Good at Maths?

[Heath68]

Hi All,
I have an excel worksheet that purports to calculate multihull performance based upon LWL, Sail area (main plus jib I think) and Displacement. All of the calculations Ive seen for calculating "speed" or potential thereof have looked at LWL/Bh.

The excel sheet seems to calculate an SA/Disp ratio and then a Base Speed in Knots. The comments say "The Multihull Dynamics, Inc. website has used the term Base Speed to do comparisons of performance potential. It results in a projected average speed of a boat over a 24 hour period under average conditions. It uses sail area, waterline length and displacement in the equation :
Base Speed = 1.7*(Lwl^0.5)*(SA^0.352)/((Disp*2240)^0.253)
(Lwl is design waterline length in feet, SA is sail area in feet squared displacement is in long tons.)
It is used in Europe and other locations for handicapping multihull races."

So my question (to anyone that's good at maths) is does this formula look correct? The reason I ask is because some cats work out much fast/slower than I would expect.

Heath

[yeloya]

This formula doesn't take into account the Lwl to hull beam ratio and wetted surface. Hull beam is something that no yard is willing to give and difficult to obtain. It shows how slick the hulls are. Everyting else equal, this makes a huge difference in the base speed.


Cheers


Yeloya

[django37]

Originally Posted by Heath68

Hi All,
I have an excel worksheet that purports to calculate multihull performance based upon LWL, Sail area (main plus jib I think) and Displacement. All of the calculations Ive seen for calculating "speed" or potential thereof have looked at LWL/Bh.

The excel sheet seems to calculate an SA/Disp ratio and then a Base Speed in Knots. The comments say "The Multihull Dynamics, Inc. website has used the term Base Speed to do comparisons of performance potential. It results in a projected average speed of a boat over a 24 hour period under average conditions. It uses sail area, waterline length and displacement in the equation :
Base Speed = 1.7*(Lwl^0.5)*(SA^0.352)/((Disp*2240)^0.253)
(Lwl is design waterline length in feet, SA is sail area in feet squared displacement is in long tons.)
It is used in Europe and other locations for handicapping multihull races."

So my question (to anyone that's good at maths) is does this formula look correct? The reason I ask is because some cats work out much fast/slower than I would expect.

Heath

This is a much too simple formula, and you cannot use dimensions given by designers or yards. You should weigh and measure each boat, because some boattypes weigh twice as much as specified by designer/yard, and some are slightly ligther (weight includes Water, diesel and waste). Yes, I have weighed and measured more than 100 cruising multihulls as rating officer in Denmark. The best of the Texel-variations are the Aussis OMR and the UK MOCRA rating rule.

Or better - look at statistics from races - where of course helmsman/crew blur the results.

[Just Another Sa]

Originally Posted by Heath68

Hi All,
I have an excel worksheet that purports to calculate multihull performance based upon LWL, Sail area (main plus jib I think) and Displacement. All of the calculations Ive seen for calculating "speed" or potential thereof have looked at LWL/Bh.

The excel sheet seems to calculate an SA/Disp ratio and then a Base Speed in Knots. The comments say "The Multihull Dynamics, Inc. website has used the term Base Speed to do comparisons of performance potential. It results in a projected average speed of a boat over a 24 hour period under average conditions. It uses sail area, waterline length and displacement in the equation :
Base Speed = 1.7*(Lwl^0.5)*(SA^0.352)/((Disp*2240)^0.253)
(Lwl is design waterline length in feet, SA is sail area in feet squared displacement is in long tons.)
It is used in Europe and other locations for handicapping multihull races."

So my question (to anyone that's good at maths) is does this formula look correct? The reason I ask is because some cats work out much fast/slower than I would expect.

Heath

In order to calculate "speed" or potential thereof, the 2 most important factors are wind over water and sea state. Any formula missing those 2 is not predicting really anything about speed, real or potential. Also righting moment for the relevant direction, not just laterally, has plenty of effect on how much sails can be up and used for propulsion. The part of sail area reefed away has no effect on speed, and any formula pretending to predict speed based on total sailarea instead of usable one is just bar talk. Typically boats can use more sails downwind than upwind in light air, the quoted formula ignores that also.
Having said all that, I must point out that formula has some limited merit while analyzing typical boats with typical dimensions of the same type, and not any with something extreme or even close to that.
If you use it to compare catamaran with bridgedeck cabin with a open bridgedeck cat, the results are nothing but misleading. The difference in windage alone is more than enough to make the results incapable of predicting even average speeds. Comparing cats and trimarans (and proas, etc) is also too far off, as there are significant differences in wetted area not taken account. And then draft of boards or keels have an effect as well as rig height, especially upwind. All that and some more combined makes such formulas very fuzzy to say the least.

[Tusitala]

unfortunately all the above is true, there's just no easy way to get a true perfomance indicator without a lot more info. a once popular method of determining power to weight ratios is called the Bruce number. take the square root of the sail area and divide it by the cube root of the displacement. an answer resulting in a number of 1.5 or above put boats into the power to weight ratio of racing boats, while a number under that was more of a cruiser. obviously taking hull shapes and dimensions into account plus exactly how much the designer was dreaming regarding displacement can infuence real world perfomance. Still, it's a simple calculation to get you in the ball park

[Heath68]

Thanks everyone for your input.. oh well.. back to the drawing board

[BigBeakie]

"This formula doesn't take into account the Lwl to hull beam ratio and wetted surface. Hull beam is something that no yard is willing to give and difficult to obtain. It shows how slick the hulls are. Everyting else equal, this makes a huge difference in the base speed."

Cheers

Yeloya

Exactly right. What we are trying to do is have a metric that puts a class of boat, in this case cruising catamarans, on a level playing field to get a feel for their performance characteristics. It is not precise, it is pretty crude, but the following is quite indicative.

Plot Lwl:Bh vs SA/Displacement. Get the data from Multihull Dynamics. Those guys get the Lwl:Bh from any source they can, but they get it. They talk directly to the designers, they get owners to measure it, they go measure it.

The Lwl:Bh is the "slipperyness" ( if there is such a word) of the hull shape. It indicates wetted surface, hull resistance, wave making characteristic, ...all rolled up into one stat. And, yes, I do realise it is not quantitative, but you can make a useful qualitative assesment between a boat with a 12:1 Lwl:Bh vs a boat that has 8:1. They will be very different. The sail power needed to get them to have the same boat speed in the same wind strength, will be very different. Or, conversely, the ability to sail in light winds, (or sail at all!) will be very different.

Then you have how heavy a boat is, the displacement, and the sail area that gives the force to move the boat. When you plot these two metrics, you get a pretty good indicator of what a boat will be like. In the ball park, anyway.

Notice that a fat hulled cat (Lwl:Bh below 9:1) with high displacement will need lots of sail area and/or higher winds to move it against the hull resistance. Notice also that a slippery boat (11:1 or better) with lower displacement would need much less sail area and/or wind to move it.

There are follow on implications for this, such as payload capacity, engine use hours, passagemaking daily distances, ease of sail handling & associated deck layout and equipment required, etc.

I would upload a sample plot showing several boats bit it's too big for CF.

[Thalas]

Speaking as a FP fanboy, I remember being very surprised that the "blocky and heavy as F*#&" Lagoons tended to do very well in the ARC rallies. How was this possible?! They had such windage when my FPs were so sleek and sexy! I'm guessing that since most crossings are downwind journeys, the windage isn't that big a factor (or may even act to push the Lagoons forward better).

There are just so many factors that affect performance. I'm curious to see how the Saona 47 performs, but at the end of the day, I'm a cruiser. Would it be fun to be on a gunboat on a beam reach racing an Outremer? Hell, yeah. But unless you're on the water, it all seems to be theoretical.

[valhalla360]

The answer is 42. (google it if you don't get it)

Way too many variables for one calculation to give a definitive measure of performance.

[Just Another Sa]

Originally Posted by BigBeakie

"This formula doesn't take into account the Lwl to hull beam ratio and wetted surface. Hull beam is something that no yard is willing to give and difficult to obtain. It shows how slick the hulls are. Everyting else equal, this makes a huge difference in the base speed."

Cheers

Yeloya

Exactly right. What we are trying to do is have a metric that puts a class of boat, in this case cruising catamarans, on a level playing field to get a feel for their performance characteristics. It is not precise, it is pretty crude, but the following is quite indicative.

Plot Lwl:Bh vs SA/Displacement. Get the data from Multihull Dynamics. Those guys get the Lwl:Bh from any source they can, but they get it. They talk directly to the designers, they get owners to measure it, they go measure it.

The Lwl:Bh is the "slipperyness" ( if there is such a word) of the hull shape. It indicates wetted surface, hull resistance, wave making characteristic, ...all rolled up into one stat. And, yes, I do realise it is not quantitative, but you can make a useful qualitative assesment between a boat with a 12:1 Lwl:Bh vs a boat that has 8:1. They will be very different. The sail power needed to get them to have the same boat speed in the same wind strength, will be very different. Or, conversely, the ability to sail in light winds, (or sail at all!) will be very different.

Then you have how heavy a boat is, the displacement, and the sail area that gives the force to move the boat. When you plot these two metrics, you get a pretty good indicator of what a boat will be like. In the ball park, anyway.

Notice that a fat hulled cat (Lwl:Bh below 9:1) with high displacement will need lots of sail area and/or higher winds to move it against the hull resistance. Notice also that a slippery boat (11:1 or better) with lower displacement would need much less sail area and/or wind to move it.

There are follow on implications for this, such as payload capacity, engine use hours, passagemaking daily distances, ease of sail handling & associated deck layout and equipment required, etc.

I would upload a sample plot showing several boats bit it's too big for CF.

In multihulls lwl / Bh is variable even with a given total weight and displacement. Heelingmoment causes lee hull to immerse more and windward hull of a cat or mainhull for trimaran to pop up. That changes lwl /Bh for all the hulls in the water. As soon as there is enough wind for that to happen those numbers treated as constants do not represent the real world and are meaningless. In a cat that means that cross sections under water will not be anywhere near semicircular. They can be close at midships, but at both ends far from that.
The minimum wetted area for a case of 25% of displacement on the windward hull and 75% on the leeward hull does not have semicircular cross sections at any displacement. Yet many people keep insisting semicircular as an optimum for minimum wetted area. And it is that but in only one given heelingmoment and one given total displacement.

Furthermore there are cases when increasing beam at a design stage decreases wetted area and even total drag at a given speed and weight and length. See for example:
https://eprints.soton.ac.uk/46442/1/071.pdf
and pay attention to Bh / draft_hull ratio, labeled as B/T ratio in the linked pdf.
If 2 boats have the same weight, the one with less lwl typically has also less wetted area. In some cases this also means it has less drag at slow speeds, in others the opposite. Near the hull speed whenever wavemaking dominates a shorter lwl has always more drag, unless we are talking about planing hulls, like most powerboats or fully foiling ones like moth.

There is even rather common mistake on the effects of prismatic coefficient. 2 different hulls can have same displacement, same length, same cross sectionals shape, and same prismatic coefficient and as a result same largest cross sectional area, while having significantly different distribution of displacement along length and different wetted area as a result. Even some documents from the same source linked above have that mistake.

I should also point out that greater drag coefficient does not necessarily mean greater drag at a given speed. This could be the case if drag is defined as a product of wetted area, speed squared and drag coefficient and water density and some constant depending on units used if the wetted area is different.

And what about the lwl/bwl ratio. There is a big difference in the results, depending on if you are comparing 2 hulls with same lwl and different displacement or 2 hulls with same displacement and different lwl.
In the document it's same lwl of 1.6 meters, and that has very significant effect on the result. The heavier model always has more drag at the same speed. there is no reason to believe same would apply if displacement would be the same.
It's not about finding sources and repeating them, but about understanding them! There are a lot of people in various forums and internet web pages who think they do understand but in fact do not.

Everything is far more complicated than those simple formulas would let you believe.

[Just Another Sa]

Originally Posted by Thalas

But unless you're on the water, it all seems to be theoretical.

Did you read the opening post on this thread?
How about the headline?
It's supposed to be theoretical, math always is, even when correctly applied to something in practice.

[arsenelupiga]

Originally Posted by Just Another Sa

Did you read the opening post on this thread?
How about the headline?
It's supposed to be theoretical, math always is, even when correctly applied to something in practice.

math is useful but if it does not describe experienced reality, is badly applied and should be thrown away and replaced. Too many try to hang on badly applied math model and twist it till infinity, I have experienced.

See monohull polar prediction math model. Noone can replicate these speeds, yet naval architects continue to use them. Totally useless application of math.

[catsketcher]

Equations are used all the time to compare boats. Our compatriots in monohulls use a variety of rules to compare boats. The winner of the Hobart race is not necessarily the first over the line but the first on corrected time - that is the time after a formula based on the rating of the boat's elapsed time is applied.

In Australia we use the OMR rule for our big races like the Gladstone. It seems to work pretty well and although line honours is well sought after the overall winner of the race is the corrected time winner.

These ratings are well developed and give a pretty good indication of a boat's performance. They have been honed over many years. They do not cover all aspects of performance - Jeff Cruise in the video attached talks of people putting blisters on the hulls to increase beam at the measurement points so the rules have to be considered against designers and builders attempts to get around them. There were even cases of builders putting hidden taps inside their multis to drain water that had been put in the floats during weighing (This designer/builder got warned off with threats - bad old days of the sport). So the rule needs to be easy to use and requires a level of self compliance but it will leave certain things out, like hull beam, as this can be "cheated" by bump points. It doesn't mean hull width is not important for speed, but as racing boats are mostly circular in hull section, the fineness ratio will be derived somewhat from other measurements like LWL and displacement. And you can't fudge this (unless you put in water during weighing!).

2016 OMR Review

As for ratings not being sailed to in the ARC there could be many reasons. The ARC has racing crews in some boats pitted against live aboard cruisers in other boats. A manufacturer could put a racing team in their cruiser and sail it to the max against a couple in a different type of cat who are under autopilot and taking it easy all the way. It is an invalid method of comparison.

It would be better to seek comparisons in a proper race, where all boats are sailed hard by race crews, like the Gladstone or even better Airlie Race week, that has around the buoy racing, windward, leeward and every thing in between.

cheers

Phil

[Thalas]

Originally Posted by Just Another Sa

Did you read the opening post on this thread?
How about the headline?
It's supposed to be theoretical, math always is, even when correctly applied to something in practice.

I did. My comment was a polite way of stating that the task was so far beyond the capabilities of a guy with a spreadsheet that it remains theoretical.

Don't get me wrong, plenty of talented people use math to do everything from launch (and now land) rockets to designing the most efficient airplane wings.
So no, math is NOT always theoretical as SpaceX is using it to attain real world results.

The problem with using this for sailing is the confluence of the surprising complexity of the elemental factors (unlike an airplane wing with very specific contortion parameters, sails have an order of magnitude more complexity in their deformation/lift characteristics) and the lack of resources to calculate due to so little payoff as opposed to the market pressure to solve cheaper rocket delivery of satellites. We're just a bunch of guys who want bragging rights. How many resources are we going to put into that?

I'm not knocking your attempt at a formula, but as you admitted off the bat, obviously it is wildly incomplete as the expectation so often does not match the real world result. I admitted in my comment that I fell into the same fallacy. On paper, I believed the FP specs should make it faster than the Lagoon. Then I look at the ARC results and they don't mesh with the results from my factored parameters.

[arsenelupiga]

Originally Posted by catsketcher

It would be better to seek comparisons in a proper race, where all boats are sailed hard by race crews, like the Gladstone or even better Airlie Race week, that has around the buoy racing, windward, leeward and every thing in between.

cheers

Phil

may i suggest that for cruiser above race results are not much relevant:

1. boats are not loaded like cruising boats but stripped down.
2. Cruisers use AP all the time and little sail trim so performance of sail trim against different conditions is more important
3. boats races are in protected waters that do not replicate conditions when passaging.

Fastest boat that behaves in race of cruisers using above guidelines would be more relevant for me.