PSN-L Email List Message

From: Brett Nordgren Brett3mr@.............
Date: Wed, 01 Aug 2007 16:56:56 -0400

```Jerry,

Your question comes up fairly regularly on the list and sometimes generates
some confusing information.  I'll try to go at it from a 'hardware store'
approach.

Most close-wound extension springs have some amount of pre-tension.  That
is, you have to pull on them with significant force before they begin to
stretch.  A so-called zero-length spring has its pre-tension force
carefully controlled to be an exact value relative to its length and spring
constant (its force increase/length increase).  To be precise, the
pre-tension force 'F' must be designed to equal the the spring's
unstretched length 'L' x its spring constant 'k'.  Most springs from the
hardware stores have pre-tensioning that is substantially less than what is
needed for them to be "zero-length".

Actually, however, there is only one situation in which such a spring is of
much interest, and that is in the particular geometry discovered by Lucien
LaCoste when he was studying designs for vertical seismometers.  Some form
of that geometry, using a zero-length spring, had been employed for many
years in LaCoste & Romberg Gravity Meters.

** When used with any other geometry, there is nothing all that magical
about the zero-length spring characteristic. **

The particular LaCoste geometry, combined with a zero-length spring, has
the property that regardless of how you position the seismic mass, up or
down, it always remains exactly balanced, that is, the spring-mass has an
infinite period of oscillation.  However, having such a setup may not be
all that good for home seismometers.  In general when folks start trying
designs which have very long natural periods, they tend to have lots of
problems with position stability, of the sort that Ted mentions in his 28
July PSN-L posting "Testing the Folded Pendulum".  When working with a very
long natural-period design, I would expect that you would need to use some
sort of electronic feedback in order to have a chance of its working reliably.

To see what a real spring looks like, I measured a Servalite #59 from the
hardware store, a spring that some others have used for their
verticals.  The results, data and a graph, are at
http://bnordgren.org/seismo/Servalite59.pdf  Its unstretched length was
about 13.8 cm, and its pre-tension was near 205g, which meant that you
might be able to call it a "6.4cm-length" spring.  In order for it to be
"zero-length" its pre-tension would need to have been about 382g, slightly
more than 86% greater than what it was.

Hope all this doesn't just add to the confusion.

Brett

At 06:36 PM 7/31/2007 -0500, you wrote:
>Not being a physics student and rather dense (yes, I admit it), will
>someone please explain what a "zero length spring" is?  I have searched on
>the net and found this law and that law, which means nothing to
>me.  Finally, I found a webpage that also called it a constant pressure
>spring and displayed a large heavy duty spring that wound around itself,
>much like an alarm clock spring.
>
>It a zero length spring simply one that returns to its original shape
>after the force is released?
>
>Thank you,
>Gerald Payton

My e-mail address above should be working, but if not
you can always use my mail form at: http://bnordgren.org/contactB.html

Jerry,
Your question comes up fairly regularly on the list and sometimes
generates some confusing information.  I'll try to go at it from a
'hardware store' approach.
Most close-wound extension springs have some amount of pre-tension.
That is, you have to pull on them with significant force before they
begin to stretch.  A so-called zero-length spring has its
pre-tension force carefully controlled to be an exact value relative to
its length and spring constant (its force increase/length
increase).  To be precise, the pre-tension force 'F' must be
designed to equal the the spring's unstretched length 'L' x its spring
constant 'k'.  Most springs from the hardware stores have
pre-tensioning that is substantially less than what is needed for them to
be "zero-length".
Actually, however, there is only one situation in which such a spring is
of much interest, and that is in the particular geometry discovered by
Lucien LaCoste when he was studying designs for vertical
seismometers.  Some form of that geometry, using a zero-length
spring, had been employed for many years in LaCoste & Romberg Gravity
Meters.
** When used with any other geometry, there is nothing all that magical
about the zero-length spring characteristic. **
The particular LaCoste geometry, combined with a zero-length spring, has
the property that regardless of how you position the seismic mass, up or
down, it always remains exactly balanced, that is, the spring-mass has an
infinite period of oscillation.  However, having such a setup may
not be all that good for home seismometers.  In general when folks
start trying designs which have very long natural periods, they tend to
have lots of problems with position stability, of the sort that Ted
mentions in his 28 July PSN-L posting "Testing the Folded
Pendulum".  When working with a very long natural-period
design, I would expect that you would need to use some sort of electronic
feedback in order to have a chance of its working reliably.
To see what a real spring looks like, I measured a Servalite #59 from the
hardware store, a spring that some others have used for their
verticals.  The results, data and a graph, are at
http://bnordgren.org/seismo/Servalite59.pdf
Its unstretched length was about 13.8 cm, and its pre-tension was near
205g, which meant that you might be able to call it a
"6.4cm-length" spring.  In order for it to be
"zero-length" its pre-tension would need to have been about
382g, slightly more than 86% greater than what it was.
Hope all this doesn't just add to the confusion.
Brett

At 06:36 PM 7/31/2007 -0500, you wrote:
Not
being a physics student and rather dense (yes, I admit it), will someone
please explain what a "zero length spring" is?  I have
searched on the net and found this law and that law, which means nothing
to me.  Finally, I found a webpage that also called it a constant
pressure spring and displayed a large heavy duty spring that wound around
itself, much like an alarm clock spring.

It a zero length spring simply one
that returns to its original shape after the force is
released?

Thank you,
Gerald
Payton

My e-mail address above should be working, but if not
you can always use my mail form at:
http://bnordgren.org/contactB.html