Ship Structure and Hull Size Limitations -- revised 5 September 2003
I have conducted an analysis of hull structures in Traveller. The short
version:
All editions of Traveller make inadequate provision for the requirements of
hull structural stability (as opposed to strength). Judging from open frame/
dispersed structure hulls (the most restrictive case), starships in Traveller
should generally be limited to 500 dtons at TL7-9, and 5,000 dtons at TL10+;
a correction to High Guard's Hull Armor Table (p. 23) is required to permit
even these modest displacements. Unarmored vessels above this displacement
are feasible, but should be considered "fragile" by Traveller standards.
Depending on one's assumptions, larger armored hulls may be possible up to
1,000,000 dtons at TL14-15, though the designer must exercise care with
extremes of density and acceleration at lower TLs and material strengths.
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
(6g) * (loaded mass) in any axis -- axial, lateral, or bending moment. This
follows High Guard, where all hulls are able to support 6g accelerations
regardless of armor factor, agility, or configuration. It 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 with 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 glosses
over their structural properties. 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.
Because of 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.
Ship Size Limits
It remains to decide what is a reasonable figure for the fraction of a ship
devoted to structure. High Guard sets the percentage of a ship's volume
dedicated to armor according to the Hull Armor table (p. 23):
Hull Armor
--------Tech Level------
7-9 10-11 12-13 14-15
Percent
of ship 4+4a 3+3a 2+2a 1+a
Formula indicates percentage of ship
required for armor (a is desired armor
factor)...
Note that the percentage is independent of drive rating: both 1g and 6g ships
have the same armor percentage. This implies that all hulls are rated for (at
least) the maximum of 6g acceleration, in accordance with my assumption
(above).
Note also that armor factor 0 still requires a fraction of the hull: 1-4%,
depending on TL. This residual hull "armor" represents the minimal structure
of the ship itself in High Guard. (The extreme example is a configuration 7
dispersed structure, which has no skin to the hull per se.)
So I started with the limits on an unarmored ship, with a percentage of the
hull dedicated to structure in accordance with the hull armor table and
rated for 6g acceration. For density I used 1 ston/m3, which seems to be
median for unarmored vessels in most versions of Traveller (where such
comparisons are possible).
The results are surprising:
TL Hull accel Hull Structure
(dton) (g) Armor
7 500 6 0.04 0.040
8 500 6 0.04 0.040
9 500 6 0.04 0.040
10 800 6 0.03 0.030
11 800 6 0.03 0.030
12 50 6 0.02 0.020
13 50 6 0.02 0.020
14 0.5 6 0.01 0.010
15 0.5 6 0.01 0.010
These are the maximum hull sizes for each combination of tech level and hull
armor/structure percentage.
Setting hull size to the maximum allowed by TL (i.e., computer, per High
Guard, p. 26), gives the following maximum accelerations instead:
TL Hull accel Hull Structure
(dton) (g) Armor
7 3000 3.3 0.04 0.040
8 3000 3.3 0.04 0.040
9 9000 2.3 0.04 0.040
10 40000 1.6 0.03 0.030
11 75000 1.3 0.03 0.030
12 900000 0.24 0.02 0.020
13 1000000 0.23 0.02 0.020
14 1000000 0.049 0.01 0.010
15 1000000 0.049 0.01 0.010
The reason for this counter-intuitive result is stability -- there is
simply not enough high tech structural material to maintain the shape of the
vessel under acceleration.
The cutoff between strength and stability requirements seems to be around
3-4%. Setting the armor factor 0 hull percentage to 4% across all TLs yields
the following results:
TL Hull accel Hull Structure
(dton) (g) Armor
7 500 6 0.04 0.040
8 500 6 0.04 0.040
9 500 6 0.04 0.040
10 5000 6 0.04 0.040
11 5000 6 0.04 0.040
12 5000 6 0.04 0.040
13 5000 6 0.04 0.040
14 5000 6 0.04 0.040
15 5000 6 0.04 0.040
In other words, the hull structural requirements portrayed in High Guard
(6g, 1-4% of hull) are physically inadequate for most unarmored vessels
above TL9; setting the minimum structure to 4% permits vessels up to
5,000 dtons.
Checking the results against the other ship design sequences in Traveller
shows that the minimum armor/structure requirements in both versions of
Fire, Fusion, and Steel are inadequate from an engineering standpoint:
the scantlings under FF&S won't support a vessel greater than 300 dtons;
for FF&S2, it's 70 dtons.
The Drive Potential table from Book 2 begins to make more sense, however.
Matching hull size against drive tech level (Book 3, p. 15), shows that
hulls in Book 2 require 3.5% of their volume or less (2.8 +/- 0.4%) as
structure:
TL Hull max Structure
(dtons) accel
9 100 6 0.023
9 200 6 0.025
9 400 6 0.027
9 600 6 0.029
9 800 6 0.030
10 1000 6 0.031
11 2000 6 0.035
13 3000 4 0.031
15 4000 3 0.028
15 5000 2 0.024
Since a ship's displacement in Book 2 does not appear to include turrets
(only 1 dton per turret of "fire control") and armor is never discussed, I
infer that the 3.5% is part of the ship's gross displacement, and only net
(internal) displacement is addressed in the rules.
For planetoid hulls, the computations are slightly different: at 20%
(standard) or 35% (buffered) of volume, the planetoid material -- equivalent
to soft steel -- has a significant effect on density. I took 0.4 ton/m3 as
a low-side value for the density of everything in a typical Traveller star-
ship, less the hull (this could be as high as 0.7 ton/m3 instead). The
results were:
Hull accel Density Structure
(dtons) (g) (ton/m3)
Standard 5300 6 1.9 0.20
Buffered 7100 6 3.1 0.35
Armored Hulls
The limitations described above will always apply to unarmored vessels, both
conventional merchant starships and open frame/dispersed structure tender
designs. If armor material does not contribute to the stability of the hull
-- that is, if armor is an applique rather than integral to the ship's
structure -- these limitations apply equally to armored vessels, and 5,000
dtons is the maximum normal displacement.
If, however, we allow the inclusion of armor in the structural material
calculations, vessels larger than 5,000 dtons are possible -- but
there are still limitations.
Once again, I had to decide on the fraction of ship's displacement devoted to
structure (though this time, including armor in the total). I chose the
maximum armor percentage allowed in High Guard (armor factor equal to TL).
This exceeds the limit of the thin-walled approximation (~20%) in some cases,
but is close enough. Note that these hulls require enormous amounts of
very dense ultratech material; again, I calculated density for the ship based
on the mass of the hull, plus 0.4 ton/m3 for everything else.
The following chart then shows the maximum hull size at each TL, based on
structural material; other limitations (e.g., computer type) are not shown.
TL Hull accel Density Structure
(dtons) (g) (ton/m3)
7 11000 6 2.8 0.32
8 12000 6 3.1 0.36
9 12000 6 3.4 0.40
10 39000 6 3.6 0.33
11 40000 6 3.9 0.36
12 630000 6 4.2 0.26
13 640000 6 4.5 0.28
14 1000000 6 2.3 0.13
15 1000000 6 2.3 0.13
Planetoid hulls with reinforcing armor is a complicated subject, involving
(as it does) two different materials, with different strengths, densities,
etc. I will leave those calculations for the interested reader.
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, if all vessels
(whether armored or not) are restricted by engineering practice and naval
architectural standards to a size where 4% of the vessel's volume is
adequate to sustain 6g nominal acceleration, then their maximum displacement
will be 5,000 dtons (~7,000 dtons for buffered planetoids). Larger vessels
and space structures are feasible, but only at the cost of greater fragility
(real or perceived) and restricted acceleration.
Using the alternate assumption that armor material counts towards structural
requirements, very large (1Mdton) armored vessels are phyically possible and
practical at high TLs -- though unarmored vessels should realistically still
be restricted to 5,000 dtons.
Copyright (c) 2003 by Christopher B. Thrash