let's build a ship

[mlangsdorf]

Originally Posted by whswhs

If we treat Dola’s fortune as a submersible... 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.

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.

[whswhs]

Originally Posted by mlangsdorf

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.

That's useful. It sounds like the Submarine lines will give a more reasonable estimate of freeboard.

And also, assuming that the upper rim of the hull is a foot or two above the top deck, there's room even for the trollwife to stand up belowdeck amidship, and the smaller crew members can move about freely. If the ship's total height were only 65 inches it would be cramped belowdeck.

[hal]

Using a prism shape, when cut through, looks like an equilateral triangle cross section with the point downwards. If you remove the tip of the triangle, you get a paralellogram (sp?) With a short parallel side on the bottom.

The bow would be a half pyramid shape (as you called it) such that you have a flat deck.

Since it will give you a height (distance between parallel sides of top and bottom), you can use loaded weight vs weight of one cubic foot of sea water per cubic foot of water at 64 lbs per cubic foot.

Example: if hull is 1000 cubic foot in volume, max capacity is 1000 x 64, or 64,000 lbs. If hull plus gear, masts, sail, sailors, food, etc Is 38,400 lbs - the waterline will be .6 x the distance between top of hull surface and bottom of hull surface. If total weight is 32,000 lbs - then 32,000/64,000 is half the max weight, and thus, waterline is half the distance between the two parallel surfaces of the parallelogram.

The same principle works with fresh water, you just need to use the weight of Fresh water instead of sea water.

[hal]

Addenda:

It occurs to me to add this:

from the top down...

Your ship hull surface at the top will comprise of a rectangle (the original Prism shape seen from the top) plus a triangle for the bow combined to make a pointed rectangle combined shape.

So the bow's shape would be that of a pyramid sliced in half as it were.

It would be so much easier if I could draw a diagram and email it to you to your email address...

:)

[Rupert]

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.

[whswhs]

Originally Posted by Rupert

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.

[whswhs]

Originally Posted by mlangsdorf

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.

[Pursuivant]

Originally Posted by whswhs

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.

[Rupert]

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.