How to calculate winch speed and lift?

[valley]

I have a cable winch 1300 lb lift. [3" cable roller] cable moves at 1/2 mph

I want to instal a larger wheel on the roller shaft that will move a rope at approx 2-3 mph.

If I use a 9" wheel will it move at 1-1/2 mpr and lift 400 plus pounds?

Maybe because I don't need a dead lift I can use a larger wheel Dia. ?
I don't need a dead lift but about a 45 degree with very little friction.

Does this sound right?

 

[BruceWard]

I do not understand the term mpr. Could you explain this unit? I assume you are stating somthing along the lines of feet per minute.

The circumfrence of the pulley (length of bottom layer) is calculated as 3.14 x diameter. A 3" spool would wind up 9.42" per rpm. A 9" spool would wind up 28.26" per rpm. Assuming the winch has sufficient torque to handle the load the 9" spool would spool at 3 times the rate of the 3 spool.

The force the winch can apply halves as the size of the spool doubles. By my math 1.5" (original axis) / 4.5 (9" spool axis) * 1300 = 433 pounds of lift.

I have seen load of a rolling load on a slope caclulated as (degrees * weight / 60 ) . Using this ofrumla your load will be around 75% of the actual weight ignoring friction.

I assume your winch is rated for first level strength and as the cable coils up the winch will become weaker.

 

[payton]

the torque on the first example is (1300 * 1.5) = 1950 inch lb
so to put 1950 inch lb on a 9" wheel you need a load of (1950 / 4.5) = 433 lb
if you assume no friction then the 433 becomes 433/cos(45) = 612 lb


the 9" wheel will pull 3 times as fast as the 3" wheel

 

[PILOON]

"the 9" wheel will pull 3 times as fast as the 3" wheel"

AND pull 3 times less weight

Since you mention rope, I presume you are not looking at very much weight therefore you could be OK.
(Poly ropes are kinda elastic, so be careful)

 

[valley]

Thanks for the help.
Correction: mpr==MPH
I Want to make a rope tow. So that we, the family, can ski in up back in winter.
This would require having a wheel where the roller is or on the roller.
I would build a cage to house the wench and the outer bearing on the wench shaft.
The grade is about 30%. With skis on there is little friction.
There would be a continuous loop, rope or cable, wench at base and pulley up top.
I was going to use a truck to drive the rope but a wench would make for a cleaner setup.
Any ideas that would add to or help would be great. Thanks for taking the time to think and post.