Good at Maths?

[Three Sisters]

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

Is there a line for this ?


wind.jpg Views: 127 Size: 86.8 KB ID: 166569" style="margin: 2px" />

[Just Another Sa]

Effect of beam to draft ratio and lwl / cubicroot(displacement) ratio on wave making drag of a hull.
Source: The Aero- and Hydromechanics of Keel Yachts by J.W. Slooff
foundable from books.google.

It is evident that Lwl/Bwl ratio has negligible effect compared to Lwl / cubicroot(displacement) ratio. In the pics Beam to draft ratio of 3:1 corresponds to Lwl/Bwl ratio of 5.04:1, while Beam to draft ratio of 6:1 corresponds to Lwl/Bwl ratio of 3.57:1
Both much wider waterlines than catamarans have of course, but negligible effect on wave making drag due to those differences. Weight / length matters far more and can not be compensated by better shape of hull.

[BigBeakie]

The subject under discussion is multihull hull forms, not displacement keeled monohull hull shapes. Extrapolating from one to the other is questionable, IMO.

If you find something from acknowledged multihull NA to the same effect (crowther, Shuttleworth, Irens, perhaps?) let us know.

I still contend that graphically plotting Lwl:Bh vs SA/Displacement is very indicative of sail performance for cats.

Can you find one that is clearly out of place?


Sent from my iPad using Cruisers Sailing Forum

[django37]

Originally Posted by Just Another Sa

It is evident that Lwl/Bwl ratio has negligible effect compared to Lwl / cubicroot(displacement) ratio. Weight / length matters far more and can not be compensated by better shape of hull.

Correct, in fact the best ratio of hullwaterline beam to hull debth is 2.5. Its difficult to understand, that some multihull designers still talk about waterlinelength to beam ratios.

[Just Another Sa]

Originally Posted by BigBeakie

The subject under discussion is multihull hull forms, not displacement keeled monohull hull shapes. Extrapolating from one to the other is questionable, IMO.

If you find something from acknowledged multihull NA to the same effect (crowther, Shuttleworth, Irens, perhaps?) let us know.

I still contend that graphically plotting Lwl:Bh vs SA/Displacement is very indicative of sail performance for cats.

Can you find one that is clearly out of place?

The effect of lwl/Bwl ratio on wave making drag is even less on narrow multihulls than on beamier monohulls. Extrapolation has nothing to do with it.
Lwl/Bwl has almost nothing to do with sailing performance of multihulls.
Even very high performance A-cats have gone for wider waterline beam.
A Class Catamarans – A Look at the State of the Art Part 2 - Carbonix

The current trend deviates significantly from the minimum wetted area ideal by being wide, very flat, and having a hard turn of the bilge.

[BigBeakie]

Well this is very good news! We can all look forward to "comfortable" cruising cats with reeealy wide hulls, and as long as they are built light, they will sail great in light airs. I want one of them! I wonder why there aren't any on the market yet?

Did you read the article you linked to? The very first sentence is: "As mentioned in Part 1, the extremely high length to beam (slenderness) ratio of each A Cat hull reduces the relative importance of wavemaking drag as a component of total drag. This is equivalent to saying that friction drag due to wetted surface is more dominant."

So the A class cats have extremely high (hull) length to (hull) beam ratios. Why? Why don't they make those RACING cats long and really fat, then?

Find me a good performance cruising cat with a Lwl:Bh of 5, 6, 7, even 8 and then we can discuss how they do it.

[Just Another Sa]

Originally Posted by BigBeakie

Well this is very good news! We can all look forward to "comfortable" cruising cats with reeealy wide hulls, and as long as they are built light, they will sail great in light airs. I want one of them! I wonder why there aren't any on the market yet?

Did you read the article you linked to? The very first sentence is: "As mentioned in Part 1, the extremely high length to beam (slenderness) ratio of each A Cat hull reduces the relative importance of wavemaking drag as a component of total drag. This is equivalent to saying that friction drag due to wetted surface is more dominant."

So the A class cats have extremely high (hull) length to (hull) beam ratios. Why? Why don't they make those RACING cats long and really fat, then?

Find me a good performance cruising cat with a Lwl:Bh of 5, 6, 7, even 8 and then we can discuss how they do it.

If you don't understand the difference between total hydrodynamic drag and wave making drag, please found out first and come back only after that to look again what I did claim and what did not.

A cruising cat with wide hulls on the waterline have excessive viscous resistance due to excessive wetted area, and are never going to perform well in light air.
Making heavy cruising cat with very narrow hulls still have excessive wavemaking resistance, and are never going to perform well in a bit more wind. You just loose the benefits for interior room a little wider hulls would have provided. But ignorant buyers can still be mislead by false claims of good performance due to high Lwl/Bwl ratio of those heavy cats.

[Just Another Sa]

Originally Posted by Just Another Sa

https://eprints.soton.ac.uk/46442/1/071.pdf

It seems some people continuing to have a debate have not bothered to read this link with some real world resistance measurements for hullforms used in typical catamarans.
In order to understand the results, it is necessary to first read chapter 4, and then 4.5.
The data is presented as resistance coefficient, and those chapters mentioned are needed to understand how to get resistance force from the coefficients. In particular it should be noted that different tests has different ratio between resistance force and resistance coefficient!
The Important conclusions are those in 7.2 and 7.3.

The relevant comparison would be either 4a vs 5c, or 5a vs 6c.
When separation between hull centerlines is 50% of lwl, and Froude number is 0.5, relevant resistance coefficients are in figures: 15d for 4a, 20d for 5c, 18d for 5a and 23d for 6c.
Wetted areas are:
0.348 for 4a, 0.277 for 5c, 0.282 for 5a, and 0.234 for 6c.
Total resistance coefficients taken from the mentioned figures at froude number 0.5 are approximately:
0.0100 for 4a, 0.00815 for 5c, 0.00835 for 5a, and 0.00725 for 6c.
Based on Chapter 4, resistance force is constant * wetted area * resistance coefficient, where the constant in the mentioned Frno is defined as 0.5 * density of water * speed^2. It is of course not a constant if any of those is changed but in the case I describe it is a constant.
Therefore the meaningfull merit for comparison is wetted area * resistance coefficient.
1000*WA*coefficient is:
3.48 for 4a, 2.26 for 5c, 2.35 for 5a, and 1.70 for 6c.
Lwl/Bwl ratios are: 10.4 for 4a, 9.9 for 5c, 12.8 for 5a, and 11.7 for 6c.
The results show that while 4a has greater Lwl/Bwl than 5c, it has much greater (+54%) total resistance. Why?
It's because because 4a is 51% heavier, while both have same lwl.
In fact the meaningfull merit for resistance comparison is 54% greater for the 51% heavier boat, or just 2% greater resistance for its weight.
So even if we are to compare resistance/weight, it turns out the greater lwl/Bwl leads to 2% greater resistance/weight at that data point of froude number = 0.5, or about 25% above hull speed.
The important conclusion of that is the same thing mentioned in chapter 7.2 and 7.3 on that pdf document!

7.2
Length:displacement ratio was found to be the predominant hull parameter, resistance decreasing with increasing length:displacement ratio as might be expected for higher speed displacement vessels.
7.3
The effect of Beam/draft on resistance was not large. ...
... In the main, increase in Beam/draft led to an increase in resistance in the lower length/displacement ratio range and a decrease in the resistance at the highest length/displacement ratio.

Heavy hulls have high drag and it's impossible to prevent that by making hulls narrower!

[catsketcher]

Thanks for the link

A few points if I may,

- the hulls tested have transoms immersed and have a deadrise of about 20 degrees. They also have low rocker (leading to the immersed transoms). This is not a typical sailing catamaran shape and may have some effect on the data.
- there is not testing done of hulls at different displacements. Catamaran hulls are interesting in that they have to be able to take a variety of loading conditions, from approximately double displacement (lee hull when flying a hull) to zero displacement (the windward hull when flying).
- Ferries and other motor cats do not need to generate significant dynamic lift to assist longitudinal stability.
- When sailing through a seaway, hull volume will be an important factor in dynamic characteristics - extra volume through wider hulls may increase pitch moment (even whilst increasing pitch damping)

So the data may be useful but it needs to balanced against what the evolution of raceboats has also developed. Theory has to be borne out by results. Hedley Nicol trimarans had wide hulls and were not as fast as early Crowthers of similar weight (although wetted area of the amas was a factor here too).

I think everyone knows that weight is a deal killer for performance and that a heavy cat will sail poorly compared to a lighter version. As most cats are semi-circular in cross section for wetted surface reasons this leads to the quick check of hull to beam ratios as a reasonable approximation for performance at a certain length. A fast cat will have less volume over a certain length and so can be narrower and shallower.

A class cats are still very thin compared to most large cats and are a hotbed of evolution. Real world testing and cut throat racing give us some of our best clues as to how sailing cats work. Interesting article from Carbonix

A Class Catamarans – A Look at the State of the Art Part 2 - Carbonix

cheers

Phil

[catsketcher]

I have one anecdote about weight.

When I first launched my 38ft cat she was just a shell with no interior (I had run out of money and the bushfire season was approaching my tree lined shed - we had fire come through 1 month after launch)

We out a 25 hp outboard on her and also put on one rudder - no interior apart from floors. She floated absurdly high - 20cm above lines - I guess she weighed half what she does cruising.

She could motor at at almost 13 knots with the motor flat out. Now she can hit 9 in week long cruise mode and 8.5 with full water (400kg)

Same hull, different loading

[Just Another Sa]

Originally Posted by catsketcher

I have one anecdote about weight.

When I first launched my 38ft cat she was just a shell with no interior (I had run out of money and the bushfire season was approaching my tree lined shed - we had fire come through 1 month after launch)

We out a 25 hp outboard on her and also put on one rudder - no interior apart from floors. She floated absurdly high - 20cm above lines - I guess she weighed half what she does cruising.

She could motor at at almost 13 knots with the motor flat out. Now she can hit 9 in week long cruise mode and 8.5 with full water (400kg)

Same hull, different loading

Double weight alone should not reduce speed of 38 ft cat from 13 knots into 9 knots with same propulsive power if the transoms are dry at full speed under full load. There must be other relevant factors present to cause that. They might or might not include at least the following:
- Unclean bottom in cruising condition.
- Reduced max power of the outboard due to increased resistance and thus reduced RPM below what is necessary to get the power it is capable of producing at higher revs.
- changed shape of propeller blades due to abrasion, cavitation, or impacts.
- Underestimate just how much heavier real world cruising load was or overestimate of how light the boat was at launch.
- Use of core material that has absorbed water and become much heavier as a result.
- wave interaction resistance peak the boat is incapable of passing in loaded condition, while it could keep a higher speed if it were already above that speed.

[Just Another Sa]

Originally Posted by BigBeakie

If you find something from acknowledged multihull NA to the same effect (crowther, Shuttleworth, Irens, perhaps?) let us know.

Guillaume Verdier:
Guillaume Verdier : «On défriche !» - Guillaume Verdier -

And especially this pic:
http://www.guillaumeverdier.com/wp-c...he-%C2%BB2.jpg
Gitana 17 cross sectional shape is substantially different from semicircular, with much wider waterlines and less hull draft regardless of the increased wetted area in static conditions. Being wider with the same length means less Lwl/Bwl ratio. But it's effect is negligible for wave making drag as they know displacement/length ratio is the important for that.

[catsketcher]

Thanks for the link

I don't think this backs up the assertion that fast multis are not slim. The hull shape in the article is flat bottomed for dynamic lift but if my translation skills are okay the drag is increased below 15 knots - pretty cool for an Ultime racer but not the shape a typical 40ft cat would be looking for - 15 knots is really fast for them. So the semi-circular hull section would be beneficial.

Also the Ulitme's themselves are very slim and have very fine hull/beam ratios so I think they still showcase the point that hull beam reduction is important in high speed performance.

So I think we still need to find a top notch multi racer with an 8-1 or 6-1 ratio. Then the race course will have shown that hull beam does not matter.

[StuM]

Originally Posted by Just Another Sa

Guillaume Verdier:
Guillaume Verdier : «On défriche !» - Guillaume Verdier -

And especially this pic:
http://www.guillaumeverdier.com/wp-c...he-%C2%BB2.jpg
Gitana 17 cross sectional shape is substantially different from semicircular, with much wider waterlines and less hull draft regardless of the increased wetted area in static conditions. Being wider with the same length means less Lwl/Bwl ratio. But it's effect is negligible for wave making drag as they know displacement/length ratio is the important for that.

Show me a cruising catamaran that regularly travels at over 15 knots and I'll accept that your link supports your argument. But the image clearly states that the "classic" i.e semi-circular shape performs better up to 15 knots.

[Just Another Sa]

Originally Posted by catsketcher

Thanks for the link

I don't think this backs up the assertion that fast multis are not slim. The hull shape in the article is flat bottomed for dynamic lift but if my translation skills are okay the drag is increased below 15 knots - pretty cool for an Ultime racer but not the shape a typical 40ft cat would be looking for - 15 knots is really fast for them. So the semi-circular hull section would be beneficial.

Also the Ulitme's themselves are very slim and have very fine hull/beam ratios so I think they still showcase the point that hull beam reduction is important in high speed performance.

So I think we still need to find a top notch multi racer with an 8-1 or 6-1 ratio. Then the race course will have shown that hull beam does not matter.

Seems that you are looking for me to prove something I have never claimed to be true.
What I have said is that reducing hull beam at waterline to substantially narrower than semi-circular hull sections require does not make the boat any faster, but instead slower. And that already proves lwl/bwl is far less important than some seem to think and weight /lwl far more important as well as wetted area, but not to the extremes. A small deviation from semi-circular hull sections does not spoil the performance in any way.