Figuring the tonnage of a flat sphere

[Bruce]

So, I know that a dton on a scale[sic] drawing for a T20 designed ship is 1.5 meters x 3.0 meters x 3.0 meters. That is the general block or space that is a dton.
So, if you want to figure out how to DRAW a circle of say 100 dtons.
Does anyone have a formula or a method of figuring out how many units of dtons that is? So when i go to draw it, I can say, this 100 dton circular hull is x number of units across. I guess I am looking for some kind of short cut so I don't have to draw a circle and count the units inside it.
When i say units, I mean the standard 1.5 x 3.0 x 3.0 meter scale.
I know pie r squared, but you must bear in mind I'm not a math wiz.

 

[TheEngineer]

Math

Hi !

area = pi*r^2 is just perfect
So
r = SQRT(area/pi)

Using 100 dTons thats 100*1,5m*3m = 450 m².
Pushed in the formula above results in
r = SQRT(450m²/PI) = 11,97 ~ 12 m radius.

OK ?

Best regards,

TE

 

[hunter]

Or search the net for cylinder volume calculators

 

[aramis]

Since a sphere is V=4/3 * Pi * r^2
and an circle is A= Pi * r^2
and an elipse is A= Pi *ra * rb
where r is uniform radius, ra is radius long, and rb is radius short

A flattened Sphere's volume should be V= 4/3 * Pi * ra^2 * rb

 

[atpollard]

The Volume of a sphere is 4/3 x Pi x r^3.

More Sphere data HERE


The Volume of a flattened sphere is 4/3 x Pi x b x a^2.
where b=radius of the short axis
and a=radius of the long axis

More sphereoid data HERE

[EDIT: Add the missing Pi]

 

[Bruce]

double check the deck

The Volume of a sphere is 4/3 x Pi x r^3.

More Sphere data HERE


The Volume of a flattened sphere is 4/3 x b x a^2.
where b=radius of the short axis
and a=radius of the long axis

More sphereoid data HERE

So if I have flattened sphere that is 3 meters in height and 12 meters in diameter the formula would look like this

4/3 x 3 x12^2 = 576
1.33 x 3 x 144 = 576

so this would be a circular slab, basically.

 

[atpollard]

Bruce,

if you really want a tall circle (like a tuna can) then it is just the area of a circle (Pi x r x r) times it's height.

More Data HERE

Don't forget that these are based on radius (half of the diameter).

12 meter radius would be 3.14 x 12 x 12 = 452.16 square meters of floor. 452.16 sq. meters x 3 meters tall = 1356.48 cubic meters. 1356.48 cubic meters x (1 dton / 13.5 cubic meters) = 100.48 dTons which is about 100 dTons.
-------------------------------------------

The flattened sphere formula is for a "flying saucer" like shape with curves everywhere (and was missing a variable - thanks Aramis).

For a flying saucer that was 3 meters tall and 24 meters across (a=24/2 = 12; b=3/2 = 1.5)

Volume = 4/3 x 3.14 x 1.5 x 12 x 12 = 904.32 cubic meters. 904.32 x (1 dton / 13.5 cubic meters) = 66.98 dTons.

 

[Bruce]

VEry helpful...

Bruce,

if you really want a tall circle (like a tuna can) then it is just the area of a circle (Pi x r x r) times it's height.

More Data HERE

Don't forget that these are based on radius (half of the diameter).

12 meter radius would be 3.14 x 12 x 12 = 452.16 square meters of floor. 452.16 sq. meters x 3 meters tall = 1356.48 cubic meters. 1356.48 cubic meters x (1 dton / 13.5 cubic meters) = 100.48 dTons which is about 100 dTons.
-------------------------------------------

The flattened sphere formula is for a "flying saucer" like shape with curves everywhere (and was missing a variable - thanks Aramis).

For a flying saucer that was 3 meters tall and 24 meters across (a=24/2 = 12; b=3/2 = 1.5)

Volume = 4/3 x 3.14 x 1.5 x 12 x 12 = 904.32 cubic meters. 904.32 x (1 dton / 13.5 cubic meters) = 66.98 dTons.

>> I guess where I always seem to get confoozeled about is diameter and radius. I like the flying saucer idea best. Tuna can just don't excite me, not like the cats.

So I have decided on a 30 meter across by 3 meters thick.

volume = 4/3 x3.14 x 1.5 x 15 x 15 = 1409.4675 = 104.405

That's pretty close, if a tad over 100 dtons. I am sure we could get the EXACT number in meters across to get to 100 dtons, but then we would end up with an odd number of squares when i go to map.

I do appreciate the help and clarifications. If I can see the formulae and examples, that means I can just plug in numbers like a monkey and get the answes I need.

 

[aramis]

Bruce:

You've mistaken cubic meters for Dtons... you've about 8 Dtons there...

a Dton is 13.5 or 14 cubic meters, or 500cu ft, depending on edition.

for that ratio, multiply by 2.4 both measures...

You're shooting for 1400 cubic meters, not 100.

 

[Bruce]

uh oh...

where did I do it wrong sir?

 

[Drakon]

reversing the process

So, I know that a dton on a scale[sic] drawing for a T20 designed ship is 1.5 meters x 3.0 meters x 3.0 meters. That is the general block or space that is a dton.
So, if you want to figure out how to DRAW a circle of say 100 dtons.
Does anyone have a formula or a method of figuring out how many units of dtons that is?

If you want to work the reverse, figuring how many tons in say, a 15 radius, 3 deck sphere, I have constructed a spreadsheet for that. How do I upload it?

But I think it's a better idea to go through the equipment list, assign each piece to one of the decks you plan on having, and work out the radius of each deck separately.

Of course if you want to do only a single deck, then forget what I said. Just figure out what it will be for a disk.

 

[TheEngineer]

Good Morning Bruce !

Guess Arams got irritated by "1409.4675 = 104.405"
For me it looks pretty.
And I would not care for a few dTons more or less, too.
But You should always have a look at the ceiling height.
Notice, that now the only location with a real ceiling height of 3m is in the center....

Regards,

TE

 

[aramis]

TE: Nope. I just missed the conversion to Dtons in there... Mea Culpa.

 

[Icosahedron]

I struggled for a long time with calculations for a 'flying saucer' that was lens shaped (ie slicing the top and bottom off a sphere and putting them together). I eventually derived the volume using volume of rotation, but I'm not sure if I ever figured out the surface area. Since you have the figures for an oblate spheroid, I'd go with that, or better still if you have multiple decks, as Drakon suggested just take each deck as a 'tin can' and leave the pointy bits as waste (or fuel).

 

[RandyT0001]

I struggled for a long time with calculations for a 'flying saucer' that was lens shaped (ie slicing the top and bottom off a sphere and putting them together). I eventually derived the volume using volume of rotation, but I'm not sure if I ever figured out the surface area.

I think your talking about a spherical cap.
http://mathworld.wolfram.com/SphericalCap.html

If you put it on a conical frustum then you might have your 'flying saucer' look.
http://mathworld.wolfram.com/SphericalCap.html

 

[Bruce]

Soooo....

To get close to 200 tons...We'll take the tuna can formula....


12 meter radius would be 3.14 x 12 x 12 = 452.16 square meters of floor. 452.16 sq. meters x 3 meters tall = 1356.48 cubic meters. 1356.48 cubic meters x (1 dton / 13.5 cubic meters) = 100.48 dTons which is about 100 dTons.

Then we slap on some suacers top and bottom....
But we will modify the size. bringing them to 22 meters across, 11 meters radius on the bottom.
20 meters and 10 meters radius on the top.

Bottom saucer:
Volume = 4/3 x 3.14 x 1.5 x 11 x 11 = 759.88 cubic meters. 759.88 x (1 dton / 13.5 cubic meters) = 56.287407 dTons

Top saucer:
Volume = 4/3 x 3.14 x 1.5 x 10 x 10 = 628.00 cubic meters. 628.00 x (1 dton / 13.5 cubic meters) = 46.518 dTons

Which puts us roughly at 203.30 [rounded up]

So our saucer would be ship would be 9 meters in height, 24 meters out at it's thickest edge, tapering at the bottom to 22 meters and 20 meters at it's top.

So the main deck, would be 3 meters thick, which is our standard and the upper and lower decks would have smaller foot prints, but the tapers could be used for fuel and waste space.

Tell me if I did this right please. OH and too everyone who has chimed in on this, thanks. When I look at the math pages, I get lost, but when I can just plug and play numbers in, I get a better sense of things. I do appreciate that.

 

[Icosahedron]

I think your talking about a spherical cap.
http://mathworld.wolfram.com/SphericalCap.html

If you put it on a conical frustum then you might have your 'flying saucer' look.
http://mathworld.wolfram.com/SphericalCap.html

Thanks for that, Randy. It's carefully filed away.
I wish I'd known about that site a couple of years ago, it would have saved many hours with pencil and eraser!