Quote:
Originally Posted by 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.
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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.
