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Mass Math.md

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Constants

Uranium Density: 0.01905 tons per liter Tank Height: 187.5cm Ballast Height: 152cm

Ballast Block

The smallest unit of ballast.

Dimensions: 4cm x 21cm x 42cm Volume: 4 * 21 * 42 / 1000 = 3.528 liters Mass: 3.528 * 0.01905 = 0.0672084 tons

Ballast Stack

The largest common unit of ballest. Contains 75 blocks arranged 1 by 2 by 37, with an additional block on top.

Mass: 5.04063 tons

That's rounded to 5 tons.

42 x 42 x 152cm

Equations

Tank Wall Thickness: Outer Diameter / 25

Configurations

Determine how many stacks can fit within the part's cylindrical frame.

Tiny (5t)

Diameter: 62.5cm Inner Diameter: 62.5 * 24 / 25 = 60cm

Ballast Side: sqrt(60^2/2) = 42.42640687 Stack Side: 42.42640687 / 42 = 1.0101525445 Stacks: 1 ^ 2 = 1

Mass: 1 * 1 = 5 tons

hole width: 46cm

Small (20t)

Diameter: 125cm Inner Diameter: 125 * 24 / 25= 120cm

Ballast Side: sqrt(120^2/2) = 84.85281374 Stack Side: 84.85281374 / 42 = 2.020305089 Stacks: 2 ^ 2 = 4

Mass: 4 * 5 = 20 tons

hole width: 88cm

Large (120t)

Diameter: 250cm Inner Diameter: 250 * 24 / 25 = 240cm

Ballast Side: sqrt(240^2/2) = 169.7056275 Stack Side: 169.7056275 / 42 = 4.0406101786 Stacks: 4 ^ 2 = 16

Mass: (16 + 8) * 5 = 120 tons

sqrt((5 * 42) ^ 2 + (2 * 42) ^ 2) = 187.8297101 cm

5 x 2 blocks is possible, therefore there's room for an additional 8 stacks

hole width: 4 * 42 + 4 = 172

Jumbo (240t)

Diameter: 375cm Inner Diameter: 375 * 24 / 25 = 360cm

Ballast Side: sqrt(360^2/2) = 254.5584412 Stack Side: 254.5584412 / 42 = 6.0609152667 Stacks: 6 ^ 2 = 36

Mass: 36 * 5 = 180 tons

Hole width: 6 * 42 + 4 = 256

sqrt((8 * 42) ^ 2 + (3 * 42) ^ 2) = 358.8481573 cm

3 x 8 blocks is possible, therefore there's room for an additional 12 stacks.

360 - 254 = 106

sqrt(42^2 + 84^2)

Textures

1 pixel per 5 centimeters

Main body height: 1,875cm

2000 - 1875 = 125 / 5 / 2 =

1875/5 = 375

Margin at top and bottom for even 400 pixels: 15 pixels

1,875 + 62.5 * 2 = 2000