After Survival Tips S1 E9 (The Trucker’s Hitch) a few readers asked me to explain further how and why the mechanical advantage varies depending on the system’s configuration. The following series of diagrams will help you visualize what’s going on. All forces are theoretical, taking no account of losses due to friction or vector components. (In some — but not all — configurations, when you pull the rope at an angle to the load you lose some of your mechanical advantage).
Fig. 1 — A simple rope with a 300 lb load.
Figure 1 illustrates a 300 lb weight hanging from a rope. The tension on the single lead of rope, unsurprisingly, is 300 lbs.
Fig. 2 — Hoisting with no mechanical advantage.
In Figure 2 we’re using a pulley to hoist a 300 lb load, but we’re gaining no mechanical advantage. The pulley is just being used to change the direction of the applied force, but it still takes 300 lbs of force to lift the 300 lb load. No matter where you stand to pull the rope (whether directly underneath, to the side, or directly above), it will still require 300 lbs of force to lift the load. It’s interesting to note that when you pull straight down, because both leads exert 300 lbs of downward force, the total tension on the upper anchor point reaches 600 lbs.
Fig. 3 — Simple hoist with a 2:1 mechanical advantage.
Now we’re getting somewhere. Figure 3 represents a hoist with a 2:1 mechanical advantage. The total 300 lb load is borne by two leads, so the force required to lift it is reduced by half. This gain is vector-dependent, so you need to pull straight up, and not to the side, to gain the full advantage.
Fig. 4 — Two-pulley system which yields a 2:1 mechanical advantage.
This setup is a combination of Figures 2 and 3. The upper pulley simply allows you to change the direction of pull with no reduction of the 2:1 advantage. Here’s some very cool trivia, though: The vector (your direction of pull) has no effect on the working load (the 300 lb weight), but it does affect the tension on the upper anchor point, which will reach a maximum of 450 lbs if you pull straight down on the rope.
Fig. 5 — Diagram of the Trucker’s Hitch, with its 3:1 mechanical advantage.
Figure 6 — Trucker’s Hitch used to tie down a kayak on a pickup truck.
Now we can represent what’s happening when you tie down your load with the Trucker’s Hitch. When you pull the rope through the loop and back to the left-hand rail of the truck bed, every pound of force puts 3 lbs of force on the right-hand cleat. Compare Figure 5 and Figure 6.
- The 300 lb weight in Figure 5 represents the fixed end of your rope on the right-hand cleat in Figure 6.
- The upper pulley represents the left-hand cleat in Figure 6 — the working end of the rope goes around the cleat like a pulley and back to the midline loop.
- The lower pulley represents the midline loop in the Trucker’s Hitch. The rope goes through the midline loop and then is tied off at the left-hand cleat or bed rail.
Now that you understand the physics of the Trucker’s Hitch let me throw a wrench in the works: Figure 4 and Figure 5 both represent what’s going on in Figure 6. They are actually the same configuration, but the mechanical advantage is 2:1 with respect to the left-hand cleat, and 3:1 with respect to the right-hand cleat. It depends on your point of reference. If you’re concerned with the work being done at the left-hand cleat, you have a 2:1 advantage. If you’re wanting to effect work on the right-hand cleat, you have a 3:1 advantage.
Isn’t the world amazing?
~SnoMan
Nice explanation and great diagrams
The top image along with figures 2 4 5 and 6 are flat out wrong, you lack a basic understanding of physics.