Cat draft

I have run into a bit of WTF

I drew up a 25' cat with 25' waterline length and 20" waterline beam and 40" height per hull with 3m overall beam. It results in a draft of 22" at 2000lb displacement

Then to check I drew a one hull only and it results around 4" draft at 1000lb displacement? Widening to 40" waterline beam results again around 4" at 2000lb

Am I missing something about draft at displacement when hulls are paired for cat or could I be looking at some sort of bug in the softwares compatibility with cats?

Thanks

 

Nope, you've just run smack dab into the "law of mechanical similitude", which is a prick to all engineers, when changing dimensions and scantlings on stuff. Simply put, things don't scale up or down as you might think. Surface area goes up or down to the 4th power, volume up times 8, while stability is times 16. Yeah a real *****, welcome to yacht design.

To make the math work in your head, picture a 12" square box. You double it's size, simple right. Well the square box goes from a single sq. ft. on each side to 4 sq. ft. on each side, even though in your head it seems like it would be two per side. The same is true of weight. If your 12" square box weighs 10 pounds, when doubled it's 80 pounds, not what seem logical at 20 pounds. Surface area goes from 6 sq. ft. to 24 sq. ft. Volume is 1 sq. ft. as a 12" box, but once doubled, is 8 cubic feet, not 2 as you head tries to wrap around it.

A 25' long 20" wide box, will have a displacement in the 2,000 pound range at 9.25" of immersion. Of course, if it's a hull shape, multiply the displacement of this hypothetical box by it's Cp, assuming there's no rocker. Lets say you have a .55 Cp, the displacement for this 25' long 20" V bottom (no rocker) will be about 1,100 pounds.

 

Man if you can get your head around that then you doing very well indeed! I just wanna take a 4x4 to mine trying to make sense of that! If I want to use a donger twice as big do I grab an 8x8 or 16x16 :/ :/ :/

So is this an actual physical state or a convention?

One block of wood on the scale is 1kg, adding a second block will read 2kg

If one of them floats 1cm deep. Throwing the other one in the bowl, they will both float 1cm deep each. Bridge them with a paddlepop stick and they will suddenly sink heaps deeper?

I really cant get my head around the law, is that an actual physical state or are the computed results ignored :/

 

No voodoo science involved here, recalculate your original computations, which have clearly suffered from an error.

 

It's not a convention, but simply physics (read reality) and yeah, at first it sucks, but do yourself a favor and draw a 12" square box. Measure the are and pick a weight. Then double it in physical size. The physics become clearer once you've done this and shows why we sometimes go crazy when a poster asks to build a replica of a 200' long frigate, just reduced to 30' (how hard could it be?).

 

What Par has told you is the absolute, not merely a convention. Mr. E is right that there is no voodoo here. It is just ordinary solid geometry at work.

Borrow some children's building blocks. Or if you have a table saw then make up 8 blocks that are shaped as cubes. The size is not important if all of the little cubes are the same.

You are going to double the dimensions of one block that is shaped like a cube.. There are three dimensions, length, width, and height. Place one block on the table, now one on top of that one, we have doubled the height, now double the width by adding two more blocks to the right or left of the first pair. Great we have doubled the size in two dimensions but we have not attended to the third dimension. Now you must add a block behind each one in the stack that you just built. That takes care of doubling the size in the depth dimension. You used 8 blocks to do this experiment.

Add to the fun by imagining that you will triple the size of the cube.......you will need 27 blocks.....keep going.....Quadruple (4 times) the size and you will need 64 blocks. All we are doing is multiplying length times width times height......4x4x4= 64

I hope that helps a little bit.

 

Hi guys, yeah going to a cube twice as big is understandable that will take 8 cubes the same size

Are you saying that choosing to use two of something as in going to a pair of connected hulls to use for a cat is scaling as in doubling the size? I fail to see where 8 hulls are getting stacked

Messabout
I start with one of your blocks 12"x12"x12" in the software. I see the draft of 1.9" at 10lb, now I want to use just two of your blocks connected and see the draft at 20lb. I increase the beam to 24" to show two blocks next to each other. The draft remains the same at 1.9" for 20lb. This is the results in the software

Question is, I feel that if the two blocks are separated and connected at the separated gap, the draft should still be in the 1.9" region at 20lb. Should it be so?

 

As far as cats are concerned, if your two hulls are identical (same length, breadth, and depth; same offsets), then a total cat displacement of 2000 lbs. implies that the displacement of each hull is 1000 lbs. This should not change even if the separation between the hulls changes.

We don't know the details of what you've done, and you haven't posted any pictures. Heck, we don't even know what software you are using.

If the calculated displacement for a single hull is not half of what is calculated for two hulls, then something is wrong; either the hulls are not identical, or there is a problem in the software you are using, or ...

 

I am using Hulls Designer from Carlson. Its just a simple proggie in which you can draw up a boat using hard chines really quickly and run nesting. So far its been great with one monohull already built and performing to spec. The cat seems to have stumped it

Both hulls are identical as you can only draw one side. I have drawn one hull and its displacement at 1000lb is good. Monohull is made by drawing half a boat, the other side builds as mirror on the wireframe model

Cat is built by drawing a complete hull away from centreline and that distance is drawn as bridgedeck. That is one hull and half bridgedeck to centreline. The other half is mirrored on the wireframe

The calculated displacement for the single hull is not half of what is calculated for the paired hulls

After the drawing, it is saved then nesting is done, shows ply sheets on which you lay all the panels and frames and save to files for cnc or hand cutting

I can upload the dxf save of the model or the .hull file

 

Saqa I think you are mostly right. I would suspect your software is not handling the catamaran configuration. Is there a setting you need to change so it shares the mass and displacement volume between two hulls? Though if its a sailing cat you may need to apply the total displacement to one hull to take account of the windward hull lifting from the water as it heels.

If you get one hull with a 4" draft given a displacement and set of dimensions then a second hull of the same dimensions will do the same even if connected together, provided of course that the mass is evenly distributed. This is a little simplistic but fundamentally you are right.

Agree with PAR as to an 8-10" draft at 1000lb, give or take a guess at your hull shape, I assumed a higher CP then went back and reread his post properly. If your original displacement of 2000lb was applied to one hull then a 22" draft would not be surprising.

 

JRD, I have been playing around with my original drawings so they have changed a lil

Currently the single hull sits 5.9" at 1000lb
9.9" at 2000lb

Its a vee hull

The paired hulls sit 4.9" at 500lb
27.4" at 1000lb
28.1" at 2000lb
The vee on the paired hulls are slighty different to the single hull now due to playing around earlier but overall simillar

 

Why is the draft important ?

 

If the boat is really going to sit 28" deep at rest then prolly be very inefficient and unusable underway if it has total hull height of 40"... time to rethink the boat!!

But if it actually is 9" or less then I am prolly n the ok side

I really have no idea if that is a reasonable reasoning or I am just speaking outa my arse..... I am very inexperienced with boat building

 

I admire your tireless enthusiasm, you are not short on perseverance !

 

Many multi hulls will favor the hull to be a semi circle , so the depth will be 1/2 the hull water line beam.

Hull Surface area slows multihulls at all speeds , the semi circle has the least area to drag thru the water.