The Practical Paddler
Getting Physical —
ItZa Drag! (Or Is It?)
By Tamia Nelson
January 26, 2010
When, not too long ago, I wrote a column entitled "The Versatile Prusik Hitch," I figured that any article on the prusik that didn't include a mention of its use in setting up a Z‑drag would be woefully incomplete. After all, the Z‑drag is a river‑rescue standby, having freed many a pinned boat from a rock's unwelcome embrace. The reasons for its popularity are easy to see. It offers a 3:1 mechanical advantage — a great help when a party is short‑handed and the river is running high and fast — while requiring only a minimal inventory of gear: a rope, a couple of prusik hitches (readily made up from high‑breaking‑strength cord), two carabiners, and one or two slings.
Here's what I had to say in the column:
Moving water exerts enormous force, and few paddlers are built like Arnold Schwarzenegger. So the Z‑drag is just the "force multiplier" we ordinary mortals need. In fact, bluewater sailors will note a close resemblance between the Z‑drag and the hauling tackle known as a "Spanish burton." Both offer a (theoretical) three‑for‑one mechanical advantage. That means you can shift a 300‑pound load with little more effort than it would take to move 100 pounds unaided, though the Z‑drag suffers somewhat in comparison with its maritime counterpart, since carabiners don't make very good pulleys. Still, even a little help goes a long way in a hard chance, and supplementary pulleys are available to improve the Z‑drag's performance.
And I illustrated the point with the following sketch:
That was then. This is now. But to be on the safe side, I suppose I'd better reiterate the cautions from my original article. The drawing above is a simplified schematic. You can't give it a once‑over and then rush out to haul your boat off a rock. Not if you value your life (and boat), anyway. In fact, you can't learn any of the techniques of whitewater rescue or salvage just by looking at a picture. You have to practice the moves in real life, under the watchful eye of someone who already knows the ropes.
'Nuff said? I hope so. In any case, back when I wrote the earlier column, I figured I'd pretty much covered the ground I wanted to cover. I'd highlighted an important application of the prusik hitch, while at the same time emphasizing the attendant hazards. In so doing, however, I accepted at face value the claim that the Z‑drag offered a 3:1 mechanical advantage. After all, no less an expert than Charlie Walbridge repeated it without question or caveat. But not all readers were convinced, and David Pitkin was one of the skeptics:
I just read your article on the prusik hitch. You say that you get a three‑to‑one advantage [with the Z‑drag]. [But y]ou need three pulleys to get that three‑to‑one advantage…. [Y]our rig shows only two pulleys, so it gives only two‑to‑one.
There was more in David's letter, but you get the point. So did I. And it gave me pause. Had I made a mistake? Had Charlie Walbridge? I voiced my misgivings to Farwell, who has greater enthusiasm for engineering calculations than I do. But to my surprise he didn't rush to blow the dust off his ancient slide rule. Instead, he suggested that we use what he calls "brute‑force methods" and…
Put the Z‑Drag to the Test
So we did. Before explaining how we went about it, though, I'd better lay out the ground rules. To begin with, then: What, exactly, do we mean when we say that the Z‑drag yields a 3:1 mechanical advantage? Well, here's one way of looking at it: If you have to shift a 300‑pound load, a Z‑drag should reduce the required force by a factor of three. In effect, the 300‑pound load has now been pared to 100 pounds, at least as far as felt effort is concerned. (I'm neglecting frictional losses here, though they mount up quickly as the number of pulleys increases.) But in physics, as in life, there's no such thing as a free lunch. You'll have to pay for all the help the Z‑drag gives you. And how do you pay? By stretching the effort out, that's how. In other words, if you need to shift the 300‑pound load a distance of 10 feet, and if you're using a Z‑drag to do the work, a total of 30 feet of line will pass through your hands, not 10. That's true if the Z‑drag really does yield a three‑for‑one mechanical advantage, at any rate. (Confused? Then check out the Wikipedia article on mechanical advantage. Or — if you'd like a more thoroughgoing explanation — get hold of a copy of the 1943 edition of Lancelot Hogben's Science for the Citizen and start reading at page 232.)
Back in the lab…er…office, our brute‑force model was now taking shape. Because our stock of disposable boats was rather low, however, we didn't want to wrap a canoe around a midstream rock in The River and rig a Z‑drag to haul it off. So we set up a table‑top experiment instead. Here's a list of the materials we used:
- About six feet of not‑too‑stretchy cord (our hauling line)
- Several boxes of shotshells, plus one box of .308 ammo (the test load)
- A small Velcro tie (the bridle around the load)
- Two short loops of lightweight cord (prusik and sling, respectively)
- Two key rings (carabiner substitutes)
- Two 6‑inch rulers
- Two twist‑ties
With this unlikely collection of odds and ends gathered from our office shelves, we had the makings of a river rescue in miniature, with the shotshells and rifle ammo standing in for the unlucky boat in my schematic sketch. (Why use shotshells and rifle ammo? Easy. The shell boxes are both heavy and compact. Plus, they were handy. In the years since we gave up hunting, we've used our remaining boxes of shells as bookends.) A leg of a worktable stood in for a riverbank tree, while the rulers and twist‑ties made it possible to measure just how far the load moved in response to every tug on the hauling line.
This is how the final setup looked:
Click here for a larger image of the rig
To repeat what I said a couple of paragraphs back: The mechanical advantage of the Z‑drag is identical to the ratio between the length of line that passes through your hands as you haul and the distance that your boat moves in response to your efforts. If you have to take up three feet of line to shift the boat just one foot, then the Z‑drag does indeed yield a 3:1 mechanical advantage.
Now we were ready to put our model of the Z‑drag to the test. Farwell got into position to haul on the cord. I set up my camera and checked that the rulers were in place. Here's how things looked at the start, with the blue arrows showing the direction of movement in the "Z":
The two‑tone background? It's a photographic artifact — the image is a composite, pieced together from two shots. Now let's take a closer look at the two rulers and the improvised twist‑tie pointers:
The ruler in the top photo measures the distance the load moves, while the one shown in the bottom panel gauges the amount of line Farwell takes in.
We're off! Farwell hauls. The boxes of shotshells slide closer. I press the shutter on my camera. And after Farwell has reeled in six inches of line, the load has traveled…
Only two inches. The ratio? Three to one, as predicted. Charlie Walbridge got it right. The Z‑drag gives riverbank salvage teams a 3:1 edge, just when it's needed most!
Not convinced? Then try the experiment yourself. But do it on a table at home — not on a raging river.
OK. The Z‑drag is an effective force multiplier, yielding the same mechanical advantage as you'd get with a bluewater sailor's Spanish burton or similar hauling tackle. But what's…
The Z‑Drag's Secret?
The prusik hitch, of course. It eliminates the need to wade all the way out to your stranded boat to fix a pulley to the bow and thread ("reeve") a line through it. This would be an easy task on Golden Pond, perhaps, but it's no small matter in a turbulent river, when just staying on your feet takes all your strength, and a single misstep can mean a long and unpleasant swim. The Z‑drag can be laid out on the riverbank, using a salvage line carried ashore by the stranded boat's crew in the aftermath of the initial accident. And the setup requires no special equipment other than the two carabiners. These take up a lot less space in your duffle than a Spanish burton.
But is the Z‑drag uniquely advantageous? In a word, no. It offers no greater mechanical assist than other three‑part purchases. And what's a "three‑part purchase," you ask? Good question. You can determine the mechanical advantage of any arrangement of pulleys (a "tackle," in other words) by counting the number of lines coming out of (or attached to) the moving pulley (moving "block" to old salts). Or — to put this in the jargon favored by sailors and other watermen — simply count the "parts" coming out of the moving block(s). That number gives the total mechanical advantage of the tackle: two parts means a two‑for‑one advantage; three parts, a three‑for‑one advantage; and so forth. The upshot? Every three‑part purchase yields a three‑for‑one mechanical advantage. It's the parts that count. The number of blocks — whether one, two, or more — is irrelevant.
In the illustration below, the first example has just a single line attached to the boat, and the sole block (in this case, the block is a 'biner) is fixed to a tree. The result? The block serves only to change the direction of pull. It offers no mechanical advantage whatsoever. The second example is different. Although a carabiner in the bow of the boat once again serves as a block, it's a moving block, and a line runs from the riverbank through the 'biner and back again. In short, two parts (lines) extend from the moving block. This tells you immediately that you'll have a 2:1 mechanical advantage when you haul on the line. That's better than nothing, but it's still not the equal of a Z‑drag.
Lastly, in the third example, we see a more elaborate hauling tackle, a true three‑part purchase. There are two carabiner‑blocks: one fixed to a tree and the other — the moving block — attached to the bow of the stranded boat. The hauling line runs from the bow of the boat to the shore and then back again, before returning a final time. In this instance, three parts come out of the moving block. Conclusion? The tackle yields a 3:1 mechanical advantage, exactly the same as that of the Z‑drag. But it won't be as easy to rig on a river!
There you have it. With David's timely letter goading us on, we put the Z‑drag to the test. And it lived up to its billing, proving itself the equal of a standard three‑part purchase. Of course, you don't need to be a physicist or an engineer to use it. You don't even have to be an old salt. You just have to learn how to set up the Z‑drag properly, with some hands‑on instruction from an experienced whitewater paddler who has a few salvage operations under his (or her) belt. Then — and only then! — you'll be ready for the day when a swift current conspires with an unforgiving rock to wrest your boat from your grasp. The good news? With a little help from the Z‑drag, it won't be at the mercy of the river for long!
The Z‑drag has winched many a pinned boat off the rocks, and most paddlers are content to accept its utility without question. But suppose you're a show‑me sort of guy (or gal). What then? Well, you can do what Farwell and I did — put the Z‑drag to the test. And here's what we learned: It passes with honors. The Z‑drag does indeed offer a 3:1 mechanical advantage, just as advertised. The proof is in the pulling. So the next time you have to get physical and pit your strength against the mighty sinews of a fast‑moving river, relax. The force is with you. In trained hands, the Z‑drag delivers.
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