In many ways calculating the destructive power of the photon torpedo is one of the simplest of all Trek technology problems. The Tech Manual states on page 129 that the photons carried by the Galaxy class contain a 1.5 kg antimatter charge. Upon reacting with an equal mass of matter, we can calculate the energy release via :

E = m x c2 (where c = the speed of light, approximately 3 x 108 m/s)
= 3 x (3 x 108)2
= 2.7 x 1017 Joules

Expressing this in Megatons is a difficult task, as we are not sure of the time scale of the explosion. However, a widely used conversion is that 1 Megaton is approximately 4 x 1015 Joules. Using this figure, we get a yield for the photon torpedo of 67.5 Megatons.

While it is possible that this energy release is channelled forwards into the shields, it is more likely that it radiates uniformly. The targets shields should thus absorb a maximum of 50% of this energy, or 33.75.

However, this is far from being a complete picture. We must also incorporate the kinetic energy of the torpedo itself. Page 129 also gives us some details of the torpedoes flight performance (edited for length at places marked ...) : "the multimode sustainer is not a true warp engine... Rather it is a miniature M/A fuel cell, which powers the sustainer coils to grab and hold a hand-off field from the launcher tube, to continue at warp if launched during warp flight by the starship... The maximum cruising velocity will follow the formula Vmax = Vl + 0.75 Vl/c, where Vl is the launch velocity. Other flight modes are triggered according to initial launch conditions. If launched during low impulse flight, the coils will drive the torpedo up to a 75% higher velocity. If launched at high sublight, the sustainer will not cross the threshold into warp, but will continue to drive the torpedo at high relativistic velocities."

Starships are normally limited to 0.25 c in Impulse flight; a torpedo launched at this speed would achieve a maximum cruise speed of 0.4375 c, or 131,250,000 m/s. Under strictly Newtonian physics, the kinetic energy is given by :

K.E. = 0.5 x mass x v2
= 0.5 x 247.5 x 131,250,0002
= 2.13 x 1018 Joules

Using the same conversion figure as before, this would add no less than 533 Megatons to the yield - a staggering near-eightfold increase!

Also, unlike the detonation energy, this energy would be delivered directly to the shields themselves rather than being radiated in all directions. The total impact would rate at nearly 567 Megatons.

Should the launching vessel choose to disregard normal speed limitations, as one might well expect during a battle, the additional energy is even more impressive. The Technical Manual says that the requirement for the E-D called for a top speed of 0.92 c (page 2). Assuming that this represents a maximum speed for both the ship and the torpedo :

Launch vessel velocity
(x c)
Torpedo velocity
(x c)
Impact energy
(Joules)
Equals
(Megatons)
Plus 50% total warhead yield
(Megatons)
0.25
0.4375
2.13 x 1018
533
567
0.40
0.70
5.46 x 1018
1,364
1,398
0.50
0.875
8.53 x 1018
2,132
2,166
0.60
0.92
9.43 x 1018
2,357
2,390
0.75
0.92
9.43 x 1018
2,357
2,390
0.80
0.92
9.43 x 1018
2,357
2,390
0.90
0.92
9.43 x 1018
2,357
2,390
0.92
0.92
9.43 x 1018
2,357
2,390


This is impressive enough, but in reality it is something of an understatement - there is no real reason why a torpedo should share the limitations of the Galaxies impulse engines, given that it is powered by a different type of system. Additionally, this chart takes no account of the relativistic mass increase; as the velocity gets closer to c, the mass of the torpedo will tend to infinity - and so will the yield.

Calculating the increased mass according to the formula m = mo/(1-(v2/c2))0.5, we get a value for m at 92% c of 632 kg. This would increase the total yield from 2,390 Megatons to 6,047 Megatons.

This trend accelerated sharply as one approaches c; at 99.99% c the torpedo would mass almost 71 times its rest mass; 17,501 kg. The total energy of an impact and detonation at this speed would be approximately 196,884 Megatons! I tend to ignore the relativistic effects because :

(a) The numbers get too damn scary!
(b) Without going into a long winded discussion of Impulse engines, it seems like Trek ships ought to be able to circumvent Relativity somehow in order to be able to attain the sort of impulse speeds they are stated to be capable of.
(c) Most importantly, it starts to become impractical to fire torpedoes at speeds close to that of light because of energy considerations.

Regarding the latter point : there must be some sort of upper limit to this thing, or we're inventing energy out of nothing. The torpedo gets its speed as a "hand off" from the parent vessel, and so at most it could receive only as much as the parent can supply. The Galaxy class seems to have a maximum engine output in the region of 107 TeraWatts (see relevant page for details). A maximum of some 10% of this is available to the launcher tube, some 1018 Watts. Using this, we can get some idea of the rates of fire that a torpedo tube could manage. Expanding our original table, then :

Launch vessel velocity
(x c)
Torpedo velocity
(x c)
Kinetic energy
(Joules)
Kinetic energy
(Megatons)
+50% warhead yield
(Megatons)
Tube Charging Time
(seconds)
Rate Of fire
(rounds/second)
0.01
0.0175
3.41 x 1015
0.85
34.6
0.0034 seconds
293
0.05
0.0875
8.53 x 1016
21.3
55
0.085 seconds
11.72
0.1
0.175
3.41 x 1017
85
119
0.341 seconds
2.93
0.25
0.4375
2.13 x 1018
533
567
2.13 seconds
0.47
0.40
0.70
5.46 x 1018
1,364
1,398
5.46 seconds
0.18
0.50
0.875
8.53 x 1018
2,132
2,166
8.53 seconds
0.12
0.60
0.92
9.43 x 1018
2,357
2,390
9.43 seconds
0.1
0.75
0.92
9.43 x 1018
2,357
2,390
9.43 seconds
0.1
0.80
0.92
9.43 x 1018
2,357
2,390
9.43 seconds
0.1
0.90
0.92
9.43 x 1018
2,357
2,390
9.43 seconds
0.1
0.92
0.92
9.43 x 1018
2,357
2,390
9.43 seconds
0.1
While there is sufficient power for many rounds per second at relatively low velocities, it is not likely in my opinion that the hardware f the launcher itself could get the torpedoes out that fast; elsewhere I have guestimated a rate of fire for the Galaxy class of about two rounds per second - the chart above indicates that this could only be achieved at relatively low impulse speeds.

The idea that the speed and rate of fire of a torpedo depends on the speed of the parent vessel is a possible explanation of why combat often seems to occur at such low speeds in Trek. Normally I chalk this up to lack of reality in the FX - a realistic space battle would look extremely dull indeed. However, ships may choose low velocities deliberately because it gives them a good rate of fire from their torpedo tubes. Alternately, a possible explanation of why ships do not use torpedoes as often as they seem able to could be that at higher velocities they can't spare the increased power requirements while still supplying shields, phasers, structural integrity and inertial damper fields, etc.


Given these figures, one can see the photon torpedo in an entirely new light. There appear to be two distinct ways of using these weapons, according to the sorts of speeds that the battle is being conducted at :

In low speed combat (less than 5% c), torpedoes can be used in large numbers at high rates of fire - as seen when the E-D fired at the Borg cube in "Best of Both Worlds", or the E-E at the Borg cube and sphere in "First Contact". In this realm the kinetic energy of the torpedo will give a significant but not overwhelming boost to the warhead (at 5% c it adds an extra 63% to the yield). Typical yields will range up to 50 - 100 Megatons or so. The upper limit to the rate of fire is unknown, but is probably at least one or two per second.

At higher speeds, the torpedo becomes essentially a kinetic energy weapon with a small warhead. The Tech Manual states that the torpedo can utilize the onboard antimatter stocks in the sustainer engine to extend its effective range, and this may even be the principle use for this material at higher speeds. With yields in the thousands of megatons the torpedo is vastly more powerful than when used at low speed, but it takes a large fraction of the ships available power to launch and can only be used very sparingly. A GCS could fire one every ten seconds at the absolute maximum, and while maintaining shields etc. probably more like one every thirty or forty seconds.

In either case, the burst fire mode could be used but with a commensurate decrease in the rate of fire.

And remember - these calculations ignore relativistic effects. Taking these into account could boost warhead yield at the top end of the speed envelope by an order of magnitude or more. Of course, they would also lower the rate of fire to a point where each torpedo would take minutes to launch - it would get to the point where a torpedo travelling at virtually at c would have near infinite energy, but would be virtually impossible to launch at all!


Last updated : 11th October 1998.
This page is Copyright Graham Kennedy 1998.
Star Trek et al is Copyright Paramount Pictures 1996/97.
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