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Old 04-01-2023, 06:07 AM   #11
whswhs
 
Join Date: Jun 2005
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Default Re: let's build a ship

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Originally Posted by Rupert View Post
My suggestion of taking the ratio of flotation/weight and multiplying it by draught to get total hull height gives a height of 115 inches, and thus a freeboard of 71 inches, just under six feet.

With a height of about 9.5 feet and an effective volume of 4915 feet if the ship is treated as a simple block this gives a top surface of ~513 square feet, and with a beam/length ratio of 1:5 a beam of just over 10 feet and a length of ~50.6 feet.

Overall the ship's probably a little wider with that being the waterline beam, and a little longer due to not being a simple block.

And yes, this gives a deck area larger than that which the surface area and armour rules do - the latter assume each face of the vehicle is 1/6th of its area, which only applies to cubes, spheres, and a few other shapes and this ship is not one of them.
I agree with your calculation's results. I thought about doing it that way, but I had doubts about whether the linear approximation was sufficiently consistent with the formula for draft. If draft is figured as the cube root of weight, then it seems as if there ought to be a cube root in the computation of total height as well, and the difference of the two ought to yield freeboard.

I certainly agree about the deck area being a function of length and beam.
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Old 04-01-2023, 06:20 AM   #12
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Default Re: let's build a ship

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Originally Posted by mlangsdorf View Post
64" of freeboard on a 44" draft seems pretty reasonable. A man of normal height, standing in a rowboat next to Dola's Fortune, can grab the top of the deck and pull himself up, but it's definitely a climb.

21" of freeboard seems dangerous low for a sea-going ship. It feels more appropriate for a recreational canoe on a placid lake than anything you'd want to take out where there are serious waves. 3 Beaufort has 2'+ waves, so you'd be pumping the bilge in weather but the mildest. The higher freeboard version doesn't run into problems until 5 Beaufort, which is edging towards severe weather.
Looking at this further, I notice that the actually usable volume of Dola's Fortune is 4096 cubic feet, of which 1245 cubic feet goes for accommodations. That leaves 2851 cubic feet. If I assume that 90% of that is full of miscellaneous cargo, that gives 51,000 pounds. That gives draft of 41 inches and freeboard of either 67 or 24 inches.

Earlier I obtained a draft of 30 inches for the empty ship, which gives freeboard of either 78 or 35 inches.

It does look as if I still need to use Submarine lines to get the full height, at least if the ship is going to be viable on blue water.
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Old 04-02-2023, 01:40 PM   #13
Polydamas
 
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Default Re: let's build a ship

I think the only way to have a useful conversation would be with links to skteches and formulas on an external site. Trying to do it on a purely verbal basis is useless.

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Originally Posted by whswhs View Post
Now, let's guess at the actual dimensions of Dola's Fortune (this is what I was puzzling over on the other thread). For this I have to extrapolate from Vehicles.

We have the area of the top deck, which is 333 square feet before deduction for the mast. If we approximate its shape as an ellipse, we can estimate the area of the rectangle that encloses it by multiplying by 4/π to get 424 square feet. If we assume a 5:1 length:beam ratio, we get 46 feet long and 9 feet wide.

If we treat Dola’s fortune as a submersible, we multiply its volume by 62.5 to get a flotation rating of 307187.5 pounds. Taking this as its loaded weight, and assuming Submarine lines, gives us draft of 9 feet. Since its draft is 44 inches with a normal load, we get freeboard of 64 inches, for total height of 9 feet from keel to top deck. Alternatively, we could use the Average multiplier of 1.2 instead of the Submarine multiplier of 2, which would give us 65 inches, resulting in a freeboard of 21 inches. Would that be better for a 49-ton sailing ship? It seems more like the dimensions I’m used to seeing.

Unfortunately, 46 feet x 9 feet x 5.3 feet is 2194 cubic feet, which is less than half of 4915 cubic feet. There’s a major error factor here somewhere. Even using 9 feet as the height only gives us 3726 cubic feet. And that’s for a rectangular solid that includes a lot of space outside the hull. Something’s not right here, but I’m not sure what.
I think beam-to-length ratio is defined under Hydrodynamic Lines vel sim.

For modelling the shape of a ship better than a rectangular prism, have you looked at reconstruction plans of various ancient ships? There are a good set for a roundship in "Kyrenia II: Building a Replica of an Ancient Greek Merchantman" (PDF coming by email)
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Last edited by Polydamas; 04-02-2023 at 02:00 PM.
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Old 04-02-2023, 02:11 PM   #14
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Default Re: let's build a ship

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I think beam-to-length ratio is defined under Hydrodynamic Lines vel sim.
It is, and in my original post I said that "it has Average hydrodynamic lines, probably at the low end of 5:1 length-to-beam ratio (p. 10)."
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Old 04-02-2023, 03:40 PM   #15
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For modelling the shape of a ship better than a rectangular prism, have you looked at reconstruction plans of various ancient ships? There are a good set for a roundship in "Kyrenia II: Building a Replica of an Ancient Greek Merchantman" (PDF coming by email)
I've received that. Thanks! From a look at the diagrams, it seems that a round ship, at least, can be approximated as an ellipsoid. Unfortunately the formulae for ellipsoids are inelegant and a pain to work with. However, in approximating the horizontal cross section as an ellipse, I got partway there, and I think that using Average lines to figure the draft may have also gone partway there, in that the increased draft from a ship with no hydrodynamic lines probably reflects the ship being wider at the top than at the bottom. So maybe I can get by with the calculations I've done here.

I don't actually want to do numerical integration of surface area and volume; if I can get something that's within a factor of 2 that's probably close enough for gaming.
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Old 04-02-2023, 04:07 PM   #16
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Default Re: let's build a ship

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If I assume that 90% of that is full of miscellaneous cargo, that gives 51,000 pounds. That gives draft of 41 inches and freeboard of either 67 or 24 inches.
That's certainly within the right range for Bronze Age ships, although a freeboard of 2 feet would be dangerously low for an ocean-going ship unless it had some mechanism to prevent water getting into the hull (like a Sealed/Waterproof deck and coamings around hatches to limit water washing across the decks from getting below decks). A freeboard of ~5-6 feet would be adequate for an open-hulled coaster or an ocean-going ship for a sea like the Mediterraneean.

OTOH, Bronze/Iron Age navigators were fearless about taking small boats with low freeboards across rough seas. (e.g., this boat). I guess they just did a lot of bailing.

I'd leave precise freeboard/draft choices up to the designer within the ranges you've worked out. Higher freeboard means slightly more seaworthy against rough seas, and slightly harder to board, but also less handy for other purposes if draft is relatively low (in particular, a shallow draft sailing ship or boat would have trouble holding a straight course when running at an angle to the wind, forcing them to "crab" to hold their course). Insufficient draft might make a ship top-heavy and prone to poor handling in rough seas or when making hard turns.

Last edited by Pursuivant; 04-02-2023 at 04:14 PM.
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Old 04-02-2023, 04:53 PM   #17
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Default Re: let's build a ship

One thing to remember is that relatively small ships like these will ride up waves rather than ploughing through them as long as the wave frequency isn't too high. Thus they don't need as much freeboard amidships as a heavier craft might.

Of course if such a small ship runs into a sudden storm (such as you can get in the Mediterranean at the beginning and end of the sailing season) or choppy waters (such as places like the Bay of Biscay can have) it can end up swamped very quickly.
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Old 04-02-2023, 05:02 PM   #18
Polydamas
 
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It is, and in my original post I said that "it has Average hydrodynamic lines, probably at the low end of 5:1 length-to-beam ratio (p. 10)."
ooh, missed that line, sorry!

The deck plan of Kyrenia II looks like a lens or a vesica pisces, but treating the ship as half an elipsoid might be easier than treating it as half a lemon. My calculus is rusty and its nice to use available formulas rather than having to derive things. This is back-of-the-envelope game math not a nautical drafting package!
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Old 04-02-2023, 09:10 PM   #19
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Default Re: let's build a ship

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I don't actually want to do numerical integration of surface area and volume; if I can get something that's within a factor of 2 that's probably close enough for gaming.
Especially if you're the GM. You'd already be the one deciding how deep the water was at any particular place.
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Old 04-02-2023, 09:21 PM   #20
whswhs
 
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Especially if you're the GM. You'd already be the one deciding how deep the water was at any particular place.
True, but actually I'm more interested in whether the belowdecks space is ample or a cramped crawlspace.
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