# What’s formula for estimating catamaran speed? Speed from length better than from design?

Discussion in 'Multihulls' started by JunkRat, Oct 31, 2020.

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### JunkRatJunior Member

Please respond with formulas and science, not opinions about what boat I should buy. Any boats mentioned are just hypothetical for example purposes.

Given basic stats and DLR, SA/D is there a formula to estimate the speed of a Catamaran on a beam reach in 20 knots of wind? This would allow me to compare widely different designs across different lengths.

I’m trying to understand all the tradeoffs. DLR and SA/D gives you an idea of how performant the boat is compared to other boats of the same length.

But I would like to compare across lengths and design types.

A 60 foot outremer has the living space of a 40-45 foot Lagoon. And costs a more.

Does a 52 foot Lagoon perform as well as a 45 foot Outremer?

Seems quite possible a heavier but longer boat may deliver same speed as a shorter, less comfortable but more performance oriented boat, at the same cost.

Also, is there a way to factor in the length/width ratio of the catamarans hulls? This seems yo be a factor but isn’t included in any formulas I’ve been using.

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### BlueBell. . . . .

JR,
Yes, but you know that already.
Long and skinny.
BB

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### Mr EfficiencySenior Member

when resistance = driving force, you get the speed figure. Obviously there is a matrix of factors, such as weight, length to beam ratio, wetted area, sail area etc, to consider.

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### oldmultiSenior Member

The simple way of doing a speed comparison is to use such formula's as Kelsall speed ratio, Bruce number, W performance factor by Bommer (?). They all work on the same basic principles length, weight and sail area which are the main speed controlling issues. If you want real refinement the OMR rule is available at the following site OMR Preamble http://www.mycq.org.au/omr/omr-preamble

This rule is used to rate multihulls in racing and gives a rating based on the true weight of the boat when sailing, the rig type and efficiency of the rig and the true sailing length of the multi when sailing. The rule is reasonably accurate as to the relative performance of a multihull compared to others. Beyond this Velocity Prediction Programs are the ultimate but are hard to use and expensive. Another approach is download the free Hullform version P9 from the following web site which will lead you to the Hullform software: https://www.storerboatplans.com/boat-design/hullform-9p-now-working-with-windows-10-download-links/ which has a section on hull drag in it after you input a close approximation of a hull shape. The hullform program demonstrates the effect of length to beam and EG weight on the drag of a hull. Have fun, there is a bit of work ahead if you want accurate answers.

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### gonzoSenior Member

The wave interference between hulls is an important factor on resistance too. Using a single hull and multiplying by two will give lower resistance values.

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### fallguySenior Member

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### DolfimanSenior Member

I have adressed the residuary drag of a sailing catamarans in a previous thread, with formulations and process valid for designs with Froude from 0,4 to 0,9-0,1 (the usual range for cruising catamarans), here attached with complete numerical examples from page 25 .
It is not an answer to your question, just an insight on the residuary drag issue involving two hulls which are, in sailing conditions, with different Lw, Bw, Displacement, Froude, ... + the wave interaction drag between them.
For the speed prediction itself, you need also to involve the friction drag component (>> to know the wetted surface and its variation with each hull displacement), the aero drag, the righting moment with heel, the sails thrust and side forces, ... in brief without a VPP integrating all that stuff, it is hasardous to discriminate two designs. It is my intention to do one day such VPP for the sailing cata issue within a spreadsheet application, but that takes time ...
Overall formulas based on ratios can be helpful to have order of magnitudes and trends, to start a new design for example, but they are not magic, a VPP tool with justificated data should be more reliable and accurate for a comparison of 2 designs.

#### Attached Files:

• ###### Residuary drag of sailing catamaran_V3.pdf
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### JunkRatJunior Member

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### JunkRatJunior Member

Turns out the Kelsall formula is even better. Simply calculate that for every boat, and then sort the results and you can see the long heavy boats mixed with the short fast boats. Then take the price and divide by the Kelsal number and you have Speed-per-dollar (roughly of course) and that number is good for comparing to your accommodations requirements.

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### guzzis3Senior Member

What is your ultimate goal ?

It sounds suspiciously like you are thinking of buying/building something. If that's the case you also need to realise that beam reach is probably the strongest point of sail for a cat. In the real world you spend half your time sailing into the wind. A boat that goes at 90 deg doesn't necessarily go well to windward. You almost might as well rank them by running speed.

If the real question is "which cats sail well?" that's a more complex answer.

And while you're on a beam reach it's not just about hull forms. The wind in your sails is trying to knock you over, so beam matters for example...

Anyway good luck.

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### DolfimanSenior Member

Following my previous quote #7, I finally did this VPP dedicated to a sailing catamaran, together with a Gene-Hull version for catamaran, posted here :
Gene-Hull Catamaran 3.0 and SA-VPP catamaran 1.0 https://www.boatdesign.net/threads/gene-hull-catamaran-3-0-and-sa-vpp-catamaran-1-0.65191/

The main feature to deal with for a sailing catamaran VPP is that the 2 hulls are in different sailing conditions (Displacement, Lwl (and consequently their Froude), Bwl, Draft Tc, wetted surface Sw, prismatic coefficient Cp, ...). Especially, the displacement distribution between the leeward hull and the windward hull is, instead of the heel angle as for a monohull, the guideline parameter to assess the sailing conditions and its limit. Order of magnitude, from the example given attached :
At heel angle 4° : D is 73% on leeward hull / 27% on windward hull
At heel angle 8° : D is 91% on leeward hull / 9% on windward hull
At heel angle 12° : D is 100% on leeward hull / 0% on windward hull (the windward hull is then off the water)

At contrary of a monohull, the heel angle variation is low and poorly informs the sailors about this displacement distribution, although a distribution roughly 70%/30% at just 4° heel within a uniform wind can become a critical 100%/0% in case of a gust. That leads to 2 very different ways of sailing a catamaran : the cruising one for which a 70%/30% can roughly be considered as a warning / a safety limit, the racing approach which at contrary try to sail at 100%/0% for an optimal speed , but needing a very reactive crew to ease the sheets when necessary.

In the figures showed in my example attached (speed, heel and displacement predictions in step 6/VPP), dashed lines are used when the windward hull displacement is less than 30% of the total, indicating that it is a more tricky sailing which requires either more attention from the crew (racing approach) or a sail area reduction (cruising approach).

An example of a 100/0 racing approach which can ended by a capsize ... ! :