Something that has bothered me for a while is the treatment of hulls on
the Hull Size table (*Fire, Fusion & Steel* p.11). The assumptions
made in the descriptive text do not tally with the figures shown on the
table.

The relationship between Rate (tons of displaced liquid hydrogen) and Volume (cubic meters, or kiloliters) is obviously correct, for it assumes a simple equation (Rate × the volume of 1 ton of liquid hydrogen). But beyond this, the table fails.

For example, taking a Rate of 1. Where 1 ton of liquid hydrogen occupies 14 cubic meters gives a total internal volume of, obviously, 14 cubic meters. All of the calculations for material use and so forth are based around a default shell 1cm thick. Thus the length (diameter) of a spherical hull should be equal to the diameter required to produce 14 cubic meters in volume, plus 2cm. The following formulae are required:

V = (4 × pi × r^3)/3, or

r = ((3 × V)/(4 × pi))^(1/3)

where

r is the radius of the sphere (half the diameter)

V is the volume of the sphere

pi is a constant equaling approximately 3.142

Thus the diameter (length) of a sphere required to enclose 14 cubic meters is 2.99m. Adding on the 1cm shell gives a grand total for the length of a spherical hull of 3.01m (rounded).

Therein lies the first problem: the value of L listed for a hull rate of 1 is 3.2m, which would require a hull thickness of 10cm to achieve.

To calculate MV, the diameter of the hull (inclusive of the shell) is fed back into the spherical volume formula, and the enclosed volume is subtracted from the result. Using a diameter of 3.01, MV is thus calculated to be 0.28 cubic meters. If the initial calculation for the diameter of the enclosed hull is rounded from 2.99m to 3m (thus giving an overall value of L of 3.02m), then the value of MV would be 0.4 cubic meters (rounding to one decimal place) - providing the value indicated on the table.

If the given value of L is used, MV comes to 3.16m - a far cry from that listed for MV.

#### MegaTraveller Compatibility

The MegaTraveller design sequences assume that one ton of liquid hydrogen occupies not 14 cubic meters, but 13.5 cubic meters (a vessel with a UCP hull rating of 100 has an internal volume of 1,350 cubic meters - see the Referee's Manual). For those looking to engender better design compatibility between T:TNE and MT (particularly useful when re-engineering MT equipment under T:NE rules), I suggest using this value of 13.5 cubic meters in place of 14 cubic meters when dealing with FF&S volumes. For simplicity's sake, multiply all volume calculations expressed in terms of liquid hydrogen (including the volume of hydrogen fuel etc.) by 0.96 before applying it to your design.

#### The Formulaic Approach

Two approaches to the design of hulls can be used: the formulaic approach, providing more accurate results, or the table approach (coupled with interpolation) for a more easily referenced angle.

For the formulaic approach, start with the desired rate of the hull, then apply the following formulae:

Vol = rate × 14 (13.5 if using the MegaTraveller Compatibility suggestion)

L (Hull length) = (2 × ((3 × V)/(4 × pi))^(1/3)) + 0.02

MV = ((4 × pi × (L/2)^3)/3) - V

VehicleMV = MV × 1.7

#### The Table Approach

This approach follows the same manner as the published FF&S rules, but replace the standard table with that shown below.

Two tables are provided. The first uses 14m³ T:NE compatibility, the second 13.5m³ MT compatibility. Vehicle MV is provided as an alternative to the Chassis Size table, FF&S p.17.

HULL SIZE (1 ton = 14 cubic meters LHYD) |
||||
---|---|---|---|---|

Rate | Vol | MV | L | VehicleMV |

1 | 14 | 0.28 | 3.01 | 0.48 |

2 | 28 | 0.45 | 3.79 | 0.76 |

3 | 42 | 0.59 | 4.33 | 1.00 |

4 | 56 | 0.71 | 4.77 | 1.21 |

5 | 70 | 0.82 | 5.13 | 1.40 |

6 | 84 | 0.93 | 5.45 | 1.58 |

7 | 98 | 1.03 | 5.74 | 1.75 |

8 | 112 | 1.13 | 6.00 | 1.92 |

9 | 126 | 1.22 | 6.24 | 2.07 |

10 | 140 | 1.31 | 6.46 | 2.22 |

15 | 210 | 1.71 | 7.39 | 2.91 |

20 | 280 | 2.08 | 8.14 | 3.53 |

25 | 350 | 2.41 | 8.76 | 4.09 |

30 | 420 | 2.72 | 9.31 | 4.62 |

35 | 490 | 3.01 | 9.80 | 5.12 |

40 | 560 | 3.29 | 10.25 | 5.60 |

45 | 630 | 3.56 | 10.65 | 6.05 |

50 | 700 | 3.82 | 11.03 | 6.49 |

55 | 770 | 4.07 | 11.39 | 6.92 |

60 | 840 | 4.31 | 11.72 | 7.33 |

65 | 910 | 4.55 | 12.04 | 7.73 |

70 | 980 | 4.78 | 12.34 | 8.13 |

75 | 1,050 | 5.00 | 12.63 | 8.51 |

80 | 1,120 | 5.22 | 12.90 | 8.88 |

85 | 1,190 | 5.44 | 13.17 | 9.25 |

90 | 1,260 | 5.65 | 13.42 | 9.61 |

95 | 1,330 | 5.86 | 13.66 | 9.96 |

100 | 1,400 | 6.06 | 13.90 | 10.30 |

200 | 2,800 | 9.62 | 17.50 | 16.35 |

300 | 4,200 | 12.60 | 20.04 | 21.43 |

400 | 5,600 | 15.27 | 22.05 | 25.95 |

500 | 7,000 | 17.71 | 23.75 | 30.11 |

600 | 8,400 | 20.00 | 25.24 | 34.00 |

700 | 9,800 | 22.17 | 26.57 | 37.68 |

800 | 11,200 | 24.23 | 27.78 | 41.19 |

900 | 12,600 | 26.21 | 28.89 | 44.55 |

1,000 | 14,000 | 28.11 | 29.92 | 47.79 |

2,000 | 28,000 | 44.62 | 37.69 | 75.86 |

3,000 | 42,000 | 58.47 | 43.14 | 99.39 |

4,000 | 56,000 | 70.82 | 47.48 | 120.40 |

5,000 | 70,000 | 82.18 | 51.15 | 139.71 |

6,000 | 84,000 | 92.80 | 54.35 | 157.76 |

7,000 | 98,000 | 102.84 | 57.21 | 174.83 |

8,000 | 112,000 | 112.42 | 59.82 | 191.11 |

9,000 | 126,000 | 121.60 | 62.21 | 206.72 |

10,000 | 140,000 | 130.45 | 64.43 | 221.76 |

20,000 | 280,000 | 207.06 | 81.18 | 352.00 |

30,000 | 420,000 | 271.31 | 92.92 | 461.23 |

40,000 | 560,000 | 328.66 | 102.27 | 558.73 |

50,000 | 700,000 | 381.38 | 110.17 | 648.34 |

60,000 | 840,000 | 430.66 | 117.07 | 732.12 |

70,000 | 980,000 | 477.27 | 123.24 | 811.36 |

80,000 | 1,120,000 | 521.70 | 128.85 | 886.89 |

90,000 | 1,260,000 | 564.31 | 134.01 | 959.33 |

100,000 | 1,400,000 | 605.37 | 138.80 | 1,029.14 |

200,000 | 2,800,000 | 960.94 | 174.87 | 1,633.60 |

300,000 | 4,200,000 | 1,259.17 | 200.17 | 2,140.59 |

400,000 | 5,600,000 | 1,525.37 | 220.32 | 2,593.12 |

500,000 | 7,000,000 | 1,770.02 | 237.33 | 3,009.03 |

600,000 | 8,400,000 | 1,998.77 | 252.19 | 3,397.91 |

700,000 | 9,800,000 | 2,215.10 | 265.49 | 3,765.66 |

800,000 | 11,200,000 | 2,421.32 | 277.57 | 4,116.25 |

900,000 | 12,600,000 | 2,619.10 | 288.69 | 4,452.48 |

1,000,000 | 14,000,000 | 2,809.68 | 299.01 | 4,776.46 |

**Rate** is the displacement of the enclosed volume of the
hull, in tons of liquid hydrogen

**Vol** is the volume of enclosed hull, useable for
installation of equipment, in cubic meters

**MV** is the material volume of the hull's shell, assuming a
shell thickness of 1cm, in cubic meters

**L** is the length of the hull (diameter for spheres), in m

**VehicleMV** is the material volume of a vehicle's chassis,
assuming a MVM of 1.7

HULL SIZE (1 ton = 13.5 cubic meters LHYD) |
||||
---|---|---|---|---|

Rate | Vol | MV | L | VehicleMV |

1 | 13.50 | 0.28 | 2.97 | 0.47 |

2 | 27.00 | 0.44 | 3.74 | 0.74 |

3 | 40.50 | 0.57 | 4.28 | 0.97 |

4 | 54.00 | 0.69 | 4.71 | 1.18 |

5 | 67.50 | 0.81 | 5.07 | 1.37 |

6 | 81.00 | 0.91 | 5.39 | 1.55 |

7 | 94.50 | 1.01 | 5.67 | 1.71 |

8 | 108.00 | 1.10 | 5.93 | 1.87 |

9 | 121.50 | 1.19 | 6.16 | 2.02 |

10 | 135.00 | 1.28 | 6.38 | 2.17 |

15 | 202.50 | 1.67 | 7.30 | 2.84 |

20 | 270.00 | 2.03 | 8.04 | 3.44 |

25 | 337.50 | 2.35 | 8.66 | 3.99 |

30 | 405.00 | 2.65 | 9.20 | 4.51 |

35 | 472.50 | 2.94 | 9.68 | 5.00 |

40 | 540.00 | 3.21 | 10.12 | 5.46 |

45 | 607.50 | 3.48 | 10.53 | 5.91 |

50 | 675.00 | 3.73 | 10.90 | 6.34 |

55 | 742.50 | 3.97 | 11.25 | 6.75 |

60 | 810.00 | 4.21 | 11.58 | 7.16 |

65 | 877.50 | 4.44 | 11.90 | 7.55 |

70 | 945.00 | 4.67 | 12.19 | 7.93 |

75 | 1,012.50 | 4.88 | 12.48 | 8.30 |

80 | 1,080.00 | 5.10 | 12.75 | 8.67 |

85 | 1,147.50 | 5.31 | 13.01 | 9.03 |

90 | 1,215.00 | 5.52 | 13.26 | 9.38 |

95 | 1,282.50 | 5.72 | 13.50 | 9.72 |

100 | 1,350.00 | 5.92 | 13.73 | 10.06 |

200 | 2,700.00 | 9.39 | 17.29 | 15.96 |

300 | 4,050.00 | 12.30 | 19.79 | 20.91 |

400 | 5,400.00 | 14.90 | 21.78 | 25.33 |

500 | 6,750.00 | 17.29 | 23.46 | 29.39 |

600 | 8,100.00 | 19.52 | 24.93 | 33.19 |

700 | 9,450.00 | 21.64 | 26.25 | 36.78 |

800 | 10,800.00 | 23.65 | 27.44 | 40.20 |

900 | 12,150.00 | 25.58 | 28.54 | 43.49 |

1,000 | 13,500.00 | 27.44 | 29.56 | 46.65 |

2,000 | 27,000.00 | 43.55 | 37.24 | 74.04 |

3,000 | 40,500.00 | 57.07 | 42.62 | 97.01 |

4,000 | 54,000.00 | 69.13 | 46.91 | 117.52 |

5,000 | 67,500.00 | 80.21 | 50.53 | 136.36 |

6,000 | 81,000.00 | 90.58 | 53.69 | 153.98 |

7,000 | 94,500.00 | 100.38 | 56.52 | 170.65 |

8,000 | 108,000.00 | 109.72 | 59.10 | 186.53 |

9,000 | 121,500.00 | 118.69 | 61.46 | 201.77 |

10,000 | 135,000.00 | 127.32 | 63.66 | 216.45 |

20,000 | 270,000.00 | 202.10 | 80.20 | 343.56 |

30,000 | 405,000.00 | 264.81 | 91.80 | 450.18 |

40,000 | 540,000.00 | 320.79 | 101.04 | 545.35 |

50,000 | 675,000.00 | 372.24 | 108.84 | 632.81 |

60,000 | 810,000.00 | 420.35 | 115.66 | 714.59 |

70,000 | 945,000.00 | 465.84 | 121.76 | 791.92 |

80,000 | 1,080,000.00 | 509.21 | 127.30 | 865.65 |

90,000 | 1,215,000.00 | 550.80 | 132.39 | 936.36 |

100,000 | 1,350,000.00 | 590.87 | 137.13 | 1,004.49 |

200,000 | 2,700,000.00 | 937.93 | 172.76 | 1,594.47 |

300,000 | 4,050,000.00 | 1,229.01 | 197.76 | 2,089.32 |

400,000 | 5,400,000.00 | 1,488.83 | 217.66 | 2,531.01 |

500,000 | 6,750,000.00 | 1,727.62 | 234.47 | 2,936.96 |

600,000 | 8,100,000.00 | 1,950.90 | 249.16 | 3,316.52 |

700,000 | 9,450,000.00 | 2,162.04 | 262.29 | 3,675.47 |

800,000 | 10,800,000.00 | 2,363.32 | 274.23 | 4,017.65 |

900,000 | 12,150,000.00 | 2,556.37 | 285.21 | 4,345.83 |

1,000,000 | 13,500,000.00 | 2,742.38 | 295.40 | 4,662.05 |

**Rate** is the displacement of the enclosed volume of the
hull, in tons of liquid hydrogen

**Vol** is the volume of enclosed hull, useable for
installation of equipment, in cubic meters

**MV** is the material volume of the hull's shell, assuming a
shell thickness of 1cm, in cubic meters

**L** is the length of the hull (diameter for spheres), in m

**VehicleMV** is the material volume of a vehicle's chassis,
assuming a MVM of 1.7

#### Material Volume & Hull Volume Usage

Because a hull thickness of 1cm has already been taken into consideration, through the formulae and the values on the tables, do not subtract total hull volume from the useable volume of the vessel if the hull has a thickness of 1cm.

Because additional hull plating does not affect a vessel's length, plating is assumed to be added inside the useable volume of the vessel. Calculate the volume occupied by additional plating by working out the total volume of the hull as per the standard FF&S rules, then subtract from this the volume of material required to plate the hull in a 1cm shell (basically, MV × hull configuration MVM).