A
Archer
Guest
In article <[email protected]>, [email protected] says...
...
> > It wouldn't surprise me a bit if you couldn't tell the difference in tension by the sound of a
> > plucked spoke, especially in a high spoke- count wheel (because the load is distributed over so
> > many spokes), but it MUST be there, and with a sensitive enough tensionometer, you could measure
> > it. Do the calculations!!!
>
> The calculations will depend on what is assumed about the relative stiffness of the spokes vs. the
> rim. If we make the assumption that the rim is infinitely stiff and the spokes are elastic (as
> Mark pointed out this is a very poor assumption for a real wheel), then your 4-spoke wheel looks
> like a rigid hoop connected to the hub with strong 'rubber-band' spokes. The rubber bands each
> have a pre-load tension of 200 lbs-f, so the hub feels a pull of 200 lbs downward from the bottom
> rubber band, a force of 200 lbs upward from the top rubber band, and cancelling 200 lb forces
> forward and backward by the two side rubber bands. Now the hub axle is pushed down by the weight
> of rider + bike in the amount of 100 lbs-f. With a rigid hoop, the rubber band on the bottom will
> get shorter and have a reduced tension while the rubber band on the top will be stretched by an
> equal amount and have an increased tension. The two side rubber bands will only have an
> insignificant increase in their lengths, so they'll have very slight tension increases which we'll
> ignore. If the bottom and top rubber bands have the same spring constant, the reduction of tension
> from the bottom one will be equal to the increase of tension in the top and the sum of these two
> effects must balance the downward force on the hub of 100 lbs-f. So the bottom spoke sees a
> reduction of its preload from 200 lbs-f to 150 lbs-f, the top spoke sees an increase from 200
> lbs-f to 250 lbs-f and the net force on the hub is balanced as expected: 250 up - 150 down - 100
> down from rider+bike = 0 net force.
Yes. That was my conclusion as well.
> The other extreme is that the rim is very flexible and the spokes are more rigid. In this case
> when the wheel is pushed down by the weight of bike+rider, the bottom of the rim deforms while the
> rest of the rim maintains its shape. In this case the bottom spoke sees a decrease in tension but
> the top and side spokes will have no change. If the force from the weight of bike+rider is 100
> lbs, then the tension in the bottom spoke must decrease by 100 lbs-f to balance it and therefore
> change from the initial preload value of 200 to 100 lbs-f while the tension in the top spoke
> remains at 200 lbs-f. The net forces on the hub are still properly balanced: 200 up - 100 down -
> 100 down from bike+rider = 0 net force.
> In the case of my actual bicycle wheels with a lightweight rim and 36 14 gauge spokes almost all
> of the radial rigidity comes from the spokes and very little from the rim (the rim alone would
> immediately collapse under my weight). Therefore it closely matches the second scenario and I'd
> expect almost no change in the tension of the top spokes when the wheel is loaded.
I would tend to disagree with your assumptions about the rigidity of even a lightweight rim (let
alone a low-spoke-count one), and would expect the results to be somewhere near the middle between
the two cases, but your analysis is good (it must be; that's exactly the way I did ti <Grin>).
Now add one more step to the analysis, and pluck the spokes in each of the analyses above, and tell
me whether or not you can hear the difference in the 4-spoke wheels' spokes. I think you will. As
for the 36-spoke wheel, because the weight is spread out among so many spokes, I'll bet you can't
hear difference in tension between them, even though it is there.
--
David Kerber An optimist says "Good morning, Lord." While a pessimist says "Good Lord,
it's morning".
Remove the ns_ from the address before e-mailing.
...
> > It wouldn't surprise me a bit if you couldn't tell the difference in tension by the sound of a
> > plucked spoke, especially in a high spoke- count wheel (because the load is distributed over so
> > many spokes), but it MUST be there, and with a sensitive enough tensionometer, you could measure
> > it. Do the calculations!!!
>
> The calculations will depend on what is assumed about the relative stiffness of the spokes vs. the
> rim. If we make the assumption that the rim is infinitely stiff and the spokes are elastic (as
> Mark pointed out this is a very poor assumption for a real wheel), then your 4-spoke wheel looks
> like a rigid hoop connected to the hub with strong 'rubber-band' spokes. The rubber bands each
> have a pre-load tension of 200 lbs-f, so the hub feels a pull of 200 lbs downward from the bottom
> rubber band, a force of 200 lbs upward from the top rubber band, and cancelling 200 lb forces
> forward and backward by the two side rubber bands. Now the hub axle is pushed down by the weight
> of rider + bike in the amount of 100 lbs-f. With a rigid hoop, the rubber band on the bottom will
> get shorter and have a reduced tension while the rubber band on the top will be stretched by an
> equal amount and have an increased tension. The two side rubber bands will only have an
> insignificant increase in their lengths, so they'll have very slight tension increases which we'll
> ignore. If the bottom and top rubber bands have the same spring constant, the reduction of tension
> from the bottom one will be equal to the increase of tension in the top and the sum of these two
> effects must balance the downward force on the hub of 100 lbs-f. So the bottom spoke sees a
> reduction of its preload from 200 lbs-f to 150 lbs-f, the top spoke sees an increase from 200
> lbs-f to 250 lbs-f and the net force on the hub is balanced as expected: 250 up - 150 down - 100
> down from rider+bike = 0 net force.
Yes. That was my conclusion as well.
> The other extreme is that the rim is very flexible and the spokes are more rigid. In this case
> when the wheel is pushed down by the weight of bike+rider, the bottom of the rim deforms while the
> rest of the rim maintains its shape. In this case the bottom spoke sees a decrease in tension but
> the top and side spokes will have no change. If the force from the weight of bike+rider is 100
> lbs, then the tension in the bottom spoke must decrease by 100 lbs-f to balance it and therefore
> change from the initial preload value of 200 to 100 lbs-f while the tension in the top spoke
> remains at 200 lbs-f. The net forces on the hub are still properly balanced: 200 up - 100 down -
> 100 down from bike+rider = 0 net force.
> In the case of my actual bicycle wheels with a lightweight rim and 36 14 gauge spokes almost all
> of the radial rigidity comes from the spokes and very little from the rim (the rim alone would
> immediately collapse under my weight). Therefore it closely matches the second scenario and I'd
> expect almost no change in the tension of the top spokes when the wheel is loaded.
I would tend to disagree with your assumptions about the rigidity of even a lightweight rim (let
alone a low-spoke-count one), and would expect the results to be somewhere near the middle between
the two cases, but your analysis is good (it must be; that's exactly the way I did ti <Grin>).
Now add one more step to the analysis, and pluck the spokes in each of the analyses above, and tell
me whether or not you can hear the difference in the 4-spoke wheels' spokes. I think you will. As
for the 36-spoke wheel, because the weight is spread out among so many spokes, I'll bet you can't
hear difference in tension between them, even though it is there.
--
David Kerber An optimist says "Good morning, Lord." While a pessimist says "Good Lord,
it's morning".
Remove the ns_ from the address before e-mailing.