Quick math help - what are the dimensions for this Capital..

[Nerhesi]

Dimensions for a 300kton Sphere/ellipsoid Capital ship.

What would r1, r2 and r3 need to be for this ship?

Trying to determine overall hull dimensions for a 300kton capital.

Is it correct to assume 1 dton = 14 cubic meters? So I'd need a geometric shape with a volume of 300,000 X 14?

Thanks

 

[Ishmael]

Here is the method I use for that sort of thing.
I is an approximation, of course...

http://forum.mongoosepublishing.com/viewtopic.php?f=89&t=56475&hilit=hull&start=39

 

[Nerhesi]

That's a round about way to figure out how many squares though...

Ultimately, I was just going to figure out correct dimensions based on volume, then inside I overlay a 1.5 by 1.5 meter grid and assume 3.0 height.

But yeah... Jesus, at 300ktons, a elipse needs to be 4.2 million cubic meters, or 300m X 170m x 165m.

The annoyance is then how "big" each deck is because you are slowly getting smaller. So you may need to break out the "slice of an elipse surface area formula" to determine each deck at 3m intervals (height of each deck)

 

[Reynard]

The formula to determine the volume of a sphere is 4/3π multiplied by r, the radius, cubed, where π, or pi, is a nonterminating and nonrepeating mathematical constant commonly rounded off to 3.1416. Since we know the volume, we can plug in the other numbers to solve for the radius, r.

 

[Nerhesi]

That I knew - no problem. I was just confirming that 1 Traveller dton is 14 m3 cubed; which that post above did confirm for me.

 

[GypsyComet]

At 55 decks high, my recommendation for deckplanning this ship is to ignore the fuel, and keep as many of the other contents away from the surface of the ship as possible.

The trick for figuring out each deck is easy with drawing software. The length vs width of each deck will always keep the same ratio (300:170), so you can whip it up *once* and scale it the other 27 times. Each size is used twice, once each above and below the equator. To get one of the dimensions of each deck other than the equator, draw up an ellipse with one of the other two ratios, either 300:165 or 170:165. You can now pull either the length or width of each deck from that, and let the deck ratio take care of the other dimension.

 

[Nerhesi]

Actually ended up being 45 decks (assuming 3 meters height per deck). I'm probably going to end up just doing 41 decks to be exact, and assume 30,000 dtons (60,000 squares) of armor are somehow accounting for the missed tonnage.

Ultimately, I ended up with an Ellipsoid that is:

157m long x 95 meters wide x 68 meters high - those are measurements yielding approximately 4.2 million cubic meters, or 300k displacement tons.

Ok.. time to get to work.. ugh.

 

[GypsyComet]

Actually ended up being 45 decks (assuming 3 meters height per deck).

Three meters of open space, or three meters from deck to deck? I ask because 45 decks is only 135m counting deck-to-deck, which matches none of your stated dimensions.

 

[Jeraa]

Actually ended up being 45 decks (assuming 3 meters height per deck). I'm probably going to end up just doing 41 decks to be exact, and assume 30,000 dtons (60,000 squares) of armor are somehow accounting for the missed tonnage.

Ultimately, I ended up with an Ellipsoid that is:

157m long x 95 meters wide x 68 meters high - those are measurements yielding approximately 4.2 million cubic meters, or 300k displacement tons.

Ok.. time to get to work.. ugh.

Unless I am missing something, that is wrong. Even assuming a rectangular prism (which would use all available space), those dimensions only total 1,014,220 cubic meters (157x95x68, or just over 1 million cubic meters), not 4.2 million. A cubic ship with dimensions of 160 meters gives a total volume of 4,096,000 cubic meters.

A 4.2 million cubic meter ship (with roughly the same proportions as your ship) would be closer to 250 meters long, 150 meters wide, and 108 meters high. And that is assuming a rectangular slab of a ship.

 

[Nerhesi]

I've blathered a bit.

The Radii are 157m, 95m, and 68m - which when plugged into 4/3πabc ends up with approximately 4.25×10^6

A 300,000 dton capital ship is 300,000 x 14 cubic meters (based on the assumption that a traveller cubic ton is 14 meters cubed), so that results in approximately 4.2 x 10^6, correct?

---------

The height, being 68m x 2 (as 68 is the radius) ends up being 136m, which is approximately 45 decks. I assume deck to deck - is this a wise ratio? or is it too little? I kind of assume 2.6 meters plus 0.4 or so of "deck floor".

What am I off on gents?

 

[Ishmael]

That's a round about way to figure out how many squares though...

I'm afraid it is not.
Given 300kdton ellipsoid hull with dimensional ratios of 4:2:1, for example.

volume= 4,200,000m^3 and a bounding box of ~8,021,400m^3
the intermediate 'boxes' volumes are the bounding box divided by the product of the dimension ratios or, ~1,002 and approximate 'box' lengths of 10m thus the apprimate dimensions will be 400:200:100 meters. This is effectively a sphere squished and stretched inside a bounding box. By working out the surface area of the bounding box itself and multiplying by .5236, you can get a dirty estimate of surface area as well.

of course, different fineness ratios will give different results.

btw, although the popular usage of 14m^3 = 1 dton, a 1.5 meter square 3 meters high as is used in many deckplans actually comes to 13.5m^3, but the difference is negligible given the leeway the number of squares in a deckplan is given.

 

[Nerhesi]

So Ishmael.. what are you saying exactly?

300k dton spheroid cap ship does or does NOT mean 600,000 1.5x1.5x3 m squares? And does that not fit in a 315 x 190 x 136 meter ellipsoid?

 

[GypsyComet]

I'm seeing the numbers flip from totals to radii, which might explain the problem...

 

[Nerhesi]

I'm seeing the numbers flip from totals to radii, which might explain the problem...

You are correct Gypsy - that was my initial mistake, I stated total length/width/height rather than the radii. Radii is correct.

 

[Ishmael]

So Ishmael.. what are you saying exactly?

I'm saying ( and showing ) that my method is not a round about way of figuring out how many squares.
It is a way of estimating the length, width and height of an ellipsoid given a volume and fineness ratios for l:w:h.
That's all...

 

[Nerhesi]

So Ishmael.. what are you saying exactly?

I'm saying ( and showing ) that my method is not a round about way of figuring out how many squares.
It is a way of estimating the length, width and height of an ellipsoid given a volume and fineness ratios for l:w:h.
That's all...

Great I thought I had done my math incorrectly. I meant it was a round-about way to determine volume, which obviously wasn't your intent - simple misunderstanding. Yeah, I just plugged in various values into the ellipsoid volume equation till I ended up with a nice ratio I liked..

 

[pasuuli]

How about a series of decks as shells in your 300kt sphere?

Assuming the outer radius is 100 meters...

(4/3 pi r cubed = 4,175,467 cubic meters = appx 300 kt)

Assuming half of the volume is dedicated to machinery and fuel...

And assuming each shell is 3 meters tall, then we have decks until we reach 50% volume, or:

Deck 1: radius 97 m, 26274 tons
Deck 2: radius 94 m, 24674 tons
Deck 3: radius 91 m, 23124 tons
Deck 4: radius 88 m, 21625 tons
Deck 5: radius 85 m, 20176 tons
Deck 6: radius 82 m, 18776 tons
Deck 7: radius 79 m, 17428 tons


More fully laid out (with total volume represented in [square brackets]):

Deck 1: radius 97 m, 26274 tons [8.7%]
Deck 2: radius 94 m, 24674 tons [16.9%]
Deck 3: radius 91 m, 23124 tons [24.6%]
Deck 4: radius 88 m, 21625 tons [31.8%]
Deck 5: radius 85 m, 20176 tons [38.6%]
Deck 6: radius 82 m, 18776 tons [44.8%]
Deck 7: radius 79 m, 17428 tons [50.6%]
Deck 8: radius 76 m, 16129 tons [56%]
Deck 9: radius 73 m, 14881 tons [61%]
Deck 10: radius 70 m, 13683 tons [65.5%]
Deck 11: radius 67 m, 12535 tons [69.7%]
Deck 12: radius 64 m, 11438 tons [73.5%]
Deck 13: radius 61 m, 10391 tons [77%]
Deck 14: radius 58 m, 9394 tons [80.1%]
Deck 15: radius 55 m, 8447 tons [82.9%]
Deck 16: radius 52 m, 7551 tons [85.5%]
Deck 17: radius 49 m, 6704 tons [87.7%]
Deck 18: radius 46 m, 5909 tons [89.7%]
Deck 19: radius 43 m, 5163 tons [91.4%]
Deck 20: radius 40 m, 4468 tons [92.9%]
Deck 21: radius 37 m, 3822 tons [94.1%]
Deck 22: radius 34 m, 3228 tons [95.2%]
Deck 23: radius 31 m, 2683 tons [96.1%]
Deck 24: radius 28 m, 2189 tons [96.8%]
Deck 25: radius 25 m, 1745 tons [97.4%]
Deck 26: radius 22 m, 1351 tons [97.9%]
Deck 27: radius 19 m, 1008 tons [98.2%]
Deck 28: radius 16 m, 714 tons [98.5%]
Deck 29: radius 13 m, 471 tons [98.6%]
Deck 30: radius 10 m, 279 tons [98.7%]
Deck 31: radius 7 m, 136 tons [98.7%]
Deck 32: radius 4 m, 44 tons [98.8%]
Deck 33: radius 1 m, 2 tons [98.8%]