More weight vs longer moment arm

[LewisM]

What is more desireable/preferrable:

1. balance a scope using the standard counterweight rod, and using many weights

or

2. balance using a longer counterweight rod with less actual counterweight mass

I understand the effective weight is the same, but is there any actual benefit/advantage/mechanical preference of one over the other?

I have a new scope coming that will require either 9kg counterweights or less actual weights on my custom counterweight rod...

[gregbradley]

Good question Lewis.

I have imaged with both. My PME has the extension and I get round stars.

I was using my PMX without an extension and got round stars with an AP140 which weighs about 20kg. Then with the Honders which weighs over 30kg and using an extension bar I was not always getting round stars initially. I moved the mounting plates so all anchors were engaging and put a dovetail on top of the mounting rings as well and I got round stars.

But the risk of an extension would be flex in the shaft. So with that in mind I suspect no extension and more weight would be better. It depends on how much overall weight your mount is able to take.

Greg.

[Spookyer]

AP advised me to keep the weight towards the top of the shaft nearer the mount. Something to do with "inertial moment"

[LewisM]

I guess I shall try both!

It is on my venerable yet slightly anaemic GPD2 which has a capacity for imaging of 10kg, so it is pushing it somewhat (but at f/5, guiding should be easier at least).

I have seen MANY others online using the same setup with round stars and no mount issues, so I know it is more than capable.

[rustigsmed]

ive heard this also, although I don't follow that advice :question: but i'm well under the mount's rated payload.

more interesting if the extra weights put you over the mount's payload vs the longer bar and under payload.

[gregbradley]

Good tip. I can see how that would be true. So I might add more weights and pull everything up and see how that goes.

Greg.

[julianh72]

You can balance a telescope with a given counterweight mass at a given offset distance, or a smaller mass at a proportionately larger distance (eg half the mass at twice the distance). The further apart the balanced masses are, the greater the Moment of Inertia:

I = m r^2

(Eg for the case of half the mass / twice the distance, you get double the Moment of Inertia.)

The bigger the Moment of Inertia, the more the telescope will tend to continue to move whenever it is disturbed; think of two pendulums of equal length, one with a small bob and the other with a large bob. They both swing with the same period, but the heavier bob will take longer to overcome friction and stop swinging. Hence it makes sense to use a larger mass at a smaller offset, all other things being equal.

[LewisM]

Given the speed of sidereal tracking, do you really think inertia will come into play to any appreciable extent?

Slewing maybe, but most imagers slew once and done for the night.

[multiweb]

My C11 assembly is now 26kg. I can tell you that inertia with lighter counterweights down the shaft affect the tiniest corrections during guiding. Go heavy and as close as you can from the RA axis to avoid unwanted oscillations and I'm not talking about backlash.

[rally]

The Paramounts allow you to change the axis drive acceleration rates, so if you have a big heavy rig like a 16" RC or 20" CDK you just reduce the value in the settings.

However when you are at or beyond the mount's capacity, the bearings are being overloaded and will deform and may degrade, likewise the surface pressures on the contact points on the drive gears will be exceeded from their design and this can also result in either permanent deformation at worst or premature wear and degradation at best.
The size, material hardness, surface pressures, load and speed are all directly related to one another in gear design.

As mentioned you can get flex in the counterbalance shaft itself.
Flex on its own probably doesnt matter much but if you get harmonic vibration happening due to the shaft being heavily stressed (or possible hysteresis in the drive systems electromechanical design) that is not so good.
That vibration can increase in amplitude if it then coincides with whatever natural harmonic resonances your mount permits - and you can end up with unmanageable vibration that will affect performance.

I made up a very large (around twice the normal diameter) custom stainless weight to be mounted at the end of the shaft on a P-ME for a friend in order to try and keep the total counterweight/telescope mass as low as possible, but this appeared to overly stress the counterbalance shaft (if you can believe that on a P-ME shaft !) and caused such a problem.
The initial solution was to go back to ordinary weights stacked hard together and an extension shaft - fully loaded, which meant a greater mass overall.
But ultimately the mount had to be replaced with a bigger mount to handle the total mass.

[Eden]

This is what I found to be the case on my mount. I could use a counter-weight extension and a single weight, but it's a bit like having a giant tuning fork connected to the RA axis...

[AndrewJ]

Agree with Julian that the longer the moment arm, the higher the Inertial moment.
This increased moment can affect the current draw and gear loading during the acceleration/deceleration phases of slews, esp if the motor has a predefined ramp up/down curve programmed in.
That said, for most scopes, if the weights are within the manufacturers tolerance, the above wouldnt be a worry, just an effect.
More of a problem is ( as others have noted ), damping oscillations if they occur.

Andrew

[multiweb]

Guiding with a shaft extension is like drawing on a post it with a ten foot pole. It can be done. With a lot of beer.

[julianh72]

The Moment of Inertia impacts the tendency of the telescope to vibrate - systems with a small Moment of Inertia are quicker and easier to damp out any vibrations, and therefore easier to achieve a stable image.

[Kunama]

An AP1200 will fix all your problems Lewis ;)

(a heavier weight closer in would be my choice)

[The Mekon]

Good posts Julianh - both of them. You have explained it well.

[LewisM]

Agreed.

I shall bolt 15kg of depleted uranium as close to the RA axis as possible.

I shall keep the extension for clubbing coconuts out of trees.

[g__day]

I remember seeing the full and detailed maths behind answering this question a few years ago - the short answer is max out your weight closer to the turning point - up to just below what your mount can quality image at. As stated above it has to do with turning moments of inertia and micro oscillations from not perfectly round and engaged gears that you wish to minimise!

[Nico13]

I'll go along with the majority here as I have seen the inertial moment errors mentioned on my NEQ6 Pro when heavily loaded and using the extention bar.
The shutter release action of the SLR I was using at the time caused serious oscillations and non round stars.

I wound up modifying the mount and fitting a screw in heavier std length CW bar with more weights and all was good :thumbsup:

[cometcatcher]

Good thread. I was just wondering about his very question myself. Now I know.

[julianh72]

There's a "double whammy" effect when it comes to the dynamics of counter-balancing an OTA with a weight on an extension arm.

Firstly, the balanced system as a whole can be thought of as a "dumb-bell" - two masses connected by a shaft. The greater the separation of the two masses, the more rotational inertia the whole system has, and the harder it is to stop it twisting and vibrating around the pivot point. (It's the principle of mid-engined sports cars having more "agility" than front-engined or rear-engined cars.) Keep the masses close to the pivot and you reduce the moment of inertia, even if the total mass has to increase to stay balanced.

There's a simple experiment you can do: take a yard broom (or a shovel or hoe) - the head of the equipment represents the OTA. Find the balance point - the overhanging handle is the counterweight. Now hold the handle at the balance point so the handle is horizontal and your arm is hanging vertically. Swing the implement so your hand is twisting clockwise and anti-clockwise - the resistance you feel in your wrist is battling the moment of inertia. Now hang a counterweight on the handle (a paint tin will do nicely) and repeat the experiment. As you progressively move the counterweight closer to the "OTA" (and adjust your grip to the new balance point), the moment of inertia reduces, and you will find it easier and easier to rotate the broom back and forth.

Secondly, the counterweight on the shaft has its own vibrational modes, just like a pendulum or tuning fork. Any given mount typically only allows us to fit a single shaft diameter, so there isn't much we can do to stiffen the shaft. The heavier the counterweight, the closer it can be to the OTA, so we are making our "pendulum" shorter and stiffer. The shorter "pendulum" will vibrate much less than a smaller weight on a longer shaft of the same diameter and material. Any vibrations of the "counterweight pendulum" are passed directly into the OTA.

[LewisM]

I think this Youtube video convinced me NOT to use an extension but to load it up on the standard shaft.

Watch his shaft CW bend (slightly).

https://www.youtube.com/watch?v=VTgkFInQTeM