The torpedo most pervasively used by the Federation in Star Trek is the Photon Torpedo. The torpedo warhead consists of a total of 1.5kg of anti-matter plus 1.5kg of conventional matter, totalling 3kg of matter. The detonation thus consists of the violent annihilation of the matter by the anti-matter. From the famous Einstein equation we can deduce that the maximum possible yield of such a detonation is 2.7e17 Joules (64.4 megatons). We know that the weapon is not 100% efficient, and that in fact the yield is closer to 48 megatons, but for this exercise (since we want to give Star Trek every advantage) we will use the theoretical yield of 64.4 megatons.
The efficiency of the torpedo as a weapon is determined by the amount of destructive energy it delivers to the target. The detonation results in a spherical explosion, which means that should the torpedo detonate against an infinitely large flat surface, then half of the energy will impact the surface, and the other half will be directed away from the surface. So already, the torpedo as a weapon is only fifty percent efficient. However, this is the theoretical maximum. In the real world, it would be somewhat less than half the total yield of the detonation.
Furthermore, if the torpedo detonates some distance away from the target, then since the energy of detonation is radiated spherically, significantly less than half the energy will actually hit the target. have a look at this diagram.
As you can see, most of the energy is directed harmlessly into space, and beyond a certain range, only an insignificant fraction of the energy will actually hit the target. However, [thanks to Lord Edam da Fromage alias Michael Griffiths for the following.] In the TM the following two statements are made with respect to photon torpedoes.
1. Photon Torpedoes are directed against threat force targets at distances
from 15km to nearly 3500000km.
2. The TNG TM says it is the responsibility of the firing ship to ensure it is outside of the "explosion hazard radius" in all situations where the target is within 25km.
The two statements together implies that photon torpedoes have a hazard radius of anywhere between 15km and 25km. It is more likely to be 15km though, since the 25km distance might include the "proximity range" at which the torpedo will detonate. For example, the torpedo may have a proximity sensor causing it to detonate within 10km of the target, and if the target is only 25km away, then the explosion could be only 15km away from the firing ship. See statement 1.
Note that the statements also mean that a photon torpedo defintely has a spherical detonation, since at this range ("Explosive hazard radius") the detonation is still a hazard to the firing ship.
At 15km, the amount of energy which would reach a 600m long starship would be about 0.004% of the total energy of detonation, or about 2.7 kilotons spread over the surface area of the starship. This works out to an approximate Intensity of 95.3 magejoules per square meter. The significance of this figure is probably that this is the amount of energy beyond which the shields cannot protect the crew with 100% efficiency. That is, there is a risk of energy leaking past the shields at an Intensity higher than this (95.3 megajoules per square meter).
The most widely used torpedo in Star Wars is the Proton Torpedo. Others include various Concussion torpedoes. Although the yield of proton torpedoes are unknown, the figures generally bandied about range from 1 kiloton to 100 kilotons, with a few interpretations claiming five to ten megatons. According to Curtis Saxton all descriptions of proton torpedoes indicate that it is a fusion device. The smallest fusion detonation that modern technology can hope to induce would be of the order of 100 kilotons, and it would take significant scientific techniques of which we are unaware to make the detonation any smaller than that. However, in the inetersts of making an absolutely fair comparison I will use the MINIMUM claimed figure of 1 kiloton.
A large nuclear detonation is difficult to control, and as we can see from the discussion about photon torpedoes, extremely wasteful. However, a smaller detonation can be controlled with the appropriate technologies, the energy harnessed and focussed. We know that proton torpedoes focus all their energy in a very tight cone towards the target. Therefore, it is very likely that the proton torpedo was deliberately downsized to 1 kiloton to facilitate the harnessing and focussing of it's energy, allowing for this increase in the weapon's destructive potential. If we assume that the entire one kiloton detonation is focussed into a conical shape with the cone having an internal angle of fifteen degrees to the cone's normal axis, then we can calculate the Intensity of this weapon as a function of the range to target when it detonates. Let us compare the performance of Proton torpedoes to Photon torpedoes as regards their Intensity (energy per unit area delivered to target).
=========================================================================== Intensity Proton Torp Range Photon Torp Range Proton Torp vs J/m2 meters meters 9.54E07 J/m2 =========================================================================== 1.86E11 10 340 1,948x 7.43E09 50 1,699 78x 1.86E09 100 3,398 19x 8.26E08 150 5,098 9x 4.64E08 200 6,797 4.9x 2.97E08 250 8,497 3.1x 2.06E08 300 10,193 2.1x 9.54E07 441 15,000 1.0x ==========================================================================
The significance of the range of 15,000m (15km) is that this is the range at which a photon torpedo is still possibly a danger to the firing ship (see points 1 and 2 above). That is, a detonation at anything less than 15 kilometers will cause some degree of damage to the firing ship. This tells us that 95.4 MegaJoules per square meter is most likely the point at which the Trek ship's shields start allowing energy to leak through and impact on the hull. As you can see, a proton torpedo detonated 10m short of the target delivers TWO THOUSAND TIMES this amount of energy to the target. A direct hit on the shield will deliver several million times this amount of energy to that portion of the shield. Thus we can see that a proton torpedo, despite it's supposedly miniscule one kiloton warhead, is in fact an extremely efficient weapon, and very likely to cause a shield or hull breach against a Federation starship even if fired singly, let alone in co-ordinated volleys.
Even at a range of 200m, the proton torpedo delivers more than five times more energy per unit area than the suposed safety level. If we were to substitute the figures used with the more pessimistic figures, i.e., 48 megatons for Star Trek as opposed to 64.4 megatons, and 100 kilotons for Star wars as opposed to 1 kiloton, then the difference in efficiency between these weapons could be increased by more than a hundredfold.
It is also a testament to an ISD's shields that various (official) sources claim that it takes 48 DIRECT HITS of snub-fighter proton torpedoes in the same shield area to cause a momentary lapse in it's shields through which to do some pinpoint hull damage, such as knocking out sensor domes or weapons batteries. If we interpret the above tables to mean that a DIRECT HIT (sub 10m range) by a proton torpedo is at least 1,948x more intense than a Federation shield's safety rating, and it takes 48 torpedoes to breach the shields, then an ISD's shields must be 93,500 times more resilient than Federation shields.
This can also be somewhat misleading, as a direct hit by a photon torpedo is several orders of magnitude greater in Intensity than that of a proton torpedo, and that same level of Intensity will be spread over a much larger area of shield. It is difficult to predict (based on these calculations) how Imperial shields will hold up to a direct hit or very close miss by a photon torpedo.
If we calculate the intensity of a direct hit (sub 10m range) by a proton torpedo, we derive a figure of 1.86E11 J/m2. Multiply by 48 to determine the 'breach level' of a Star Destroyer's shields, and we get 8.92E12 J/m2. As a rough rule of thumb, we can assume that an Intensity of 8.92E12 J/m2 is sufficient to momentarily breach an ISD-I's shields. A photon torpedo would have to detonate at a range of approximately 120 meters or less to exceed this Intensity. Working with shorter ranges becomes mathematically difficult, especially for the proton torpedoes because the 'shaped' detonation impacts on a shield area which is a very small fraction of 1 square meter, artificially inflating the Intensity on a shield area tending to the microscopic. This is not true because the PROTON warhead has a finitely sized warhead.
However, it is safe to say that where the Federation can use (10km to 15km) proximity detonated torpedoes against ships similar to their own and expect to damage them, the same is not true for ISD's. They would have to score a direct hit (or close to it) to score any real damage.
There is also a down side to this efficiency. A photon torpedo which detonates inside the hull of a starship delivers all of it's 64.4 megatons to the target, while a proton torpedo will merely blow a small hole through the ship. Similarly, a photon torpedo detonated near a starship will always deliver some of it's energy to the target, whereas a proton torpedo will only damage targets inside it's cone of destruction. It is therefore possible that a ship can be bracketed by multiple photon torpedoes, their combined energy damaging the starship, whereas the same is not true for proton torpedoes. If you imagine a large cardboard box, and detonate a grenade nearby, you will always damage the box, but you may only fling it around a bit. However, if you fire bullets at the box, you will very easily punch holes in the box, but if you miss, there is no damage whatsoever to the box. By the same token, proton torpedoes are very efficient at 'punching holes' in ships, but only when they hit the target, or catch the target in their destructive cone. This is the job they were designed to do.