Inclined Cableway Trolley Question

[ForestMoon]

Hi all,

First post, please be gentle

I saw this picture online (

https://www.aditnow.co.uk/SuperSize/Inclined-Cableway_49382/)

of an inclined cableway trolley. What I understand from this picture is that the trolley is supported on a main carrying wire rope and a second rope is used to control the descent of the trolley along the carrying rope (connected to a winch probably). The pulley systems would then allow to lower the load when the trolley hits the cable clips, stopping its motion and allowing the loose given by the winch to be transferred to the load.

My question is: wouldn't the trolley need to be heavier than the load to ensure that the correct motion order be respected (the load should not be lowered when the trolley is mid-span on the carrying rope for example)? From this picture, even with the triple load reduction factor, it may seem that the trolley is barely heavier, especially if the cart is not empty. Am I missing something? Is my intuition failing?

Thank you all,

 

[3DDave]

Even if the trolley weighs nothing the load will be pulled up to the trolley as long as the tension required to to pull the trolley up is greater than 1/3 the weight of the load, or about 20 degrees slope. (Edit: arcsin, not arctan)

 

[ForestMoon]

3DDave,

Okay I think I got it.

Denoting P the load, W the weight of the trolley, N the pulley ratio and θ the slope angle, ascent or descent of the trolley along the carrying rope occurs first if:

[pre](P + W) sin(θ) > P/N[/pre]​

Thanks a lot,

 

[Denial]

Generalising 3DDave's result.[ ] Let m be the mass of the trolley, and M be the mass of the lifted load. Then the critical angle for the main wire rope is
Θ_c = arcsin(M/(3(M+m)))
[ ] [ ] [ ] [Edit:[ ] arctan changed to arcsin.]

However, after thinking a bit more on it, I don't believe the problem as shown is this simple.[ ] Consider the situation when the entire load is held stationary somewhere along its inclined path.[ ] The system has two degrees of freedom, but only one restraint (that being the control rope).[ ] It remains a mechanism.[ ] If the slope is greater than Θ_c then m slides down, lifting M as it goes.[ ] If the slope is less than Θ_c then M drops and moves m up the incline as it does so.

If I am right, there must be some other device that stabilises things, a device not shown in the photo.[ ] But what?

 

[MintJulep]

Goes down light.
Comes up heavy.
It's a quarry. No need to send rocks down.

 

[berkshire]

This looks like a running sky line yarder as used by lumberjacks.
B.E.

You are judged not by what you know, but by what you can do.

 

[Denial]

Thanks for your brief insight, MintJulep.[ ] I think it completes the picture, for me at least.[ ] If the device is used as you suggest, then:
»[ ] On the way up, the "critical angle" θ_cd will be relatively high, with an upper limit of arcsin(1/3) as per 3DDave's contribution.[ ] (And please note here that he got it right with arcsin whereas I got it wrong with arctan.)
»[ ] On the way down, the critical angle θ_cu will be relatively small, with a lower limit of zero.

Depending upon the actual slope of the cable (θ), we can identify three possible situations.

Low slope[&nbsp;] θ[&nbsp;]<[&nbsp;]θ_cd[&nbsp;]<[&nbsp;]θ_cu[&nbsp;].[&nbsp;] When lowering, the load will first descend vertically.[&nbsp;] This descent will have to be terminated by some sort of stop attached to the control rope.[&nbsp;] Then and only then can the inclined combined travel begin.[&nbsp;] When raising, the reverse happens and the trolley's inclined travel occurs before the load's vertical travel.

High slope[&nbsp;] θ_cd[&nbsp;]<[&nbsp;]θ_cu[&nbsp;]<[&nbsp;]θ_[&nbsp;].[&nbsp;] When lowering, the trolley will first roll down the cable, then when it hits that small stop the load will descend vertically.[&nbsp;] When raising, the load will ascend vertically until it hits the trolley, then the combined unit will travel up the inclined cable.

Intermediate slope[&nbsp;] θ_cd[&nbsp;]<[&nbsp;]θ[&nbsp;]<[&nbsp;]θ_cu[&nbsp;].[&nbsp;] When lowering, the trolley will first roll down the cable, then when it hits that small stop the load will descend vertically.[&nbsp;] Then and only then can the inclined combined travel begin. When raising, the trolley's inclined travel occurs before the load's vertical travel.

I suspect that the only acceptable result is the "high slope" one. If so, this could be achieved either by setting the cable's slope, by putting limits on the m:M ratio, or by changing the number of rope falls between the trolley and the load.