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Old 03-30-2023, 09:56 PM   #1
whswhs
 
Join Date: Jun 2005
Location: Lawrence, KS
Default let's build a ship

As an application of the discussion of ship design using GURPS Vehicles in another thread, I'm going to do a version of the ship from a recent campaign of mine.

Dola's Fortune is a Bronze Age merchant ship sailing a sea that's narrower than the Atlantic Ocean, but larger than the Mediterranean Sea. It has a mixed crew of various races of different sizes. Its crew includes half a dozen sailors, standing watch two at a time. Going by Vehicles (p. 75), the sum of its mast heights is 64 feet. At TL1, it can only have one mast (p. 9), so that mast is 64 feet. This requires a body volume of at least 4096 cubic feet (p. 9). The mast's volume is 26 cubic feet (p. 17).

It has a flotation hull. Since it's design for exploration rather than carrying bulk cargo, it has Average hydrodynamic lines, probably at the low end of 5:1 length-to-beam ratio (p, 10).This requires an increase in its volume by a factor of 1.2 to 4915 cubic feet (p. 16). Multiplying this by 52 pounds per cubic foot (p. 11) gives it a flotation rating of 255,590 pounds.

The mast carries a square-rigged sail with an area of 1638 square feet (p. 30). This weighs 1638 pounds and costs $1638. Thrust is 3276 pounds for a fresh breeze.

The controls are primitive and require one watchstander (p. 73) who occupies a roomy exposed crew station on deck (p. 75) that weighs 40 pounds, occupies 20 cubic feet, and costs $100. The crew, the armed guard, and the owners aboard sleep in hammocks (p. 77). Ten of these are for SM -1, weigh a total of 500 pounds, occupy 500 cubic feet, and cost $100; five are for SM 0, weigh a total of 500 pounds, occupy 500 cubic feet, and cost $100; one is for SM +1, weighs 225 pounds, occupies 225 cubic feet, and costs $45. The ship is large enough to have a bilge pump for free (p. 66). The total volume these take up is 1245 cubic feet, which leaves 3670 cubic feet.

The area of the body is 2000 square feet (p. 18). The area of the mast is 60 square feet. We assume that the structure is light, typical of sailboats, and expensive; this gives the body a weight of 15,000 pounds and a cost of $10,000 (p. 19). The mast weighs 720 pounds and costs $600 (p. 20). The body has 1500 hit points, and the mast has 120 hit points.

Dola's Fortune has heavy compartmentalization, which weighs 1500 pounds and costs $1500.

The body is armored at DR 6 on all sides except the top, which is DR 2. The armor is expensive wood. That's 9000 pounds and $4500 for the hull, and 600 pounds and $300 for the top deck (pp. 21-23). The PD is 2 for the top deck and 3 for the other faces (p. 24). The area of the top deck is 333 square feet, divided by 2 to leave room for the mast, to give 166 square feet (p. 94). Waterproofing Dola's Fortune costs $4120.

Total empty weight is 28,223 pounds. Crew weight is 3361 pounds. When empty, Dola's Fortune has a draft of 2.53 feet or 30 inches (p. 132). That leaves unused flotation of 227,367 pounds. I'll assume loose cargo at 20 pounds/cubic foot (p. 26) and 90% of the unused volume filled with cargo, for 66,000 pounds of cargo, bringing loaded weight to 97,584 pounds; that takes draft to 3.68 feet or 44 inches.

Size modifier per Vehicles is +6. Price is $21,503, which implies a maintenance interval of 136 hours, or about 45 minutes per day; this can be covered by crew members with Carpentry skill (p. 146). HT is calculated at 8 (p. 26).

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 Dolaís 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 Iím 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. Thereís a major error factor here somewhere. Even using 9 feet as the height only gives us 3726 cubic feet. And thatís for a rectangular solid that includes a lot of space outside the hull. Somethingís not right here, but Iím not sure what.
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Old 03-30-2023, 10:23 PM   #2
whswhs
 
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Default Re: let's build a ship

Hmmm. If we assume that Dola's Fortune is a half ellipsoid, with the full ellipsoid having a volume of 9830 cubic feet, then dividing by 4π/3 and by deck height of 9 feet gives us 261 square feet. Assuming a length:beam ratio of 5:1, we get length of 72 feet and beam of 14 feet. Multiplying 72 x 14 x 18 gives 18,144 cubic feet, or 9072 cubic feet for the lower half; that's certainly big enough to enclose 4915 cubic feet. Maybe it's TOO big . . .
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Old 03-31-2023, 02:30 AM   #3
johndallman
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Default Re: let's build a ship

Quote:
Originally Posted by whswhs View Post
Multiplying 72 x 14 x 18 gives 18,144 cubic feet, or 9072 cubic feet for the lower half; that's certainly big enough to enclose 4915 cubic feet. Maybe it's TOO big . . .
It isn't. You're calculating the "Block coefficient" there, one of several numbers used to measure hull forms. Low-tech ships generally have lower block coefficients than modern ones; yours is about 0.54, which is perfectly reasonable.
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Old 03-31-2023, 01:24 PM   #4
hal
 
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Default Re: let's build a ship

If instead of going the route you're going, you went for an approximation using a prism for the hull?

If you know the depth of your hull along with its length and breadth, you could cheat by using a prism for the main body whose depth is longer than what you need. Then calculate the volume of the prism whose depth is just the tip of the prism you don't need for your hull (thus, getting a smooth bottom). For instance, if you had a prism that measured 20 feet from the flat surface to its "ridge" line, figure out the volume of that prism. Next, figure out the volume of a prism that was 10' from its apex to its base. Subtract that smaller volume from the larger and you will have the basic hull's volume. To that, add a BEAK that is essentially a pyramid like shape to simulate its bow.

That should mostly describe an early bronze age style trireme or bireme no?
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Old 03-31-2023, 02:31 PM   #5
whswhs
 
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Default Re: let's build a ship

Quote:
Originally Posted by hal View Post
If instead of going the route you're going, you went for an approximation using a prism for the hull?

If you know the depth of your hull along with its length and breadth, you could cheat by using a prism for the main body whose depth is longer than what you need. Then calculate the volume of the prism whose depth is just the tip of the prism you don't need for your hull (thus, getting a smooth bottom). For instance, if you had a prism that measured 20 feet from the flat surface to its "ridge" line, figure out the volume of that prism. Next, figure out the volume of a prism that was 10' from its apex to its base. Subtract that smaller volume from the larger and you will have the basic hull's volume. To that, add a BEAK that is essentially a pyramid like shape to simulate its bow.

That should mostly describe an early bronze age style trireme or bireme no?
It's possible that it would. But I can't visualize the shape you have in mind from your description. Is it a stretched four-sided pyramid, or half of a pyramid (pointed at the front, flat at the back), or something else?
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Old 03-31-2023, 02:51 PM   #6
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Default Re: let's build a ship

Quote:
Originally Posted by whswhs View Post
If we treat Dolaís 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.
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Old 03-31-2023, 03:48 PM   #7
whswhs
 
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Default Re: let's build a ship

Quote:
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.
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.
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Old 03-31-2023, 09:15 PM   #8
hal
 
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Default Re: let's build a ship

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.
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Old 03-31-2023, 09:19 PM   #9
hal
 
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Default Re: let's build a ship

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...

:)
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Old 03-31-2023, 10:53 PM   #10
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Default Re: let's build a ship

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.
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