Figuring out the torque required to rotate a dome

In summary, Hutchphd is looking for a way to rotate a heavy dome using a minimal amount of torque. He understands that friction will be a major factor in determining the amount of torque needed, but is unsure of how to calculate it. If there is no friction and the dome can be rotated for an arbitrarily long time, the world's smallest motor could be used.
  • #1
doopa
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TL;DR Summary
I'm trying to calculate the minimum torque needed to rotate a fairly heavy dome and I'm a bit lost on how to approach this issue.
Hello,

Assuming the dome will not spiral away using a single motor and is set up in a manner such that it would rotate in place, I want to find the minimum torque needed to rotate a fairly heavy dome if a motor was located on the dome's inner face.

I understand that this is an issue that deals with the moment of inertia, but I'm not entirely sure how to apply it to this specific problem. Any input on the issue is much appreciated.
 
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  • #2
We need specifics: size, weight, rate and acceleration.
 
  • #3
If there is no friction and you can take an arbitrarilly long time then the world's smallest motor will work.
Clearly these are two things that need to be specified (and you need to know/calculate the moment of inertia of the shell...that is straightforward with help)
 
  • #4
hutchphd said:
If there is no friction and you can take an arbitrarilly long time then the world's smallest motor will work.
Clearly these are two things that need to be specified (and you need to know/calculate the moment of inertia of the shell...that is straightforward with help)
Just to be clear, @hutchphd said two things. Friction is the second thing.
 
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  • #5
Welcome!
A heavy dome rotating about a vertical axis like the one in the picture?

e-elt.jpg
 
  • #6
Usually it's all about friction. Once the dome is moving it usually takes less torque than what is required to get it moving. Is it possible to just measure it? Can you push on the dome and measure the force needed to get it moving?
 
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  • #7
Lnewqban said:
Welcome!
A heavy dome rotating about a vertical axis like the one in the picture?

View attachment 305357

Yes! It is actually quite the coincidence that you brought up an image of an observatory because that is what I intend on building.
 
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  • #8
How big? How heavy? Can you just rotate it by hand, or will it be so large that it will definitely require external power to rotate?

Please share as many details as you can.
 
  • #9
hutchphd said:
If there is no friction and you can take an arbitrarilly long time then the world's smallest motor will work.
Clearly these are two things that need to be specified (and you need to know/calculate the moment of inertia of the shell...that is straightforward with help)
I see, so figuring out the moment of inertia will give an idea on the torque necessary to move the dome itself, assuming friction is negligible. And then after finding that, I would just add the torque required to overcome friction to my previous result, correct?
 
  • #10
doopa said:
I see, so figuring out the moment of inertia will give an idea on the torque necessary to move the dome itself, assuming friction is negligible. And then after finding that, I would just add the torque required to overcome friction to my previous result, correct?
No. Your MOI is negligible, and bearing friction will dominate. I have a crystal ball in front of me that tells me that...
 
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  • #11
How is the dome supported. It could be low friction but not without a lot of engineering effort. Then any additional force (torque) will cause the dome to (angularly) accelerate
 
  • #12
doopa said:
Yes! It is actually quite the coincidence that you brought up an image of an observatory because that is what I intend on building.
I never would have guessed! :biggrin::wink:
 
  • #13
hutchphd said:
How is the dome supported. It could be low friction but not without a lot of engineering effort. Then any additional force (torque) will cause the dome to (angularly) accelerate
The plan is to rest the dome on top of an open cylinder and create a platform on the top of the cylinder so that a motor could rotate the dome. I don't have an idea on the exact material I will use for the platform, but I have a feeling it will end up being made of wood or some 3D printed material.
 
  • #14
doopa said:
The plan is to rest the dome on top of an open cylinder and create a platform on the top of the cylinder so that a motor could rotate the dome. I don't have an idea on the exact material I will use for the platform, but I have a feeling it will end up being made of wood or some 3D printed material.
I didn't quite understand this. Will you have some type of bearings or wheels to support the weight of the dome and allow it to rotate?
 
  • #15
phyzguy said:
I didn't quite understand this. Will you have some type of bearings or wheels to support the weight of the dome and allow it to rotate?
There will be wheels attached to the motor. The wheels themselves will be on the platform and that allow the dome to rotate. Sorry if I wasn't clear on that.
 
  • #16
doopa said:
Yes! It is actually quite the coincidence that you brought up an image of an observatory because that is what I intend on building.
Practically, you could use almost any torque, because your rotational velocity can be very small in this case.
The inertia of that big mass should be considered for starting and precisely stopping the rotation.
The friction of all the driving and guide wheels, electrical tracks and transmission mechanisms, under windy conditions, should be also considered.

It seems to me that this analysis may be a little early in this project, if structural solutions have not been engineered yet.
 
  • #17
Well, I can give you an idea from an astronomical dome that I'm familiar with. The dome is about 10 meters in diameter and covered with metal sheeting. It probably weighs several tons, but I don't really know how much it weighs. It is supported on about 100 wheels that run in a track around the perimeter of the dome. Four of these wheels have 3/4 HP motors that drive the rotation of the dome, spaced 90 degrees apart around the dome. Your dome is probably smaller and lighter so could use smaller motors.
 
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1. What is torque and how does it relate to rotating a dome?

Torque is a measure of the rotational force applied to an object. In the case of rotating a dome, torque is the force needed to overcome the resistance of the dome's weight and inertia to cause it to rotate.

2. How do you calculate the torque required to rotate a dome?

The torque required to rotate a dome can be calculated using the formula T = F x r, where T is torque, F is the force applied, and r is the distance from the center of rotation to the point where the force is applied. This formula applies to both rotational and linear motion.

3. What factors affect the torque required to rotate a dome?

The torque required to rotate a dome is affected by several factors, including the weight and shape of the dome, the material it is made of, the friction between the dome and its support structure, and the speed at which it is being rotated.

4. How can you determine the minimum torque needed to rotate a dome?

To determine the minimum torque needed to rotate a dome, you must first calculate the dome's moment of inertia, which takes into account its mass and distribution of weight. Then, using the formula T = I x α, where T is torque, I is moment of inertia, and α is angular acceleration, you can calculate the minimum torque required to overcome the dome's inertia and cause it to rotate at a desired speed.

5. Is there a maximum torque that can be applied to rotate a dome?

Yes, there is a maximum torque that can be applied to rotate a dome. This is limited by the strength and stability of the dome's support structure and the materials it is made of. Applying too much torque can cause the dome to deform or collapse, so it is important to carefully calculate and monitor the torque being applied.

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