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The Shape of Beer: the Answer

To review, here is last week’s Puzzle:

When a beer can is full, its vertical center of gravity (VCG) is half the can’s height.

When it is partly full, its VCG is somewhat lower.

When it is empty, the VCG is again half the height of the can.

When is the can’s VCG at its lowest? 

The answer starts with knowing that there is a VCG of the can, and a separate VCG of the cylinder of beer inside the can, and that the two combine to produce a third VCG. All three points coincide when the can is full. The can’s VCG doesn’t ever change, but when you start drinking the beer’s VCG gets lower, and so does the combined VCG, but only until no part of the beer is above the combined VCG.

Before then, that VCG moves downwards. If you remove any more beer, it VCG starts to move upwards. So the elegant, obvious-once-stated answer is that the combined VCG is lowest when it coincides with the top surface of the beer.

Another approach is to turn the beer can into a pendulum, perhaps using the tab as an attachment point for the string. The period of a pendulum’s swing is proportional to the distance of the weight’s VCG from the pivot point. So even though the beer can gets lighter with successive sips, its VCG gets further from the pivot point, and you can time the swing to find the longest period. At which point the top surface of the beer will be as above.

One of my favorite entries came from Mike Madden, who got bogged down in calculations, so decided to take another approach. As he wrote, “Out came the precision equipment (scales, beer can, inclined plane (2 rulers and a rubber band — a ruler for the can to sit on, one to measure the vertical height and a rubber band to make a stop  so the can didn’t slide down the ramp). Full, the can tipped at about 23 degrees from the horizontal (that is, the back end of the 12 “ramp was about 4 3/4”  off the table). Since a thing tips over when its center of gravity is outside its base, I was encouraged to find that a right triangle from the VCG of the can to a point on the circumference of the base was 23 degrees, too…

“Anyway, after some playing around, It looks like the most stable VCG (tipping at about 36 degrees) is when the can is a little less than 1/3 full, putting the VCG … at about 1/6 the height of the can…”

This is consistent with results gotten by other means. I will note here that any specific result depends entirely on the relative density of the beer (or other liquid), and the dimensions and materials of the can. Heavier cans will contribute more to the result, lighter ones, less. Same for the contents.

Most entrants thought the answer was when the weight of the beer was the same as the weight of the can. This has a certain intuitive appeal, but it can be dismissed, with no need for calculus, by imagining a can that weighed the same as the beer it contained, when the can was full. The VCG would still start dropping when you started sipping.

Some entries were less than, um, scientific, but possessed of admirable practical consideration. For example, Greg Bridges wrote, “Open the beer, drink it, drop can on floor sideways, flatten with foot. VCG is now .005cm from the bottom, assuming the can has a standard industry sidewall thickness… Don’t think you can get much lower than that.”

Okay, now for the winner. I am happy to say that it came from Aaron Drake, who provided a hand-written work of art: pages of calculations that prove in-depth what other methods can only approximate. If you would like to enjoy a little algebra ecstasy, see below. In closing, Aaron also made use of the fact that rum is lighter than beer. He wrote, “In conclusion, on lighter air days when a higher VCG is desired… bring rum.”

To view Aaron’s work of art, see:

https://drive.google.com/file/d/1IpOAJ6izP9iW3Gc9BaBLu3bucb0JVN21/view?usp=sharing

Congratulations, Aaron! You have won a bottle of amazing beer, courtesy of Propolis Brewing, here in Port Townsend. Be in touch with me to arrange shipping. Or, if you are in the neighborhood, you can visit the brewery in person, and get one of their beer flights.

As for how all this relates to rigging, the lower the VCG of a hull, the more wind energy it can absorb without falling over. On vessels with ballast keels, the lead is the beer, and the hull and rig are the can. But even without ballast keels, VCG can be lowered, by judicious hull construction, lighter spars, and where you stow all the crap you bring aboard.

 

Coming on Friday: The Old Ways

Next week’s Puzzle: Rigging the Bathroom

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Adventures in Maintenance: Smorgasbord

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  1. The Pub

In Ross Norgrove’s classic book Cruising Rigs and Rigging, he tells the tale of the crew of a trading ketch in New Zealand, long ago. The skipper and mate took the train out of town to visit their farmstead for the day, leaving the crew to end-for-end all the halyards and sheets. Not a horrible job, but a slow one, involving unreeving, reversing, and rereeving, then cutting off the old splices, whipping those ends, and then putting new splices into the other ends. It was a small port town, and they were tied right up to the shore, and right across the train tracks was a pub. When it opened for business, someone got the idea of dragging the ends of the lines over there to work on, leaving the blocks attached to the boat.

All went wonderfully well, with locals buying them beer, the crew reciprocating in kind, with a helping of sea stories to entertain everyone. At the end of the delirious day, just as the sailors were preparing to drag their work back to the boat, the bartender announced there’d be a farewell round of drinks, on the house. They were just setting down to enjoy this unexpected parting gift when the train carrying the skipper and mate came back to town, and severed every single line.

 

2. Slush

We sent a new hire aloft to “slush” some standing rigging. Slush is a mixture of tar and/or paint and/or fish oil and/or Marvel Mystery Oil and/or pretty much whatever gummy, stinky liquid that a rigging shop might decide should be painted onto served rigging, to act as a preservative. No matter what is in it, slush is an awful, viscous mess until it cures, and riggers are expected to apply it while hanging above pristine yacht decks. There are ways to minimize the likelihood of spatter, but there are even more ways to spatter, with no shortage of stories about teak, canvas, and humans doused by what amounts to aromatic indelible ink.

So when we sent our apprentice up, we made it clear that the slush must not be spilled. Not one drop, we said. And up she went and immediately tipped the bucket into her lap. The rest of us were attending to matters below, and didn’t hear her gasp of anguish, and didn’t see her desperately trying to squeegee the goo back into the bucket. Nor did we see how, once it was clear that only a limited amount was going to be recoverable, she began to distribute it into her clothing, and into the fabric of the bosun’s chair, in an attempt to prevent drips. She succeeded at this, and spent the next couple of hours slushing the rigging by extracting tar from herself as well as the bucket. When she got back to deck, gloriously stained, we asked her why she hadn’t just come down right away. She said she it was partly because she was embarrassed, but mostly because she thought I would let her go if she didn’t get the job done. She really, really wanted to be a rigger. And she turned out to be a great one. To this day I am sure, when she is around, that I detect of whiff of pine tar.

3. The Topmast

A topmast was going up on a big schooner. This job is accomplished using a heelrope, which is rove through the bottom of the mast, up to the lower mast cap. The mast is hoisted aloft on the heelrope, and threaded up through a pair of “doublings,” basically a couple of brackets to secure the bottom of the topmast to the top of the lower mast. The arrangement looks like this model when it is in it doublings:

Topmast doublings

The lower doubling is rectangular, at the height of the crosstrees. The upper doubling is seated, at its aft end, onto the lower mast cap. It has a round hole in its forward end. The topmast goes up through both holes.

The rigging has to be put on after the top of the mast has cleared the upper doubling. You basically thread this tree-size spar through the doublings, and pause with the head of the topmast just above the lower mast cap. Then you slip all the gear on, and when you are done you send it the rest of the way up.

sending-up-main-tgallant-mast- on Picton Castle

A topmast going up through the upper doubling, on the bark Picton Castle. Our protagonist would have climbed up on top of the upper doubling, once the topmast was a few feet further along.

 

This can be an awkward process, because if you are standing on the crosstrees – the logical place – the top of the topmast might be well above your head, and you have to strain to get the (heavy) rigging up and over the topmast’s top. You can also sit on the lower mast’s cap, but this is awkward, too. So on this schooner the mate decided he would stand on the cap, and work from there. This is crazy, but not altogether unheard of. True, he was over eighty feet above deck, perched on something the size of a large dinner plate, but on the other hand he had several feet of topmast right in front of him, providing a stout and secure handhold. So he proceeded, hanging shrouds and stays and blocks. He was almost done when the heelrope broke.

The topmast immediately plummeted to – and then through – the deck, shedding all that rigging as it went, leaving the mate, as he put it, “Holding air.” He stood there for a moment, and then somehow, with extraordinary care and agility, he got himself down off that dinner plate. He has been a fan of carefully-inspected heelropes, plus backup heelropes, ever since.

4. Soap

Many years ago, some New Zealanders sailed into Port Townsend, and came to visit Hasse’s sail loft. They proved to be knowledgeable voyagers, full of useful information, even though their accent was a bit opaque to local ears. One of their suggestions was for a brand of soap that they had found to be excellent for getting stains out of Dacron sails. The sailmakers thought this was great, and one of them asked the Kiwis if the soap was good for anything else.

“Oh, yiss,” one of them said, “You kin also wash yer dicks with it.”

There was a moment of stunned silence, and then everyone except the puzzled visitors fell to the floor laughing. When they finally got their breath, they explained the misunderstanding, at which point the other Kiwi carefully said, “Oh, no, we mean it is really good on wood.” At which point everyone fell down laughing, again. Two nations, divided by a common language.

 

Do you have an Adventure in Maintenance story that the world needs to hear? Send it in, and I will find a home for it in a future post. Write to btoss@me.com. If I feel the need to edit it, I will run any changes by you before posting.

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Puzzle Contest: The Shape of Beer

Here is a classic, beer-themed puzzle that happens to have a direct bearing on sailboat rigging efficiency:

When a beer can is full, its vertical center of gravity (VCG) is half the can’s height. When it is partly full, its VCG is somewhat lower. When it is empty, the VCG is again half the height of the can. When is the can’s VCG at its lowest? 

Use whatever numbers you like for weight of beer and can. There are answers requiring fairly dense calculations, and at least one that is obvious once stated. Have at it.

Send your answers to puzzle@briontoss.com. Please don’t give your answer away on line; we’ll be posting the most interesting answers, even if they aren’t correct, so you will have a platform for your intelligence and/or smartassedness.

The deadline for entries is noon, Pacific Time, April 2nd. The winner, randomly drawn from the pool (keg?) of correct entries, will be announced on the 4th, and will receive a 25 oz. bottle (not a can) of Propolis, an internationally-acclaimed, gold-medal-winning, really, really delicious beer that happens to be made here in Port Townsend. By our daughter and her sweetie. To learn more about this beer, visit Propolis.

 

The Client From Hell

 

Our clients tend to be wonderfully self-selecting; if they were the kind of jerks that we would rather not deal with, they probably wouldn’t be into cruising under sail to begin with. Year after year we see the truth of this, in the form of a succession of sailors who are perceptive, resourceful, generous, sensible, and infectiously enthusiastic, to name just a few of their virtues. Plus they pay their bills on time, and have even been known to complain that the bill wasn’t high enough.

If you think I’m exaggerating, bear in mind that it takes a rare kind of individual even to consider the cruising life. We are talking about people who convert a large amount of money – often every available bit of their money –  into  a small, fragile, unstable parody of a living space. Their goal is to pilot that wobbly space into harm’s way, in circumstances where the chance of trouble of one sort or another is high, and where the chance of aid varies from slim to nonexistent. In addition, a cruising boat takes its occupants, by its nature, into alien lands, among alien peoples, just for the sake of doing so. Again, it’s a rare type of person who finds all of this attractive, and in almost every case it is a type that is wonderful to be around.

Every once in a while, however, we encounter  a cruiser who obviously got lost en route to a strip mine, who possesses all the charm and social grace of a flatulent badger, who is by turns insulting, distrustful, querulous, and parsimonious.  This is the kind of person who interprets  my every suggestion as a thinly-disguised attempt to add to the cost of the project, who dismisses my hard-won experience as so much empty opinion, and who regards their own completely baseless opinions as the height of wisdom.

Or to put it another way, these infuriating individuals cause me to re-examine my precious-but-often-deluded beliefs. They refuse to accept unquestioningly that I am an infallible source of wisdom. They insist, whether they are aware of it or not, that I pay serious attention to the ideals and standards that are at the heart of this business.

It is possible to be nice as well as usefully critical, but my experience is that people who like and trust us are reluctant to point out issues, even when they see them., so we get a lot fewer corrections from nice people. We can easily miss shortcomings they don’t notice, or don’t bring up. Of course, it is wonderful when people that I respect in turn respect me. It is gratifying when they confirm, both in the yard and in subsequent correspondence from far-off places, that our ingenious and elegant work actually did what we said it would do: make cruising under sail easier, more efficient, safer, and more comfortable. But one of the consequences of having a swelled head is that it tends to squeeze one’s eyes shut. Unhappy clients, lacking though they might be in social graces, can open our eyes to errors, to less-than-ideal solutions, to missed opportunities. It is just a painful way to get educated.

How, then can we maintain our quality control without going through conflict? Can we, on our own, motivate ourselves to keep our standards up, to seek continually to achieve the Perfect Gang? We can, but we rarely do. No matter our sense of pride and ethics, we are understandably inclined to think the best about ourselves. Even with a generous helping of spiritual aspiration,  virtue only enables one to seek knowledge, and to act on what one knows; it cannot guarantee full or accurate perception. Far from it; no matter how principled we might be – or think we are – we have an innate need to feel that we have achieved competence in the world. We all aspire to be respected by others, and it can be tempting to think that we inherently deserve respect, even if that feeling is based on the flimsiest of evidence. That’s why it can be mighty handy to have someone around who is skeptical, or even just plain rude. Not attractive characteristics, to be sure, but there is an old saying that goes, “Pay attention to people who don’t like you, for they will tell you your faults.”

An example: We did a furler, mainsheet, and a few other upgrades for a visiting cruiser.  We installed the brand of furler he insisted on having, even though it was a brand that we advised against. He was similarly dismissive of several other of our suggestions. This behavior annoyed us no end, but that was nothing compared to how we felt when he informed us that we were responsible for his having to recut his Genoa after the new furler was installed. It turns out that the brand he had chosen features a very high standard drum height, much higher than that of his old furler, so that the sail was now way too long to fit the furler. It would have been relatively easy to modify the new unit’s drum height  beforehand — all it takes is a few minutes with a hacksaw and a drill press — but we hadn’t discussed the height change with him.

On the one hand, he was the know-it-all who had insisted on the superiority of his chosen brand; we just installed the thing. On the other hand, installation of anything in a cruising rig must always be more than a matter of cutting, drilling, and tapping.  There is always a design component, and  there are always hardware quirks and requirements to be met, if one wants to avoid ending up hip deep in  a can of variables. One design detail with cruising vessel Genoas is that the tack should properly be at least a little bit higher than the bow pulpit railing. That way the foot of the sail won’t chafe on the pulpit, the crew will be able to see under the sail when under way, and the sail is much less likely to scoop up an errant wave at sea. The old furler had the tack right at the deck as for a racing boat; it was just wrong for a cruising boat. We knew this, but we were just too miffed to stop and think about it, let alone talk it over with the client. Granted, the guy had an attitude problem, but so did we.

One more example: I am in the habit of thinking out loud around clients. Often I will do this consciously, with the intent of including them in the process of selecting and installing the things that will make their rigs work. I want them to know why we’re doing what we’re doing. If they seem particularly receptive, I’ll go on in detail, describing options and variants of options, working with them towards an ideal. Or that’s the intent; sometimes I just think out loud. The latter is probably what was going on one day when I brought up the subject of a client’s bobstay. This is a man who one would not ordinarily describe as cheerful. Far from it. From the very beginning, when I was even slower than usual at getting an inspection done, our relationship had bordered on the adversarial. Maybe it’s just that peppy and dour don’t mesh real well, but it wasn’t just my perception; no one in the shop wanted to work with him either, and a couple of times we seriously considered suggesting that he take his job down the road.

Anyway, back to the bobstay. Originally, I’d suggested reinforcing the cranse iron and stem fitting for this highly-loaded stay, but the more I looked at it, the less vital the reinforcement seemed. The sprit was very short, very stout, and very well-secured to the boat. In addition, there was a Solent Stay throughbolted to the stem that was going to take the storm stays’l loads, and the relative angle of jibstay and bobstay was unusually favorable. So I mentioned to the client that maybe the reinforcing wasn’t so vital after all, then moved on to other topics. The next day the client gave me a firm lecture, saying that he feared that, as the job rushed to completion that I was trying to cut corners in order to finish on time. I thought, “Oh, boy, Lone Ranger shot with silver bullet,”  but realized that communication is every bit as much a skill as splicing or trigonometric calculations. Yes, the client saw my words in the worst possible light, but he wasn’t the one babbling on with every thought that came into his head. We ended up reinforcing that cranse iron, which cost the client needless expense, because I could not get him off a path that I had unwittingly set him on.

Well, we finally restepped that man’s mast. It had been a big, thorough job, involving just about everything that could be done, including the masthead, mast step, halyards, reefs, vang, mainsheet, all kinds of deck gear. Everything went beautifully, with every member of our team working at full efficiency, swarming all over the boat leading lines, attaching terminals, hanging the foil and boom — it was a joy. At one point, when I was on shore to set the rake of the mast, I happened to strike up a conversation with the owner. It was the first real conversation we had ever had, and in it he revealed, in a few halting words, a deep appreciation for history, spoke of considerable experience in commercial vessels, and shared a few thoughts on the nature of cruising. It was all very self-effacing, even shy, and I realized that, no matter his faults, I had severely misunderstood him, and had thereby missed out on some great conversations, as well as making the job more difficult than it needed to be. We stood there together in a light drizzle, watching the rig come together, relaxing for a blessed moment.

Many years ago, our dear friend Mary Tietjen, a woman with vast skill and experience at running organizations, did us the incomparable favor of running a series of strategic planning sessions for our business. The whole crew participated, and one of the topics we brought up was “The Client from Hell”. We described some of these people, and asked what, oh what we could do to avoid them. At the time, I found her response a bit depressing. Now it seems like a good thing. She took a long, slow look at each one of us, then replied in her laconic drawl, “There’s things you can do to make things better. But there will always be a client from hell”.

 

 

 

 

Extavagant Purchase

Extravagant Purchase, the Answer

 

The old-school version of the answer is below. It is also a fuller answer, with commentary, but if you’d like to see the video version, I have uploaded it here: https://www.youtube.com/watch?v=MdxwhcmDj-8

Now on with actual text.

 

Last week’s Puzzle set a new high for views, a new high for entries – and a new low for correct answers. This was a tough one, and I commend all of you who worked at trying to figure it out. Note: I say this as one who didn’t have the right answer, either. That’s right, when I put it up, I was certain I knew the answer, but it turns out that I didn’t. More on this in a bit. Meanwhile the challenge was to determine the mechanical advantage of the arrangement below.

Let’s look at the three component purchases. The purchase in the middle has a 4:1 advantage*. That means that for every pound of tension you apply to the end, you get 4 pounds of tension pulling down on the topmost block. Mechanical advantage is “…the ratio of the force that performs the useful work of a machine to the force that is applied to the machine” (Merriam-Webster).

The line that goes through the topmost block produces a 2:1 advantage. This means that if you pull down on either end with one pound of force, you get two pounds of tension on the topmost block.

The purchase on the left is also 4:1. It uses a fiddle block instead of an ordinary double, but the power is the same. This purchase is attached to the line that goes through the topmost block, making a “compound purchase” in which the two advantages are multiplied. 4×2=8, so the compound purchase is 8:1.

Most entrants simply added this 8:1 purchase to the central 4:1 purchase, for a total purchase of 12:1. But remember, you have applied a one-pound downward pull on both ends to get the resulting twelve pounds of tension, so the actual mechanical advantage is 12:2, or 6:1.

That’s right, the combined effect of both purchases produces a lower mechanical advantage than the compound purchase by itself, which sounds crazy. At least it did to me until Bob Downes, BTYR’s resident genius, showed me the details. Basically, the total tension is higher with both systems engaged, but the relative input efficiency drops.

Out of all of the answers we got, only 6 were correct, and out of that group, our randomly-selected winner is … Matt Barnett! Take a bow, Matt, and be in touch with me about where to send your copy of Finding Pax.

I offered bonus points for an approximate range of motion for the assembly, and entrants were far more successful here. As many of you determined, the topmost block had a total range of motion of approximately one foot. Even if we made the rope ends longer, total range would only gain another 6” or so. This rather limits the utility of this arrangement, and it would take real finesse to keep an even load on both ends. Reader Theresa Danks imagined some sailors trying to make this setup work, and concluded that, “If they all quit in disgust at the ridiculous rigging job, there’s no mechanical advantage at all.” Well put.

 

Note that if you were to let go of the whip tackle and kept pulling on the center tackle, the range of motion would be a little over three feet (whoop de doo), but you’d have to give up a full third of your power to get it, and this would happen at the end of the hoist, where loads are usually highest. Some readers nevertheless attempted to come up with practical applications, suggesting everything from mainsheet to boat hoist to shiftable tackle to backstay adjuster, but far superior arrangements for all of these uses are readily available; this is just a ludicrously bad arrangement for use as anything. Except as a puzzle.

 

*We do not have space here to describe how a block-and-tackle accomplishes this gain. Another time.

If you didn’t win Kaci’s book, and haven’t read it yet, do yourself a big favor and get a copy. You can contact Kaci at Finding Pax,Or you can order it through all the stores and sites.

Be sure to visit the rest of our site, too, for books, dvd’s, tools, rope, workshops, and a whole bunch of rigging services.

Posting on Friday the 23rd: The Client From Hell

Mark 2

Mark in the Army

 

He was not after a career in the army. He enlisted instead of being drafted, as did most of the soldiers in that war. He was idealistic and gung ho, but he also knew that by enlisting he’d get better educational options. This habit of earnestness and pragmatism is still with him. He signed up for clerk-typist school, then went on to Airborne, the second step on his chosen path. If he had completed training there, he was planning to take the steps to become a Green Beret, largely, he said, because of the training in languages and medicine he would get. We joked with him about this, saying that when he was done with all his classes he would be able to parachute behind enemy lines to perform surgery on a French typewriter. He laughed, a little.

But on his 3rd jump for the 82nd he injured his hip, and after his 5th jump it was clear that the injury wasn’t a slight one, so the Army put him into the typing pool at Fort Benning, and after a while they sent him to Vietnam. There he was put into a holding company, which is where they would they keep newcomers until they found a place for them walking point somewhere. But the clerk who interviewed him looked at his papers, and said, “Can you type?” Mark ripped through an exam at 60 words per minute, clear text on five carbon copies with a manual typewriter, and the next thing you know he’s interviewing newcomers at 2 Field Force, command center for 3-Corps, in the southern part of the country.

A little context:

In 1969, when Mark enlisted, Neil Armstrong walked on the moon, the Jumbo Jet made its debut, the Beatles gave their last live show, Charles Manson killed people, Woodstock inspired and entertained people, and 11,616 U.S. service members died in action. This last is of course an appalling number, but it was actually almost 3,000 fewer than the year before. The war was beginning to wind down.

Things were more intense in 1970, when he arrived in Vietnam. On the one hand, the Beatles broke up, Joplin died, Hendrix died, perhaps not coincidentally heavy metal was born, and the Ford Pinto made its fiery debut. On the other hand Apollo 13 managed to get home safely, the world celebrated the first Earth Day, the Nuclear Non-Proliferation Treaty was signed, the Azwan High Dam was completed, cigarettes were banned from U.S. television, and Muhammed Ali knocked out Jerry Quarry. But to return to the first hand, Nixon ordered the invasion of Cambodia, protests against the war turned violent in the U.S., a Communist peace treaty delegation rejected Nixon’s October 7 peace proposal as “a maneuver to deceive world opinion,” and another 6,081 U.S. troops died. As in every year of the war, many more soldiers were grievously injured than killed, and many, many more civilians were injured or killed than soldiers. On the whole it was a lousy year, though perhaps my recollection is colored by the fact that my brother suffered a freak gunshot wound in late April. More on that later. Meanwhile, let me tell you about his job.

Imagine that you are a clerk, riding in a helicopter. You can hear bullets spanging off the armored bottom of the helicopter, because you need to visit the firebases out in the countryside. In the process, you must fly over many, many hostile people armed with AK-47’s. In this war, no soldiers really qualify as REMF’s (rear-echelon-you-can-fill-in-the-rest), because there is nothing remotely like a secure rear echelon here. Every base in the country is subject to various forms of attack at any time, from harassing fire to full-on assaults. Even social clubs in Saigon got bombed if GI’s are known to frequent them.

So Mark was a clerk, but he spent a good deal of time under fire. The reason Mark needed to visit all those fire bases is that his job was to count bodies, living and dead. He and maybe another dozen clerks like him had to track how many soldiers were supposed to be in each unit, how many were on leave, how many had rotated out, how many had been sidelined by injuries, how many of those were likely to return to duty, and of course how many had been killed. With the data he collected, the Army decided how many people to send where.

Mark did not know what difficulties were ahead of him when he arrived. He considered himself extremely lucky to be in a place with tennis courts, a swimming pool, and other amenities. Those amenties were there in part because field troops would rotate through the base for 13-day leaves, so he saw a steady parade of Aussies, Koreans, and assorted VIP’s, as well as G.I.’s. It was an interesting place to be. Then, three weeks in, he got shot.

Here is how it happened. He was asleep in a top bunk of his hooch (hut). A friend was reading in the bunk below. Somewhere outside someone – could have been friend, could have been foe – fired off a 7.62mm heavy machine gun round. It arced in through the roof of the hooch, burrowed laterally into his left latissimus, and came to a stop less than an inch short of his spine. He stirred, but did not wake. A little later another friend passed by, and noticed that there was a lot of blood on the mattress. At first they all thought it was a rat bite – there were a lot of those – but a medic said, “I know this will sound crazy, but I think this soldier’s been shot.” So they half-carried him down the street to the hospital, and he got a second hole in his back, to dig the bullet out. He still carries it with him.

This was not a heroic wound. Mark’s heroism lies in this: he stayed in that place, and continued to do his job. He interviewed the new guys, sent them off to places that he knew were as likely as not to kill or maim them. He saw every variety of spook, sniper, and Montagnard, plus the Green Berets that he had wanted to join, when they would cruise through to meet with the generals, in a bunker 65 feet below the clerks’ office. He heard their stories. Decades later he remembers the “horrible, gut-wrenching feeling, knowing how badly things were going.” His disillusionment, begun almost immediately after enlisting, became stronger, veered into bitterness, veered towards despair, But he kept doing his job, to the best of his abilities.

Decades have passed. Mark has made a good career in title insurance, raised two splendid daughters, endured some non-splendid marriages. He writes poetry, officiates at weddings, is a good and generous man. But the war is still with him. I finally realized this one day when I asked him how long he had spent over there. He looked at me for a moment, then said, “Eleven months, four days, six hours, thirty-two minutes, and twelve seconds. Approximately.”

 

Extravagant Purchase Puzzle Update

We have definitely struck a chord with the current Puzzle (see below), with by far the most entries — and the widest range of answers — that we’ve seen before. And as of today, only two of the entries are correct.

For those few of you who are posting the correct answer on Facebook, you do realize that this is a contest, right? This means that the people who figure things out for themselves will have their odds of winning diminished by those who copy your work. So enter, but save the bragging for later, okay?

By way of coaching, I will stress that equal downward force is applied to both tackles. One of them will come in faster, but neither will go slack. Assume a constant load of 1 pound (or whatever else you choose), and go from there. So to review, here is the Puzzle:

Puzzle Contest: Extravagant Purchase

Extavagant Purchase

Puzzle Contest: Extravagant Purchase

Above is a very odd block-and-tackle configuration. Odd, as in has-no-practical-use. But rather than waste it, we’ve made it this week’s Puzzle: What mechanical advantage does this configuration have?

Assume that the sheaves have no friction, that all leads are parallel, and that equal force is exerted, straight down, on both tackle ends (arrows). The uppermost block will move toward the deck.

You don’t need to explain your answer in order to win, but as long as you get the purchase number right, your explanation doesn’t have to make sense, so hey, go for it.

Bonus points if you can approximate the maximum range of motion, up and down, of the uppermost block. Assume that the fiddle block is one foot long, and that the tackles end at the arrows.

Send your entry to puzzle@briontoss.com. The winner will be randomly selected from the pool of correct entries. Deadline for entries is noon Pacific time, Monday, March 19th.

This week’s Fabulous Prize is an autographed first edition of Kaci Cronkhite’s wonderful best-seller, Finding Pax. You can find out more about this wonderful book  here

Note: Painter Frank Hanavan recently posted our Puzzle’s photograph, from Petersson’s book on ship model rigging. It appears to be a nice enough book, but the image, as near as I can tell, shows a configuration that has never been found outside the pages of that book. If such is not the case, please let me know.

 

Pnuema, A Vessel of Resonance

Adventures in Maintenance: Achieving Resonance

My friends Melissa and Guy Stevens were somewhere in the middle of the Pacific Ocean, in their sloop Pneuma, when they discovered that they couldn’t lower their Genoa. They wanted to get it down for a bit of repair, but the halyard swivel on their Genoa furler kept hitting an obstruction, and wouldn’t slide down the foil. For all you non-sailors, the Genoa is the big sail at the front of the boat, and the furler is like a huge roll-up windowblind. The one one Pneuma was about fifty feet long.

The stuck furler didn’t make for an emergency, because conditions were about as calm and unthreatening as they could possibly be, with absolutely no wind, and a sea so calm and flat that it scarcely seemed a sea at all. Ordinarily, going aloft anywhere but in a marina is something to be avoided, at least in small craft, but in this case it made perfect sense for Guy to get his climbing harness on, and get up there to see what the problem was.

The furler was a Profurl, and it quickly became evident that the problem was a fairly common one, specific to this brand. Every furler brand has its quirks, and one of Profurl’s is that the foil sections are held together by machine screws that are coated, at the factory, with a threadlocker (Loctite is the best know type of threadlocker).

This threadlocker for this brand is on the screws,  is dry when you get the furler kit, and is activated once you screw thread the screws into the foils. Or that’s the way it is supposed to work; there seems to be more threadlocker on some kits’ screws than others. And maybe sometimes the formulation isn’t quite right, or the stuff is old, so it won’t stick as well as it should. In any event, while the screws in most Profurls stay obediently in place, you occasionally hear about situations like this one, where the sail can’t be lowered because, in the course of sailing, the foil has rattled and twisted, the screws have backed out, and their heads are now projecting past the surface. The swivel, which goes up and down with the sail, fits closely around the foil; this one couldn’t get past the loosened screws.

Some sailors, either because it’s an emergency or because it’s just how they do things, have forced the sail down when confronted with this problem, hauling mightily on the luff of the sail. This can work, if the crewmembers are heavy and/or panicked enough, as the halyard swivel has a plastic inner lining. So with sufficient force you can make the screw head(s) carve channels up the inside of the lining, which of course damages said lining, and does nothing to address the root cause of the problem, so the screws can continue to work their way out, making it even harder to raise or lower the sail next time, as well as gouging even deeper channels.

Since most roller-furler jibs get left on the stay for years at a time, it sometimes happens that, especially on long voyages, the screws can fall completely out of the foil, with no one the wiser, which means that the foil sections are no longer held together, which means that, depending on the quality of the installation, they can drift apart to varying degrees. The most common consequence of this is that a bight of the sail’s luff herniates out between sections, making it impossible to lower the sail. There are other possible consequences, but thinking about them just depresses me, so I’ll leave them to your imagination. The short form is that you don’t want those screws to back out, which is why Harken, for instance has you pretty much cover all parts in 5200 adhesive that they don’t bathe in red Loctite, and why Schaefer, to take another example, puts their units together with stainless rivets.

Oh, and a perverse alternative Profurl scenario involves the fact that thread-locking adhesives also function, to a certain extent, to isolate dissimilar metals. So if the insufficiently-coated screws don’t back out, that just means they will stay in place, becoming one with the adjacent aluminum through the wonders of galvanic action, until not only will they not back out if you should want them to; you’ll be tempted to use explosive devices to budge them, should you ever need to disassemble the foil for repair. What typically happens in this case, if explosives aren’t handy, is that first you’ll strip out a couple of screw heads trying to remove them, then progress through penetrating oil, impact driver, easy-outs, heat, cursing, and utter despair, at which point you will pause to regroup, then attack anew with a sharp drill bit. This will remove the screw, but will also almost certainly chowder the threads on the (expensive, impossible-to-find-in-the-remote-port-you-are-doing-this-repair-in) aluminum bearing holder that the screws are tapped into, and very likely also chowder the holes in the foil itself. In addition, you are liable to discover, once you slide the ruined bearing holder out of the foil, that though the heat you applied earlier might not have loosened the screws, it did manage to turn the equally hard-to-find internal plastic bearings to slag.

Well, Melissa and Guy are not the sort of people to let teensy screws get away with things like the above, which is why Guy was up there on that flat calm day. He first detached the head of the sail from the swivel, so that Melissa could gather the sail in on deck. Then he got to work with a little baggy of spare teensy screws (they are easy to drop, so bring spares), a screwdriver (on a lanyard, of course), and some fresh Loctite. He was up on two halyards (a primary and a safety), plus he had an approximately 2’ tether looped around the stay to hold him close enough to the foil to do the work. He made his way down, section by section, removing screws, coating them with Loctite, and putting them back in.

All went well until he was about halfway down, at which point Melissa called up to him.

“Hey Guy!”, she said.

“Yeah?”, replied Guy.

“Swell!”, said Melissa, and pointed off to one side.

Guy looked, and saw the glassy, otherwise utterly flat and featureless surface of the ocean broken by a single, large, rapidly moving swell. It was coming from directly abeam. “Hold on!” shouted Melissa. Unfortunately the only thing available to hold onto was the foil, a device designed to rotate under load. As the swell reached Pneuma, a series of intimately linked, harmonic mathematical elements were put into action. The speed, height, and steepness of the swell, Guy’s mass, his position relative to the boat’s axis of rotation and center of gravity, the length of exposed halyard, the boats’ lateral roll period, and the length of the tether, all came into perfect alignment, such that as the boat rocked, it swung Guy forcefully, unstoppably around the stay. Fast. Because the stay was angled, it meant that he was swung forward and up, with an apogee in front of the stay, and higher than the starting point. Which meant that there was now an opportunity for gravity to accelerate the second half of the rotation. As an engineer I know put it, Guy “achieved resonance.” Aided by the continued, wonderfully complementary continuing gyration of the boat, he was swung around again. And again. And again, faster and faster, as the halyards spiraled around the foil, shortening as they went, until there was no slack left, and Guy came to a very abrupt stop with his face mashed against the foil.

At this point, as often happens in times of stress, he was able to be aware of several things at once; the impact of the foil, the warmth of the sun, the color of the sky, and of course the sound of Melissa falling down laughing at the sight of him pulling a stunt worthy of Buster Keaton. But in almost the same instant he was also aware that the boat’s ongoing motion was causing him to unwind, about as forcefully as he had wound. All the requisite inertial and geometric properties remained in utter accord, and he orbited the stay, slower and slower, until he was back where he had started, and then continued to wind up in the other direction, faster and faster, once again fetching up abruptly. This went on several more times, we’re not sure how many, as Guy was kind of occupied with the whole acrobatic thing, and Melissa was pounding one hand on the deck and laughing so hard she was having trouble breathing, let alone counting.

Eventually, long after the swell had gone by, the boat stopped rocking, and Guy stopped spinning. Melissa kept laughing, but she was able to tend him on the halyards as, bruised but unbowed, he finished the job.

Got a Profurl? Fine furlers, very reliable. But you might want to check those screws.

 

For more on Melissa and Guy’s adventures, and a lot of valuable advice, visit realworldcruising.com.

Enjoy the story? Looking for more? You’re in luck! “Falling,” which in includes this and other tales from aloft, both thrilling and amusing, is now for sale on Amazon.com in handy e-book form! Or click here to get it on Apple iBooks!

From dropped tools to collapsed towers to near-fatal falls, the litany of accidents and near-accidents is long… and the sometimes miraculous outcomes are both instructive and thought-provoking.

Not a technical manual, “Falling” is nonetheless a must-have companion in the library of anyone working at heights.

Whether Helm or Not, 2, The Winner!

Whether Helm or Not, 2, The Winner!

Whether Helm or Not, 2

We had a veritable flood of entries to this week’s Puzzle. To review, it went like this:

Some cruising sailors entered a local race series, and to improve their chances they decided to lighten ship. They took off their diving gear, books, extra clothing, and all the other stuff that tends to accumulate on a cruising vessel. They even offloaded their chain rodes and anchors, figuring they wouldn’t need them to go around the buoys, sent down some spare halyards, and retuned the rig.

The boat was definitely faster after all this, but the sailors were shocked that what had previously been a significant amount of weather helm had suddenly become an alarming amount of lee helm. What factor or factors might have caused this?

Things got off to a slightly rough start when Bob Perry, the Pope of Yacht Design, got the idea that I was promoting an antique method of determining helm balance in the design stage. See, in the old days, naval artichokes saw that getting hulls and sails to balance was tricky, so they came up with rules of thumb to determine how hull area and shape would relate to sail area and shape. The method worked, sort of, but it also produced a lot of vessels with infamously bad helm manners. You can read more about this in Skene’s Elements of Yacht Design. Nowadays things are more refined, and you can find more reliable methods in books like Bob’s, Larsson and Eliasson, and others. The basic idea is that the aerodynamic focal point of the sails (center of effort, or CE) needs to line up pretty closely with the hydrodynamic focal point of the hull (center of lateral resistance, or CLR). In the real world, when the vessel is under way, heel, drag, wind direction, and a host of other variables make this a fairly complex thing to determine. But when it is right, the boat will have a slight tendency to round up. When it is wrong the boat will have a violent tendency to round up (too much weather helm), or a ghastly, terrifying tendency to fall off (lee helm).

I started to detail just the basics of this relationship in preparing this post, and after several pages realized that there was far too much to say just to answer a puzzle. The short form is that, as with the previous puzzle about the effects of running rigging on weather helm, just about everything you do can have a measurable effect on helm balance, inducing either weather helm or lee helm. Just walking around on your boat while it is underway can have such an effect.

One of our more comprehensive entries came from rock star sailmaker Emiliano Marino*, author of The Sailmaker’s Apprentice. He wrote,

“Offhand, I’d say if their ground tackle was stowed up forward and they cleared it out; that would lighten and raise the bow… tending to increase lee helm [this is true for most but not all boats, BT].

“Removing anything aloft would reduce heel, which would also increase lee helm.

“And if, in retuning the rig, they did anything to bring the rig, sails, and sail power forward, that too would increase lee helm. Crew size, weight and position could be a factor.

“Mostly, I’d guess that the weight of all the beer stowed in the lazarette for the race was the culprit.”

To that I would add that, if the rig had been too slack before, the mast would have gone further to leeward, especially when loaded up and on the wind. This is a big cause of weather helm. With a proper tune, the mast would stay further uphill, and this could contribute to moving things toward lee helm. Likewise if the mast had previously been straight, and the tune imposed a proper bend, the CE would have moved forward some.

So, our randomly selected winner from our pool of even remotely correct entries is… Richard Shearley! Be in touch about where to send your Fabulous Prize, which is an autographed copy of Bob Perry’s Yacht Design According to Perry.

Thanks to all of you for your entries! Next week’s Puzzle: Extravagant Purchase.

 

*He also recently added to our list of the tiny number of running rigging pieces that do not, in normal use, affect helm balance: a tripping reef clewline.

 

PS,

My regular Friday blog post this week is Adventures in Maintenance: Achieving Resonance

 

 

 

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