Quick Question

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.

 

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.

 

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...

 

Stability

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

 

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.

 

real examples

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

 

Hmm... like I said... quick question...
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?