endmass of the shaft would be 8.5 g

Decreasing the diameter of this cue to 1.1 cm (11mm) results in an endmass of 6.08g, a cueball to endmass ratio of 28:1.

Looking at table 1, it is seen that this approximates the 30:1 table entry, that corresponds to a pivot point of 15.4" and squirt of 1.59 degrees.

So, just turning down a regular maple shaft from 13mm to 11mm gets you a 0.74 degree reduction in deflection for a 75% english shot, which is about 0.6" at 50 inches.

Now, if I am not mistaken, the values in Shepard's table are for (the dreaded) parallel english. So the result of narrowing the diameter is a cue much more forgiving of off-center hits, but I do not see that an 11mm shaft is any better than a 13mm shaft when each has english applied by pivoting at the natural pivot point of the cue.
 
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I knew I should have bought the Rosseta Stone! It sounds like all that is being said here is that the lighter then end of the cue, the lower the deflection?

Chris
 
Yes........I must agree. However, I think you're overlooking the Earths elliptical rotation in your equations. :eek:
 
hdgis1 said:
I knew I should have bought the Rosseta Stone! It sounds like all that is being said here is that the lighter then end of the cue, the lower the deflection?

Chris
Click to expand...

Well, you can also consider that there have been reports that certain "high performance low deflection shafts" have pivot points in the neighborhood of 14", and the above calculations would imply that this is roughly equivalent to a standard shaft turned down to 11 mm.

Also, knowing that the density of graphite is about 3 times higher than maple, it raises the question of why McDermott cored their cues with it. It also explains why they narrowed the shaft.

Furthermore, if you are going to have your cue lathed, you might as well know ahead of time a reasonable estimate of what improvement (or at least what change) you can expect.
 
DeadCrab:
... I do not see that an 11mm shaft is any better than a 13mm shaft when each has english applied by pivoting at the natural pivot point of the cue.
Click to expand...

This is only true if simple pivoting is a reliable way to compensate for squirt. But because of swerve pivoting is a complex maneuver made more difficult by higher squirt.

pj
chgo
 
Dead Crab said:
I offer the following, based largely on Ron Shepard's work:
http://billiards.colostate.edu/physics/Shepard_squirt.pdf

Based on the data in table I, my own McDermott cue which has a pivot point of about 10.5" and a 13mm diameter probably has a cueball mass:endmass ratio of about 20/1.
Click to expand...
I think the data in Shepards's paper is a little misleading. For more info, see:

Dead Crab said:
I calculate that the contribution of endmass of the cue is limited to the last 2.67cm of your typical 1.3cm maple shaft. The assumptions used in this computation are a cue ball mass of 170g, density of maple wood of 0.6 g/cc, and pro taper. Ratio of ball mass to cue endmass of 20:1. the endmass of the shaft would be 8.5 g
Click to expand...
Based on my tests, the length that contributes to endmass is typically closer to 6 inches (15 cm). For more info, see the article and analysis links here:

Dead Crab said:
just turning down a regular maple shaft ... gets you a ... reduction in deflection
Click to expand...
This is most certainly true. You can also use a shorter and lighter (or no) ferrule and drill out the shaft core. Anything that lightens the end of the shaft reduces CB deflection (AKA "squirt"). For more info, see:

Regards,
Dave
 
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