# True Displacement

Sometimes when voyagers are evaluating boats they compare data for similar boats. This data may include the ballast ratio, the displacement/length (D-L) ratio and the sail area/displacement (SA-D) ratio. All of these numbers are commonly taken as measures of performance - the higher the ballast ratio, the lower the D-L ratio, and the higher the SA-D ratio, the better the performance is likely to be. The displacement number used in these formulas should approximate the weight of the boat with all normal equipment and crew on board, the tanks half-filled and the lockers filled with half a full load of food and beverages (in other words, what you would expect to find about midway through a voyage). This is known as half load displacement. In reality, boat builders will use everything from this number to a “lightly loaded” formula (a couple people with no account for non-standard gear and equipment, minimal stores on board and tanks half full) to the construction weight of the boat with nothing on board (the dry weight or light ship weight), or even the designed weight (which is almost always exceeded during the building process, often by a substantial amount).

The use of artificially low displacement numbers skews the ballast ratio upward, the D-L ratio downward and the SA-D ratio upwards. The lighter the boat, the more the numbers are likely to be distorted by leaving a realistic payload out of the calculations. The net result is that typical published ratios are, at best, of marginal utility when comparing boats and, at worst, are downright deceptive.

Our Pacific Seacraft 40

Let’s look, for example, at the displacement of our Pacific Seacraft 40. The published displacement of 24,000 lbs is based on light local sailing. This includes the tanks half full and some gear and supplies on board - i.e., a nominal half load displacement of a stock factory boat.

I performed a rough weight audit on our boat and discovered that our heavy-duty DC system (total battery capacity of 700 amp-hours, two alternators, cabling, DC to AC inverter, wind generator and solar panels) weighs in at around 800 lbs, probably less than half of which is included in the manufacturer’s published displacement. We also have between 400 and 500 lbs in ground tackle. The water tanks, when half full, weigh 700 lbs, the diesel 200 lbs. The dinghy and outboard, plus fuel, weigh 250 lbs, the wind vane and autopilot 60 lbs. This is around 2,500 lbs, much of which will be found on any offshore voyaging boat, all of which will be added before the first crewmember steps on board and less than half of which is included in the published displacement figure. Then there are all kinds of tools and spares.

People average out at 160 lbs. Clothes, books and gear (including such things as crockery, cutlery and galley utensils) weigh in at around 100 lbs per person. Food and beverages are around 6 lbs per person per day, which is to say 200 lbs per person for a moderate voyaging range. When these kinds of numbers are added to the weight of non-standard equipment, the total added weight for a crew of four is soon up around 4,000 lbs, whereas, when I checked with Bill Crealock, the designer of the Pacific Seacraft 40, I found that the total added weight in his light local sailing condition is 1,200 lbs.??

To be fair to Pacific Seacraft, most designers and manufacturers don’t even attempt to approximate half load displacement. The majority of published displacement figures are based on some form of light ship weight, which includes little more than the boat, and does not always include even such basic items as sails, minimum ground tackle and legally-required safety equipment. All too often, these numbers are derived from calculations made by the designer rather than the actual build weight of the boat, which almost always exceeds the calculated weight. The longer a boat has been in production, the more the weight tends to go up as upgrades and changes are made. In going beyond light ship weight, manufacturers such as Pacific Seacraft are, to some extent, stacking the deck against themselves in terms of making comparisons with other boats.

Recently, I saw a set of figures for a popular racer/voyager that showed a listed displacement of 28,500 lbs, an actual weight from the builder with a full set of voyaging options of 34,500 lbs, and a fully-loaded weight of 39,500 lbs! Clearly, for coastal voyaging, these numbers are likely to be lower; nevertheless, the point remains the same - accurate displacement figures are dependent on a realistic assessment of weight.

With this is mind, a minimum of 2,500 lbs should be added to most published displacement figures to get a ballpark half load displacement for coastal voyaging. For offshore voyaging, 3,750 lbs should be added. Most long-term voyagers and liveaboards will add considerably more weight than this (it would not be unreasonable to up the coastal add-on to 3,750 lbs and the offshore number to 5,000 lbs), while weight-conscious racer/voyagers may add less.

Though these numbers will give a reasonable displacement approximation, a better solution is to define your personal voyaging style and thus the weight that you will introduce to a boat, and derive from this what I will call a personal increment number (PIN). This process is described in detail in the sidebar. Armed with your PIN and the published displacement numbers for boats of interest to you, you can determine realistic displacement numbers in voyaging trim.

Now let’s determine a ballast ratio, a D-L ratio and an SA-D ratio that is somewhat closer to reality than most published numbers. You may be a little shocked at how the ballast ratio goes down, the D-L ratio up and the SA-D ratio down!

Ballast ratio

The higher the ballast ratio, the heavier the keel in relation to the rest of a boat and, all other things being equal, the stiffer the boat. This translates into a greater ability to carry sail to windward. However, all other things are not equal! Given two boats with the same ballast ratio, one might have lead ballast in a bulb on a deep fin keel and the other might have internal iron ballast with a shoal draft. The former will be substantially stiffer. As such, the ballast ratio can only be used as a very broad indicator of a boat’s stability, and in fact its utility is significantly limited to comparing boats with a similar hull form.

With these issues in mind, we can say that the lower limit for the ballast ratio of a 35-foot to 45-foot voyaging boat at a realistic half load displacement should be around 0.30, with ratios up to 0.40 possible on modern boats where the hull weight has been minimized by the use of high-tech construction techniques and materials. It should be noted, however, that at these higher ballast ratios the trade-off for a stiffer boat is a less comfortable motion.

Let’s look at our Pacific Seacraft 40. It has a shoal draft option (5’ 2”) with a ballast weight of 8,880 lbs and a published displacement of 24,280 lbs (light local sailing weight according to the manufacturer’s literature) for a nominal ballast ratio of 0.37. The light ship weight is 23,080 lbs. If we arbitrarily add 2,500 lbs to the light ship weight to approximate the half load displacement in coastal voyaging trim, we get a ballast ratio of 0.35. With a 3,750-lb payload (half load displacement in offshore voyaging trim) this drops to 0.33. With a 5,000-lb payload (full load displacement in offshore voyaging trim) we get 0.32. These figures are still above my 0.30 threshold but significantly lower than the published number.

Using published displacement figures (as opposed to a realistic half load displacement), most modern boats have a ballast ratio higher than 0.30. However, when I looked at a sample of modern boats and tried to assess numbers that I felt approximated coastal voyaging trim, a number of the lighter boats dropped below this threshold; while in offshore, voyaging trim fell below it even more.

D-L ratio

The addition of a substantial amount of weight to a boat with lightweight construction will have a disproportionately greater impact on the ratios and on the boat’s performance, than the addition of the same weight to a heavier boat. The farther it is intended to voyage offshore and the longer the voyage, the greater the load the boat is likely to carry. In general, a moderate to heavy displacement boat will be able to absorb the load better than a light displacement boat. The heavier boat will also have a more comfortable motion in a seaway.

Another formula - the D-L ratio - can be used to quantify a boat’s heaviness. The formula is:

Displacement in long tons/([0.01 x waterline length]3)

A long ton = 2,240 lbs

To make realistic comparisons between boats as you will use them, you need to calculate your PIN for the displacement figure before calculating D-L ratios.

Looking at our Pacific Seacraft 40:

Half load displacement (light ship + 3,750 lbs) = 26,830 lbs

26,830/2,240 = 11.98 long tons

LWL = 31.25 feet

(0.01 x 31.25)3 = 0.0305

Therefore:

D-L ratio = 11.98/0.0305 = 393 long tons/foot (as opposed to the published figure of 355)

This is very much at the heavy end of things for a contemporary boat, although it should be noted that this is mostly because of the boat’s relatively short waterline and long overhangs, which tend to skew the numbers upward. This is also the case for many older designs. A number of modern boats, especially those influenced by the IMS rule, have almost no overhangs, so the LWL is close to the overall length. It is interesting to note that if the same design philosophy were to be used on the Pacific Seacraft 40, with the displacement kept constant, the D-L ratio would go from 393 down to 187!

In point of fact, with a PIN of 3,750 lbs the boat sinks almost three inches, which, because of its long overhangs, increases its LWL by more than nine inches, bringing the D-L ratio back down to 366. For the rough and ready purposes of comparing boats, I believe this sinkage factor can be ignored, particularly since an accurate lines plan, which is not likely to be available, is needed to calculate it. However, it is important to bear in mind that the longer the overhangs and the shallower the angle between the overhangs and the surface of the water, the more the D-L ratio will be distorted upward by adding weight without accounting for its impact on the waterline.

Extremely lightweight boats may have a D-L ratio in voyaging trim below 100. Older voyaging boats commonly exceed 400. The higher the ratio, the greater the volume below the waterline, which translates into comfortable interiors with plenty of fuel and water capacity but often with a significant performance penalty. A good range for contemporary voyaging boats would be between 250 and 400 (using a realistic half load displacement number). The longer the boat in relation to a given payload, the lower the D-L ratio should be. (Once you get into the realm of 50-foot and longer boats designed for a single voyaging couple, it should be below 200.)

SA-D ratio

It is commonly assumed that a moderately heavy displacement boat, especially one loaded with stores, will be a dog to sail. This is often the case but need not be. So long as the boat is given adequate sail area to compensate for the weight and so long as it is stiff enough to stand up under this sail area, there is no reason for it not to have excellent performance.

The key parameter here is the SA-D ratio, which is calculated for a sloop or cutter by determining the nominal area of the mainsail and the foretriangle in square feet, and dividing their sum by the boat’s displacement in cubic feet taken to the two-thirds power. The equation is:

SA-D ratio = [(I x J)/2 + (P x E)/2]/(Displacement in cubic feet)0.67

Where:

I = the height of the foretriangle

J = the horizontal distance from the forward side of the mast to the bottom of the headstay

P = the hoist of the mainsail

E = the foot of the mainsail

[Editor’s Note: The figures for this section reflect a mathematical correction of the figures published in Nigel Calder’s Cruising Handbook.] Let’s look at our Pacific Seacraft 40 with a half load displacement of 26,830 lbs. Sea water weighs 64 lbs per cubic foot, so the boat displaces 419 cubic feet (26,830/64). The displacement of 419 to the two-thirds power (or the power of 0.67) is 57.13. According to some of Pacific Seacraft’s literature, the boat’s sail area is 1,032 square feet. Using these two figures, divide the sail area by the displacement (1,032/57.13) to get an SA-D ratio of 18.06.

However, in this case, the staysail was used to calculate the sail area, which is improper use of the formula (in other literature the staysail is excluded). Without the staysail, the sail area drops to 846 square feet, and the SA-D ratio to 14.81. A ratio of 15 to 16 is considered acceptable for a traditional voyaging boat; 17 to 19 is typical for performance cruisers; 20 to 22 is on the high side.

My own inclination would be to aim for something around 18, which is on the performance end of things, because in many ways it is easier to reef down in a blow than it is to increase the sail area in a calm.??

In conditions where both the staysail and headsail are flown, the Pacific Seacraft has a fair amount of sail power, so long as the boat is stiff enough to carry this sail area (it is of no use at all if the boat can’t carry it without excessive heeling). The British boating magazine, Yachting Monthly, conducted a boat test in relatively heavy weather and commented that the “Pacific Seacraft 40 gives a sprightly performance, mainly due to its large sail area.” If the staysail is taken out of the picture (which it will be quite often, especially when off the wind), in light airs (which are encountered by voyagers far more than heavy weather), the basic sailplan is likely to leave the boat underpowered, especially when loaded for voyaging. Decent light air sails will be needed.

Once again, when comparing boats it is important to use a realistic SA-D ratio. Not only do boat builders commonly exaggerate the sail area of their boats, but they also use some form of light ship displacement. Taken together, these result in completely unrealistic SA-D ratios. If the numbers are reworked using 100 percent of the sail area and a realistic half load displacement, it is not uncommon for the SA-D ratio to drop by three full points (e.g., from 17 to 14).