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I'll add - in fear that I have provided fuel to the fire !
Wall thickness does increase the strength of a pipe for a given diameter but it is the increase in outside diameter that provides the greatest increase in strength/rigidity (or rather lack of flexure).
Vibration at the frequencies we can hear is almost completely irrelevant.
Its only very, very low frequencies that might cause a problem.
Yes, I know, I have read all the various posts and threads on astro forums over the years by would be engineers who say it matters or are just repeating what they heard.
It does not matter if the pier is otherwise rigid.
The real issue is the purpose of a pier in astronomy ?
In partiocular astrophotography because for visual astronomy these things are not so important.
The piers purpose is to provide a rigid support base that is mostly free of LOW frequency vibration that has a high enough amplitude to affect the image on a CCD (these are not audible sounds in the 1-5Khz range, they are very low frequencies usually well below 50Hz.
But more specifically and most importantly it is designed to ensure that there is the least amount of deflection when lateral loads of the order of a few Kgs are applied to the top of the pier/mount etc - either as a result of wind on the OTA, imbalance of the Mount and OTA as it moves throughout its range and to resist the opposing forces when fast slewing.
Being rigid means it transfers these forces into the ground where they will do the least harm and allow the system to settle very quickly.
Since we are asking the pier to resist deflecting by arc seconds or less - the pier has to be substantially stronger and more rigid than ordinary engineering would dictate on the normal basis of material limits and stengths for what are in effect quite trivial loads.
We want the pier to deflect less than the image scale of the system or maximum resolving capability of the system - preferably half or better.
Filling your pier with sand may make you feel happy that you have done something about it and it will change and subdue the resonant pitch of your pier at frequencies that have nothing to do with a pier deflecting arc seconds under a lateral mechanical load.
If you fill a hollow steel pier with concrete you will increase its strength (improve the modulus of elasticity) and that will help, but the preference would be going an extra couple of inches larger in diameter.
Loose sand doesnt add any strength !
I would start at 10.75" and look to 12" with 1/2" wall thickness or greater, but if you dont have a suitable mount (without backlash) and very solidly built and an optical system that is already rigid and without flexure all the way through - eg threaded adapters, solid focussers and rotators etc, solid attachment to mount etc then it may be a moot point what your pier construction is.
Calculating pier deflection (cylindrical beam) is a trivial engineering exercise for those who have studied it or wish to repeat it - the relevant function for calculating the moment of inertia OD (Outside diameter) in inches and ID in inches - pi = 3.142
i = pi * (OD^4-ID^4) / 64
deflection angle in radians is
(W * L^2) / (2 * E * I)
Where
L is the length of the pier in inches
W is the lateral load in lbs
i is the value from the first equation
E is the modulus of elasticity of steel = 3.00E+7 (Concrete without reo is approx 3.60E+4)
As you can see the function shows that it is proportional to the diameter to the fourth power ie (OD * OD * OD * OD) that means that a small increase in OD yields a large improvement.
Hope that helps
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