How do I calculate the dia of wire rope for aerial ropeway of 1 ton capacity ?

Question

I am designing a aerial ropeway. Somebody please help me with the design calculations for the wire rope to be used.

Answer 1

The tension on a highline (aerial ropeway) is dependent on the sag consideration of the system. The smaller the sag, the more tension force will be on the highline. However, too much sag will make it more difficult to move a load from one end of the highline to the other end. Normally a sag equal to 2% of the span of the highline is used. Thus the tension on the highline is:

T = P/(2 sinA)

Where:

T = the tension on the highline

P = the load

A = the angle the rope makes with the horizontal when the load is at the middle of the highline

For a 2% sag:

tanA = 0.02L/0.5L = 0.04

But for small angles, the sine of the angle is approximately equal to the tangent of the angle. Hence for a 1ton (2200lbs) load, the tension on the highline is:

T =2200/(2 x 0.04) = 27500 lbs

Wire ropes are normally rated at their breaking strength. So if you consider a factor of safety of 5, the breaking strength of the wire rope that you need should be;

T' = 27500 x 5 = 137500 lbs. Thus select a wire rope diameter which has a breaking strength of not less than this.

There are other factors that must be considered in selecting the wire rope to be used.

a. Construction.

Wire ropes made of lesser number of wire strands are normally stronger than those with more wire strands of the same diameter but are less flexible. Since a trolley would be running on the highline, it would be preferred to use the more flexible wire rope construction like a 6 x 37 so that the wire rope will not kink even if the diameter of the sheaves of the trolley are smaller. Sheaves with diameter of 16 times the diameter of the wire rope can be used for a 6x37 construction but for a 6x19 wire rope construction, the sheaves should at least be 21 times the diameter of the wire rope.

b. Core type

Wire ropes with independent wire rope core are stronger than those with fiber core, but cost more.

c. Type of wire material

High grade plow steel (HGPS) wire ropes are stronger than ordinary improved plow steel (IPS)  wire ropes.

d. Lay

The abrasion resistance of lang lay wire ropes are better than the regular lay because of the longer crown of wire strands where the sheaves bear on.