Does an MA system put more load on the anchor?
Warning to non-enginerds: this question gets a little technical, feel free to skip it if you want. The takeaway is YES, it usually does, so make your anchor extra stout. If you want to know why, read on.
Ahh yes, this is a very interesting question, and one subject to much debate on the inter-webs.
Lots of folks think that an MA system always magnifies the load on the anchor. For example, if you have a 2:1 system lifting a 100 kg load, then the anchor is holding 200 kg. A 3:1 system, the anchor is holding 300 kg, etc.
This is NOT correct!
Theoretically, an MA system does not put more force on the anchor.
In the real world, with friction, you can magnify forces on the anchor.
Let's first have a look some ground rules, and then we’ll get into the friction part.
The higher the MA of the system, the more force goes to the anchor.
Let's have a look at the diagram below, made with the clever software vRigger. Assuming no friction in the system, and a load of 100 kg, there's quite a large difference in the load that gets transmitted to the anchor with the 2 to 1 compared to the 3 to 1. This is a pretty straightforward rule that applies to all MA systems.
Why is this? The lower the MA of the system, the more of the load you’re supporting with your hand, and the less goes to the anchor. With a 2:1 system, about half the load is on your hand and half is on the anchor. With a three to one system, roughly 1/3 of the load is on your hand and the other 2/3 of the load is on the anchor.
made with vrigger software
A redirect on the anchor for pulling increases the force on the anchor.
This is a great rule to keep in mind when you want to reduce forces on your anchor, such as crevasse rescue with one buried dead man.
Check out the example below with a 2:1. With the standard set up on the left, about 0.5 times the load goes to the anchor. But when you redirect as shown on the right, about 1.5 times the force of the load goes onto the anchor.
made with vrigger software
In the real world, friction can magnifies force on the anchor.
Let's revisit Sticky, who is pulling a simple 1:1 pull, redirected through the pulley high up in the tree. Only this time, instead of the tree branch conveniently hanging out over the edge of the cliff, the tree is set back, so the rope is running over a rock ledge. For this discussion, let's say that Sticky needs to pull with an extra 50 pounds of effort to overcome the friction of the rope running over the ledge. For her to lift the 100 pound load, she needs to generate 150 pounds of effort.
If she pulls with 150 pounds of effort to raise the load, that means there is now 150 pounds on the strand coming out the other side of the pulley. Which means the anchor is holding 300 pounds rather than 200 pounds. Remember, when you redirect your pull, that redirect point will receive twice the force that you apply.
Note that this does not have anything to do with the actual mechanical advantage of the system. Instead, it's an example of how friction in your hauling system can result in increased forces on your anchor, regardless of the mechanical advantage you’re using.
Is this a problem? Maybe, maybe not. Do you have an anchor on a stout tree limb or three well equalized points of rock protection? Probably not.
Or, is your anchor a a vertical snow picket, and you're about to set up a 3 to 1 haul with two strong people trying to pull somebody out of a crevasse? Then, that lone anchor might be a significant problem. Take a few more minutes and make a deadman anchor from that picket, or better yet, two that share the load.
With this in mind, let's consider a real world crevasse rescue scenario.
One person from your 3 person rope team fell into a crevasse. The rope going to them is cut deeply into the crevasse lip, adding a lot of friction.
You only have 50% efficient carabiners instead of 90% efficient pulleys.
On your alpine climb, you’re using small diameter, stretchy dynamic ropes.
You set up at 3:1 Z drag, and you and your partner both start pulling with your entire body weight. To move the load, your pulling force has to overcome all the extra friction from the carabiners, the rope against the snow, (and the inefficiency of the stretchy rope) and that pulling force has to be transmitted to the anchor. How much force? Hard to exactly say, but two people pulling as hard as they can on a Z drag with a lot of real world friction can generate a BUNCH! That extra force has to be absorbed by something - most of it’s going onto the anchor. (Better bury another picket as a deadman!)
You may be thinking: “Here I am with my buddy, and we’re both pulling as hard as we can on this 3:1 Z drag, trying to lift our 150 pound partner out of the crevasse. Me and my partner weigh a combined 300 pounds, so in theory, if we’re pulling with a 3 to 1 we should be creating 900 pounds of pulling force, but we’re still only barely lifting my 150 pound friend. This is way harder than it should be . . .”
Here's another way to handle that crevasse rescue scenario.
Your three person team is carrying high-efficiency pulleys, a Micro Traxion or two, and enough extra rope with each and person to be able to drop a loop down to the person in the hole.
After your buddy falls in, can you drop a loop of rope to them which they clipped to the harness with a Traxion. You also prepare the lip on top, knocking down some loose snow and putting an ice ax underneath the dropped loop to help reduce friction.
The victim, who is functional, can greatly help in this process by pulling down on one of the draft strands. This effectively reduces his weight and friction on the other strand that’s being pulled.
Now, the two partners on top can easily pull up the victim, and have a minimum load on the anchor.
To use a more extreme example, let’s say you get your car stuck in a ditch, and you rig a 9:1 with a big tree as anchor to try to pull it out. Now you have basically a tug of war between the tree and your car. When you pull onto 9:1, the anchor (in theory) gets your pulling force multiplied by 8.
Now, say someone else steps up to help you pull. How much force on the anchor components can two strong people apply? That’s now the force of two people pulling multiplied by eight. Now you’re probably getting pretty close to the safe working limits of some of your equipment. There’s a chance the weakest links on the system could start to fail, like prusiks sliding or breaking or even hardware failing. Hopefully the car moves before anything breaks or slips, but the point is, your anchor and the components of your pulley system need to be stout enough to handle these magnified forces.
So, here is the final answer - In the real world, mechanical advantage systems often result in extra force on the anchor, because of the extra effort needed to overcome friction. The greater the MA of your system, and the heavier the load you’re trying to lift, and the more friction is involved, the stronger your anchor needs to be.
This is discussed in the excellent book “The Mountain Guide Manual”, by Marc Chauvin and Rob Coppolillo, pg 276.
