Funny but serious by all accounts!!

[daltontrees]

It can't be! If you pull 2 foot through but only go up 1 foot, your rope must be magically getting longer.

 

The double rope technique (that I am aware of) is a re-directed 1:1 system.

 

Look here: Pulley Systems | ropebook

 

No no no. You pull 2 foot through. The rope shortens by 1 foot on one side of the crotch and 1 foot on the other side of the crotch. To go up a foot you have to shorten both sides of the pulley/crotch by a foot. To do that you needs to shorten the whole rope by 2 feet.

[Amelanchier]

Its not that complicated.

 

Complicated enough that no-one explained that the mechanical advantage of a system depended on your frame of reference within it...

[daltontrees]

Uh oh, looks like saome basic physics is needed here. Don't run away, it's fairly easy.

 

You need only one equation. F=ma. Force equals mass times acceleration.

 

When you are hanging on a single line the force on the branch equals your mass (and the mass of teh rope and the harness etc.) times the acceleration which if you are static is the gravitational acceleration. it is about 9.8 m/s/s. Call it 10.

 

100kg x 10 m/s/s = 1000 Newtons (the unit of force). Or 1kN.

 

If you think about it, this is why gear rated to say 30kN can hold 3 tonnes or 3000kg. F = m a.

 

So in the example, the rope is resisting all of this force, so the load on it is 1000N. every action has an equal and opposite reaction. One of Newton's laws of dynamics.

 

But if you pull up on the single line to go up the ways, and you accelerate at 2 m/s/s, you are adding that much to the acceleration of gravity, so the load becomes 100kg x 12 m/s/s = 1200 Newtons.

 

The load on the rope therefore depends on how fast you go up, and is only greater than the static load while you accelerate upwards.

 

It might not be surprising to know then that if you start to descend, the load on the rope decreases.

 

Using a doubled rope is a little more complicated. When static, the load on teh branch is still 1000N, but the load on each half of the rope is 500N.

 

As you ascend, the load on each side is increased by half the additional total load. If you were accelerating upward at 2 m/s/s, the additional load on each side of the rope is equivalent to 1 m/s/s which means each side is loaded 10 + 1 m/s/s = 11 m/s/s times half the deadwweight. Using f=ma again, the load is therefore 11 x 500kg = 600N.

 

With ropes of standard rating 3kN or 3000N, neither SRT nor DdRT will come anywher near breaking strain. To do that you would need to (using our F=ma in reverse now) accelerate at a = F/m = 3000/100 = 30 m/s/s.

That is, your upward speed would need to increase by 30 metres per second per second. After the first second you would have to be travelling at 30 metres per second. Now I don't care how fast SRT is, that aint going to happen unless you're being hoisted by a medieval battle trebuchet.

 

The modest DdRT man would by comparison have to be pulling through 60 metres of rope a second and be body thrusting like Beyonce on speed.

[daltontrees]

And that, my Arbfriends, is how to kill a thread!

[Amelanchier]

Wouldn't descending involve an acceleration as well?

 

Rise Lazarus...

[daltontrees]

Wouldn't descending involve an acceleration as well?

 

Rise Lazarus...

 

The descending climber would be accelerating, which is taking soem of the force that otherwise gravitational acceleeration would take. So if you descend and accel;erate downwards at 2m/s/s the effective gravitational acceleration is reduced from 10 to 8 m/s/s, reducing the effective load. The potential energy released is absorbed in the crotch and the hitch, manifesting itself as heat and/or mechanical damage.

 

Reductio ad absurdum: if you cut the hitch like Adam did to dolly, the acceleration of dolly equals gravitational acceleration, and the load on the curtain rail is (10 - 10) x dolly's weight. This will equal zero, there is no longer any load on the curtain rail or the rope.

[Amelanchier]

On second thoughts Laz - get your head down. Nothing to see here

[daltontrees]

LAZZzzzzz......

[Adam Bourne]

Nice read dalton

[Joe Newton]

Sod this, I'm getting a MEWP.

 

Seriously though, Dalton explained it comprehensively enough for me to just about wrap my little brain around.

 

Got any explanation for descending on a line to static?(I.e. Abseiling down using your hitch then coming to a stop)