Ratios for dummies

Practical: What the numbers mean

Ever seen funny-looking numbers in the stats box at the end of a boat review? Weird stuff like ballast/displacement = 0.35 or SA/disp = 16.7? John Champion explains what they mean and how to use them to help you determine which boat is right for you.

The complexity of modern life seems to accelerate in direct proportion to computer technology. As soon as new hardware and more powerful software allow a deeper analysis of a concept some bright soul is leaping on the opportunity to rip out a doctoral thesis.

This situation applies equally to yacht design and some of the things being considered, studied, designed and built are quite incredible. Canting keels, canards (an additional rudder forward of the keel) and trim tabs on keels, to name a few. Add new, lightweight materials and construction methods and it becomes clear that the days of chicken wire and cement are receding. Some of these innovations are finding the way from the top-end race scene to general sailing and can be expected to reach the average (what's that?) cruiser in time. So while we wait for our own PhD to arrive in the post a little discussion on ratios will allow a better understanding of what the magazine reviews are talking about and perhaps steer us a little more efficiently towards the vessel we want to buy.

Insight into performance
Each ratio is intended to indicate an insight to a vessel's performance and is probably, these days, to the modern yacht designer what the bulldozer is to the landscape gardener - a basic tool to hack out a starting point for all the finer work.

In this instance the word "indicate" is used precisely because two vessels can share an identical ratio but yet be vastly different.

There are many ratios, some of disgusting complexity but those commonly seen in magazines are:

* Ballast/displacement
* Sail-area/displacement
* Displacement/length
* Theoretical hull speed

Ballast
Easiest of all to calculate is the ballast-to-displacement ratio. This is the only one that doesn't involve a formula and requires only dividing the yacht's stated ballast by total displacement. For example, my boat, a Hunter production boat, Rancho Relaxo, has a displacement of 17400 pounds (divide by 2.205 if you insist on kilos, but don't try metric conversion on the other ratios because most were developed for imperial measurements) and ballast of 7900 pounds.

Do the sum and the ballast/displacement ratio is 0.454. This simply means the ballast makes up 45.4 percent of the total displacement or yacht's weight.

The theory of this ratio is to indicate the boat's "stiffness", which is resistance to heeling or ability to stand up under sail. Forty-five percent is a high figure and indicates that Rancho should be able to stand a formidable amount of sail before reefing is required.

Draught
But the ratio tells only part of the story. Keel design and material tell another tale. Draught obviously has great bearing on a yacht's stiffness and it would be an argumentative skipper indeed that ever claimed a shoal-draught version performed better than the deep-keeled sister ship. In essence, the deeper the weight the stiffer the boat and here is when construction comes in.

Many modern fin keels resemble slim, deep blades holding a whopping great lead torpedo. This has the significant benefit of putting the greatest amount of weight as low as possible and so providing the maximum righting moment for the weight. The designer then can lower the total ballast, considerably lighten the boat and improve performance in exchange for the extra draught.

Consider production yachts that offer deep and shoal-draught models: additional ballast is nearly always present on the shoal version to offset the reduced depth, which naturally means you are sailing a heavier boat.

The ballast material is also important. Cast-iron is often used in place of lead, being cheaper and certainly a bit lighter. This has the disadvantage of requiring more material, which keeps weight higher in the construction and is hence not so efficient as a lead equivalent but certainly explains why Rancho carries such a high ratio, in case you were wondering.

Naturally there is much more to the keel story. Lateral area (long or full-keeled vessels) often steer beautifully straight with little more than balanced sails but our narrow-minded ratio takes no heed of this fact or of draught, keel shape or material. Many ratios are calculated on a lightship basis. Add gear, crew, fuel and water and things may be very different.

Sail-area/displacement ratio
This tricky little number is a bit more complex to calculate and might well send you round the bend without a scientific or financial calculator, so see a maths teacher if you want to try it at home. Imperial measurements please Ð displacement in pounds and sail area in square feet are required.

The intention is to tell us the boat's power potential under sail Ð in essence the amount of sail area in proportion to the vessel's displacement. Common sense here: take the Endeavour out in five knots of wind with just a storm jib and see how fast you go. On the other hand try a Hobie cat in 35 knots with full sail. A high sail-area-to-displacement ratio points toward a boat that can perform handsomely in light air and will probably need to be reefed before too long. A very low ratio might well indicate more breeze will be required before sailing becomes a viable option. But consider Ð if the ratio is low enough you may never need to reef!

Most boats fall into a middle-ground solution that will have a little light-wind credibility but won't require reefing in 10 knots of breeze. Motor-sailers can be expected to have a far lower value than performance yachts. Measurements should be for 100 percent of the sail plan, so no overlapping sails, please, and ignore the huge roach on your new Volvo 70. Most reviews report the 100 percent-sail-area value, so if you see a ratio that seems way out of the bell curve for the particular type of vessel at least now you can check it.

Indicative values

Motor-sailers below 14
Ocean Cruisers 14-17
Coastal Cruisers 16-18
Ocean racers 18-20
Radical racers 20 plus

* Values from celebrated US naval architects Ted Brewer Yacht Design.

Displacement/length ratio
D/L is displacement to waterline length
D/L = (Disp/2240)/(0.01 x LWL)3

Use imperial measurements for this because the formula requires conversion into tons, not tonnes.

This last common ratio broadly indicates how heavily built our prospective vessel is. Material plays a great part here. The average 40ft/12-metre glass monohull probably comes in around 8000kg - far less if it is a whiz-bang carbon and epoxy number. The higher the number the greater weight for the given length and hence the construction is indicated as heavier. Very low numbers point towards racing exotics.

You should expect the 40ft steely to have a considerably higher ratio than, for example, a Sydney 38.

A low ratio will probably mean better acceleration and superior light-wind performance, which should come as no surprise. Multihull fans are born with this knowledge Ð light means fast, heavy means slow.

Because multihulls rely solely on form stability (beam) and carry no ballast they generally have low displacement/length ratios and moderately high sail-area-to-displacement ratios for the same reason.

The downside of light displacement is load-bearing capacity. Light vessels are affected far more by an increased payload. By way of confirmation try this exercise in pure science: strap a 10kg pack on a greyhound and see how fast it runs. Now take the same pack and load a bull terrier of identical length.

The heavier and more muscular dog will bear the additional weight far better and maintain a higher speed over time.

Most ratios can be misleading and this one is no exception. Waterline length on monohulls varies at different levels of heel. A yacht with long overhangs will increase the waterline significantly when heeled and this changes everything. Another ratio Ð calculated at average angles of heel for upwind sailing Ð may present a very different.

How they rate

Very light racer 100-150
Light cruiser/racer 150-200
Light cruiser 200-250
Average cruiser 250-300
Heavy cruiser 300-350

* Ratings again as per Mr Brewer. Seems most boats these days seem to fit into the 150-250 bracket.

Theoretical hull speed
Hull speed = square root of length waterline multiplied by 1.34 (simply take the waterline length in feet, get its square root and multiply by 1.34)
HSPD = SQRT(LWL) x 1.34

This one is seldom seen in yacht reviews but is worth mentioning because we were speaking of speed potential. Another little formula will help us determine the theoretical hull speed of our boat, which will give us a benchmark of performance to work towards. Assuming our yacht has a hull speed of 6.5 knots, and we are hooting along in a blow at sevens and occasionally surfing faster, it is probably futile (and unwise) to call for more sail. Conversely, if the best we can get is five knots in the same conditions we might wish to examine our sail trim or configuration for improvement. This formula is only for displacement hulls so don't send abusive letters because your ski boat goes much faster!

As mentioned most yachts are capable of exceeding hull speed if conditions are suitable - occasional surfing and planing are common. Naturally, again the heeled waterline will be different to the measured waterline so some differences are to be expected.

Apples with apples
All these ratios (and there are a heap more) have a purpose, which is very specific and the usefulness for comparing very different boats is going to be marginal, if not truly misleading. However, if you wanted to buy, say a 38-foot fibreglass monohull and compared various makes and models, the numbers should then provide a reasonable insight into some build and performance characteristics. At the very least you'll have an idea what the magazine reviews are talking about.

John Champion isa regular contributor to CH on practical matters. He lives in the Whitsundays and works in the bareboat industry.

how we measure stability
Stability is measured in a number of ways but two key factors are the centre of gravity and the centre of buoyancy.

Keeping heavy objects (such as engines) as low as possible helps the centre of gravity stay low. This in turn has the benefit of supplying a greater righting moment as the boat heels. The centre of gravity is the point at which the vessel's weight acts vertically to press downwards. Essentially, the lower the centre of gravity the greater will be a boat's inherent stability. This is an essential part of the the keel's job in monohulls.

The centre of buoyancy is much the opposite and is the point where the water pushes the vessel upwards. As a boat heels the centre of buoyancy is moved outboard and the flotation acts to correct the heel. This is known as form stability and is the reason catamarans and other unballasted boats stay upright.

Designers graph the interaction between the centre of gravity and the centre of buoyancy to produce a stability curve. This will supply the angle of vanishing stability, which indicates at what level of heel the boat is capable of self-righting and when she will capsize. This data is sometimes supplied with new vessel specifications and sometimes not. Higher numbers indicate a greater righting moment and ultimately a higher resistance to capsize. Some yacht races (notably Sydney to Hobart after the 1998 event) require a minimum documented angle of vanishing stability as a condition of entry. Another consideration is the angle of down-flooding which tells at what level of heel water will flood the vessel.

Needless to say, this is a pretty important and specialised area and the domain of naval architects.

Ratios are primarily meant to give an insight in comparing boats of similar size and construction. See the examples below of various GRP production yachts.

Ballast/disp Disp/length Sail-area/disp
Catalina Morgan 440 0.37 180 18.39
Dufour 455 0.29 172 16.8
Najad 440 0.34 222 15.4
Jeanneau 45DS 0.28 194 16.8