This paper is a comparative analysis between the various Star Fleet starships as presented in the Star Fleet Technical Manual. The entire exercise shows how to derive esoteric details about starships based upon scanty information and some well-placed educated guesses.
In many cases given some elbow grease and simple mathematics, undisclosed but interesting quantities and relationships can be extrapolated from known "facts." All of the information is presented with the understanding that it is only a first-order approximation; the author appreciates any comments, suggestions, or improvements, should any reader feel strong enough about it to write.
An example of design data that can be extrapolated is the actual volume inside a starship. Luckily we have been given lengths, breadths, depths, and diameters in good detail. These are complemented by the various blueprints available, a necessity for this sort of work.
The first step, then, is to approximate the size of the starship involved using common geometrical solids whose volumes are known from simple equations. To simplify our comparison though, let's examine the starships involved and make a few assumptions.
The first ship in our comparison is the Constitution Class heavy cruiser which should be familiar to all by now.
The second ship is the Federation Class dreadnought, roughly in appearance to a "fat" heavy cruiser with an additional warp nacelle attached to the rear of the primary hull, extending lengthwise above the secondary hull.
Third is the Saladin Class destroyer, constructed of a primary hull (in this context, the term "primary hull" should be understood as including the interconnecting dorsal) connected to a single warp nacelle.
Last comes the Ptolemy Class transport/tug, in essence a primary hull with two warp nacelles and a "tow pad" used for connecting the different forms of cargo carriers.
The values used for the heavy cruiser class are transferred directly to the calculations for the destroyer and transport classes; without additional reference material, and judging by their similar appearance, this seems safe enough for our purposes.
For our first-order math we approximate the various ship sections as follows. The primary hull is comprised of a flat wide cylinder, with a cone of smaller radius but larger height on top and below. The interconnecting dorsal is approximated as a rectangular solid.
The secondary hull is approximated as a simple cylinder as are the warp nacelles. The support pylons to the nacelles and the tug's "tow pad" were neglected. The values used in the computations were measured carefully using scales given on the blueprints, but do represent some "trimming" by eye to account for large variations away from the approximating shape.
An example of this is the aft section of the heavy cruiser secondary hull. It tapers quickly below the hangar deck, and the value used for the secondary hull diameter tries to take this into account, and is definitely not the maximum diameter listed in the reference material. The dreadnought secondary hull, though, is not as irregular, and the value used reflects this.
This is also true for the top and bottom cones for both ships. The values used for calculating are shown in Table 1.
|Saucer Diameter||132 m||122 m||122 m||122 m|
|Saucer Height||5.88 m||5.88 m||5.88 m||5.88 m|
|T/B Cone Diameter||82.4 m||58.8 m||58.8 m||58.8 m|
|T/B Cone Height||13.5 m||11.8 m||11.8 m||11.8 m|
|Dorsal Height||18.2 m||17.6 m||17.6 m||17.6 m|
|Dorsal Length||25.3 m||27.8 m||27.8 m||27.8 m|
|Dorsal Width||4.71 m||4.90 m||4.90 m||4.90 m|
|Secondary Hull Diameter||29.0 m||30.0 m||n/a||n/a|
|Secondary Hull Length||129 m||105 m||n/a||n/a|
|Nacelle Diameter||18.2 m||18.2 m||18.2 m||18.2 m|
|Nacelle Length||141 m||141 m||141 m||141 m|
From geometry it is known that the volume of a cylinder is:
and that of a cone:
and that of a rectangular solid:
all where R = Radius, H = Height, L = Length, and W = Width. Using these equations the separate volumes are calculated and shown in Table 2. Note that the Top/Bottom Cone Volume figure represents the sum of both cones, not just one.
|Saucer Volume||80.5e3 m^3||68.7e3 m^3||68.7e3 m^3||68.7e3 m^3|
|T/B Volume||48.0e3 m^3||21.4e3 m^3||21.4e3 m^3||21.4e3 m^3|
|Dorsal Volume||2.17e3 m^3||2.40e3 m^3||2.40e3 m^3||2.40e3 m^3|
|Primary Hull Volume||131e3 m^3||92.5e3 m^3||92.5e3 m^3||92.5e3 m^3|
|Secondary Hull Volume||85.2e3 m^3||74.2e3 m^3||n/a||n/a|
|USABLE VOLUME||216e3 m^3||167e3 m^3||92.5e3 m^3||92.5e3 m^3|
|Nacelle Volume||36.7e3 m^3||36.7e3 m^3||36.7e3 m^3||36.7e3 m^3|
|Number of Nacelles||3||2||1||2|
|Total Nacelle Volume||110e3 m^3||73.4e3 m^3||36.7e3 m^3||73.4e3 m^3|
|TOTAL VOLUME||326e3 m^3||240e3 m^3||129e3 m^3||166e3 m^3|
At this point we compute our first practical quantity, "usable volume" in a given starship. This number, the sum of the volumes of the primary and secondary hulls, is the amount of space accessible to the crew to live and work in. Let's examine these values.
For a dreadnought the usable volume is 216 thousand cubic meters. A heavy cruiser comes in at 167 thousand cubic meters while the destroyer and the transport trail at slightly under 100 thousand cubic meters. What do these numbers mean?
Imagine a cubic solid (like, say, a Borg ship) 55 meters (180 feet) on a side. That is how big the Enterprise is to those inside her. Another way to look at this is that this is equivalent to 300 good-sized (2000 sq. ft.) houses. A dreadnought is more like 400! These ships really are moving cities. (Well ... moving neighborhoods at least.)
Adding the usable volume to the volume of a single warp nacelle times the number of nacelles per ship yields the total volume for each ship. This is the vessel's displacement used for warp calculations.
The total DWT (deadweight tonnage) for each class is given in the references as well. Although there are several ways to interpret DWT, these calculations assume that the ship in question is rated at maximum capacity (fully laden).
References give the DWT of a dreadnought at 285000 metric tons (t), a heavy cruiser at 190000t, a destroyer at 95000t, and a transport at 126500t. A comparison of ship structures, along with some unusual subtraction, yields the DWT of the various parts of the ships.
Subtracting a transport from a heavy cruiser gives the DWT of the secondary hull: 63500t.
Subtracting a destroyer from a transport gives the DWT of a single warp nacelle: 31500t.
Subtracting two warp nacelles and a secondary hull from a heavy cruiser gives the DWT of the primary hull: 63500t. (Note the similarity in mass between primary and secondary hull.) All these values are summarized in Table 3.
|Primary Hull DWT||89.9e3 t||63.5e3 t||63.5e3 t||63.5e3 t|
|Secondary Hull DWT||72.9e3 t||63.5e3 t||n/a||n/a|
|USABLE DWT||163e3 t||127e3 t||63.5e3 t||63.5e3 t|
|Nacelle DWT||31.5e3 t||31.5e3 t||31.5e3 t||31.5e3 t|
|Total Nacelle DWT||94.5e3 t||63.0e3 t||31.5e3 t||63.0e3 t|
|TOTAL DWT||257e3 t
(285e3 t spec'd)
|190e3 t||95.0e3 t||127e3 t|
|Primary Hull DWT/VOL||0.687 t/m^3||0.687 t/m^3||0.687 t/m^3||0.687 t/m^3|
|Secondary Hull DWT/VOL||0.856 t/m^3||0.856 t/m^3||n/a||n/a|
|Nacelle DWT/VOL||0.859 g/cm^3||0.859 g/cm^3||0.859 g/cm^3||0.859 g/cm^3|
Density computations are also computed (where one t = 1e6 g). Note that the primary hull is significantly less dense than the remainder of the ship, understandable given that it is largely comprised of living space for the crew.
The secondary hull is more dense in that it houses much heavy machinery and bulk cargo storage (plus the bowling balls!). The warp engines are lighter than expected, barely more dense than the secondary hull. This is a subtle reminder of the sophistication of 23rd century warp engine technology.
Let's do a quick parenthetical calculation: Assume (this, by no means, is a safe assumption) that the metal structure of the ship has a density on a par with good steel, about 8 g/cm3. For a heavy cruiser with a rated usable DWT of 130000t this gives a material volume of about 16000 cubic meters, roughly 10% of the total usable volume.
This number would seem to agree with a visual approximation based upon the deck plans. Also, interesting enough, notice that a heavy cruiser primary hull (without the dorsal) would displace about 90000t of water but weigh less than 65000t. Ever wonder after an emergency saucer separation how they land the thing? They don't have to; it floats! (In fact it looks like the entire ship would - go figure.)
Unfortunately these results do not apply easily to the dreadnought. Though the warp nacelles are the same, the primary hull and secondary hull are significantly different in size. We must be creative in order to find these values.
An examination of the deck plans for the heavy cruiser and the dreadnought shows that the primary and secondary hulls are alike in construction. Using our values for the DWT of each section and the volume of that section, we can compute an average DWT/VOL (t/m3).
Now using the average DWT/VOL and our observation that the construction of the heavy cruiser and the dreadnought is similar, we can calculate backwards to get the DWT values for the primary and secondary hull of the dreadnought. This produces the values shown in the dreadnought column.
Notice that when we add these two numbers (plus the three nacelles) we get a total DWT of about 260000t, noticeably short of the specified value of 285000t. Where is the rest?
My conjecture, given the nature of the craft, is that it is found in additional hull shielding and/or improved (read "thicker") bulkheads. When designing a warship it must be able to absorb more damage. This would increase the DWT while not significantly affecting the total volume. I invite discussion on this discrepancy.
Those interested in warp drive theory should note the interesting ratio DWT/Warp Nacelle, shown in Table 4. Throughout the design comparison a limit on the potential of the warp engines appears; we see that a single warp nacelle can "warp" space for about 95000t of mass (see explanation of transport warp speed below).
|DWT/Warp Nacelle||95.0e3 t/nac||95.0e3 t/nac||95.0e3 t/nac||63.3e3 t/nac|
|Maximum Warp Factor||10||8||8||8|
Notice also, given the different maximum warp factor for the dreadnought, that maximum warp speed does not seem to be dependent on this constant. Although this factor might be related to the volume/nacelle involved I tend to doubt it; these starships are obviously not designed to optimize volume. Instead, I believe that the dreadnought warp engines are used more strenuously in an expectedly shorter time frame and that this accounts for the incongruity.
Table 5 shows an analysis of the five standard types of cargo carriers towed by the transport class. Although identical in shape, the given DWT ratings, coupled with the deck plans of the MK4 personnel carrier, reveal the internal structure of the remaining carriers quite well - the enormous difference in the DWT show them to be very densely packed indeed.
|MK1 -- LIQUID||20m||200m||251e3 m^3||122e3 t||0.486 t/nac|
|MK2 -- DRY BULK||20m||200m||251e3 m^3||122e3 t||0.486 t/nac|
|MK3 -- REEFERS||20m||200m||251e3 m^3||122e3 t||0.486 t/nac|
|MK4 -- PEOPLE||20m||200m||251e3 m^3||80.0e3 t||0.319 t/nac|
|MK5 -- PRODUCTS||20m||200m||251e3 m^3||122e3 t||0.486 t/nac|
Considering the two carrier limit placed upon the transport class, the constraints upon the warp engines of the transport ship are shown in Table 6 for the heaviest and lightest loads possible. Although I have never seen any actual specifications it is unreasonable to assume that a laden transport can travel at warp speeds approaching its unladen value.
This is reflected in the case shown for the 2 MK1 example where the DWT/Nacelle ratio is greater than that for the non-transport classes. One can postulate that the ship is moving at slower warp speeds, producing less strain on the engines and allowing the 13% relaxation from the "limit."In the case for 2 MK4 carriers we see that the ratio is lower than expected. I would speculate that for this example this is due to a difficulty in adapting the warp field around the bulky shape (and quite possibly, the cargo), as well as an understandable respect for the safety margins involved considering the awful consequences of a warp accident.
Star Fleet Technical Manual, Franz Joseph Designs, Ballantine Books, 1975.
General Plans, Constitution Class, U.S.S. Enterprise, Franz Joseph Designs, 7404.12.
Dreadnought Blueprints, U.S.S. Federation Class, Stardraft Productions, 7912.12.