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Sailboat ratios: SA/DISP; DISP/LOA

SA/Disp; Disp/LOA

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#101 12 metre

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Posted 15 July 2014 - 06:42 PM

Worth taking a look at the law of mechanical similitude (scaling) as it applies to sailboats:

 

http://www.books-for...rent-sizes.html

 

In summary, if you double the dimensions of a sailboat (hull & rig)

L, B, and Draft  will double (21)

SA and WS will increase by 4 times (22 )

Displacement will increase by 8 times (23 )

Stability will increase by 16 times (24)

 

So besides having the advantage of a longer sailing length, a proportionately bigger boat has the same SA/WS, but much greater sail carrying ability.  This means you can either increase SA while holding the hull dimension constant (increasing SA/WS), or hold SA constant while reducing beam which reduces WS, again increasing the SA/WS. 

 

This explains why larger cruising boats tend to have greater L/B ratios (i.e. relatively skinnier)



#102 Grey Dawn

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Posted 15 July 2014 - 09:14 PM

Good explanation. In other words, bigger is better, as we suspected. Also more expensive. Do $ go as the cube of dimension like displacement?



#103 12 metre

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Posted 15 July 2014 - 10:27 PM

Good explanation. In other words, bigger is better, as we suspected. Also more expensive. Do $ go as the cube of dimension like displacement?

Oh yeah, forgot to mention that one. 

 

Pretty much. Would give a decent ball park number.  Certainly better than using LOA alone, for which there is no correlation

 

Of course, it goes without saying that the $/lb  (or $/L3) is not going to be the same for a Catalina and a Swan. 



#104 DDW

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Posted 16 July 2014 - 02:03 AM

Good explanation. In other words, bigger is better, as we suspected. Also more expensive. Do $ go as the cube of dimension like displacement?

 

Yep, both for purchase and maintenance. Peculiarly though, berthing costs only go up as ^1 of length, even though the boats take ^2 in space in the marina. A few marinas are catching on to this and making adjustments.



#105 Grey Dawn

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Posted 16 July 2014 - 02:21 AM

I just checked the prices of new Jeanneau cruisers on Yachtworld and they do seem to increase roughly as the cube of length. It's about $150K for 33 feet going to $1300K for 64 feet. The extras add a lot of variation in the price and, of course, there are more of them in the big boats. 



#106 Alex W

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Posted 16 July 2014 - 04:42 AM

Good explanation. In other words, bigger is better, as we suspected. Also more expensive. Do $ go as the cube of dimension like displacement?

 

Yep, both for purchase and maintenance. Peculiarly though, berthing costs only go up as ^1 of length, even though the boats take ^2 in space in the marina. A few marinas are catching on to this and making adjustments.

 

Shilshole Bay Marina does.  It's a big reason for me having a 29.5' boat (they include the bow pulpit, so +1' on LOA on most designs).  A 30' slip is $332/mo, or $11.09/foot, while a 34' slip (next size up) is $406.64/mo or $11.96/foot.   The extra per foot is to account for the slip being wider.  That $900/year is a pretty big difference and covers haul outs and bottom paint every other year.



#107 boat_alexandra

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Posted 16 July 2014 - 09:59 AM

I think the calculation doesn't take into account the higher windspeeds aloft, which gives further advantage to the larger boat.

 

Bigger isn't better, it's just faster.

 

It costs $100 per month in the marina (or $4 per day) for a 27ft boat.   It's based on length, so catamarans are the same heh.

 

 So I'm anchored.. what's the point in paying when you can anchor?  



#108 Py26129

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Posted 16 July 2014 - 02:06 PM

 

Good explanation. In other words, bigger is better, as we suspected. Also more expensive. Do $ go as the cube of dimension like displacement?

 

Yep, both for purchase and maintenance. Peculiarly though, berthing costs only go up as ^1 of length, even though the boats take ^2 in space in the marina. A few marinas are catching on to this and making adjustments.

 

Shilshole Bay Marina does.  It's a big reason for me having a 29.5' boat (they include the bow pulpit, so +1' on LOA on most designs).  A 30' slip is $332/mo, or $11.09/foot, while a 34' slip (next size up) is $406.64/mo or $11.96/foot.   The extra per foot is to account for the slip being wider.  That $900/year is a pretty big difference and covers haul outs and bottom paint every other year.

 Our club has not caught on yet but I fear I may be on my way to teaching them :-(  

 

Fees are calculated based on the following formula:  Your bill = length x beam x $$$$ ,  where $$$ was around $3.50 last time I cared to check and length is advertised length. For billing purposes an IP31's  length = 31'.  Actual length wiht the bow sprit is 34'4"  add the davits + dinghy and we're looking at pretty close to 40' overall. 



#109 SemiSalt

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Posted 16 July 2014 - 02:10 PM

You can look at the variation by size either way. If you adopt the big boat as the norm, you will say that as boats get smaller, it gets harder to get enough stability. Hence small boats tend to be beamier than large boats.

The fact that designers use the D/L ratio suggests that, to a first order of approximation, the different sizes are more similar than different.

#110 Islander Jack

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Posted 19 July 2014 - 05:28 AM

Do $ go as the cube of dimension like displacement?

 

Yes, and for the price of a cubic foot of seawater, you can have yourself a unitless ratio.



#111 Bull City

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Posted 21 July 2014 - 06:36 PM

As you may have seen on other threads, I may be moving from a J-22 to an H-Boat. I don't want to go into the "why and wherefore" here, but I have noticed some interesting things in comparing sail and hull dimensions:

 

                      J-22               H-Boat

LOA               22.5'                27.25'
LWL               19.0                 20.70

SA                 223.0               260.0*

DISP             1,790                3,200
SA/DISP         24.2                  19.1

DISP/LWL     116.5                161.0

 

* I've run into differing figures, so I'm using the average.

 

Here are line drawings of the H-Boat:

 

lines 0
 

How would the performance of the boats compare?

 

 



#112 12 metre

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Posted 21 July 2014 - 07:13 PM

Based strictly on the numbers (not taking into account foil/rig efficiency) and assuming good sails and smooth/fair bottoms on both, I suspect the H-Boat to have a slight edge in just about all conditions except downhill in a stiff breeze.  But I believe they would be similar performers overall.



#113 mrming

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Posted 21 July 2014 - 07:25 PM

Based strictly on the numbers (not taking into account foil/rig efficiency) and assuming good sails and smooth/fair bottoms on both, I suspect the H-Boat to have a slight edge in just about all conditions except downhill in a stiff breeze.  But I believe they would be similar performers overall.


Yep - the J/22 will probably be quicker to accelerate in the very light, but the H Boat hull shape is very easily driven and it won't take much breeze before it gets up to speed and will edge out the J with it's slightly longer waterline length.

Things may be fairer on PHRF, but on IRC you could forget trying to race the H Boat in a J/22.

#114 Bull City

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Posted 21 July 2014 - 11:51 PM

PHRF mean reported ratings:

 

H-Boat:     198

J22:           201

J22 ODR:  189

 

The last time I raced our J22 with main & class jib only, our local PHRF asshole rated me 177.



#115 Bob Perry

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Posted 22 July 2014 - 03:16 PM

Based on those numbers I'd say the J22 would be much faster in light air. I suspect the SA/wetted surface ratio is much better on the J and that's what you are after for light air.



#116 carcrash

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Posted 22 July 2014 - 10:37 PM

Since this is Cruising Anarchy, cruise on over to this article by Starzinger. It was published in Cruising awhile back and he makes a pretty good case that average speeds over long periods can be explained by two numbers: SA/D and LWL. Vastly simplifying, LWL says how fast you can go and SA/D says how often you do that in real world weather.


One point raised in the article is that rigging stresses (loads), when high, cause cruisers to slow down.

I think this is exactly on target. When I was young, it seemed I could do anything, load was wonderful, it meant we were sailing fast. And when things went wrong, it was just the owner's ample checkbook taking the hit, us young buck crew would quickly heal, casts were cool.

Now, Its my money, and I don't want to keep earning more to replace money spent on a blown up chute. Now, I get hurt easily, and heal slowly, and sometimes, people my age don't heal at all.

So load has become something to avoid. I mean, really, really avoid.

So low D/L becomes important for a cruising boat. Really, really important. Its the primary driver for loads (therefore injury) and cost. For a given budget, and everyone has a budget, you can afford a certain amount of load, a certain amount of material (mass).

To go cruising, I want to carry along 5500 lbs of stuff, including full tanks, dinghys, food, clothes, rode, sails, tools, etc. I want a certain amount of volume for living spaces.

So what I have been doing is coming up with the lightest floating container for that stuff and volume, that has the lowest loads on every element.

Its different. That is for sure. Working structural details, so maybe this is the last design spiral, but I have sad that before. I will post pictures only when construction starts.




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