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# Calculating torque applied to a drum by a rope or cable of some diameter

## Calculating torque applied to a drum by a rope or cable of some diameter

(OP)
Hi there,

Lets say I have a drum of radius (R). Attached to the drum is a spool of rope or cable of diameter (D) with a weight attached to the end. I wish to calculate the torque applied to the drum. The strands of the rope (or cable) are under tension on the outside of the bend radius while the strands on the inside of the bend are under less tension (maybe even compression). Therefore, what is the correct radius to use to calculate the torque applied to the drum? Would you use the diameter of the drum itself assuming an infinitely thin rope, or would you account for the thickness of the rope in making this determination?

For example, would the torque be
1) T = maR
2) T = ma(R+D)
3) T = ma(R+(D/2))
4) something else

Note: m = mass, a = accelerates due to gravity.

### RE: Calculating torque applied to a drum by a rope or cable of some diameter

Typically rope is made with a spiral so all fibers change places from inner to outer along the bend to prevent any average difference in tension. Some rope has straight core, but I would avoid using it on a drum. It is more useful for structural purposes, such as suspension bridges.

It's unlikely to matter unless the rope is of considerable diameter. If so, then the center of the rope is the average location for the applied load. Too small a drum causes the fibers in the rope to slide on one another to equalize the load, increasing wear and decreasing strength so I would avoid cases where the rope diameter is considered.

If you are using torque on the drum to pull the rope it would be conservative to add a bit to the drum radius. If the rope is pulled to drive the drum then it would be conservative to use the drum diameter and ignore the rope diameter.

### RE: Calculating torque applied to a drum by a rope or cable of some diameter

Hi jared1313

I would use the drum diameter as a starting point, however as the rope wraps around the drum and the rope builds up upon itself the torque will increase due to the increased radius.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Calculating torque applied to a drum by a rope or cable of some diameter

jared - General thoughts:
1) Since you used the word "weight" describing the object attached to the rope, I assumed you knew it's actual weight. But then you use formulas involving mass. If you already know the weight (force) you don't need those formulas.
2) In most real-world cases the diameter of a single wrap of rope will be a non-issue because its effect on the calculation of torque is so minor. However if you have multiple wraps you should use the radius to the centerline of the outer layer as your torque arm length.
3) Although an interesting discussion, any variation in actual tension throughout the length of rope is also a non-issue. Assuming that the weight is suspended directly from the drum (the rope does not go around other pulleys) then the bottom line is that the drum must exert enough torque to equal that created by the weight at the efffective torque arm radius.

Very simple formula: Torque = Weight x Torque Arm Length.

### RE: Calculating torque applied to a drum by a rope or cable of some diameter

Homework problem .....

MJCronin
Sr. Process Engineer

### RE: Calculating torque applied to a drum by a rope or cable of some diameter

The centerline of the rope is the line of action of rope tension.

### RE: Calculating torque applied to a drum by a rope or cable of some diameter

(OP)
No, this is not a homework problem but rather a personal project to accurately measure torque on a drum. Additionally, this is only considering a single layer of windings.

So it seems that the effect of the torque arm not being equal to the diameter of the drum is usually negligible if the diameter of the rope is very small relative to diameter of the drum in addition to using spiraled rope. From what I am seeing, the spirals help to distribute the compressive and tensile loads evenly throughout the rope. This seems to make sense to me now that I think about it. Unfortunately, I don't feel the rope I am using is a little large in diameter relative to the drum it is winding on. The drum will likely be between 1" and 1.5" in diameter while the rope is about about 1/8" in diameter. I do not know the minimum suggested bend radius, but I suppose I should find out. Since my rope will be wrapped relatively tightly, I think I may need to consider using compositepro's suggestion that the middle of the rope is the line of action of rope tension.

### RE: Calculating torque applied to a drum by a rope or cable of some diameter

generally the required torque is needed to identify the drive of the winch (hydraulic motor, gearbox, etc). So, what we did is identify the load to be lifted, radius of the drum, diameter of the wire rope and calculate the torque at the inner layer and outer/final layer and you have to consider the radius of the wire rope cross section for that.

you can refer to BS2573-2 and BS 5500:1982 (not sure what's the latest edition) for further reference.

R.Efendy

### RE: Calculating torque applied to a drum by a rope or cable of some diameter

Often small diameters like that won't stay round. So far ignoring the diameter is 12.5% error at worst - often that won't be the largest unknown.

### RE: Calculating torque applied to a drum by a rope or cable of some diameter

If you draw an FBD there is no doubt that the centreline of the rope is the effective point of application of the force. If the rope squishes radially that moves the hanging rope inwards a bit.

Are you interested in the crush strength of the drum?

Cheers

Greg Locock

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