Vessel Weights and Measures

Archimedes in studyWe are frequently asked, “What is the displacement of your vessel?” It seems to be the question of the month and appears to have spilled over from the marketing of the hypothetical “ocean going trawler”, cast iron bathtubs presumably trumping canoes.

The inquiry is generally a quest for some comforting number demonstrating due diligence, but in the absence of qualifiers, that simple number will be an abstraction of little value and will probably be misleading. There is no end of unqualified opinions proffered; you must have heavy displacement, you must have light displacement, (do I look fat in these jeans?), depending on who is trying to sell what against whom, never mind defining what is meant by heavy or light.

What most people really want to know is if a vessel’s buoyancy is appropriate for the intended usage, setting aside the jargon. (How that buoyancy has to be manifest may be the stuff of another diatribe on “stability and seaworthiness” one day soon?)

Years ago when I was first tentatively testing the connection between the mathematically abstract and reality, (about to launch a vessel whose waterline I had predicted with ‘rithmetic), I was approached by a good fellow who had been employed that spring to apply bottom paint. He was unsullied by any prior marine background so had an enviable perspective on all things nautical.

“That special paint I have been putting on, its amazing stuff! How does it know?” sez he.

“Know what?” sez I.

“Where to float the boat,” sez he. “I have been watching the boats being launched and they all float with just a little of the paint showing.”

I tried to explain a little of the theory of displacement but I didn’t sound all that convincing apparently for he looked at me askance, then at a curvaceous boat bottom, then went resentfully about his business, pretty certain I was having a joke at his expense. I guess the paint label looked more authoritative than I sounded. I don’t blame him; I rather preferred his approach too. I presume this is the origin of the expression, “He’s as smart as paint.”

Before Archimedes sat in his bath and subsequently expounded the mathematical principles governing floating and waterlines, all kinds of objects happily floated as they wished, in complete ignorance of his theories. They still do.

Archimedes Eureka

The Eureka moment came when the great thinker realized that his floating body “displaced”, or pushed aside only the quantity of water that would have a weight to equal his own. Any volume he had to spare, once this condition was met, projected up above the surface, (presuming his ass wasn’t aground). The nice thing is, all objects once afloat, display indisputably, their right displacement and true waterline.

Pigs can swimImagine the ancient shipbuilders, launching enormous oared galleys for hundreds of years and apparently completely ignorant of the necessity of knowing their ship’s displacement number. Perhaps they did know all along but didn’t have the academic credentials to publish, but still, what good is a “comparative weight of water” number when real demonstrations are floating in the harbour; full size model tank testing in fact.

The vast majority of vessels have been built without much, if any, application of numbers, other than tallying the cost. You would tell your shipwright; “I need 20 cannons” or “I have 200 wine bottles to carry” and that’s what he would use to make an educated guess based on experience as to which pieces of wood to use. Occasionally some extra things got added along the way, excusing him if the results didn’t look particularly well planned, but as long as everyone was happy.

Happy Boating

Recognizing the mathematical principles of floatation were of limited practical application to shipbuilders, even after Archimedes, until somebody figured out how to measure the volume of an irregular three dimensional shape, cubes for example being simple and accurate to work out, spheres less so, and ship hulls just not on. It wasn’t until the mid 1700’s that a method of mathematical approximation was developed which was used right up until the advent of the three dimensional computer model. “Simpson’s multipliers” give the designer some comfort but have limitations. The nicely affordable computer program I use now has taken some anxiety away from launch day; it measures the volumes of complex shapes to several decimal places in only a second. Some of the adventure has been lost.

Once you know the volume of the portion the hull you hope will be immersed, you can figure out what an equal volume of water would weigh, (see next paragraph!). That would also be the weight of the vessel if it actually floated at that immersion. This is the “displacement” number that we have been seeking. It is specific to that hull shape floating at that particular waterline and really represents a volume measurement given in variable weight terms, just to confuse.

The density of water changes in accordance with its salinity and temperature. We can reasonably ignore the temperature but fresh water is about 62 lb./cu.ft. and salt water is about 64 lb./cu.ft. This is enough of a difference to require that the designer consider what happens when his creampuff navigates the inland waterways, so a qualifier is really necessary, and the displacement number should be followed by either (fw) or (sw) if he is being exacting.

By creating a series of volume calculations for several hypothetical waterlines, even cock-eyed ones, a chart can be generated to suggest where the vessel will float at various weights and crazy angles. Smarter (more expensive) marine design computer programs will do this for you, but if you like an interval for contemplation now and then you can make up a traditional chart that looks like this.

Link to enlarge Hydrostatic Curves chart

You may notice that the official title for this figuring is “hydrostatics”, the significant part being the “static”. As soon as the boat moves through the water or encounters anything but a flat calm surface, the numbers are spilled about in concert with its rolls, heaves, and pitches; (“hydrodynamics”, let’s just not go there).

These abstract figures are really defining the nature of the hull in terms of the shape of the depression it makes in the water. The values plotted or noted to help imagine what will happen as the weight load on the submerged portion of the hull varies in magnitude or position, so to be meaningful, the design exercise also now requires the generation of a “weight study” to collate the weights of all the vessel’s components and burdens in various states.

This is a drudgery that represents the flip side of the displacement calculation; if you don’t have some confidence in what the conglomeration will weigh, and how the weight will be distributed, the displacement numbers are of little use. Other than a spread sheet program, the computer offers no shortcuts; so weight studies unfortunately may tend to be somewhat cursory, (at the designer’s considerable risk). At its best though, the study will include everything you can think of that may be part of, or carried aboard the vessel in all conceivable circumstances.

Since things change, like more or less fuel or water, there needs to be a number of weight studies in fact, representing different conditions of loading. The placement of discretionary weights, like provisions or a dinghy, will tilt the vessel one way or another and the studies must take the shifting centre of gravity into account. Venturing a little farther into the abstract, the hull tilts and sinks until it finds a position in which the buoyant effort pushing upward finds equilibrium with the weight pushing downward. When this stability is established, the vessel will hopefully be afloat, upright, and acceptably close to level (it makes your racy lines look better), the actual waterline will be wherever it is.

Elephant's equilibrium established

So, the weight study and the hydrostatics, including the displacement numbers, must go hand in hand to have a practical application, making comparisons of different vessels in anything other than broad brushstroke highly problematic.

It is virtually impossible to determine the weight of a vessel at any given time by using a weigh scale so the design procedure is reversed once the vessel is afloat and the actual floating waterline is compared with the hydrostatics, taking into consideration the properties of the water, and a weight is pronounced based on the properties of the hull. You just observe how she floats.

Cargo vessel operators, (and insurers), pay closer attention to these issues of floatation and hydrostatics than what is customary for pleasure vessels. You will see this illustrated in any commercial harbour as “Plimsol marks”, (the meaning of which is shown in the diagram below), safe operational loading being tailored to suit the prevailing conditions. You may also see the expected difference between floating in fresh vs. salt water.

Plimsol mark
Plimsol marks

The weight of the vessel in the picture obviously varies considerably so its displacement has changed accordingly, it being relatively low when the picture was taken. The vertical numbers on the ship show the distance down to its keel. They serve as the draft marks, (useful if you distrust your depth sounder). The ship’s officers observe the draft marks and compare them with an on board hydrostatic chart to see how much the cargo weighs and decide if the distribution is acceptable. There appears to have been some dispute over where the Plimsol marks should be in this case. Maybe somebody goofed the calculations, or maybe the bottom has been dented in somewhat, changing the hydrostatics?

Well below the DWLFor a medium sized pleasure vessel, peering over the side to get an idea of whether you have any bottom paint still visible above the water is the equivalent way of deciding when to stop bringing junk on board. The builder’s application of bottom substituting for the Plimsol mark.

For the purpose of providing a benchmark for calculations, a hull design will very early on have a DWL, (design waterline), established. This is primarily a geometric plane from which measurements can be taken and for this purpose it can be established at any convenient altitude, even above or below the vessel, but the designer will generally place it, well in advance of the rest of the design, where he hopes its real world designator will occur. (This is his first chance to declare his authority over nature.) As the weight study progresses in concert with the developing design of the whole vessel, the DWL frequently proves to have been ambitious, its associated displacement being insufficient to accommodate the loads. Nonetheless, that displacement number frequently gets tagged on to the hull design and tends to be quoted rather liberally perhaps, well after it has lost its practical authority.

If you are just looking at a raw hull design with a nice waterline stripe provided, an associated displacement number will impart some sense of the floatation capacity but may have little to do with a finished vessel, fully provisioned and ready to depart on an extended voyage.

Right displacement

In practical terms, the displacement will vary considerably for any vessel and any published number that has been provided without qualifications is largely useless. It is usually the number associated with the DWL. Common boatyard practice is to use the DWL as measuring point above which to extend the bottom paint, usually several inches, in anticipation of floating in the real world. Boats tend to float lower as they get older due to the accumulation of junk so most hull re-paint jobs are accompanied by an upward adjustment of the waterline striping and the old scum line is thereby covered by nice new bottom paint. (Also, the apparently lower topsides look sleeker, so the bill gets paid more willingly.)

You often see vessels being compared or evaluated based on some totally unqualified displacement numbers or their “displacement to sail area ratio”. It’s tough to see how this serves a potential owner as anything other than an exercise in abstraction. A cruising catamaran will weigh something like 30%+ more when departing for a sea voyage than it did when it was launched totally empty. What particular displacement number does a potential owner want to hear?

In the broadest sense, for like vessels, lower hull displacement numbers would suggest a predilection to race while higher numbers would suggest a predilection to carry cargo. The catamaran mantra “lighter is better”, as a generalization, is a good thing to keep in mind however when designing any vessel; taking extraneous weight along for a ride is never desirable. It benefits the owner if the all-up weight of the cruising package includes more of his stuff and less of the builder’s materials. The builder may use costlier materials or technology to save some structural weight to the degree it is practical. But realistically, overburdening a lean machine may seriously detract from the enjoyment and piece of mind that a voyage with a more relaxed design could have provided.

Paradoxically, higher catamaran weights (necessarily supported by higher displacement volumes) generate higher stability figures. This is why capsizes are frequent in light racing cats but very rare in cruising vessels of the same approximate dimension envelope. A lighter displacement hull design may not automatically be assumed to be a good or bad thing; it depends on what you are going to do with the boat.

It all depends on what you are going to do with the boat

If we haven’t driven him away in bafflement by now, how might we then help the potential cruising catamaran sailor when he asks for a displacement number in hopes of evaluating what we have to offer?

  • 1) Demonstrate that there is enough buoyancy available at a practical waterline to float the vessel itself and all his stuff safely and comfortably.
  • 2) In the absence of a floating demonstration vessel, provide fully qualified numbers and justify their derivation if the mathematical model is helpful.
  • 3) Avoid simplistic numerical comparisons with other vessel that may be entirely misleading out of context.
  • 4) Help him get a grasp of the underlying concepts of floatation and stability, it may be fun! And give him something to contemplate when stuck in commuter traffic.
  • 5) Use plain language and analogy wherever you can. (Perhaps I should heed my own advice).

It would be unfortunate if our man reached a decision by comparing mathematical terms specific to different hulls, each with its own unique draft, profile, section shape, appendages and weight loading.

Does the design “do it for you” or not? That is the question.

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