In a message dated 2008/02/17, PETERS_RD@.......... writes:

Hi Randall,

       I hear what you say about pendulums and agree with it. However, I am 
having a little bit of a problem in relating this to seismometers, in which the 
principle is that the mass stays still - it is the Earth which moves / 
accelerates!

       Before we try to reinvent the wheel, perhaps we should consider the 
history of  past seismometer and linkage types?

       A simple vertical pendulum depends for the resonant period on the 
length of it's suspension. It is desirable to keep this ~1 second , ~25 cm, on 
grounds of physical size, ease of construction and freedom from environmental 
effects. 

       We can keep about this size, but get much longer periods if we use 
either a garden gate suspension, a Romberg linkage or a Folded pendulum 
construction. However, the gg uses two flexures and the other designs use at least 4 
sets of flexures, which can, but not necessarily do, limit their performance. 
Won't this seriously muck up your suspension flex loss problems, Randall? The 
reason why you are using ball on a plane bearings for the Volksmeter?

       The Australians claim to have got about 90 seconds from a folded 
pendulum. However, in practical experiments making up simple FP constructions, it 
seemed to be difficult to get beyond about 10 seconds. Both the Teds found 
similar problems. And there is still the huge tilt sensitivity. I do wonder if the 
Aussies left something a bit critical out of their write up? 

       Historically, the period of simple pendulums has been varied by 
reducing the vertical force on the mass. This has been done with a vertically 
mounted spring under the mass, by fitting repelling magnets on the mass and on the 
ground and by providing a solenoid field to attract some iron attached to the 
mass. 

       2 second Willmore vertical seismometers were extended to about 20 
seconds with a spring and there are several other examples applied to inverted 
pendulums.

       There is no reason in principle why you could not feed a fraction of a 
position signal back to a vertical coil mounted on the mass, to directly 
reduce the horizontal centring force. I would expect to be able to get x3, maybe 
x10 increase in the period this way. This is an example of positive feedback 
less than that required to make the pendulum oscillate. An analogy would be to 
reduce the strength of the spring in a vertical seismometer.

       Note that some quite complicated and critical spring designs have used 
for LaCoste and Streckeisen vertical seismometers. The 'trick' here is to 
offset the gravitational load in such a way that the force change for a small 
vertical movement is also very small.
 
       Regarding loss in suspension systems, the sequence for reducing the 
loss appears to be Cardan single wires/foils, crossed wires/foils, ball on a 
plane, crossed cylinders and best of all, rolling wires/foils. Note that I have 
deliberately missed out point in a cup and knife edge suspensions, which are 
both profoundly unsatisfactory. 

In a message dated 2008/02/17, charles.r.patton@........ writes:

> There is another possibility rather than the moving pivot as you describe.  
> Keeping in mind that the basic pendulum period is due to the change in 
> height of the bob during the swing that sets the period, then if we flatten the 
> swing, the period will increase.  Therefore starting with the concept that the 
> upper pivot, rather than the customary shape, a point on a flat supporting 
> surface, is a flat rolling on a curved 
> surface.  If this curved surface is such that the height of pendulum is 
> constant over the swing, then the period is infinite.  Obviously a bit much.  It 
> also has the problem that the surface is not round, but increasingly steep 
> off the center, a recipe for slipping.  

    I am having great difficulty in visualising this. It seems that the 
bearing plate would have to rotate in the opposite sense to the pendulum? It is not 
just the height change that matters; the angle is also important.

So we marry > that with the old Rollamite bearings, to prevent side slip, and 
> put on 
> (immerse in?) lots of lubricant to prevent stiction.

       Uh Uh! Any liquid lubricant will really foul up such a suspension! 
Liquid flow and surface tension spring to mind. The contact friction is highly 
variable between lubricated rolling surfaces. You might try fluon spray or dry 
moly, or rely in the oxide coating. 

       Regards,

       Chris Chapman   
In a me=
ssage dated 2008/02/17, PETERS_RD@.......... writes:



Hi Randall,



       I hear what you say about pendulums and=
 agree with it. However, I am having a little bit of a problem in relating t=
his to seismometers, in which the principle is that the mass stays still - i=
t is the Earth which moves / accelerates!



       Before we try to reinvent the wheel, pe=
rhaps we should consider the history of  past seismometer and linkage t=
ypes?



       A simple vertical pendulum depends for=20=
the resonant period on the length of it's suspension. It is desirable to kee=
p this ~1 second , ~25 cm, on grounds of physical size, ease of construction=
 and freedom from environmental effects. 



       We can keep about this size, but get mu=
ch longer periods if we use either a garden gate suspension, a Romberg linka=
ge or a Folded pendulum construction. However, the gg uses two flexures and=20=
the other designs use at least 4 sets of flexures, which can, but not necess=
arily do, limit their performance. Won't this seriously muck up your suspens=
ion flex loss problems, Randall? The reason why you are using ball on a plan=
e bearings for the Volksmeter?



       The Australians claim to have got about=
 90 seconds from a folded pendulum. However, in practical experiments making=
 up simple FP constructions, it seemed to be difficult to get beyond about 1=
0 seconds. Both the Teds found similar problems. And there is still the huge=
 tilt sensitivity. I do wonder if the Aussies left something a bit critical=20=
out of their write up? 



       Historically, the period of simple pend=
ulums has been varied by reducing the vertical force on the mass. This has b=
een done with a vertically mounted spring under the mass, by fitting repelli=
ng magnets on the mass and on the ground and by providing a solenoid field t=
o attract some iron attached to the mass. 



       2 second Willmore vertical seismometers=
 were extended to about 20 seconds with a spring and there are several other=
 examples applied to inverted pendulums.



       There is no reason in principle why you=
 could not feed a fraction of a position signal back to a vertical coil moun=
ted on the mass, to directly reduce the horizontal centring force. I would e=
xpect to be able to get x3, maybe x10 increase in the period this way. This=20=
is an example of positive feedback less than that required to make the pendu=
lum oscillate. An analogy would be to reduce the strength of the spring in a=
 vertical seismometer.



       Note that some quite complicated and cr=
itical spring designs have used for LaCoste and Streckeisen vertical seismom=
eters. The 'trick' here is to offset the gravitational load in such a way th=
at the force change for a small vertical movement is also very small.

 

       Regarding loss in suspension systems, t=
he sequence for reducing the loss appears to be Cardan single wires/foils, c=
rossed wires/foils, ball on a plane, crossed cylinders and best of all, roll=
ing wires/foils. Note that I have deliberately missed out point in a cup and=
 knife edge suspensions, which are both profoundly unsatisfactory. 



In a message dated 2008/02/17, charles.r.patton@........ writes:



There is another possibility ra=
ther than the moving pivot as you describe.  Keeping in mind that the b=
asic pendulum period is due to the change in height of the bob during the sw=
ing that sets the period, then if we flatten the swing, the period will incr=
ease.  Therefore starting with the concept that the upper pivot, rather=
 than the customary shape, a point on a flat supporting surface, is a flat r=
olling on a curved 

surface.  If this curved surface is such that the height of pendulum is=
 constant over the swing, then the period is infinite.  Obviously a bit=
 much.  It also has the problem that the surface is not round, but incr=
easingly steep off the center, a recipe for slipping.  



    I am having great difficulty in visualising this. It seem=
s that the bearing plate would have to rotate in the opposite sense to the p=
endulum? It is not just the height change that matters; the angle is also im=
portant.



So we marry 
that with the old=20=
Rollamite bearings, to prevent side slip, and put on 

(immerse in?) lots of lubricant to prevent stiction
.



       Uh Uh! Any liquid lubricant will reall=
y foul up such a suspension! Liquid flow and surface tension spring to mind=
.. The contact friction is highly variable between lubricated rolling surface=
s. You might try fluon spray or dry moly, or rely in the oxide coating. 



       Regards,



       Chris Chapman