Toward a useful definition of Sportboat

For several years Singlehanded Sailing Society has had a Sportboat class in its races. We used the same definition as did the Yacht Racing Association of San Francisco: a Sportboat is a boat with a displacement-to-length ratio or DLR of 105 or less.

Aside: For anyone not familiar with DLR, some explanation is in order. First of all, the phrase displacement-to-length ratio is a misnomer. The cube of the length is used to calculate the ratio, because if a given object is scaled up or down, the weight changes as the cube of the change in length. That is, if you make something twice as long, with the same proportions and materials, it'll be eight times as heavy. By cubing the length, the ratios will be comparable between little boats and big boats. Secondly, the length in the formula is the waterline length or LWL. We don't care too much about what's hanging out over the water. Third, this ratio is obviously not dimensionless, so we need to agree on the dimensions to use in the calculation. By convention, displacement is in long tons (pounds divided by 2240) and waterline length is in hundreds-of-feet -- for example, if the waterline length is 24'6" we use .245. DLRs for sailboats can range from well under 100 for stripped-out racing boats, to around 200 for modern racer/cruisers, to 400 for crab crushers.


Santa Cruz 27
D=3300, LWL=24, DLR=107
Sportboat?


But there's a problem with setting the Sportboat cutoff at 105. The Santa Cruz 27, Bill Lee's classic 1970s design, is generally accepted as a sportboat on San Francisco Bay, but it teeters right on the edge of that definition. The early examples were lighter, but most of them (according to their PHRF certificates) weigh 3300 lb on a 24' waterline, giving a DLR of 106.6! A Mini TransAt that raced occasionally with SSS in 2007, a boat that sure seems like a sportboat to me, also has a DLR of 106 and change. So when I signed on as SSS race chair for 2008, the first change I made was to raise the Sportboat cutoff to 108.




Thompson T650
D=1918, LWL=19.8, DLR=110
Sportboat?



I thought I was so clever. Then I received a race entry for a Thompson T650. Teeny little boat, very cool, certainly a sportboat, right? Its cert read: D=1918, LWL=19.8 ... DLR=110! So should we bump up the Sportboat cutoff a little further still? Or is something else going on here?


Hunter 54
D=20500, LWL=43.5, DLR=111
Sportboat???????


A while back I looked at the specs of a very different boat, a 1982 Hunter 54. An SSS member races one of these successfully. It's a fast boat (PHRF 39), certainly not a sportboat, but look at that DLR, 111! Barely heavier for its length than the little T650. Obviously DLR doesn't tell the whole story. Empirically, we have to say that a small boat can be considered a sportboat with a relatively high DLR, while a big boat may not be a sportboat even if its DLR is pretty darn low. Makes sense: a light boat can get up on a plane more easily than a big boat, even if it is a bit heavier for its size. So ...

Let's invent a new formula and call it the length-weighted displacement-to-length ratio, or LDLR. Instead of using the cube of the waterline length in the denominator, we'll raise LWL only to the 2.5 power. This yields a higher number for big boats and a smaller number for small boats, which is what we want. And since the result isn't going to be directly comparable to DLR numbers anyway, we'll get rid of the long tons and hundreds of feet, and just use pounds and feet ... much simpler to calculate. The formula is:

LDLR = D / LWL^2.5

It remains to calculate the LDLR for a range of boats. We need to choose a cutoff point that classifies average-sized boats (as Sportboats or not) in about the same way as the 108 DLR does. Then we must test the formula on a few outliers - small boats that are fairly light but clearly not sportboats, and large boats that by consensus are sportboats - to see if they get pushed into the wrong category.

LDR & LDLR for selected boats
Sportboat cutoff: 108 for DLR, 1.20 for LDLR
Scroll down for the table; I haven't figured out how to get rid of all that blank space.

Type	D	LWL	DLR	Sportboat?	LDLR	Sportboat?
Santa Cruz 27	3300	24.0	107	yes	1.169	yes
Thompson T650	1918	19.8	110	no	1.099	yes
Catalina 22	2150	19.4	132	no	1.297	no
Hunter 54	20500	43.5	111	no	1.643	no
Santa Cruz 50	15000	46.5	67	yes	1.017	yes
1D 35	6500	31.5	93	yes	1.167	yes

We seem to be on the right track with the LDLR formula and a Sportboat cutoff of 1.200. We've ruled the T650 into the Sportboat class and not changed any others of this sample. I'll collect a few more boat specs when I get a chance and add to this table.