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Neville's Magic Hull Shape

Although the maiden voyage of Robert Beebe's Passagemaker was more than 30 years ago, the concept of traveling offshore for large distances is still a new concept to many boaters. Today, even experienced yachtsmen are seeing powerboats in a whole new light. And many of these people are trading in sailboats with revised dreams of motoring off into the sunset.

To no one's great surprise, the number of yachts advertised as the "perfect boat to do just that" keeps increasing. Many are new designs. Some have been around for years. Each, however, is touted as fulfilling the offshore needs of this new category of boat buyer. The good news is that some of these boats actually do that and do it quite well. But, of course, some do not.

Finding the right boat for you often means two things: Knowing what you want, and separating fact from fiction.

Brutal honesty is important. Be able to admit to the salesman and, more importantly, to yourself, what kind of passagemaking you are really likely to do? Here the key words are "really likely." If you are actually going to be crossing oceans, you are probably looking at one kind of boat. If, however, "really likely" means driving "the ditch" to Florida, or skipping across the Gulf Stream to cruise the Bahamas, or doing the Inside Passage to Alaska (all admirable goals), a totally different boat may be a better choice.

One of the most significant factors in picking the right boat is hull shape. Unfortunately it is also one of the most illusive. What a boat looks like above the waterline and what it looks like below the waterline sometimes have little, if any, relationship to one another. A salty traditional looking boat up top may be riding on the bottom of a modem planing hull. The opposite can also be true. Knowing what lies above and below the waterline is a big part of separating fact from fiction.

Initially, Forget Size And Price

Often the most important tool in your arsenal is simple comparison. Look at as many boats as you can, and look at them critically. Don't be too concerned if the boat is the right size for you. At this stage the interior doesn't have to make sense to you and you don't even have to be able to afford that specific boat. You are just looking at overall shape. Look at the best, most expensive boats, even if they are outside your price range. What would be the best boat if money were not a concern?

If you have narrowed down your list of requirements (read, you are not looking for a boat that does everything well), you will hopefully begin to see similarities in the underwater shape of the boats that attract you.

Just as important, you'll also notice boats that are quite different. Quite different means questions to be answered. You are trying to teach your eye to identify the "norm." Radical departures from that norm may be reasonable if you fully understand all the tradeoffs, but such departures make me nervous. As in most areas of life you almost never get something for nothing.

So, your search has led you to order brochures for every boat from 40 to 60 feet. You've read articles about folks who have actually made the kind of trips you want to make. Maybe you've even chatted with owners on the Internet, at owner rendezvous, or at the yacht club bar. How do you make sense of it all?

Unfortunately, looking only at published boat data often tricks the brain into "apple and orange" comparisons. One good alternative is to supplement the things you have learned with what designers refer to as coefficients of form.

These coefficients are numbers that help to compare the general relationship of things like size, weight, and speed. They help you to quantify the difference between two boats of the same general size. They also allow you to more honestly compare relationships between two vessels of quite different size. Regardless of how similar they appear, two boats with quite different coefficients are quite different boats.

Example 1: The displacement boat that you have been looking at can be ordered with bigger engines if you want higher speed. Is it a good displacement boat?

Example 2: The 50 foot waterline boat you really like weighs 80,000 lb., but you prefer a boat 5 feet shorter. What might it be expected to weigh?

These are the kind of questions that coefficients of form can help with. Some of the coefficients you will probably recognize. Others may be new, but all of them offer you tools to help in your quest for the perfect boat.

Speed Length Ratio (S/L ratio)

The search for speed in vessels ranging from canoes to ships has had more influence on hull shape than any other single factor. Boat speed is not an absolute, and there are many variables in the speed equation. For example, speed is closely tied to length.

Picture this: A 750-foot ship is motoring near shore at 25 knots. There is hardly a ripple around the boat as it glides through the water with seemingly little effort. Sightseers are foolishly racing the behemoth in their 24-footer and barely keeping up. Unlike the ship's calm demeanor, the little boat, on the other hand, is surging out of the water as the crew hangs on for dear life. The water surrounding the 24-footer is all froth and foam. This image gives a visual picture of the relationship speed length ratio. The mathematics are this:

S/L ratio = speed (knots) / √waterline length (feet)

The speed of 25 knots divided by the square root of the ship's 750-foot waterline equates to a S/L ratio of 0.91 for the ship. As we will discuss, that is a very low number. The ship is operating at a very efficient rate relative to its own length. Relatively speaking, the horsepower required to move the vessel at this speed is also quite low.

The small boat is also traveling at 25 knots, which, divided by the square root of 24, produces a S/L ratio of 5.1, quite high in the planing range. Such a speed in a small boat requires a relatively massive amount of horsepower. The big ship is efficient at 25 knots, the small boat is not.

Think about it in reverse. The 750-foot ship would have to be traveling at 140 knots to match the small boat's 5.1 speed to length ratio. Now that is a formidable image!

The S/Lratio is more than just a mathematical relationship. In fact, it is also the key to understanding a real world force that every vessel must overcome. A boat or ship traveling through water generates a bow wave. That bow wave gets longer as the speed of the boat increases. When the speed increases to the point where the S/Lratio equals about 1.34, the bow wave produced becomes as long as the vessel itself. When this happens, the vessel must be able to climb up over its own bow wave to go any faster.

As the boat attempts to do so, a tremendous amount of additional resistance is created. Semi-displacement and planing hulls can overcome this resistance to differing degrees. Boats designed for purely displacement speed operation, however, never can do so. That is why they have a finite top speed--and no increase in engine horsepower can overcome that.

Speed length ratio is a good key to the speed range in which the boat can travel.

But caution: If the boat is capable of traveling at higher speed (as with those optional "bigger engines"), than it is NOT a true displacement hull. Such is the case in our Example 1. It is simply a boat that has been under-powered to operate within a slower speed range. To get the most out of the S/L ratio, you need to determine the maximum speed the boat is capable of.

Again, a planing hull traveling at very slow speeds is operating as a displacement boat. That does not mean it has a true displacement hull shape. Likewise, that salty looking boat chugging along at 9 knots could just as easily be an under-powered semi-placement or planing hull form. Speed potential is the key.

Displacement Length Ratio (D/L ratio)

The displacement length ratio is a tool used to evaluate how much a boat weighs (therefore how much water it displaces) relative to its own length. The D/L ratio offers a means of comparing the weights of boats of different lengths.

This coefficient is not tied to a physical phenomenon as is the S/Lratio. Instead it works as a guide with a range of numbers. D/L values tend to creep up as boat size goes down. The D/L of a 50-foot trawler might be 340. On the other land, the D/L of a 70-foot trawler might only be 290. even so, the D/L ratio will normally point clearly to the general characteristics of the boats you are comparing. The calculation is as follows:

D/L ratio = displacement / (0.01 x waterline length)^3

Where displacement is in long tons (one long ton equals 2,240 lb.) and the waterline length is in feet.

In our example 2, we could use this formula to determine a reasonable weight for a similar 45-foot boat. The D/L for the 50-footer using the above calculation would be 286. We could use this number to calculate that the weight of a similar 45-footer, with the same D/L value, would be about 58,380 lb. That would be 286 time the quantity (0.01 times 45) cubed. This give us the vessel's weight in long tons., which is multiplied by 2,240 to convert the weight to pounds.

One shortcoming of the D/L ratio is that it is a condition-sensitive calculation. By that I mean you will get decidedly different numbers depending upon whether the boat is fully loaded, at half load, or empty. Therefore, it is helpful (although not always easy to find out) if you know what load condition the published displacement represents.

Was the boat carrying full fuel and water tanks, passengers, and complete stores ready to leave the docks—or was it the empty weight or the boat measured on the truck at the time of delivery? More often than not, the weight used is somewhere in between. Even with this ambiguity, the D/L ratio can still help you identify boats that seem to be too heavy or light for their appearance. If, for example, you find a boat with a massive D/L ratio compared to other boats its size, you should ask yourself why. Is there really a hull design argument that supports that huge volume, or is it just a way of fitting a massive interior into too short a boat? A worthy question indeed!

Block Coefficient (Cb)


The block coefficient is a non-dimensional way of comparing undetWater shape. You can visualize the Cb by imagining a rectangular block of wood that is the same waterline length, waterline beam, and draft as the hull you are evaluating. The Cb is the percentage of the original block that would remain after the shape of the hull is carved away. The calculation of block coefficient is:

Cb = volume of displacement [cubic feet] (waterline length x waterline beam x draft)

Where volume of displacement (in cubic feet) equals displacement (in pounds) divided by 64 (the weight of a cubic foot of seawater).

A barge illustrates a good example of block coefficient. Its Cb would be very high, maybe 0.85. The value would be high because the shape of a barge very closely resembles the equivalent block of wood that it would be carved out of. Most yacht shapes, however, are much lower, ranging from about 0.25 to 0.50. Again, the higher the number (the closer to a Cb of 1.0) the fuller, or bulkier the vessel. The optimum Cb varies with boat type and size.

Cb also changes depending on whether or not the keel is included in the measurement. To be most conventional, you would exclude the keel from the overall draft. To do so, however you must first estimate how much of a reduction in draft would occur by eliminating the keel. Since we are using Cb purely as a mechanism for comparing several existing boats, there is still value in using the Cb even if it includes the whole keel. The only difference will be that the numbers might seem skewed when compared to other published block coefficients-but there are very few published coefficients anyway.

Consider two boats: One has a 52-foot LWL, a 15.5-foot beam, a 5-foot draft, and displaces 42,000 lb. The second boat has a 60-foot waterline with an 18-foot beam and a 4.5-foot draft, and displaces 75,000 lbs. The first hull has a Cb of 0.163, including the keel. The second has a Cb of 0.241. This shows that the hull form of the first boat is not nearly as full as that of the second boat. Among other things, that means the second hull will take more horsepower to push through the water.

Prismatic Coefficient (Cp)

Prismatic Co

The prismatic coefficient is a similar non­-dimensional coefficient, and it is an even more valuable tool for the designer. Unfortunately, you need to know the area of a section of the hull, usually amidships. The Cp compares the shape of the hull not to a block, but to a prism with a base the same shape as the midship section and a length the same as the waterline length. It is a more valuable number and its relationship to speed in yachts is better documented than the block coefficient.

Cp = displacement [cubic feet] / (waterline length X underwater area of the largest section)

Where volume of displacement (in cubic feet) equals displacement (in pounds) divided by 64. Since you have to measure or estimate the size of that midship section, this is probably not a likely do-it-yourself project (unless you are really dedicated). It must have real value to the potential buyer, however, as evidenced by the growing number of builders and designers who include this measurement data in their advertising and boat literature.

Like the block coefficient, the higher the number the fuller the vessel, i.e. the closer the boat is to, in this case, the shape of a prism. The Cp tells you how much has been removed from the ends of the boat and therefore how fine the shape is. We said the Cp is valuable in understanding the design speed of the ves.sel. There is a widely published table (shown below) of the optimum prismatic coefficient for any given speed length ratio.

S/L ratio VS. Optimum Cb

S/L ratio VS. Optimum Cb

This table illustrates that boats designed to reach higher speeds should have a Cp approaching 0.70. Those designed for displacement speeds might have Cp values between 0.52 and 0.62. The higher number of the faster boat would be a reflection of the broad planing surface required for this type of boat. If you know the prismatic coefficient you have an idea as to what speed the hull was designed for.

Measure, Formulate, Compare

There are still other coefficients that can be useful in evaluating hull form. Beam to length ratio is simply a division of those two entities. Draft to length is similar. You could even make up your own coefficient, such as gallons of fuel to full displacement. Use whatever helps you to make sense of all the variations between two vessels.

So now, in addition to all those glossy brochures, you are also armed with a stack of legal pads full of notes and calculations. You can make spreadsheets, tables and bar graphs. You can even make pie charts. But the question still remains—how do you evaluate what's out there?

Hull shape tells it all. Whether you're talking about tug boat, Eurocruiser, jet ski, or the boat of your dreams, there are basically three different hull shapes to consider. Each is good for its own specific purpose The problems usually begin when someone thinks he is getting one thing and really winds up with something quite different.

Whether we're talking 10 feet or 100 feet, all hulls operate in either the displacement speed range, the semi-displacement (AKA semi-planing) speed range, or planing speed range. First, you need to decide which range is appropriate for the kind of cruising you want to do. Second, you want to make sure a given hull is not only operating in that range, but that it was designed to be optimum within that range.

Displacement Hulls

When rough, serious offshore conditions are expected, the most efficient, most comfortable and the safest (albeit slowest) boat on long passages is a full displacement vessel. Often, though not always, this boat has a round bilge hull form.

You can probably make a case (and I am sure some will) that the round bilge form is the most efficient. Outside of using a model in a test tank, however, I'm not sure that the differences between rounded and the more angular chine forms are as apparent as some believe. Certainly commercial vessels (with chines) have been operating quite efficiently for the better part of this century.

The use of chines is often related to ease of construction. Metal boats, for example, are much easier to fabricate with chines. And the chine form is sometimes desirable for other reasons. On several occasions, we've used chines to give a vessel slightly greater resistance to initial rolling. Chines can also help a boat track better, which actually improves efficiency.

So it seems clear that very efficient displacement hulls can be built with or without chines.

As we have discussed, true displacement hulls reach maximum speed at a S/Lratio of roughly 1.34. That is the number traditionally used, although with lighter and improved engines, we've seen it to be practical to push some displacement vessels up to S/Lratios of about 1.42. If you add more horsepower, hoping to make these hulls go even faster, you are just wasting money. Trying to climb its own bow wave, an over-powered displacement speed boat does what every tugboat does-it squats down deeper into the water just hoping to get out of the way of the massive wave that is being dragged along behind it. Not a pretty sight!

Because of the combination of its hull shape and weight, a displacement boat sits in the water, not on top of it. This is true no matter what speed the hull is traveling. And, as we have said, it also doesn't matter if the underwater shape, as seen from the bow, is rounded or has one or more chines.

The quarter beam buttock is another good indication of speed potential. The quarter beam WHAT you say? The quarter beam buttock is an imaginary line that traces the path the water tries to follow along the hull bottom. Draw an imaginary line on the bottom of the boat so that it runs fore and aft and parallels the centerline. Locate this line half way between the centerline and the maximum waterline beam. That is one quarter of the beam if you consider both sides.


Specifically, the quarter beam buttock on a displacement boat is relatively steep, often in excess of 7 degrees. Because of this angle, much like air flowing past an aircraft wing, the water tends to separate from the hull, and, as it does not follow easily around the hull's shape, no significant vertical lift is produced which might add additional hull speed. As a result, the boat reaches its theoretical top speed and stays there. (This may also explain somewhat the tendency of a double-ended hull to squat down into the water as it reaches its top speed. The parting of the waters, so to speak, creates a suction that pulls down the stem.)

The good news of all of this is that, within their operating range, full displacement boats are extremely efficient objects to move through the water. Remember the ship example? This efficiency equates to very modest horsepower requirements, which can be easily accommodated by engines designed to put out such moderate power for hours, days, even weeks without serious risk of mechanical problems.

The other good news is that the displacement speed hull form is really quite forgiving. What that means is that there is no one perfect shape, and many different full displacement hull shapes have been drawn that work, and work well.

Some people portray this subject as being technically difficult and complex, but, if the truth were known, it really isn't. Designers have a lot of latitude in designing successful displacement hulls, evidenced by the great number of successful boat designs. But we are living in a high-tech world, with high-tech solutions for everything, so it is no surprise to see some people trying to profit by developing high-tech "solutions" for the full displacement hull form.

Semi-Displacement Hulls

These boats are a bit trickier They operate within S/L rage of 1.34 and 2.5. Calculating the D/L ratio, these hulls fall within the value of 225-300. Semi-displacement boats are neither, "fish nor fowl."

As the boat starts moving fast enough to try and climb over its own bow wave, completely different hull characteristics come into play. First, weight becomes a critical factor. If the boat is too heavy, it simply cannot make it. Second, the bottom shape must allow must allow some lift to start to develop, particularly aft.

Some boaters (and some designers) scoff at semi-displacement designs, and wonder why anyone would even want to operate in this range. It is arguably inefficient, and it consumes a great deal of horsepower energy.

But there is something to be said for semi-displacement. Despite coefficients or other quasi-engineering/scientific mumbo jumbo—for modest size vessels, this is really an extremely desirable speed range.

The augment is an old one, " I can travel along leisurely, but boy, when I want to kick ip up, I can get home ahead of that storm." A semi-displacement boat makes a lot of sense if you are likely to find yourself in that situation. They are not the vessel for transoceanic travel, but the are great if making landfall a daily occurrence.

Actually, many of the negatives that seem to apply to semi-displacement boats are a result of what you might call the "modernization" of that hull form. Today we think of semi-displacement hull forms as inefficient. These boats use an enormous amount of fuel at high speed. At low speed they are reasonably efficient, but at a price of a corky, un­comfortable motion in a seaway. In the worst of circumstances, ultimate stability is a definite concern.

Most of these "modem" forms have an underwater hull shape that has a striking resemblance to faster planing hulls. This wasn't always so. Earlier in the century (when huge engines weren't an option), long narrow semi-displacement boats were among the most prized race horses of the era. Un­fortunately, with few of today's boat owners latching on to the minimalist philosophy such boats required, these beauties are largely ghosts of the past.

Still and all, today's modern semi­-displacement hull offers what many owners want-speed, but only when they want it. These modern hulls are most commonly hard chine shapes, although the Maine lobster boat hull form has defied that trend for decades. Be cautious here, as overweight or under-powered planing hulls are often disguised as semi­ displacement boats. Measuring the quarter beam buttock, the best semi-displacement hull angle is around 4 degrees (which is, quite properly, between the optimum for either a planing hull or a displacement hull).

Another place that semi-displacement hulls become very desirable is when overall boat length decreases. For the very small motoryachts, an S/L of 1.34 may be just be too slow to be practical. Displacement speeds are a hard sell for boats under about 30 feet.


What if you want to travel at higher speeds of, say, S/L ratio 2.6? That would be 18 knots in a 50-foot boat. Any way you look at it, you are now talking planing boat. Now trust our counselors, there is nothing inherently wrong with traveling at those speeds in moderation. Sometimes reality must take a front seat. In spite of serious offshore ambitions, many of us are still forced to make it back to work on Mondays. Whatever the story, planing boats can deliver the goods, getting you there in the shortest amount of time, weather permitting.

Planing boats are generally designed for speed length ratios in excess of about 2.5. They are always chined hull forms. These boats are generally beamy and always have very broad transoms. At these higher operating speeds, a planing boat succeeds in climbing up over top its own bow wave, being dynamically supported by the water instead of simply sitting in it like a displacement boat.

At plane there is actually a reduction in resistance since the boat has been lifted up out of the water. This results in less hull, or wetted surface, in the water, therefore less resistance. That is why it is not uncommon to be able to throttle back when "on plane."

More traditional designs tend toward V­-shaped sections which flatten as they move aft, and they often have a skeg to provide directional stability. Although these shapes offer excellent speed potential, they can pound like the devil in a seaway, especially if the forward sections are concave.

The more contemporary deep V-shape was developed to overcome this problem offshore. These newer designs reach a constant, more pronounced, V-shape amidships and maintain that angle (called deadrise relative to the waterplane) all the way aft to the transom. Deep V-types have a much more comfortable ride in open water. They rely on their V-shape for directional stability rather than skegs.

On plane, speed is largely a function of how much horsepower you add to the equation. You go from thinking of cruising boats with engines of 100, 200, or at most 300 horsepower, to boats with 500, 700, 900 or more horsepower.

In terms of D/L ratio, planing boats come in between about 130 and 225. The angle of the quarter beam buttock will be less than 2 degrees and often level with the waterplane. This allows the water to track easily along the hull bottom and promotes the dynamic lift necessary to reach these higher speeds.

Planing boats offer speed. The penalty for this speed potential is efficiency and ride. In a seaway, these hulls can inflict serious punishment. In ultimate conditions, they may not even have a chance at survival.

Running at speed, fuel consumption will seriously limit your offshore range. That may be a good thing, however, since most of us wouldn't want to be out there anyway.

As you might expect, planing boats are extremely weight sensitive, meaning that if they get too heavy for any reason, they simply won't perform at all.

Now remember, if you drop your speed enough, it's still possible to make serious distances even in a planing hull. I have known professional captains who have driven sport fishermen to Hawaii on delivery. You can do it. That doesn't mean, however, that it is a pleasant ride or an enjoyable experience.

Your Own Magic Shape

So what's the best hull form for you?

The good news is that it is entirely your choice. The bad news is... that it is entirely your choice.

A planing hull, I believe, is appropriate for a half day's run offshore, depending how well equipped she is. Fuel costs will be substantial and comfort questionable in any kind of a seaway, but everything comes with its own price tag. Then again, everything comes with its own rewards.

For coastwise work, a semi-planing boat is quite suitable. Whether it is considered the best of both worlds, or the worst, remains a matter of perception. "Modern" incarnations of the semi-displacement hull form often guzzle fuel at their best efficiency, and are uncomfortable at their worst.

More traditional examples of the semi-displacement concept are higher on the efficiency charts, but often provide minimal accommodations for any given length. Still, both con­temporary and traditional hulls are great boats when operated in their prime.

Consider semi-displacement boats for work that is not more than maybe 100 miles offshore. Getting to a safe haven is still a serious consideration.

If you are really heading offshore, you will (no surprise) want a full displacement boat. Look for a boat with a D/L ratio of between 300 and 350 for a 55-foot boat, slightly lower for larger boats and slightly higher for smaller ones. A D/L of 200 is extreme, as is 500.

The boat should be designed for a maximum speed/length ratio of 1.34 and a working S/Lratio of about 1.1. In a fiberglass boat I'd look for a round bilged hull form with a fairly hard tum of bilge. I wouldn't want a boat that rolls too much. In a metal boat, a chine would be fully suitable.

The choice might be even easier in a perfect world. Unfortunately, many of us are still forced into practical compromises. If that is your situation, my professional advice is—do the best you can.

You see, I have a great respect for people who just find a way to solve the problem and get where they want to be. I'm not suggesting that you should strike out in a late model old town canoe. But, by the same token, if you are really serious, don't wait until everything is perfect.

Compromise on overall boat size if you must. Compromise your course of travel if you must, but find a way to do it. There are souls among us who are compelled to hold on for years (and often forever) until they can afford, or design, or imagine that perfect boat. You know the boat—the one with the right accommodations, the best pedigree, or THAT MAGIC HULL SHAPE.

You also probably recognize the owners. they are among the ones who, not surprisingly, never leave home.