I have completed my preliminary analysis of hull structures in Traveller.
The short version: at TL14-15, using bonded superdense, most combinations of
displacement, density, and acceleration **are** feasible up to
1,000,000 dtons. At progressively lower TLs and material strengths, however,
the extremes become less and less feasible. This particularly affects
heavily armored non- starships and planetoids with high accelerations --
i.e., monitors and battleriders. The long version follows.

#### Methods and Assumptions

A spacecraft hull can be modeled to first order as a free-standing column, "resting" on its drives. (This is analogous to treating a water-borne vessel as a beam supported along its length, which is the standard starting point for naval architecture.) For my analysis, I have slavishly followed the method outlined in Space Mission Analysis and Design, 3d. ed. (SMAD III), Wertz and Larson (ed.s), 1999, pp. 459-494. I assume (with SMAD III) that the column is thin walled (radius/thickness < 0.1), supported only by its walls (monocoque construction), with its mass uniformly distributed along its length.

For dimensions, I used the "large cylinder" values from Fire, Fusion, & Steel (1996): length:beam = 3.5:1. Most canonical ships for which dimensions are given (e.g., Kinunir, Azhanti High Lightning, the deckplans in Traders and Gunboats) are closer to these proportions than to the other choices for cylinder (actually, AHL is more like 7:1). They are also the best match for the dimensions specified for GT vessels (per GURPS Space).

For loading, I assumed that the hull is constructed to withstand forces equal to (drive rating) * (loaded mass) in any axis -- axial, lateral, or bending moment. This is likely to overestimate normal loads, but seriously underestimate loads from aerodynamic forces, occasional collisions, and weapons effects. Other than this, I did not provide for unusually high margins of safety in the designs (beyond what SMAD III recommends: 1.1 for yield strength, 1.25 for ultimate strength). This is consistent current shipbuilding practice, and with descriptions of naval design standards in canon:

"In emergencies, the [Azhanti High Lightning] can utilize its limited streamlining to allow a direct fuel skim of a gas giant... There are three dangers to this procedure; all are called for by the very design of the ship, by the costs of the design, and the realities of structural integrity... "Loss of Fuel Deck Integrity. The severe buffeting may cause one or more fuel decks to leak or buckle, resulting in a failure to retain fuel. This is an accepted part of the total ship design... While there is a potential loss of 9600 tons of fuel, the actual loss is statistically much less, and is considered to be acceptable by the naval authorities." Supplement 5, p. 43. (1980)

Finally, I had to make some assumptions about the properties of ultratech hull materials, particularly crystaliron, superdense, and bonded superdense. Each of these is rated in canon for density and for "toughness" relative to hard steel. Fire, Fusion, & Steel (1993), p. 37, describes "toughness" in detail:

"Face-hardened armor is an illustration of two competing values in armor plate which, for purposes of simplicity, we gloss over in Traveller, those properties being hardness and toughness. Hardness is the ability to resist any deformation at all, and it is usually associated with a certain brittleness. Toughness is the ability of the armor to absorb energy without shattering, and usually is associated with a certain elastic character. By way of illustration, glass is extremely hard but not very tough. Rubber is very tough but not extremely hard.

"Armor which is very hard will cause small shells to shatter when they hit it and cause no damage, but larger shells will shatter the armor and pass completely through it. Tough armor does not suffer the massive shattering that hard armor does. Face-hardened armor combines both characteristics in one plate by taking a plate of very tough armor and hardening only the face of it. Small shots shatter against it while larger shots crack only the outer surface and are stopped by the more elastic part of the plate.

"Although this is an interesting subject with some interesting effects on armor and protection, we have decided for purposes of game simplicity, to lump both characteristics into a generalized "toughness" rating, which represents the ability of armor to resist penetration by all projectiles."

This discussion focuses on the properties of materials as armor, and gloss over their structural properties (not surprising, from what was originally a wargames company). Toughness as an engineering quantity is the total amount of energy a material can absorb before it ruptures; for a ductile material, toughness is roughly equal to its ultimate strength times its maximum elongation (how far it can stretch before it breaks); for a brittle material, it is about half that much (and they don't stretch very far). Hardness is basically given by the ratio of stress (force applied) to strain (amount of stretching), up to the point where brittle materials break and ductile materials are permanently deformed.

Based on this, I have based the assumed structural properties of the ultratech materials on hard steel; this seemed to be the most reasonable approach. I multiplied both the yield and ultimate stresses (strengths) by the listed Toughness. I kept the stress/strain ratio (Young's modulus) and maximum elongation the same. (I'll address the effects of varying the hardness towards the end.)

#### Results

In accordance with SMAD III, there are actually two requirements that a hull must fulfill: strength and stability. That is, the structure must not only be strong enough to support the required loads, but it must also be stiff enough to resist buckling under them. These two requirements lead to two different formulae for hull structural volume (in m3):

- Strength: Structure = vol^(4/3) * a * p / (1000 * T)
- Stability: Structure = vol^(1.15) * (a * p)^(0.453) / 300

where

- vol = total displacement of hull, m3
- a = rated acceleration, g's
- p = mass density of vessel (loaded mass/volume), ston/m3
- T = Toughness, where hard steel = 2.86

The actual structural volume is the greater of the two results. Structural mass is the volume multiplied by the density of the material.

The formula for strength is reasonably exact; note that the exponent is 4/3, not 3/2 (as in FF&S2). I derived the formula for stability empirically from the data -- the relationships are complex and (per SMAD III) practical experience has led to a number of necessary "fudges" to meet margins of safety. This formula overestimates the required volume for stability by up to 10% in some cases.

Strength requirements dominate for low-tech materials and very large or heavy vessels. Stability comes into play for small and light vessels using high-tech materials, which otherwise would have very thin (but strong) structural members.

Notice that this leads to an iterative process, as the structural mass affects the overall density of the vessel. This is not ideal for simplicity, but as Dr. Akins says:

"3. Design is an iterative process. The necessary number of iterations is one more than the number you have currently done. This is true at any point in time."

#### Ship Size Limits

It remains to decide what is a reasonable limit on the fraction of a ship devoted to structure. Rather than chase through components and capabilities (which in any case are different for each Traveller version), I chose 20% as my cutoff. Not only is this the limit of the thin-walled approximation, but it is also the canonical structural percentage for planetoid hulls (which are supposed to be tunneled). Note that 20% of a hull is an enormous amount of ultratech material: for superdense and its derivatives, the density of such a hull starts at 3 tons/m3 and goes up.

The following four charts show the maximum acceleration that can be supported by 20% hull volume devoted to structure, for a selection of materials and displacements. The last chart is slightly different: it shows the same data for standard and buffered planetoids (assuming that nickel-iron is equivalent to soft steel). The ranges of density (p) are representative; although most canonical ships (disregarding the 60 ton/m3 monstrosities in Fighting Ships of the Shattered Imperium) hover around 1 ton/m3, at 20% required structural volume the densities will be much higher.

1 ton per cubic meter | ||||
---|---|---|---|---|

Hull Disp. | Hard Steel (TL6-9) | Crystaliron (TL10-11) | Superdense (TL12-13) | Bonded Superdense (TL14-15) |

60,000 | 6g | 6g | 6g | 6g |

100,000 | 5g | 6g | 6g | 6g |

200,000 | 4g | 6g | 6g | 6g |

500,000 | 3g | 6g | 6g | 6g |

1,000,000 | 2g | 6g | 6g | 6g |

3 tons per cubic meter | ||||

2,000 | 6g | 6g | 6g | 6g |

4,000 | 5g | 6g | 6g | 6g |

7,000 | 4g | 6g | 6g | 6g |

18,000 | 3g | 6g | 6g | 6g |

60,000 | 2g | 6g | 6g | 6g |

100,000 | 2g | 6g | 6g | 6g |

200,000 | 2g | 5g | 6g | 6g |

500,000 | 1g | 4g | 6g | 6g |

800,000 | - | 4g | 6g | 6g |

1,000,000 | - | 3g | 5g | 6g |

8 tons per cubic meter | ||||

100 | 5g | 6g | 6g | 6g |

200 | 4g | 6g | 6g | 6g |

400 | 3g | 6g | 6g | 6g |

1,600 | 2g | 6g | 6g | 6g |

8,000 | 1g | 6g | 6g | 6g |

12,000 | 1g | 5g | 6g | 6g |

14,000 | - | 5g | 6g | 6g |

20,000 | - | 4g | 6g | 6g |

40,000 | - | 3g | 6g | 6g |

60,000 | - | 3g | 5g | 6g |

70,000 | - | 2g | 5g | 6g |

100,000 | - | 2g | 4g | 6g |

200,000 | - | 2g | 3g | 6g |

300,000 | - | 1g | 3g | 6g |

500,000 | - | 1g | 2g | 5g |

1,000,000 | - | 1g | 2g | 4g |

Planetoids (Soft Steel) | ||||

Hull Disp. | Standard (3 t/cu m) |
Standard (8 t/cu m) |
Buffered (3 t/cu m) |
Buffered (8 t/cu m) |

100 | 6g | 5g | 6g | 6g |

200 | 6g | 5g | 6g | 6g |

400 | 6g | 4g | 6g | 5g |

600 | 6g | 3g | 6g | 5g |

1,000 | 6g | 3g | 6g | 4g |

1,200 | 6g | 3g | 6g | 4g |

1,600 | 5g | 2g | 6g | 4g |

2,000 | 5g | 1g | 6g | 3g |

4,000 | 4g | 1g | 6g | 3g |

6,000 | 4g | 1g | 6g | 3g |

9,000 | 3g | 1g | 6g | 2g |

10,000 | 3g | 1g | 5g | 1g |

14,000 | 3g | 1g | 5g | 1g |

20,000 | 3g | - | 4g | 1g |

30,000 | 2g | - | 4g | 1g |

50,000 | 2g | - | 3g | 1g |

70,000 | 2g | - | 3g | 1g |

100,000 | 2g | - | 2g | - |

200,000 | 1g | - | 2g | - |

1,000,000 | - | - | 1g | - |

Standard hulls use 20% structural materials; buffered hulls 35%.

#### Other Variables

I did not consider the effect of configuration on the structural volume requirement. Although the answer rests on geometry, it is not as simple as calculating relative surface areas for a given volume. One point that is available from inspection: cone and wedge configurations will require less structure per unit volume than cylinders; spheres and spheroids will almost certainly require more.

I mentioned the stress/strain ratio (E, Young's modulus) and its effect on structure. If a different relation between Toughness and E is desired, the final volume required for stability (not strength) is divided by (k^0.368), where k is the ratio of the selected E to the E of hard steel (196e9 N/m2).

#### Conclusion

Well, now we know. To the extent that my assumptions are valid, very large (1Mdton) vessels are physically possible and practical at high TLs, so long as care is taken with acceleration and density. Persons interested in restricting the size of vessels in their Traveller campaigns will have to look elsewhere -- to populations and economics, jump drive limitations, available strengths of materials, etc.

One interesting result (and one that I did not expect) is that what limitations there are fall most heavily on those vessels that have traditionally considered "easy" to design: planetoids and battleriders or monitors. This supports the canonical picture of hordes of (relatively) small system defense boats in preference to large battlestations, and serves to level the playing field somewhat between jump-capable battleships and battleriders.