# Mathematical Equation to figure out Horse power....

#### JP12687

##### Active Member
I am attempting to design/build a turntable for my stage. I was wondering how you would deterine the right size motor for doing this. I need an euation that will tell me how fast it will spin, using hte size of the motor and the size of the circle. I hope that makes sence to someone cuz its been confusing me for a few days now....

well i dont know about motors, but at my sleepaway camp we had a turntable on stage that was our entire set for chicago, it was really cool but i wont get into the details of it now... anyway there were a few stagehands below it whose job was to push. so if you have extra people who feel like sitting below a platform for a few hours you can always do that and make your job easier.

haha well i know exacly how(or relativly so with a little playing...) to make it with a motor...and i have about 4 different options in terms of motors, ranging form a little 7.5 HP electric motor allthe way up to a 75hp Gas motor...i just want to see which i have ot use..i would love to use the little electric...but i'm trying to figure out how fast it would move....

The speed of the rotation will depend on the sheave sizes or gear box. I think most electric motors have standard speeds (1,200 rpm, 1,800 rpm, 3,600 rpm; off hand, I don't know if there are lower ones or not.)

But the key is the rpm of the drive that you'll be using after the gearbox or final sheave if you have a belt system. And then you need the diameter of the the drum/pulley that will drive the table. I'm assuming that the drum will then drive a belt/cable that goes around the revolving table. The belt speed will be the drum rpm times the drum circumference. Now apply the belt speed to the circumferance of the revolve and you'll get the rpm of the revolve.

Example: Say the drum is 1 foot diameter, circumference of 3.14 feet, and the drum speed is 10 rpm. The belt speed is 3.14 x 10 = 31.4 feet per minute. Now say the revolve is 20 feet diameter, circumference = 62.8 feet. One revolution of the revolve will be completed in 62.8 feet / 31.4 ft per minute = 2 minutes.

I don't know how to calculate how much power you need, but the power does not affect the speed (other than having enough power to turn the thing.) (Its been a long time since physics - I know its a simple calculation. Maybe a torque calculation...)

Joe

So do you think a 7.5 horsepower motor would be enough to spin a 20ft diamiter table?

Or

Are you saying the horse power doesnt really matter only the RPM does...as long as the table its self is light enough to be turned by 7.5 horspower. Correct?

O yea and any suggestions on how to build one would be appreciated i have a few ideas...just having trouble getting it on paper

I honestly have no idea about this. I've never researched or trie to build a truntable. There are numerous discussions about building revolve's on rats and stagecraft. I'd search both of those places for some good info.

I agree with the Rats' and Stagecraft research. While I in the past have helped construct one or two, and assembled more, as for motor type, that was handled by people other than me. I do know that you will need to in addition to stying what size the turntable is know about how much weight is going to need to get into rotation, much less how fast from zero stop. There is also factors such as height and working space or type of revolve you have in mind be it mounted under or beside the revolve.

The type of rotating system will also play into this due to resistance.

Hardest part is getting the thin moving.

A large truck tire attached to a gear box and moving the platform from it's side will take a lot less effort to make the thing move than a mini-2" wheel or gear. A 18" gear on the other hand while slower in gear ratio will take less effort also than a 2" gear. This after the gear box in converting the motor's turn to something with enough torque to get it moving.

Just a random thought as I think the primary step. After that, the operating speed.

Dont want to sound too stupid...but What are the URLs for Rats' and Stagecraft...

In my opinion, for something of that size and scope, it might be a better idea to turn it over to a professional in that field, or at least seek their advice.

That first reply I made was too late at night. After posting I checked bdesmond's reference – looks like its on the right track. Weight AND speed of the revolve determine the horsepower. That's what I was alluding to at the end of that first reply. I also think that the solution is beyond a few posts at this site. And I now apologize in advance for what will be a lengthy reply…

I'd look into a theater reference text about how to make and power a revolve. The reference I had shows a motorized drum and cable. And I suppose you can have a direct drive too. But motorized rotating equipment and moving cables are dangerous things – you may just want to make the revolve manually operated/pushed. Also, the noise of the motor and idler pulleys and gear reduction need to be considered – I'm not altogether sure that you want the motor on the stage. And then once you get this mass moving, you have to stop it.

Be that as it may, I tracked down a couple equations that may help:

First, the power equation, torque times angular speed (rad/minute). Then, convert ft-lb/minute to horsepower.

Rotation speed is a given. (Can't help you as to what it should be – there are safety issues and noise issues, but it would have to be as slow as practical, but it may be a function of your drive.) But there's that torque variable. Torque is inertia momentum times angular acceleration. (That's from the old physics book I dug up – Resnick and Halliday.) But if the speed is constant then acceleration is zero – and that obviously isn’t the answer.

So I searched for horizontal torque and came across an equation at flo-tork.com. They have an equation for the friction torque of a horizontal table. The equation is Weight x coefficient of friction x bearing radius. Now assuming that the trolley wheels are on the outer edge, that would be bearing radius. (Okay, there may be additional interior trolley wheels, but we'll be conservative.) The weight would be the weight of the revolve, the wheels, the set, the props, any thing permanently on the revolve. Then I'd add a safety factor – maybe even 100% more or 750 lb minimum to account for unknowns and stuff like people taking a ride or major design changes. The coefficient of friction (unitless) appears to be a bit of a "fudge factor". It may be high at the start, but very low once it gets moving. I found a conservative reference of 0.8 to start and maybe as low as 0.015 once it gets rolling. But I'd use the higher number.

Now, an example. 20 feet diameter revolve (Radius = 10 feet). Weight of Revolve. Assuming typical platform construction applies, then by my own experience, a 4 x 4 section (16 square feet) weighs about 90 lbs. The revolve, at 20 feet diameter, has an area of 314 square feet. So the weight is about 314 x 90 /16 = 1,800 lb (!!!). Assume 500 lb for set/wall, so the total is 2,300 lb. Safety factor of 2, so 4,600 lb. Finally, assume a relatively slow rotation speed of 1 rpm.

Friction Torque = 4,600 lb x 0.8 x 10 feet = 36,800 ft-lb

Power is Torque x rotation speed (radians/time) = 36,800 ft-lb x 2 x pi/minute x 1 minute/60 seconds = 3,863 ft-lb/sec (Note - 1 rpm = 2 x pi rad/min)

550 ft-lb/sec = 1 hp

So 3,853 ft-lb/sec x 1 hp/550 ft-lb/sec = 7 hp.

There are probably other minor inefficiencies in the system, and the 7.5 hp motor probably won't be enough, under these conditions and assumptions.

Now, based on the above, you really need to either go to the library and/or book store to get some better design references; or (as Supercow suggested) track down a professional or someone who has designed these. And again, consider safety and noise.

Joe

One might also go with a few smaller horse power motors depending upon their drive system, but excellent figuring Joe!

Wonder what's more effective some sort of worm drive gear or moving wheels to make it move. Perhaps four inner wheels at these center caster positions as opposed to a center gear or what ever drive hub. A few smaller motors when spaced out from the center would have a bit of mechanical advantage in getting the thing running which might also help in the motors being smaller.

Think there is a missing figure here as to at what point or type of drive you are moving the platform with. A motor mounted upstage and to the outside of the platform when riding the edge of it would certainly need less torque than one attempting to move the platform from it's center in a cable/gear/what ever type of drive. In my case and the ones I remember seeing, the type of drive had center support casters (center of the individual platforms not the centeral pivot point) that were moving the platform when it's bottom was provided a well supported road for the casters to run on. Such platforms had about a 6" clearance but were aluminum or steel in frame if I remember correctly. (Been about 10 years now.)

In noting these center casters and the road for them, there is two types of revolves. Those that use casters mounted to the platform, and those that use casters mounted to a frame below it and tracks under the frame of the platform to ride on. Both systems have their advantages but the frame layed out on the stage where a platform sits on the casters is a little more easy to lay out and use - much less make move in the above multiple motor method.

Good luck on the center pivot, very hard to do well.

Replies
13
Views
1K
Replies
0
Views
768
Replies
0
Views
748
Replies
0
Views
625
Replies
0
Views
605