Quick Question

[Mat-C]

Quick question.
I was just looking at a pic of a 70ft boat designed by Bolger. The boat had an 12 foot beam... very long and slim.
Made me wonder.
All other things remaining the same, if you simply shortened the boat to say 35 feet, would it be any more stable?
(Yes, I know, the displacement would have to come down too...)

[PAR]

Oh if it were only as simple as this. The short answer is no it will not be more stable. The reason is the physical laws of relativity and mechanical similitude. You see things don't scale up and down proportionately, which is the rub. If you don't go far in terms of scale difference, then there are rudimentary formulas (none work very well) and rules of thumb (ditto) that apply, but a 50% reduction means a whole new design and whatever the previous design was or had, no longer applies. For example, lets take your 70 footer and half it (I know you only want to half the length, but lets just have some fun to keep the math simple). The surface area decreases by 4 times, which is cool because you have less boat to build, but you'll have 8 times less volume! The butt kicker is the stability will decrease by a factor of 16 times less then the previous model (can you say OUCH). What's that sound? Yes, the smacking sound of your kissing the idea good bye. Yep, I'm a butt head at times, we all have skills.

If you want a 35' x 12' boat, there are quite a few to pick from and no smacking sounds. In other words, if you want to make the 70' Bolger, a 65' truncated Bolger, then yes, you can because it's a less then 10% reduction, but much over 15% and you can toss every design element out the window, because you're starting from scratch.

[Submarine Tom]

Nicely put PAR. Yes, all of it...

-Tom

[Mat-C]

Thanks PAR...
1st up, apologies, I got my boats confused... I was thinking about the 50 ft Wyoming that you posted about elsewhere, so the dimensions were actually 50 x 8.5ft...
But that's imaterial... I don't want to scale the boat at all... it was a purely acedemic question.... I was looking at the Whyoming and thinking... gee that's long and skinny, I wonder how stable it is (yes I understand that long and skinny doesn't necessarily equate to lower stability) and then I wondered, but if it was shorter, would it actually be any more stable...?
So, if the beam was the same, the LCG the same and (unlikely) the weight the same, would the stability be any different?

[PAR]

A fat boat will have more initial stability then a skinny one, so a 50' x 10' will have more initial stability then a 50' x 8', given the same hull form. The problem is stability is measured a few different ways. For example a narrow, but longer boat will have less stability issues then a shorter but wider version in some conditions. In other words, the subject can get pretty complicated fairly quickly when attempting to make these types of comparisons.

[Mat-C]

Thanks...understand all that, but will a 40 x 8 have more / less / same stability as a 50 x 8... again, all else being equal and without 'external conditions' effecting things?

[PAR]

In a perfect world situation, a fatter beam/length ratio boat has an advantage only in initial stability, but less in other areas which real world yachts have to contend, such as longitudinal and maximum positive stability, for example.

To directly answer you, yes the fatter boat is more stable in some regards, but yachts don't work in perfect world fluids or environments, they get tossed around like a rubber duck in a bath tub at times, which is when you really start thinking about righting arms, roll moments, where the PFD's are located and angles of positive stability.

[DCockey]

Thanks PAR...
1st up, apologies, I got my boats confused... I was thinking about the 50 ft Wyoming that you posted about elsewhere, so the dimensions were actually 50 x 8.5ft...
But that's imaterial... I don't want to scale the boat at all... it was a purely acedemic question.... I was looking at the Whyoming and thinking... gee that's long and skinny, I wonder how stable it is (yes I understand that long and skinny doesn't necessarily equate to lower stability) and then I wondered, but if it was shorter, would it actually be any more stable...?
So, if the beam was the same, the LCG the same and (unlikely) the weight the same, would the stability be any different?

Boat is scaled in length only with the beam and draft remaining unchanged. Sections remain the same but the distance between stations changes.

If the total weight stays the same then the boat will trim lower when scaled to a shorter length. Whether it's more or less stable will depend on the hull shape.

If the total weight scales in proportion to the length change with the LCG staying at the same relative location (same station) and the Vertical CG staying at the same height, then the transverse stability in terms of forces and moments will be reduced in proportion to the length change. The non-dimensional transverse stability (normalized by the weight) will be unchanged.

[Paul Kotzebue]

Quick question.
I was just looking at a pic of a 70ft boat designed by Bolger. The boat had an 12 foot beam... very long and slim.
Made me wonder.
All other things remaining the same, if you simply shortened the boat to say 35 feet, would it be any more stable?
(Yes, I know, the displacement would have to come down too...)

If the boat is being scaled in one direction only (length), then according to the laws of mechanical similitude, displacement, wetted surface, and stability would be one half of the original. The "laws of relativity" do not apply ...

[cor]

When people see long skinny boats they often think of tippey unstable boats (like a canoe).

A better way to think through this problem is to think of the short boat first. If you had a boat that was 8x25 that would seem normal and no one would worry about the stability. If you take the same boat and "strecth" it out to 8x50, the stability is not going to decrease. Actually the stability will increase (about double). Making a boat long does not make it into a tippey canoe.

As Par mentioned there is a lot more to figuring out the stability than just the length and width.

[DCockey]

If the boat is being scaled in one direction only (length), then according to the laws of mechanical similitude, displacement, wetted surface, and stability would be one half of the original. The "laws of relativity" do not apply ...

That would be the dimensional stability in terms of roll vs applied forces and moments.

If same number of passengers move to the rail of both boats then the half-length boat will roll more. But if the half-length boat is only carrying half the number of passengers then it will roll the same amount as the full length boat.

Roll period would not change with the length only scaling.

How the applied forces and moments would change with scaling of the length varies with the causes of those forces and moments.

So it gets back to what is meant by "stability".

[Paul Kotzebue]

So it gets back to what is meant by "stability".

In this context I interpret "stability" to be equivalent to "righting moment".

[ancient kayaker]

Quick question ... All other things remaining the same, if you simply shortened the boat to say 35 feet, would it be any more stable? ...

Shortening the boat reduces the ratio of length/beam; short beamy boats of the same displacement tend to be more stable than long skinny ones. When it comes to stability, size matters more than length/beam ratio, for example RMS Queen Elizabeth, with length 1,031 ft and beam 118 ft has L/B = 8.7 which is “skinnier” than your examples but a lot more stable! As a general rule, if you make any single dimension of a boat smaller it will be less stable.

It depends what you mean by “stability”. You’d might assume it meant how much the boat resists heeling when you walk from one side of the deck to the other, which is how Paul K interprets your question; and he is correct of course. PAR, on the other hand has spent a lifetime trying to get customers to be realistic about their next boat so he is just as concerned with how boats handle in heavy weather, how far it will tip without flipping and whether it will keep its crew alive after a capsize: “stability” references probably fill up a yard or two of his bookshelves :) As a canoe and kayak paddler, I get :mad: when folk write about tippy canoes ... I’d want it to stay more or less level as some power boat’s wash passed underneath; righting moment is a good thing that I can have too much of!

Nonetheless, it’s an interesting mind experiment to scale a boat in one direction at a time. If you halve the length of a boat its righting moment will be halved - along with its displacement of course. Let’s not even think about what that does to the performance. Do the same across the beam and it can get strange; it might flop over on its side unless you reduce the depth at the same time so let’s halve beam and depth. Now the displacement is down to 1/4 but stability went down to 1/8th. So what happens to the righting moment if we just halve the depth? Not an awful lot, actually; for the first couple of degrees anyway. But in the previous case we had to reduce the depth and beam together so the metacentric height didn’t go nuts: but that’s another story ...

If you want to pursue it further, this expert is your man http://www.boatdesign.net/forums/boat-design/center-flotation-calculation-implications-30857-18.html#post353422


Well, that's what you get when you ask a quick question ;)

[wimal]

I would say the discussion of stability should be based on the righting lever than the moment as the righting moment would depend on the displacement of the vessel as well, and other reasons is that we always use righting lever and the area under the righting lever as a criterion to measure the adequate stability of a vessel. When the length of the vessel is shorten to half of it the righting lever may remain almost same provided that the breadth, draft and depth of the vessel remain same. The righting lever is the perpendicular distance between the line of action of buoyancy force and center of gravity. As long as vessel 's draft and hull shape remain same, transverse movement of the center of buoyancy relative to the center of gravity with the angle of inclination of the vessel would be almost same irrespective of the length. The advantage of vessel with high L/B ratio is for the resistance as economical speed depend on V/Sqrt(L) or Froude no. This would reduce the wave resistance and hence power required to propel a unit displacement of the vessel reduces. However as the length/beam increases the bending moments would be critical factor and the structural strength of hull is more important. This is just share my views on your discussion.

[aranda1984]

When it comes to stability, we have to talk about longitudinal and transverse stability.

I am talking sailboats here...

If you double the length of a boat at the same beam, you actually increase the wetted surface by 4 times (area squared) and the displacement by 8 times (cubed) and the longitudinal stability by 16 times. (The wind forces will be about 8 times more if the sail area is proportionally increased.

The transverse stability number created by catamaran designer James Wharram and his engineers is as follows:

Windspeed in MPH=(the square root of W times 0.5 BOA), times 0.682;
divided by (0.001785 times SA times H); and the whole thing multiplied by 0.555.

Where:

W=weight of boat in pounds
SA=Working sail area
H=Height of center of sail area from the waterline
BOA= Beam overall

LOA is not in the equation since a longer boat a racer can be lighter then a cruiser of half that size!
It is the total weight of the boat and the beam that matters and the center of the sail area the most...
This makes engineering sense since we are talking about forces acting on a certain radius trying to flip over a certain weight.

Regards,

Stephen I. M.

[DCockey]

When it comes to stability, we have to talk about longitudinal and transverse stability.

I am talking sailboats here...

If you double the length of a boat at the same beam, you actually increase the wetted surface by 4 times (area squared) and the displacement by 8 times (cubed) and the longitudinal stability by 16 times. (The wind forces will be about 8 times more if the sail area is proportionally increased.
..........

These comments relate to a different question than asked in this string. They are about what happens if all dimensions of a boat are doubled (or halved).

The question here is:
"So, if the beam was the same, the LCG the same and (unlikely) the weight the same, would the stability be any different?"In other words the LENGTH ONLY IS CHANGED, the cross sections are not. In this case if the length is halved the displacement is one-half and the wetted area is one-half.

As for stability, in this case the righting moment at a given heel angle) will also be one half. The GZ curve will be unchanged. (Righting moment is moment arm from GZ curve multiplied by displacement.)

The design which prompted the question above is a long, narrow powerboat, not a sailboat. Changing the length only of a sailboat design brings up the question of how the sail plan would be altered. It shouldn't be be scaled with the length, and the arrangement and possibly type of sails would likely be be changed if the change in length is substantial.

[Milan]

… Changing the length only of a sailboat design brings up the question of how the sail plan would be altered. It shouldn't be be scaled with the length, and the arrangement and possibly type of sails would likely be be changed if the change in length is substantial.

Bolger also designed some very narrow sailing boats. “Insolent 60” for example, 60 ft long 8ft wide.

As of altering sail plane, there are basically two ways to choose from: one is tall mast, (tall for the hull beam), and corresponding very deep fin, or keeping draft same and enlarging sail area with a second mast.

[terhohalme]

If you double the length of a boat at the same beam, you actually increase the wetted surface by 4 times (area squared) and the displacement by 8 times (cubed) and the longitudinal stability by 16 times.

Only if your ratios (Length/Beam, Length/Draft) and the shape of boats are similar. Then the beam also must be twise the original, not the same...

Have a cucumber, cut it on the middle. Now you have "same beam". Put one end on the scale and then the other end on the scale. Summarize results. How about your displacement? Or wetted surface?

Sometimes just use your own head instead of repeating sentences from others or text books.

To the original question, if beam is same, waterplane coefficient and block coefficient are same, the metacentric radius is only a inversed function of draft. When displacement is same, the daft is halved and metacentric radius is doubled. Now if the center of gravity from keel line stays original, the stability (GM = metacentric height) is almost doubled.

Complicated, but not difficult...

[aranda1984]

The original question was about a 70' long boat with a 12' beam....
If you scale this boat down to 35' length and if you want to scale everything to 1/2 size, at 6' beam (less wall thickness of the hull) you got nothing but a long row boat!

This is why the "cutting the cucumber into half" eaxample is probably what the original intention was behind the question.

I talked about a sail boat, because the forces are simpler to comprehend...
I have not seen the picture of the boat in question, but I would be surprised if anybody who built a sleek beauty like this would make it an ugly high house boat like structure.

Now I am assuming things.. we are all assuming things.. and we know what can happen when we are assuming things...

Regards,

Stephen

[Paul Kotzebue]

If you double the length of a boat at the same beam, you actually increase the wetted surface by 4 times (area squared) and the displacement by 8 times (cubed) and the longitudinal stability by 16 times.

That statement is not correct as written. If length, beam, and depth are all doubled the boat will then have 4 times the wetted surface, 8 times the displacement, and 16 times the righting moment. This assumes the weight and location of the center of gravity also scale proportionally.

[bruceb]

Many wooden work boat builders used to take a given "design" and add or subtract stations to vary the length plus or minus 15-20%. A 20% increase would usually give about a 40% increase in fish you could haul and a much "stiffer" feel when you were loading over the rail. If they could afford the engine/fuel/crew, the longer boat was also faster. Some of the older "up east" yards can probably still give details. I used to stay at a boat yard in the Med that seemed to specialize in adding extensions to all sizes of yachts and work boats-40's to 100+', they didn't seem concerned about adding 10-15' to an 80' boat. I asked how they decided how much to add- the answer was how big the cabin/swim platform needed to be- the boats always preformed "better". They always had plenty to business:) B

[Mat-C]

Hmm... like I said... quick question...:p
Thanks for all the replies. I was indeed thinking mainly about initial stability...

Since that was such a simple question ;) can I now expand on the idea...?

If I have a design for a say 30 x 10ft. For arguments sake, lets say its a hard chine displacement power boat that weighs 5 tons. Now, to increase the hull speed, I decide to stretch the boat to say 50ft, but don't need any more actual accomodation. So I keep essentially the same shape and still 10ft beam, but increase displacement by as little as possible.
What is likely to be the effect on ht einitial stability?