Building a Ski Rope Tow. Need help with motor sizing

[JesseWendt]

Need help with motor sizing/torque calculation - Building a Ski Rope Tow.

I am building a homemade ropetow in my backyard. I have done a lot of research and unfortunately I have been away from physics for about 15 years, so I am having trouble calculating my motor size and transmission options. I will lie out what I am trying to accomplish below.

Here are the specs:

-The hill is 300 feet long at a 20% grade
-The rope is approximately 650 feet long and 200 lbs.
-I can use anywhere between a 1 to 2 hp motor operating at 1750 RPMs (would prefer to stay on 110 power and definitely can't go to 3 phase)
-The gear reducer can be 10:1 15:1 or 20:1
-The pulleys to attach to the output shaft range from 6" to 14" mostly in even numbers.
-I would like to be able to pull three 200 lb people up said rope at once
-I would like the rope speed to be approximately 7-10 fps.

I am open to ideas. I have nothing purchased at this point.

My plan was to use a 15:1 reducer with a 14" pulley for speed that works out to

1750rpm/15 = 116.667 RPM output

circumference of pulley is 3.663'

speed is 427.39011 feet/minute or 7.1 fps

This would be completely fine for speed if it can handle the load. My biggest concern is not overloading the motor.

Any help or suggestions would be appreciated.

Jesse

 

[turbo]

Not to be a wet blanket, but have you considered any kind of fail-safe or cut-off? As a kid, I saw a young girl get hauled up the mountain because her long hair got entrapped in the tow-rope. Not really fun.

Rope-tows are inherently dangerous if used with standard twisted ropes. It may be possible to source some braided ropes, such are used on paper machines, and that could help with the safety issue. Teufelberger makes braided ropes, for instance.

 

[JesseWendt]

Yep. I have that covered with switches at the top and bottom and a trip line that will kill the motor.

 

[CWatters]

-The hill is 300 feet long at a 20% grade
-The rope is approximately 650 feet long and 200 lbs.
-I can use anywhere between a 1 to 2 hp motor operating at 1750 RPMs (would prefer to stay on 110 power and definitely can't go to 3 phase)
-The gear reducer can be 10:1 15:1 or 20:1
-The pulleys to attach to the output shaft range from 6" to 14" mostly in even numbers.
-I would like to be able to pull three 200 lb people up said rope at once
-I would like the rope speed to be approximately 7-10 fps.

Sorry I work in metric..

600lbs is about 300kg
300ft at 20% is about 60ft or 20 meters
300/10 = 30 seconds

Power = energy/time = mgh/t = 300*9.8*20/30 = 1960W = 2.6bhp

That's the power required to lift the weight of the people up the hill in the stated time assuming no friction, so the actual power required is going to be significantly more than that.

I've no data on the force required to pull a skier through snow.

PS: Also need to account for losses in the motor and gearbox etc.

 

[K^2]

My plan was to use a 15:1 reducer with a 14" pulley for speed that works out to

1750rpm/15 = 116.667 RPM output

circumference of pulley is 3.663'

speed is 427.39011 feet/minute or 7.1 fps

This would be completely fine for speed if it can handle the load. My biggest concern is not overloading the motor.

Seems a little fast to me. Tow lifts I've seen go less than half of that.

But if these are the metrics you insist on, you should expect about 0.6HP per 180lb person. But since the pull is unlikely to be even, I'd go with a 2HP motor to be safe.