Virtual Capstan

[Richard Brekne]

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Ok... I see it now... yes I aggree that viewing this in terms of a second class
lever with the fulcrum at the whippen center, load at the capstan (what is
relieved from the capstan as it were) and input at the whippen magnet gives a very
nice way of figureing out the net yeild of the device. Took me a bit... but I
understand you now. :)

Using some real magnet weights and force levels from what I have plugged into your
leverage.. we have more or less what I have measured empirically.

I'm useing 1 magnet on an assembly weighing a total of 2 grams, and 2 magnets on
the keystick weighing a total of 2.5 grams.

Secureing one magnet to the scale (super glue :) ) and holding as steady as my
hand would allow for at about 8 mm over gave approximately 60 grams << weight >>
on the scale. At 17 mm -- 5 grams,  12 mm -- 15 grams, at 6 mm 80 grams.

These are reaaaaall rough estimates... tommorrow I contrive some sort of jig to
get a more accurate reading... but if we accept those and adjust the figures below
to basically match we get....

Ron Nossaman wrote:

>
> The first group defines leverage ratios and weights.
>
> center rail to magnet           moment3 95
> center rail to capstan          moment2 120
> keytop to center rail           moment1 220
> wip center to capstan           moment4 63
> wip center to magnet            moment5 80
> keytop to capstan               lever1          0.55
> keytop to magnet                lever2          0.43
> wip center to magnet            lever3          1.27
> magnet weight                           1.25
> wippen magnet assy weight               2.0
> key magnet assy weight                  2.5
>
> no magnet - weight on capstan   92         DW=  50.18
> This is what it takes in weight on the capstan to produce 50g DW. I don't
> care how it got there.
>
> add magnet weight to wippen             94.53      DW=  51.57
> A 2.0g weight adds 2.53g at the capstan. This is a second class lever,
> where the effect of the force (weight) is amplified.
>
> add magnet weight to key                96.24      DW=  52.49
> Add 2.5g inside capstan position, equivalent of +1.94g at capstan. First
> class lever, shorter moment arm, effective weight at capstan is less than
> that applied.
>
> define magnet lift                      7
> Approximate amount that made DW come out to about where it started - break even.
>
> add magnet lift to key                  100.20     DW=  54.65
> Magnet force pressing down on key. Effective force at capstan less than
> applied, just as with magnet weight. -5 gram at magnet yields 3.96 grams at
> capstan
>
> subtract magnet lift from key           91.31      DW=  49.8 (ok..grin.. 0.4
> grams off starting point)
> Second class lever, effective weight reduction at capstan is more than that
> applied. -5g at magnet equivalent to -6.35g at capstan.
>
> The static weight of the magnets (4.5g) add 4.48g at the capstan. The
> magnetic repulsion adds another 3.56g, and lifts 6.35g.
>
> At 60g magnet lift, adjusting the gap smaller, roughly this would result.
>
> no magnet - weight on capstan   92         DW=  50.18
> add magnet weight to wippen             94.53      DW=  51.57
> add magnet weight to key                96.24      DW=  52.49
> define magnet lift                      60
> add magnet lift to key                  143.74     DW=  78.4
> subtract magnet lift from key           67.54      DW=  36.8
>
> Here, the static weight of the magnets (4.5) add the same 4.48g at the
> capstan. The magnetic repulsion adds another 47.5g, and lifts 76.2g,
> reducing DW.
>

Interesting to note that tho the leverages between our two models differ a good
deal...the DW I got on my model at what very roughly looks to give 60 grams lift
(8 mm) yielded 44 grams DW, and this ended up at 37 grams. I suppose this could be
explained partially because you had a bit larger distance between magnet placement
and capstan (yours yielded more lifting power as it was closer to the balance
rail)  and because our key ratios differed by 0.4

Nice exercise... and thanks for the lesson in looking at different leverage
moments. This will make it much easier to see exactly whats going on.

Cheers
RicB


--
Richard Brekne
RPT, N.P.T.F.
UiB, Bergen, Norway
mailto:rbrekne@broadpark.no
http://home.broadpark.no/~rbrekne/ricmain.html
http://www.hf.uib.no/grieg/personer/cv_RB.html


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