Sailboat Ratios

[GordMay]

Sailboat Ratios

There are many ratios that can be used to compare boat design dimensions, many of which are mainly of interest to professional boat designers. Here's a few ratios of use to the average boatowner (or wannabe) in comparing boats.

General Sailing Categories (in order of descending performance):
Racer
Racer/Cruiser
Cruiser/Racer
Cruiser


Displacement/Waterline Length - D/L
(Displacement/2240)/[(Waterline x 0.01)^3]
This is probably the commonest of these measures, and indicates whether a particular boat is "heavy" (eg a cruising design) or "light" (eg a racing design) for its length. Because it is "non-dimensional" (achieved using a cube of waterline length) this ratio can be used to compare boats regardless of their length and the resulting ratios can be categorized as follows:

Very light Under 90 - 100
Light 90 - 180 ~or~ 100 - 250
Medium 180 - 270 ~or~ 250 - 300
Heavy Over 270 - 300

In general, a boat with a lower D/L will have better light air performance for a given sail area but it will be more sensitive to loading, likely to have a less comfortable ride in a sea and will likely need to shorten sail sooner. Exact values differ between experts.


LWL to Beam:
LWL/B = LWL / Beam
This is the waterline length divided by the overall beam. All other factors being equal (of course they never are) the longer boat will be faster (in displacement mode, not planing/surfing). Waterline beam might be interesting to know but it is not a commonly reported figure.
A medium value would be 2.7, whereas 3.0 would be high, and 2.3 would be low


Motion Comfort:
The higher the number the more comfort in a sea. This figure of merit was developed by the Yacht designer Ted Brewer and is meant to compare the motion comfort of boats of similar size and types. A higher value is better (if you like comfort). Smaller and beamier boats tend to have a lower ratio. This is best used to compare boats of similar size.


Pounds per Inch Immersion:
LBS/IN = WPA x 64 / 12
The weight required to sink the yacht one inch. If the boat is in fresh water multiply the result by 0.975. If you know the beam at the waterline (BWL) multipy the result by BWL/Beam.

Sail Area to Displacement:
Sail Area with 100% foresail/((Displacement/64)^2/3)
The sail area is the total of the main sail and the area of the front triangle. Mainly it is a "power to weight" ratio so that a boat with a higher value will accelerate better and be a better light air performer. It will reach hull speed with less wind and need to reduce sail sooner if it is to avoid being over-canvassed in a blow.
A racing boat typically has large sail area and low displacement.
Motorsailers 10 ➛ 13 (underpowered)
Cruisers 12 - 15
Cruiser-Racers 16 - 18
Racer-Cruiser 18 - 20 (high performance)
Racers above 20.
High-Performance Racers have ratios above 24


Capsize Ratio:
CSF = Beam / (Disp/64.2)1/3
A lower value is supposed to indicate a boat is less likely to capsize. A value less than 2 is considered to be relatively good; the boat should be relatively safe in bad conditions. The higher the number above 2 the more vulnerable the boat. This is just a rough figure of merit and controversial as to its use, and the cutoff value of “2" is somewhat arbitrary.


Ballast Ratio (%) - BR
(Ballast/Displacement) x 100
The ballast ratio shows what proportion of the total displacement is ballast and can give an indication of how "stiff" (i.e. a greater resistance to heeling) or "tender" a particular boat is. Racing boats tend to have higher BR's then cruising boats.

However, use this value with care. Keep in mind that one boat may have the ballast at the bottom of a deep keel and another in a shallow keel. As a result, two boats with the same ballast ratio could have very different "righting moments" which is what actually determines how "stiff" (or otherwise) it is, depending on the location of the ballast and hull shape.

Some manufacturers who offer shoal and deep keel versions of the same boats (eg Catalina, Hunter) actually increase the amount of ballast in the shoal keel versions to help maintain a similar righting moment. In some cases this works well but in others it can mean that the shoal draft boat has a higher ballast ratio and yet still has a lower righting moment (so is less stiff) than it's deep keel counterpart.


Hull Speed - HSPD
Square Root(Waterline) x 1.34
Displacement (ie non-planing) hulls theoretical maximum speed is governed by the length of the wave created as the boat moves through the water. Since longer waterline lengths create longer waves they are able to go faster. Keep in mind that hulls are usually designed so that waterline length will increase as the boat heels increasing the maximum speed and also that in some circumstances (eg surfing down large waves) the boat ceases to be a true displacement hull and can exceed the theoretical maximum.



Metrics Formulae (in British system)

Sail Area - Displacement Ratio = Sail Area / (Displacement in Cubic Feet)2/3
Displacement - Length Ratio = Long Ton displacement / (0.01 x LWL)3
Theoretical Hull Speed = 1.34 x Square Root of LWL
Motion Comfort = Displacement / ( 2/3 x [(0.7 x LWL) + (1/3 x LOA)] x Beam3/4
Balast - Displacement Ratio = ballast/ displacement x 100
Capsize Screening Formula = Beam / (Displacement in Cubic Feet)1/3

In the above formulae:
Displacement in Cubic Feet = displacement in lbs / 64
Displacement in Long Tons = displacement in lbs / 2240

[ozskip]

Here is a site that may interest http://www.image-ination.com/sailcalc.html[/URL] Greg

[GordMay]

Thanks Greg (for the link), to Carl's Sail Calculator v2.72, which is a great tool that allows you to look up sailboat parameters in a large database of boats, or enter your own boat and compare to the others. In addition, for any boat you can calculate a set of quantities that will help you measure how it will perform.

Here’s some additional links regarding “ Hull Shape and Performance”:

“Estimating Stability” - by John Holtrop: http://www.johnsboatstuff.com/Articles/estimati.htm

“Calculating a Personal Increment Number” - By Nigel Calder
http://www.sailmag.com/SAILcalder.pdf

“Sailboat Design & Stability” - US Sailing (includes an on-line calculator)
http://www.sailingusa.info/design_winds.htm

Regards,
Gord May

[Jeff H]

Hi Gordon,

Nice to see that you are still posting high quality, general information posts.

As you probably recall, I am always cautious about relying on the 'numbers' when comparing boats. They really provide almost no useful information unless viewed judicuiously with regards to all of the other factors that contribute to the behaivor of a boat.

I do want to touch on a couple specific points in your posting. In a general sense this information seems to be an older interpretation of some of these ratios than the current thinking. I would say that much of the descriptions included would be true of boats built perhaps 20 years ago, but are less true of the better modern designs. To touch on this more specifically:


Displacement/Waterline Length - D/L :

The most recent scale on relative D/L has changed to reflect the current trend in longer waterline lengths over older boats. This trend would make it seem that boats have gotten much lighter than they actually have. Boats of a given length on deck weigh pretty much what they did 10- 15 years ago but their waterline lengths are much longer. When looking at more modern designs the scale looks something like:
ULDB: 90 - 110
Very Light: 110 - 140
Moderately light: 140-180
Moderately heavy 180 - 200
Heavy Over 200 or so

I also disagree with some of the statement:
"In general, a boat with a lower D/L will have better light air performance for a given sail area but it will be more sensitive to loading, likely to have a less comfortable ride in a sea and will likely need to shorten sail sooner."

This is not true when comparing the compartatively shorter waterline boats of 10-15 years ago to the newer longer waterline boats. Even though the longer waterline boats would appear to be lighter because of their lower D/L ratios, they are actually of very similar weights. That being the case they are generally more comfortable in a seaway, and can carry sail area longer than an equal LOA, equal weight boat on a shorter waterline. Similarly, given their longer waterline lengths they can often carry more load as a percentage of their displacement than a boat than an equal LOA, equal weight boat on a shorter waterline. In otherwords given the changes in design that have happened in the past 10-15 years you cannot simply compare L/D ratios and expect to have accurate information regarding senitivity to loading, need for sail changes, or motion comfort.


Capsize screen and Motion Comfort:
Both of these formulas are worse than useless. I know that I have explained this on this forum before but here it is again, both of these formulas were developed at a time when boats were a lot more similar to each other than they are today. These formulas have extremely limited utility in comparing boats that are not extremely similar.

Neither formula contains almost any of the real factors that control motion comfort or seaworthiness. Neither formula contains such factors as the vertical center of gravity or bouyancy, neither contains weight or buoyancy distribution, and neither contains any data on dampening, which really are the major factors that control motion comfort or likelihood of capsize.

I typically give this example to explain just how useless and dangerously misleading these formulas can be. If we had two boats that were virtually identical except that one had a 1000 pound weight at the top of the mast. (Yes, I know that no one would install a 1000 lb weight at the top of the mast.) The boat with the weight up its mast would appear to be less prone to capsize under the capsize screen formula, and would appear to be more comfortable under the Motion Comfort ratio. Nothing would be further than the truth. That is why I see these formulas as being worse than useless.

Sail Area to Displacement:
Again how these numbers are assigned is somewhat misleading. They would be reasonably accurate for older designs which has comparatively high vertical centers of gravity and were designed to carry very large genoas.

These numbers are quite small for newer designs which tend to have comparatively low vertical centers of gravity relative to the vertical centers of buoyancy (which comes from the more frequent use of bulb keels and the shallower canoe bodies permitted by the longer waterline lengths.) The numbers are also low because better sail handling gear and greater stability has allowed boats to stand up to a larger standing sail plan without having to shorten sail. The better modern designs are generally being designed to operate with minimally overlapping headsails which make for easier tacks, wider wind ranges, and greater flexibility.

I would expet the assignement of these ratios on more modern designs to look more like:

Motorsailers 10 - 13 (underpowered)
Cruisers 12 - 18
Performance Cruiser-18 - 21
Racer-Cruiser 20 - 22 (high performance)
Racers above 22.
High-Performance Racers have ratios above 24

Hullspeed:
Again, this is an area where we see the 1.34 times the square root of the waterline length tossed about like it is gospel. The reality is the more moderate versions of the newer finer bow, fuller stern types have proven to be closer to 'semi-displacement' type hullforms and so routinely sail in a range of 1.5 times the square root of the waterline length.

In the most past issue of Sailing World there was an interesting couple paragraphs dealing with theoretical hull speed which touched on this very issue. I am quoting here:

“Waterline’s affect on hull speed is theoretical and not absolute. As a hull goes faster, the bow wave stretches to the point where the bow and stern wave become on wave cycle, whose wavelength is equal to the waterline length. This brings us to wave theory. “

“The speed of a wave (in knots) is equal to the square root of the wavelength (in feet) multiplied by 1.34. If your boat has a waterline length of 32 feet, the theoretical hull speed is 7.6 knots. The waterline length is thought to limit the hull speed because if the boat goes any faster the stern waves has to move further back taking the trough between it and the bow wave along with it. As the trough moves aft, it causes the stern to drop, making the boat sail uphill.”

“Except for planning designs, sailboats typically can’t generate enough power to go any faster and climb their own bow wave. But a boat with extra volume in the stern can exceed its theoretical hull speed because the extra bouyancy prevents the stern from dropping into the trough. By the same token, a fine-ended design might not achieve its theoretical hull speed if buoyancy in the stern is insufficient.” (Written by Steve Killing and Doug Hunter).

It was also thought that older designs which had longer heeled waterlines than their upright waterlines would sail at 1.34 times the square root of their heeled waterline length. That simply has not proven to be the case. While there may be some modest gains in speed when heeled, the gain is minute when compared to the speed of a boat with waterline length equal to the heeled waterline length of the boat with long overhangs.

Respectfully,
Jeff

[GordMay]

JeffH: As always, I appreciate your insightful and knowledgeable additions & corrections to my obviously incomplete posting.
Your general cautions regarding the utility of these ratios is right on the money.
Thanks, also, for presenting a more modern view of some of the numbers. Admittedly, I’m and old out of date landlubber.
And ...
Thanks for the J-28 information on Sailnet - I appreciate it.
Regards,
Gord

[GordMay]

Jeff: You're reference to "Sailing World" got me looking, and I found these from 'Sail'

“SAIL” Magazine’s 2005 Buyers Guide Online Articles:
http://www.sailbuyersguide.com/articles/default.cfm
Including
“Comparing the Ratios - by Jay E. Paris
Discusses ‘D/L’, and ‘SA/D’
http://www.sailbuyersguide.com/artic...gTheRatios.cfm
and
“Stability and the GZ curve” - by P.N.
http://www.sailbuyersguide.com/artic...TheGZCurve.cfm
and more ...

[witchcraft]

We like Carls Sail Pro Calculator. It has been useful for comparison purposes, of boats of similiar sizes.
We have forwarded this along to others who are looking at a couple of different boats, to assist them with comparing the vessels for cruising.
Cheers
Witchcraft

[Jeff H]

I would suggest that you also include a link to this discussion. While Carl's calculator is a helpful resource, it is generally misunderstood by those who have not actually looked at the formulas or analyzed their implications. Without carfully evaluating the specifics of the boat in question, the results may be next to useless in terms of the reality of the situation.

Jeff

[dustman]

I feel like it is worthy of note that vessels with long thin, well shaped hulls do not suffer the same fate as short fat boats, due to the fact that they do not create significant bow waves to climb.

[Don C L]

Originally Posted by Jeff H

It was also thought that older designs which had longer heeled waterlines than their upright waterlines would sail at 1.34 times the square root of their heeled waterline length. That simply has not proven to be the case. While there may be some modest gains in speed when heeled, the gain is minute when compared to the speed of a boat with waterline length equal to the heeled waterline length of the boat with long overhangs.

Respectfully,
Jeff

So do you not get the benefit of less wetted surface when not heeled in those older designs or is that a myth?

I too hold all the numbers in suspicion since I have a narrow, relatively tender boat that, once heeled, has a different response that does not seem accounted for in the numbers. And as well, though it may be knocked down or capsized more easily than a flatter, beamier hull, it is far more likely to bounce back up, which is of more interest to me.

[GordMay]

Carl's Sail Calculator v3.55 ➥ Sail Calculator Pro v3.54 - 3200+ boats

[Mike OReilly]

Thanks for the updated link Gord. I like Carl’s database. It’s interesting and fun to play with comparisons. From my limited experience I actually find the comparisons do generally track with reality, but I completely agree with Jeff’s earlier cautions that you have to be comparing apples to apples.

[Jeff H]

Originally Posted by dustman

I feel like it is worthy of note that vessels with long thin, well shaped hulls do not suffer the same fate as short fat boats, due to the fact that they do not create significant bow waves to climb.

This is partially true for the current generation of extreme width Open Class derived race boats. They tend to have comparatively full bow's so that they can plane earlier in lighter winds and so that they don't bury thier bow's when they collide with the back of a wave at very high speed (15-25 knots) while heavy air reaching.

Those boats actually produce very high upwind performance because they have huge sail plans that they can carry into pretty high winds due to their enormous stability and also because they have extremely efficient foils(both keels and rudders). They don't point as high as prior generation IMS derived designs but have a much better VMG because of thier higher speeds. They are typically in semi-displacement mode and so well exceed hull speed in winds above 6-8 knots.

Both of the IMS and the Open Class derived designs will outpoint and have better speed on all points of sail than the earlier longer overhang shorter water line boats. In the case of the IMS style boats they typically have a very fine entry which minimizes wave formation and produce much smaller bow waves than long overhang-short waterline boats. The net result is that thise boats not only shift to semi-displacement mode much sooner and easily exceed hull speed, but they also offer much better motion comfort in roll and pitch. That is why virtually all of the major cruising boat builders have shifted to that hull form.

Jeff

[Jeff H]

Originally Posted by Don C L

So do you not get the benefit of less wetted surface when not heeled in those older designs or is that a myth?

I too hold all the numbers in suspicion since I have a narrow, relatively tender boat that, once heeled, has a different response that does not seem accounted for in the numbers. And as well, though it may be knocked down or capsized more easily than a flatter, beamier hull, it is far more likely to bounce back up, which is of more interest to me.

The hulls on the current crop of extreme beam race boats do have a lot of wetted surface, but these tend to be very light boats for their length and are carefully shaped to minimize wetted surface. They also have very efficient keel and rudder foils so they actually have less wetted surface than either a similar length or similar displacement long overhang-short waterline boat.

What is not really apparent is that the water plane of these boats at any angle of heel (except perhaps dead flat-and even when dead flat it's narrower than it appears) is surprisingly narrow. It's all in how they are shaped.

These boats have huge amounts of stability and so can carry very large sail plans that allow them to have really exceptional light air performance despite their larger wetted surface.

Amazingly enough these boats typically have very high angles of the limit of positive stability and are self righting from inversion despite their large form stability.

Jeff

[Don C L]

Originally Posted by Jeff H

Amazingly enough these boats typically have very high angles of the limit of positive stability and are self righting from inversion despite their large form stability.

Jeff

I too find that amazing. Know of any videos and/or GZ curves for those boats offhand? Is this due to the deep keels with bulbs making them so unstable when inverted?