Thank you Peak Rescue Institute
Let’s begin with manual hauls. When you talk about manual hauls or mechanical advantage, you have to talk about work. Work is done when force moves an object. Well, what’s this thing called force? Force is simply a push or pull that causes an action. And in fact, force can be measured with something as simple as a spring scale.
Now, what does mechanical advantage do? It helps us do work easier. Mechanical advantage makes work simpler, and given the right tools, it can make work safer. But overall, the way we think of mechanical advantage, it will make work easier for us.
Now, man makes simple machines to create this mechanical advantage. Some of the simple machines, for example, are…
- incline planes
What do those simple machines do? They just simply decrease the force required to move a load.
Now let’s get some examples out here.
Weight at the base of a building. It takes a lot of work to move this weight straight up. No? Simple machine, an incline plane. Move the rock. We’ve all done this all the time. Incline plane is a simple machine. Makes work easier. Now what’s the difference between the load moving from here to here? From here to here? (see below)
The force is over a greater distance.
Or another way to consider levers…
Let me give you another example of an incline plane, a screw.
What is a screw, but an incline plane wrapped around a nail? If you have a nail, takes a great force perhaps to pound it into wood. Compared to a screw, it goes in equally as fine, but what’s the difference?
It’s easier to do. It takes less force. What’s the other thing? It takes longer.
So there’s a price to pay with this mechanical advantage stuff. Another simple machine, a lever. A lever with a fulcrum. Simple machine, for example, a teeter totter. Let’s look at this a little closer.
We’ll put a weight on a lever. This is the fulcrum, and hopefully I can balance this. The lever is in balance. No? One ounce is holding one ounce in balance. Simple. We’ve seen this all the time. Let’s change some weight. Now one ounce is holding two ounces in balance. How can one ounce hold two ounces?
Leverage, right. We’ll continue. See where this is going. One ounce is now holding three ounces.
All right, let’s continue more. One ounce is now going to hold five ounces. This lever, a great simple machine. There’s no magic to it. Didn’t create energy, but what changed? How could this one ounce now hold five ounces? What changed?
The distance. The lever arm changed. I’m foreshadowing here. This is going to be a common theme, or it has been thus far from what I’ve talked about. So all I’ve done is move the fulcrum. I didn’t change the force. The force remained one. The distance though, the distance, the force traveled, that’s what changed.
Now, what’s a wheel? As it turns out, a wheel is a circular lever. A circular lever. The axle of the wheel is the fulcrum. Make sense? Now let’s look at this. This is what we get to work with, pulleys. What’s a pulley? A pulley is a wheel. A pulley is a wheel with a string around it. What does a pulley do? A pulley simply changes the direction of a flexible material. The flexible material that we’re going to use is a rope. All this does is change the direction of the force.
Now, pulleys can create mechanical advantage. Let’s talk about what mechanical advantage is. Just simply as a definition is a relationship between how much load can be moved and how much force it takes to move it. And it can be given in this simple equation.
For us. The force in will be the haul. The force out will be the load. As an example, if one pound of weight can move or hold steady one pound of load, or if one pound can hold one pound, that’s called a one to one mechanical advantage. If one pound can hold two pounds, it’s called a two to one mechanical advantage. If one pound can hold three pounds, it’s called a three to one mechanical advantage, et cetera, et cetera.
Now, how do pulls create mechanical advantage? There’s no electricity in it. How does it manifest this energy? Well, nothing in the world in physics is free. So with that mind, what’s the cost? The cost is endurance. Mechanical advantage spreads the weight of the load over a distance. The distance for us will be the distance of the rope.
As an example,
- if you move a load one foot with a one foot pull, that’s a one-to-one mechanical advantage.
- If you move a load one foot with a two foot pull, two to one mechanical advantage.
- One foot pull with a three, a one foot load raise was a three foot pull, three to one mechanical advantage, et cetera, et cetera.
Now, when we talk about pulleys and mechanical advantage, we have to talk about the systems that they create. So pulleys can be fixed moveable or a combination of both. This pulley system is fixed. The pulley is fixed at the anchor. This is called a one-to-one mechanical advantage.
What’s an example of a one-to-one mechanical advantage? How’s about a flag on a flag pole? Pull up the halyard, the flag goes up. A one-to-one mechanical advantage. Simply all a fixed pulley does is change the direction of force around itself. It creates no mechanical advantage. Then you guys ask yourself, “it seemed easier to pull a flag up”. Well, simply it is because you’re working with gravity. It’s much easier to pull down with gravity than to pull straight up. Nothing changes as far as force goes.
So we have a three pound load. What do you expect to happen?
Three pounds to lift it.
Three pounds to lift the load and hopefully given the magic of science three pounds on this side is directed around the pulley. Three pounds on the opposite side, one to one mechanical advantage with a fixed pulling.
Now somebody tell me what’s going on top. Holy cow. What’s going on? Does that make sense to you guys? So now you have three pounds on this side of the line and you have three pounds on the opposite side of the line.
That’s six pounds.
You have six pounds at the anchor. When you guys put fixed pulleys in anchors, you can double the load. There’s the example right there, right there for you to see.
Now what’s the other way we measure mechanical advantage of pulls.
All right. Let’s check that out. This, as it turns out, is about one foot. Yeah. Pretty close. So let’s measure. Okay. That’ll be there. We’ll measure from that point. That’ll be one foot right about there. What do you think? Boom. One foot. One to one mechanical advantage. Good. Let’s carry on.
So we’ve talked about a fixed pulley. How’s about a moveable pulley?
Moveable pulleys, think of it as two ropes lifting one load. With a two to one mechanical advantage. That’s essentially what’s happening. In effect, half the load is on one side and half the load is on the other. So the load is three pounds, correct? Somebody with good eyes tell the crowd.
Okay. What’s the load here? About half right?
About one and a half because that’s two and that’s about one and a half on that side as well. So two to one mechanical advantage utilizes the moveable pulley. The pulley is at the load. It’s moving. Fair enough? Everybody understand that? Really? I’m testing you right now.
What should I feel if I’m hauling? One and a half? All right. Load is three. Put it in static mode. It’s about one and a half. It’s a fixed pulley at the anchor. It simply becomes a change of direction. Okay. Check this out. It’s two to one about. Actually the change of direction may put more efficiency into the system.
So we’re talking about pulley systems. What else can they be? A mixture of both. They can be not only fixed, but they can be moveable. So this is the combination of a fixed and a moveable pulley.
Let’s make it a reasonable haul. Three pounds at the load. One pound at the haul. What should be right here? What kind of load do you think will be there? Two pounds.
The load of three is divided, two plus one is three. So the point being again, three to one mechanical advantage, this load is displaced over three lines. We saw the result experimentally. Holy cow, that weighs three pounds. I’m only lifting one pound.
Three pound load with a five to one mechanical advantage one, we should feel one fifth of the load, correct? Or about 10 ounces. So a little less than a pound, three quarters of a pound. Let’s just give it that.
Let’s look at this five to one mechanical advantage I’ve created. All I’ve simply done is laced the rope back and forth between the fixed pulleys and the moveable pulleys. The load is displaced over how many lines? Five!
Three pounds is lifted by slightly less than a pound. This is a five to one mechanical advantage. I’ve lost a few of you, but that’s cool. We can bring you back with some one-on-one education.
The T-Method (Tension Method)
We can measure mechanical advantage simply using scales or a measuring stick to measure how far we’ve pulled the load versus how far the load moved. I want you guys to leave here knowing how to calculate mechanical advantage for any pulley system. And we’re going to use the T Method. The rules for the T Method are few, but they’re terribly simple. Now I’m going to preface all this when saying how simple is a T Method? Well, it only requires addition.
And for the most part, until you get into mechanical advantages that are really huge, and typically you’ll never see, all you have to do is to be able to add digits one through nine. So you have to be able to add, you have to be able to add single digits. Sound like a method? Let’s go over it.
T Method, or tension method. I’m going to go over these and we’ll work some problems. Okay.
- You assign one unit of tension at the haul. You’ll understand all this once we go through it.
- Two, the tension on one side of the pulley equals tension on the other side of the pulley. We just saw that that’s a true fact right here.
- Beginning at the haul… You have to be able to trace the rope either with your finger, a pencil or your imagination. You have to, at the beginning, trace the rope through the pulley system. When you reach a pulley, add the units at the pulley.
- Total all the units of tension that reach the load.
- And the last one, the mechanical advantage is a ratio between the total units at the load and one unit of tension that you’ve hauled.
1:1 No MA
Let us begin. What do you want to calculate a one-to-one mechanical advantage? Let’s start with the hard one. One to one mechanical advantage. Anchor. We have a fixed pulley. We have a load. And we have a rope going around a fixed pulley. And this is the haul.
Okay. Let’s go through the T Method. One, you assign one unit of tension at the haul. Truth be told? This could be called anything. One unit of fluff. One unit of goodness, anything. But it is just one.
You start off with the unit of one. You have to trace the rope. This is the hard part. When you get to a pulley, what do you do? The force on one side of the pulley equals the force on the other side of the pulley. They’re not… Pulleys aren’t magical. They don’t suddenly make energy.
So here’s the addition. At that pulley, you add one plus one, which equals two. There’s still one unit of force on the line. Follow line that down. The one unit of force goes to the load. Total the units of tension that reach the load. The unit of tension that reaches the load is one. Remember, the mechanical advantage is the ratio between the total units at the load and the one unit at the hall. One to one.
Okay. Let’s continue.
The line is anchored around a pulley. The load is connected to the movable pulley. Start with one unit at the haul. One unit at the haul, you trace the line down. You come to a junction or the pulley. One unit comes in. One unit comes out. You add the units at the pulley, which is two. So there’s two units here. One continues up, it terminates.
The mechanical advantage is the ratio of the load, which is two compared to the haul, which is one.
Hey, how do you check your work? The load has to equal the haul line, plus the unit that is terminated at the haul. One plus one equals two. Good? Let’s continue.
Three to one. The line comes from the load around a pulley to another pulley, to the haul line. The pulley is connected to that line via a prusik. Three to one? Let’s find out.
One unit of haul. One unit at the haul, trace the line. We come to a pulley. There’s one unit on this side of the pulley, an equal amount on the opposite side. So one plus one, there’s two units at that pulley. Continue to trace a line. There’s still one unit.
Trace a line. There’s one unit on this side of the pulley, an equal amount on the opposite side. There’s two units here, correct? There’s still one unit on the line. Uh-oh it just connected to the two units. One, this one unit plus two units continues down to the load. Two plus one is three. The ratio, the units that have reached the load versus the haul.
That’s almost as complicated as it gets. You may have to add more numbers. You may have to go around more pulleys, but that’s the T Method.
Let’s do some more stuff.
Okay. Now Let’s see if you guys really know what’s going on. There’s the load. We’ll connect a line to it around a pulley, around another pulley. Continuing up around another pulley at the anchor… around another pulley to a haul. Connect this to this. Connect that, to that with another prusik… Any guesses? Just off the top of your head.
Let’s check it out. What do you do? Begin with a unit of one at the haul, trace the line. You reach a junction or a pulley. There’s unit of one on this side of the pulley. A unit of one on the opposite side. One plus one is two at the pulley. There’s still a unit of one here. Correct? Continues down line. Oh, another junction, hit a pulley. One and one, so there’s unit of two on that side continuing. Ah, one plus two. Now we have three on this line. Does that make sense?
So now coming into this pulley, we have a force of three coming out of the pulley. We have…
Three. The force coming in is the same force that comes out. Nothing changes. Three plus three is what? Six. So there’s a unit of three coming up the line, correct? It reaches this pulley. So there’s three on that side. Three on the opposite side, six up here. So there’s three units coming down the line meeting six units. Three plus six is nine. I’m going, “Oh, well I think it’s nine.” So as it turns out, this is a nine to one mechanical advantage.
The Progression Scale
Peace on your Days!