There was a complete explanation of this in Racecar Engineering a year or
two ago. it seems that the taper is the trick - even the taper center lock
bolts that modern race cars use exhibit this tightening /loosening to some
degree. Per the article I recall that there are two modern designs, with
the taper acting in different ways, so that the tightening action is
opposite so that the threads have to be opposite for each design to get the
desired effect. So it's likely that inertia of the ears has nothing at all
to do with the effect - especially since the article also noted that at
constant speeds (ie no acceleration) the nuts would tighten up if loose,
when on the correct side of the car.
Nice bit o'calculation, tho...
Brian
At 04:00 PM 04/19/2000 -0400, Carl McLelland wrote:
>Thanks to all who responded to my question of why one of my knockoff's
>tightened after racing. Your responses (1) generated some brain functions on
>my part and (2) answered a question of why the knockoff threads are
>directional (clockwise tighten on left side and counterclockwise tighten on
>right side) and why they "unscrew" if mounted on the wrong side.
>
>I whipped out the old and trusted Basic Motion and Accident Reconstruction
>formula's from Northwestern University Traffic Institute, put my solar
>calculator under the heat lamp, and went to work!
>
>Here's what I came up with (subject to variations and adaptations based upon
>unknown variables...... {check my math Lou... make sure I'm doing this
>right!})
>
>FACTS:
>Ole NEWTON said that an object at rest or in constant motion will continue
>to do so until acted upon by another force (in this case, acceleration or
>deceleration).
>My 2 earred knockoff's weigh approx. 23.3 ounces each.
>The total diameter (ear to ear) of the knockoff's is 6.5".
>The diameter of the knockoff base is 3.5".
>The ear height (from the knockoff base) is 1.5", so I'm assuming the
>center-of-mass of the ear to be .75" or a 5" diameter relative to the center
>of the axle.
>The tire circumference (21" diameter) is 65.97" or 5.498'.
>At 60 mph (88fps) the tire rotates 16.006 revolutions per second or 960.35
>rpm.
>The center-of-mass of the ears has a 15.71" circumference, and at 60mph
>(88fps) travels 251.45 inches per second (20.95fps).
>
>ASSUMPTIONS:
>20% of the weight of the knockoff is in the ears, so the weight of the ears
>totals 4.66 ounces.
>The wheel could feasibly rotate (on the splines) during acceleration and
>braking an equal amount so this motion cancels itself, providing (1) the
>knockoff rotates with the wheel or (2) does not rotate on the hub.
>At 60mph (88fps) the center-of-mass of the ears possess 31.759 foot ounces
>(1.985 foot pounds) of Kinetic Energy.
>Drag Factor (during braking) of 0.80% for an acceleration rate of <->25.76
>feet/second/second.
>Acceleration 0 to 60 in 10 seconds for an acceleration rate of +8.80
>feet/second/second.
>
>FINDINGS:
>During constant acceleration a force (energy) of 17.468 foot pounds/second
>is generated to accelerate (LOOSTEN) the knockoff on the hub.
>During constant deceleration (braking) a force (energy) of 51.137 foot
>pounds/second is generated to accelerate (TIGHTEN) the knockoff on the hub.
>
>These forces should remain constant until the mechanical drag of the
>metal/metal surfaces of the wheel and knockoff PLUS the hub to knockoff
>overcame the Kinetic Energy of the knockoff and prevented further loostening
>or tightening.
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