Hanging your husband

A reader writes:

How is it possible that I can belay my husband when rock climbing? He is almost twice my weight.

At our local climbing gym, the top of the "cliff" has a cylinder, which the climbing rope is thrown over, wrapped around, and falls down off the other side (i.e., it's touching 540° of the cylinder). The employees say that it works because the rope is wrapped around the cylinder twice. I'd like a more scientific explanation, though: does wrapping it actually increase the amount I can lift? Is it just friction?

As another data point, I belayed him once on an incorrectly-set-up wall where the rope was only thrown over the cylinder, not wrapped around it. I felt alarmingly weightless when supporting my husband's weight, but my feet stayed on the ground.


Yes, belaying really is pretty much all about friction.

When you wrap a rope around an object a few times and pull on both ends, there's enormous friction between the rope and the object, even if the object's smooth. If the tension on one end of the rope, plus the friction, exceeds the tension on the other end, nothing moves (the exact numbers can be calculated using the "capstan equation"). So you can belay your husband. Actually, with enough turns around the cylinder and assuming the cylinder and the rope are strong enough, you could belay anything at all. (Getting a grand piano, a garbage truck, the USS Nimitz or the planet Mercury into the climbing gym is left as an exercise for the reader.)

When either end of the line is slack, which is the case most of the time, almost all of the friction disappears and it's easy for the climber to proceed upward while the belayer takes up the slack.

What you can't do, of course, is actually lift whatever's on the other end of the belaying line. Trying to do that puts you on the wrong end of the equation; you'd have to pull with a force greater than the mass on the other end of the line, plus the friction, which gets worse the harder you pull. In this situation, with a few turns around the cylinder, the world's strongest man would be unable to hoist a small child. If you add another, movable smooth cylinder, though, or preferably an actual pulley, you can make a block and tackle and lift arbitrarily large loads by applying a smaller force over a longer distance.

Standard yachting capstans (the things that you are apparently legally required to see people frantically cranking whenever TV news reports on a yacht race) are pretty interesting, too. They contain a planetary gearset that only operates when the capstan's being turned in one direction. Turn the capstan crank that way, and the gearset turns the outer barrel of the capstan at a fraction of the speed at which you turn the crank, making it possible to apply a strong pull to a line under tension. Turn the capstan the other way, though, and the gears lock up and connect the barrel directly to the crank, allowing you to let the rope out again quickly.

(Well, that's the way the old one depicted in one of my favourite toilet books worked, anyway. I'm sure there are now also capstans that can turn the barrel faster than the crank. They probably have infinitely variable transmissions in them by now.)

Psycho Science, as I have brilliantly decided to call it, is a new regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.

7 Responses to “Hanging your husband”

  1. iworm Says:

    A nice example of friction was on QI t'other day:


    Illustrates rather neatly (and amusingly) the "power" of friction.

    • Anne Says:

      I thought a rather nice solution would have been to tear the interleaved phone books in half - not as hard as it looks; apparently the trick is to shear them a little so that you start tearing the sheets one-by-one.

  2. yetanotherdan Says:

    I'm pretty sure the capstan crank only works for tightening - it's either really fast at tightening (i.e. lifting a sail up) and then you turn it the other way when you need some more gearing/force (i.e. the sail is taut/full of wind or for trimming). So if you tack you can take up the slack quickly, then apply some geared force to trim. Something like that anyway.

  3. charleso Says:

    Modern yacht main working all in one winches tend to work in 3 modes:
    1) no winch handle in the socket or no pressure on it - capstan locked to hold lines
    2) winch handle turned one way - capstan turns at high speed usually direct to winch in fast when low load on line
    3) Winch handle turned other way - capstans turns at lower geared speed to winch line when loaded

    To hold the line it is either cleated off in a jam cleat *before* the winch which allows one winch to serve a bank of lines - usual for lines used to haul sails and set up rig - or it is cleated off after the winch so it can be rapidly eased or hardened - usual for the sail sheets that need to be constantly tuned. Most winches dedicated to sail rather than rig handling are self tailing, here an arm strips the turn off the capstan into a rubber grip ring on the top of the capstan. This means the winch itself keeps the pressure on the capstan ("tailing") and it's safe to leave like that to hold the rope. This makes sail triming much easier but means the winch is dedicated.

    To ease a line it's not done with the gears. The line is put back onto the winch if needed, un cleated and then the tension lowered so the friction drops and it pays out. This action needs to be done with care as if the line surges the loops can jump about and lock over each other leading to a riding turn where the line is locked on the winch. That's a sailors nightmare as you now have to get *another* line onto the loaded line in order to take the tension off the locked rope. Most folks will therefore pay off the rope in one hand and keep the other hand flat lightly on the turns on the winch on the outside - no chance of the hand being trapped but it will stop the loops jumping and you can feel if it's getting too energetic and slow things down.

    Average 30-40 foot yachts tend to have a pair of dedicated winches for the foresail, and then a pair of general winches with cleat banks for the rigging and main sail.

    Larger or racing dedicated yachts will tend to have more dedicated winches to reflect the larger crews and faster pace (as well as deeper pockets!) and the largest will seperate the winch drive into a seperate pedsatal with handles that the mad rugby player like crew member can crank like crazy while other crew use a gear box to connect it to a specific capstan and handle the rope. Even here the bi direction gear is the norm, if you watch them you will see a frantic crank one way to get the line in and then a rapid direction change to get the tension and power on quickly.

  4. Dr Nick Says:

    Even a carabiner is enough to generate a fair bit of friction. I have used a pulley to belay a climber of similar weight, and it's like trying to belay someone 50% heavier over a crab (especially if it's wearing a monocle and top hat. Whoops, wrong post). With a crab and a couple of runners, it's possible to catch a lead fall on the rope above the belay device. Again, this is the voice of experience, though it's not a trick I'd recommend.

    If you do find you're being lifted, then you need to look at anchoring yourself to the ground. This is standard practice in gyms, since you've often got a waif of a climber belaying a front row forward, or similar situations. Outdoors you look for big rocks, trees, or places to set natural gear. Very rarely there will be bolts for this purpose, but that's normally in situations where the belayer is at risk of falling themselves (e.g. on a ledge halfway up the cliff).

  5. David Richfield Says:

    It's good practice when out on the rock for a belayer's harness to be tied to something solid , especially if the belayer is much lighter than the climber. This keeps the belayer from being hoisted into the air if the climber falls.

  6. Mayhem Says:

    Not quite. It is better for the main carabiner in the belay system to be anchored rather than the harness - that way if the belayer needs to get out of the system (say to lend the climber some assistance) it is relatively easy to do so, and they can still be safely attached to the hill while doing so rather than having to take off their harness.

    The indoor climbing centre approach of simply clipping into the harness belay loop wins on convenience and helps prevent novices crossloading the biner, but isn't such a good practice if doing mountaineering or multi-pitch routes outdoors.

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