Thoughts on longer counterweight shafts

[g__day]

What do folk think of using longer counter weight shafts on larger scopes?

Given that a longer shaft may have slightly more flex, more weight, but it would give you a much greater turning moment - you could counterbalance your OTA with significantly less weight. All this should mean much less wear and tear on your mount and its gears - even if its all perfectly balanced?

Am I missing anything here? If I was to place a 50% longer counterweight shaft on my CG5 I could counterbalance my scopes with 50% less weight - which seems very sensible to me.

Any idea where you might purchase a longer bar?

[Dennis]

Hmm, that's an interesting question; I look forward to the replies from the mechanical engineers and wizards. Simplistically, (or even ignorantly!), I would have thought that the force “experienced” by the bearings would be the same.

That is, they would not "know" the difference between lighter weights on a long shaft and heavier weights on a short shaft?

Cheers

Dennis

[JohnG]

I was always under the impression that it was better to have more weight closer to the turning axis, having a longer counterweight bar will introduce more flexure and a greater swing radius.

As far as weight on the bearings, it should not have any effect, no matter what you are doing you are still balancing the OTA so the weights should not be an issue.

I prefer the weight in close to the head, to me you have much better control of how it is distributed ie: I place a slight presure on my RA worm to maintain a slight imbalance, when I swing through the Meridian to the other side, that weight has to be moved to maintain that slight imbalance, a lot easier to do than mucking around at the end of a long shaft.

There is a method of calculating weight on the Robin Casady site.

Cheers

JohnG

[g__day]

Guys,

From 5 years of physics and 2 of engineering that thinking about forces simply isn't right. You have a few forces to think about:

1. Dead weight on the bearings = OTA + bar + mount head + counterweights

- a longer counterweight bar will dramatically lower your counterweight and so dramtically lower the weight your mount has to carry

2. Turning moment and inertia (think of a ice skater doing pirouttes, pull your arms in and you turn faster to conserve angular momentum, but you are also decreasing weight making in an inexact comparision).

- The turning moment will be zero if the scope and counter weights are balanced. When you wish to move the scope lengthening the bar will make it easier for althought your weight is further out - your weight is linearly smaller, so less energy will be required (its like picking up a bowling ball striaght up or picking up a shot put with your arm almost fully extended). Now try and throw both those balls over arm - bet the shotput goes alot further! Adversely - it will take more force to stop the turn you have started!

* * * * * * *

More weight on the bearings that is moving will produce more wear and tear, put simply weight * coeffiecent of friction = work done. More weight = more work, thats why its harder to push a car than a bike with the same sized wheels - the car weights much more.

Yes a longer bar has more flex - but 15 kgs on a 30 cm bar versus 10 kgs on a 45 cm bar or 3 kg on a 1.5 metre bar will all be roughly equivalent - in fact the lighter weight at a greater distance may just flex less!

The bar in question is 2cm diameter - of probably 0.5% carbon steel - call it a mild peroeutectic steel with minimal heat treatment. Well anything under 100 kgs at lengths that are a less than half a metre are simply too small to flex a bar that short more than a few micrometres. So without a micrometer it would be hard to tell any flex in the bar with the human eye. You'd have more worry that the longer bar will expand more in the heat and so throw off your balance by a few tenths of a newton of force.

[JohnG]

Well, to me, you have answered your own question, I really don't know why it was asked. :shrug:

I will stick with convention and the learned wisdom of a lot of very experienced people and have my weights up close to the head, I certainly don't have any flexure, vibration or balance problems to worry about.

Good luck on your project.

You might want to have a look at this:

http://www.tfn.net/~blombard/book/8-GermanEquatorialMts.pdf

Cheers

JohnG

[sheeny]

G'Day g_day,

There is one aspect of this that you have over-looked - vibration.

You are right in what you say, reducing the total mass of the OTA/counter weight assembly will reduce the load on the bearings, hence reducing friction in the bearings and reducing load on the drive gears... but I think you might be placing more importance on this than it warrants. If your scope is well balanced, even just slightly (and deliberately) unbalanced to minimise backlash, the "war and tear" on the bearings will certainly be insignificant and the that on the gears should be well within the design loadings anyway.

I would doubt that, if you actually do the experiment, when you lengthen the counterweight rod by 50% you can actually use 50% less counterweight. It may be close, but I'd almost be preared to bet it's not exactly that amount - beause the mass of the moving parts in the mount (RA axis, etc) are not negligible.

Most precision rolling bearings require some sort of minimum load to work efficiently. This may be achieved by preloading (like in your car or trailer wheel bearings) or it may require a minimum load. I doubt this is significant to your mount! I just mention this FYI - I have encountered some classic engineering design problems that "no-one could solve", but in actual fact the bearings were over designed - they didn't have enough load on the bearing for them to work properly.

The biggest issue I think you may notice with a longer counterweight shaft will be vibration. Lengthening the shaft (I.e. the radius of the counterweight from the RA axis) will decrease the resonant frequency of the counterweight. As well as the static deflection of the shaft increasing (as you've already acknowledged) the amplitude of any vibration will increase, because it is now a softer "sprung" mass spring system. The amount of damping in the system is essentially unchanged, so any knocks to the scope will take longer to settle as well as being more noticable.

I think if you go for a longer counterweight shaft and less mass you will find a degradation in the stability of your scope. It will be more sensible to movement, bumps, gusts of wind, etc. I wouldn't go that way, but if you want to do the experiment, I'd love the see the results! Set it up, give it a bump test and time how long it takes for the view to settle and compare it to your standard setup. Maybe it's not significant...:shrug: . I think it probably is though.

Al.

[jase]

Other than balancing heavier equipment, I don't see any major benefits. If there were, I'm sure mount manufacturers would make them longer.

Let’s take Bisque and Astro-physics for example. Both make some impressive (to say the least) mounts. At present both present CW shaft extensions as optional add-ons.

http://www.astro-physics.com/products/mounts/1200gto/1200upgrades.htm#m12601c

https://www.bisque.com/help/paramountme/counterweight_shafts.htm

There are other mount manufacturers that have similar options.

Comes back to personal preference - add heavier weights to a "standard" shaft or extend the shaft and use the original weights (just further down the shaft). The net affect is the same.:)

[g__day]

JohnG - no I just corrected some basic errors two folks thinking about the forces involved - that doesn't definitely answer my question - it merely pointed out fallacies in trivailsing this problem too far to get your answer - as pointed out by the very next reply.

Al - your'e totally right I haven't considered any of vibration, nor resonant frequencies. There must be an ideal bar lenght for a carrying capacity and set of materials; but I wonder what formulea determines this. I think vibration would increase with a longer shaft holding a lighter mass, but possibly the vibration is minimal. As is I assume the bar isn't normally vibrating unless forces are acting on it. Mines in a shed - so rule out wind etc. That leaves bumps or movement due to the motors, particularly RA.

Personally I ponder having too light a weight means too much momentum to absorb when you are nearing completion of a goto movement.

If I can find a mild steel bar 50 cm by 2 cm I might thread it so I can conduct this experiment to see what results. Also I may dash an e-mail off to Celestron to see what their engineers think!

Jase - great links - thanks!

PS

A Paramount at $16K would be my dream!

[sheeny]

g_day,

OK... now you've done it! I've opened my dynamics book!:scared: :lol:

The formula for the approximate natural frequency of a cantilevered beam with a mass on the end is:

omega = 1.56 *sqrt( E * I /( m * L^3))

where,

omega is the natural frequency in radians per sec
E is Young's modulus of the beam material (207GPa for steel)
I is the second moment of inertia for the beam
m is the mass
L is the length of the beam

So you see, as the length of the beam (radius to the counterweight) increases the natural frequency of the counterweight and beam decreases very quickly.

For a given amount of energy (say your standard "1 swear-word-bump-the-forehead-on-the-back-of-the-OTA":lol: ) as the natural frequency reduces, the amplitude of vibration increases. So any given movement or bump on the scope will cause a greater disturbance for the scope.

So I would expect that with a longer shaft and lighter counterweight, the scope will be less stable - or any movement or bumps will result in larger movement and longer time to settle.

This is why large mass and stiff stuctures are desirable things in telescopes.

Al.

[g__day]

I think your very right there, you could dampen vibrations, - by sandwhiching rubber between your weights and the bar, but a L^3 function shouldn't be ignored (actually for my case with the reduction in mass this would be a case of the square root of a doubling (rather than tripling) of resonant frequencies (which one of those links suggests keep above 30 Hertz (200 Hz would be ideal). This change would shift RF by 40% downwards (not a great thing if RF is already low).

* * * * *

Another thing I was pondering was using a flatter weight (like weightlifters do). Its a variation of the above - using a broader (fatter) weight to lower the centre of mass of say 15 Kg by a good 5 - 7 cm. Instead of three weights on the bar (standing 12 cm high), use (even) fewer weight that only stands 3 cm high and lower it further down the bar.

Be interesting to experiement - but first I have to stablise my pier with added welding of struts.

Thanks guys!

[AstroJunk]

Just make sure a longer bar doesn't snag on your tripod legs - I have a pier so it isn't a factor.

(you can all get back to your physics now;))

[g__day]

I built my own pier (and astro lab) too - its the only way too go!

[mark curtis]

One does what one must do. I use a large refractor on a german EQ mount with various instrument packages and eye pieces of greatly differing weight. I built a dec counterweight/ guid scope mount that seems to work for all but one configuration, And for that one I am to the point that I might just duct tape the cat to the scope:D for balance.With all the extra weight i have added for balance i have had no ill effects in this systems 2 years of operation.
Here is a pic of my system, like I say it works for everything but one thing and amazingly that one thing is a really hefty 2" eyepiece, This dang thing weighs than an olympus OM-1 camera and when it's on a barlow i just cant balance it.