April Puzzler Winners

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This month's Fair Leads is the result of our April Puzzler, which generated a record number of entrants, some of whom came up with some answers that were just too good to leave unpublished. The puzzle, itself contributed by Spartalk regular Russel Turpin, ran like this:

"When a beer can is full, its vertical center of gravity is half the can's height. When it is partly full, its vertical center of gravity 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 Most Creative Award went to Andrew Falcon, who wrote,

"The VCG of a beer can is lowest when it is full, but not of beer (well, okay, you can leave the beer in, but it's really a bit of a waste). This is because the can will float if empty. After the beer is consumed, well offshore, say at approximately 11 degrees 22 minutes N, 142 degrees 35 minutes E, said beer can is tossed overboard, refills with salt water, and sinks. Its eventual VCG will be approximately 35,838 feet below sea level, and you really can't get any lower than that."

Others, like Brent Trockman, at least started out on a more serious note, though I suspect that the latter part of his essay was several beers along. Here's his entry:

Because the mass of the aluminium is less than that of the beer, the VCG is more effected by the mass of the beer than that of the can. If we were to weigh the empty can and find its weight at, say 2 oz., and then put a little shy of 2 oz, of beer in the can, the VCG would be at its lowest point possible. This is a little less than half a swallow of beer.

The reason for this is because the moment arm of the empty can above the beer (and thus above the VCG) would be less than that of the lower portion of empty can plus the beer. In this case, with just a half swallow of beer in the can, the balance point, or VCG would be at its lowest. This is why you should drink it fast. This is only theory however, because with drinkable beer, as you tip the can over to do the test, the beer spreads out, and eventually spills in the cockpit, leaving us with a VCG right in the center of the can. Same with using hot,molten lead for ballast, it has the same mass as solid lead, but as the boat heels, the molten lead pours into the shower sump, settee and eventually right into the cabin, which decreases the righting moment of the ballast and subsequently raises the VCG of the unfortunate vessel described above. Comfort factor goes way down as this occurs. Definitely not the way to go on a proper sailing yacht.

The more beer you put in the can, the more effect the beer has on the VCG and the higher the VCG would move. This is the same as loading the deck of your boat with alot of junk; it raises the VCG. This is why big ol' cans of Fosters have a higher VCG than a normal, 12 oz. can of Coors. I won't drink Budweiser. Half full would put the VCG at a little higher than the 1/4 height spot, 1/4 full would put the VCG at a little higher than the 1/8 height spot, until the weight of the beer is less than the weight of the can, at which time the moment arm of the can becomes a more significant factor in determining the VCG, and it, the VCG, again gets higher.

At this point I didn't remember how to use the scale and such to actually weigh the can and do some simple math on paper in order to arrive at the exact fill spot on the can, but we will get pretty darn close to optimal if we just put about the same weight of beer as aluminum into the can.

I think this is why a 50% ballast ratio in a boat is kinda cool, as it puts the VCG of the yacht at its lowest point. Barring other factors, the boat just can't stay upside down for long. Of course, a 12 foot blade shaped keel with less ballast in a bulb at the lower end can also move the VCG down as well, but that would be like using a beer can extension, which is not practical to most sailors. It is just another gadget to break at a bad time, when something important is taking place. Proper keel design is like proper beer can design: the idea is that the can tips over just enough. Drinking beer out of a frisbee is for my friend's dog. Drinking beer out of one of those yard things in the brewery is also silly. Just use a can, why make such a fuss?

Of course, you have to take into account the form stability of the beer can. It has very hard bilges and thus resists heeling initially. But, due to the overly high topsides, if it finally does go over, it is very hard to right again, it usually just rolls around the cabin sole. If we had a couple of oz. of frozen beer in the bottom of the can, and the motion was lively enough (like on a sled) the can would have the best chance of righting itself.

This is probably just what Brion does when you hire him to do a consultation. He gets out a can of beer and writes the name of your boat on a little piece of masking tape and then puts it on the can. Then he drinks part of it and thinks about how heavy the new rig will be, and what effect this has on the righting moment. Sure enough, the more he drinks, the more time he spends on your consultation and the less your boat heels over, due to all the whiz bang spars and terminals which reduce the weight aloft. But careful, if he continues to drink, and you start to lose ballast, it could end up just like one of those fools who saws off the bottom of his keel to get a shoal draft boat, without adding a bulb at the end, and the boat has big trouble. Make sure he doesn't drink too much on your consultation.

You know, I'm really not sure this is clear, so I will stop now. In fact, it just dawned on me, THIS IS A TRICK QUESTION!! What kind of skipper would allow partially full cans of beer on his boat? They are either full or empty, no? In that case, disregard all the nonsense above and remember that the VCG should always in the middle of a beer can on a proper sailing vessel.

Umm, thanks Brent. Moving on to something really elegant, my old friend Brent Benson submitted a "Pendulum Method":

Open can; bend tab so the ring is exactly centered on the can top.

Attach string of convenient length to the ring,, and tie the other end to a fixed object such that the can can swing as a pendulum. of fairly low amplitude.

Time the period of the pendulum over a fairly large number of swings, perhaps such that the total time is around 100 seconds. Use your digital multifunction watch for accuracy.

Sip some beer and retime the same number of swings. Do not change the string. You can use a dipstick method to determine the height of the remaining beer.

Repeat many times.

You will observe that the time keeps getting slightly longer until you have drunk 297 ml of beer, 58 ml left, and the height of the beer left in the can is 2.0 cm. This is for a 12 oz can with height 12 cm, and a string of negligible mass. Then it will decrease until the beer is gone.

When the time is the longest, the VCG is be the lowest.

Repeat the experiment [many trials] and average the results to get the most accurate results. Accuracy is also better if person doing the timing is not the one sipping the beer.

The period of a pendulum depends only on it's effective length, which is the distance from the pivot point and the VCG.

But perhaps the most practical entry came from RW Salnick, "Friend of John Barleycorn and and aluminum industry refugee", who wrote:

"Rule of thumb: When the VCG starts to rise, it's past time for a fresh beverage..."

Fair leads,
Brion Toss