At 04:38 PM 3/22/2000 -0800, you wrote:
>Hi Brett --
>
>Nice to hear from you again.

You too, Karl, it's been a while.

>I have constructed a 1:1 model of the STS-1 leaf spring, based on the
>sketch in the paper referenced by Sean-Thomas.  By the way, I can send
>electronic copies of the article to anyone that wants them.  I have done
>testing with several variations in dimensions and don't see any significant
>"zero length" effect (which, incidentally, I think might be more properly
>termed infinite length).

In looking at the first results of the numbers, it became apparent what 
they were doing.  The major spring effect was from the bending effect at 
the ends, not the end forces.  It's working more like the mainspring of a 
clock than like a coil spring.

Imagine a leaf spring with each of its ends attached to the side of a round 
stick, so that by twisting the two sticks, you could make the spring form 
into a curve.  If you only twist and don't push or pull on the ends, the 
curve will be an arc of a circle.  Now, by just twisting, formin the spring 
into a half circle.  Then start pulling to the sides to make the ends of 
the spring separate more.  To keep the ends vertical (parallel), you will 
have to twist harder.  Pull apart more, twist more.  That's what seems to 
be happening to the spring in the STS-1.  The end *force* exerted by the 
spring is actually trying to make the boom rotate downward.  However the 
twist (the end moment) is a substantially greater effect, and is working in 
the direction to lift the mass.  In that configuration, as the beam tips up 
and down, the end moment changes very little.  With everything balanced, 
beam tilt has very little effect on the spring moment which equals very 
little change on the force supporting the mass which means long period.

If you look at pictures of the STS-1, you can see the flattened curve the 
spring takes when the end forces  applied to the spring are directed 
outwards, rather than inwards, as you might expect to have.  To get that in 
your prototype, you need to be sure the spring is the length given in the 
article, so that it has to flatten out somewhat.  Also, it appears that the 
STS-1 must be using fairly thin spring material.  With something like 
0.008" for a single spring, the model started looking fairly 
reasonable.  0.018" material bent that sharply would take a very permanent 
set.  Over a +/- 5 degree boom motion, the lifting force looked to be 
changing by less than 0.6%  Don't know what that implies for natural 
period, but pretty long for a first try.  Maybe too good; I need to go over 
the numbers more closely to be sure they are all making sense.

Still need much more playing to understand what's happening, particularly 
to find a configuration where the beam will sit stable at zero without 
help.  As you can tell, this is still all real preliminary.

Regards,
Brett

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