The Weak Hull Fallacy

Pro-Wars debaters like to claim that the hulls of Federation starships are thin, weak affairs, and some Rabid Warsies have even claimed that small arms fire (say, from a modern M-16) could pierce them!   Meanwhile, the faction claims stunning hull strengths for their own vessels. So, let's take a look at these myths, using some collision examples from both universes.

Ramming of the U.S.S. Odyssey

Examination of the ramming of the Odyssey from "The Jem'Hadar"[DS9], using the video capture provided by Mike Wong at stardestroyer.net, edited from a video capture from Stardock Alpha. The frame rate is 30fps.

(Background) In 2370, the Federation made first contact with the Dominion. The Dominion had destroyed Federation and allied ships and colonies in the Gamma Quadrant, as a show of force. In order to test the waters and perform a threat assessment, the Galaxy Class starship Odyssey was sent through the wormhole, accompanied at Sisko's insistence by three Starfleet Danube Class runabouts. Soon, they were under attack by three Dominion "battlebug" Attack Fighters. For the first time, Starfleet learned of the Dominion's phased polaron beam weapons, and the Odyssey's shields were ineffective. Captain Keogh ordered shield energies rerouted, and when he finally came to realize that the fight was hopeless, he ordered a withdrawal. One of the Dominion ships, however, was also given an order . . . the Dominion wanted to make it clear that the Federation was not welcome. In a move which foreshadowed later engagements in the Dominion War, the Dominion Attack Fighter rammed the Odyssey, resulting in her complete destruction a few seconds later.

The Dominion ship's ramming run involved turning the ship as it passed below the saucer, so that a direct hit could be scored on the engineering hull. Our first sight of the nose of the Dominion ship occurs at Frame 10 of the provided video capture, with the observation of the tail occurring at Frame 20. It should be noted, though, that the ship is not at a perfect angle for speed determination. Actual speed should be higher.

Frame 10:
The Jem'Hadar nose enters the frame, with the starboard warp nacelle also clearly visible.

Frame 20:
The Jem'Hadar tail has cleared the top limit of the frame.

The accepted length of a Galaxy Class starship is 642 meters, so determining the length of the Dominion ship is a simple affair of measuring it at closest approach.

Frame 65:
One frame before impact

The width of the ship appears to be at least 100 meters, suggesting a length (based on the studio model) of approximately 95 meters.  On the other hand, the crashed Jem'Hadar ship from "The Ship"[DS9-5], which had at least 15 meters hanging out of a rockface, is said to be embedded 90 meters into the rock.  And, as seen at the end of the episode, the vessel is visually indistinguishable from the class of ship above.   Nevertheless, we'll use 95 meters as a rough low-end estimate.

For the ship to move its own length of 95 meters in 10 frames at 30fps suggests a velocity of 285 meters per second, though uncertainties exist due to the angle of the ship's approach, and the fact that it is executing an upward turn. (Strangely, the ship seemed to be moving much, much faster in the prior shot, suggesting either rapid slow-down or slow-motion in this scene.)

To determine the kinetic energy involved, we would need to know the mass of the Jem'Hadar attack ship.  As this has never been stated, we'll have to guess.  First, based on a 3-D model of the vessel, the volume of the Jem'Hadar ship is approximately 40,000m³ .  The Jem'Hadar design ethic does not involve a lot of open spaces aboard a ship . . . as Dax noted in "The Ship", the Jem'Hadar "travel light" . . . no cargo bays were found aboard the vessel, and the ship's bridge and corridors would qualify as small and cramped.   Nonetheless, if we assume that only about 15 percent of the ship were taken up by bulkheads, structural supports, and other various components, then we would have a metal volume of about 6,000m³.

Alas, the density of the hull materials in use aboard Jem'Hadar ships is not known. If we assumed that the ship is made of iron, we could make a guess. Iron's density is approximately 7600 kilograms per cubic meter. Mass equals density times volume, so the mass of the ship would be 45,600,000 kilograms, or 45,600 metric tons.

This agrees well with certain lower-limits.  We know, for instance, that the Intrepid Class Starships weigh in at 700,000 metric tons.  If we used that as a baseline and estimated the ship's mass accordingly from the differences in volume, the Jem'Hadar ship should weigh in at about 45,000 metric tons. Using known Constitution Class mass, the ship could mass as much as 155,000 metric tons.   The true value should probably be in between the two . . . we'll use 80,000 metric tons, 15,000 less than the median 90,000 metric ton value.

Now, we know the speed and the mass, so we have all we need to do the math for kinetic energy:

KE = (1/2)mv^2
KE = (.5)(80000000)(285)^2
KE = (40000000)(81225)
KE = 3,249,000,000,000 joules

So, the kinetic energy of the Jem'Hadar vessel is estimated to be about 3.25e12J, or about 3.25 terajoules. Again, this is only an estimate . . . the Dominion Attack Fighter may be composed of far lighter materials, or materials far more dense.  However, 3.25e12J is a fair guess.

The damage to the Odyssey was extensive, but surprisingly limited. As you can see below, the entire navigational deflector array and a large chunk behind it was destroyed, the hull fractured all the way up the interconnecting dorsal, and a large fragment of one of the vessels went flying into the warp nacelle, where it sheared off the Bussard ramscoop. The visibly damaged area does not include the warp core, though it should only be about 20 meters away from the burning mass at the front of the secondary hull and it is hard to tell if internal damage extends that far. What is truly remarkable is that more of the ship was not destroyed by the collision. The damaged areas (not counting the nacelle) are confined to a box roughly 100 meters long, 100 meters tall, and about 130 meters wide.  

Based on a Lightwave model of the Enterprise-D, chopped up in keeping with the missing parts by reader "D-Five", the actual missing volume as seen in the image below is well under 230,000m³.  The model was upscaled quite a bit to avoid error, and based on the images of the model as chopped there was more of the ship present than is missing in the scene below, which also drives the estimate upward.  Assuming 5-10 percent of that area were composed of superstructure, that's 16,500-23,000m³ of material destroyed.

A Higher-Res Version of Frame 129:
Damage to USS Odyssey approximately two seconds after impact

Whatever her resistance to the damage, it was still extensive and not survivable. Approximately 3.76 seconds after the collision, the ship exploded due to what appeared to be a core breach.

Note:
I am intentionally ignoring the possibility of a Jem'Hadar core breach in this analysis, opting instead for the most conservative view possible. However, very fine and convincing arguments can be and have been made for such a breach, given the following:

Frame 67
Two frames into "impact"

The above frame offers the clearest view of what can also be seen in frame 66, the first frame of apparent impact. Note that the Jem'Hadar ship is exploding from within, even in areas not in contact with the Odyssey (for instance, the starboard warp nacelle). When compared to the behavior of Jem'Hadar ships colliding with Klingon vessels, the argument for a core breach is quite solidified (i.e. the other JH ships didn't blow apart in this fashion). However, given that a core breach is incalculable, and that a ramming offers the most basic and conservative estimate, I have chosen to leave that matter be.

Ramming of a Klingon Attack Cruiser

Two Jem'Hadar fighters slam into a Vor'Cha.  

(Coming Soon)

Ramming of a Klingon Bird-of-Prey

One Jem'Hadar fighter slams into a BoP

(Coming Soon)

Crash of an Intrepid Class Starship

In ratings symbolism, Voyager crashes into Dante's worst circle of Hell.

(Coming Soon)

Crash of a Trade Federation Command Sphere on Geonosis

(Coming Soon)

Asteroid Collision with Imperial Star Destroyer

Examination of the asteroid collision with an Imperial Star Destroyer bridge tower in The Empire Strikes Back, using the video capture provided by Mike Wong at www.stardestroyer.net, frame rate 24 fps.

(Background) A collision visually similar to the Odyssey destruction occurs in TESB, during the hunt for the Millennium Falcon. Darth Vader has ordered the pursuit of the Falcon to continue, even after the Falcon enters a dense, violent asteroid field in the Hoth system. An unspecified time later, the Imperial ships have taken damage, presumably disabling the shields of one unlucky Star Destroyer. Suddenly, a large asteroid zips into frame, colliding with the bridge tower of the Star Destroyer. The novelisation also suggests that the entire ship was destroyed, presumably after the collision, but that is not relevant for our purposes.

This calculation will be a little more difficult. The Odyssey calc involved a more easily determined "projectile speed", owing to the orientation as it came into view. The asteroid, however, comes from almost directly behind the camera to strike the Star Destroyer.

The asteroid enters the top of the picture at Frame 29, becoming completely visible by Frame 35, .25 seconds later. Unfortunately, the trajectory is such that it is difficult to tell how far it actually travels. So, we'll work backwards. First, let's estimate the size of the asteroid upon impact. Impact occurs at Frame 50.

Frame 50:
Collision

Two methods of scaling the asteroid can be used. One would be to use the shield/scanner globes atop the ship, which Curtis Saxton claims to be 43 meters in diameter. The second would be to measure along the upright portion on the portside of the bridge tower. Either method yields a figure of approximately 80m x 60m x 60m, give or take a few meters.

(Correction: I recently discovered that Saxton's universal globe figure is in error for the ISD-II subclass (referred to as such because a different, more detailed model was built after the more simplistic ISDs used in ANH). This page gives a well-researched bridge tower width in the 270 meter range. If that were correct, the bridge globes of the ISD-II would only be about 31.5 meters in diameter. This is confirmed by measurements of the entire 1600-meter ISD vs. the globes in this picture, so I will use 31.5 meters for the actual globe size from here on out, as well as the 270 meter figure for the tower face width. As a result, the asteroid is actually only 57m x 42m x 42m, give or take a few meters. I shall simply revise what follows, but I wanted to mention the reason I use the 31.5m globe figure for the benefit of the readers.)

So, now we know the size, roughly. Let's figure out how far away the thing is at Frame 50. Then, we'll figure out how far away it is at Frame 35, and we'll know roughly how far it went. As I read it, for 35 mm film, the asteroid size on Frame 50 corresponds to 3.73mm. If the asteroid is 57 meters long, this means that at impact on Frame 50, the asteroid distance was:

ObjectDistance/ObjectLength = ImageDistancetoLens/ImageLengthonFilm

or . . .

OD/57m = 35mm/3.73mm

OD = 9.38 x 57m

OD = 534.8 meters

Okay, cool. That works out to within my eyeball estimation, so that's good. Now, let's figure out how far away that bad boy was at Frame 35.

Frame 35:
Asteroid Fully Visible

Using the same methods and the same asteroid axis (adjusting for the funky angle), I read the asteroid as being 10.4mm. So:

OD/57m = 35mm/10.4mm
OD = 3.365 x 57m
OD = 191.8 meters

Fantastic. We now know that the asteroid travelled about 343 meters in the space of 15 frames, and at 24fps that works out to a speed of 548.8 meters per second. That's a nice clip . . . about 1,200 miles per hour.

Alright, time to get the mass. To do that, we need to know the volume and the density, which we can estimate. The asteroid is roughly cylindrical, so we'll estimate the volume to be 78,970 cubic meters. The density of your average asteroid is between 2000 and 3000 kg/m³, but we'll use the 3000 kg/m³ figure as a comfortable middle between the density of the moon (3300) and a silicate asteroid like 433 Eros (2600). This may, therefore, be an overestimation (most Sol system asteroids have densities of half of this figure).

We therefore arrive at 236,910,000 kilograms for the asteroid, or 236,910 metric tons. At a speed of 549m/s, the kinetic energy is:

KE = (.5)(236,910,000)(549)^2
KE = 35,702,455,455,000 joules

That's about 3.57e13 joules, or about 36 terajoules.

(A word of caution: the asteroid is rotating when hits, but I'm ill-prepared to factor in rotational energies. It does turn about 90 degrees in about a second, so the energies could be important or unimportant, depending on the nature of the impact. However, I doubt the asteroid's rotational energies would be a huge factor.)

The collision does severe damage to the Star Destroyer, utterly annihilating the bridge tower and interconnecting neck. It would have been nice to see what it would have done against the primary dagger-hull, but we are not so lucky.

Frame 73:
Damage to Star Destroyer

For estimating the size of the bridge tower, I shall use the corrected 31.5 meter figure for the shield/scanner globes (thereby working backward from the 270m to 31.5m figure), and the larger version of the following picture of ISD bridge towers from Saxton's site:

ISD Bridge Tower from TESB

Judging from the globes, the tower face is 268.3 meters wide, and the main bulk is 72 meters tall at the thickest point, tapering down to about 33.5 meters at the edges. The main bulk is in the neighborhood of 65 meters long, though this is an eyeball-underestimation. When all is said and done, it works out to a volume of about 939,000 m³. Again, this is just for the main, wide bulk of the bridge tower, and does not cover the scanner/shield domes, the thingy in the middle, or the interconnecting neck. The neck, just by eyeballing it, is 50m x 120m x 150m (though I have underestimated the length and height, I imagine), for a volume of 900,000 m³. Altogether, that's 1,839,000 m³ obliterated by the asteroid. Given the shape of the components and the common pro-Wars claims of ridiculously thick armor, I think it safe to say that at least 10-15% of this would be hull, structural support, and equipment, or between 183,900m³ and 275,850m³ of material.

It should be noted, however, that these calculations do not attempt to tackle the issue of whether or not additional damage beneath the bridge tower occurred. Unfortunately, our view is obscured by the debris. Given that most of the bridge tower was destroyed without direct contact from the projectile, the issue of additional primary hull damage is an open question. In any event, the TESB novel suggests that the ship was destroyed, so we must assume that it either took additional hits as it listed out of control, or simply exploded due to some sort of reactor failure.

Conclusions

With the two examples completed thus far, much can be inferred. The Star Destroyer took a hit approximately 11 times more energetic than the Galaxy Class starship, losing between 8 and 16.7 times the mass. This suggests that Star Destroyer hulls and Galaxy Class hulls are about equal in their resistance to kinetic impact. Granted, these are not rigid figures . . . I have been very conservative toward Star Trek and comparatively liberal toward Star Wars, in the hopes of avoiding bias. For example, though my volume figures for the Star Destroyer are fairly close underestimations, my Galaxy Class volume figures are gross overestimations. 

One calculation I have not made would involve stress per square meter. The Jem'Hadar starship was a denser projectile, with more of the mass striking in a smaller area. The asteroid, on the other hand, was less dense, with the collision occuring over a much larger area. I think such a calculation would rule strongly in the Federation's favor. Also, the Jem'Hadar ship seemed to make a mostly dead-on collision with a concave joint, whereas the asteroid hit a corner of the blocky ISD bridge tower. I would also wish to discover how areas of the ISD which were not under direct strain at the time seemed to dissociate and fragment with such ease.

There's also momentum to consider.  The impact against the ISD had only 5.7 times the momentum of the Jem'Hadar ship colliding against the Odyssey, doing far more than 5.7 times the damage.  However, because the KE values look better, they are the ones being employed.

It is also worth noting that the Jem'Hadar vessel seemed to disappear rather quickly, dissociating almost as fast as the asteroid did. There are several possible explanations, none of them certain: a self-destruct, containment breach, et cetera. What is clear is that at the moment of impact, the warp engines and thorax all appeared to explode individually. If some sort of self-destruct was used, it can be assumed that this would drive up the relevant energy considerably. A self-destruct is also the only explanation which fits the fact that the battlebug's port nacelle didn't appear to do any damage at the location where it would have been expected to hit. It may also explain how so much damage occurred in a downward direction, whereas the battlebug seemed to be aimed at and collide with the engineering hull neck joint, just aft of the torpedo launcher.

In any event, both collisions resulted in the destruction of the ships.

I think the safest conclusion to make is that the hull strengths are roughly equal in regards to impact resistance, and in reference to these two canon examples.

Mike Wong of StarDestroyer.Net has also posted analyses of collision events. However, his figures are replete with error. First, he suggests that the bridge tower asteroid was 70 meters and spherical. Then, he uses a density for the asteroid roughly twice that of any known asteroid. Finally, he estimates the speed to be 1000 meters per second, when photographic analysis shows the speed was approximately half of this. In other words, he made it bigger, heavier, and faster, thereby bumping up the kinetic energy to a whopping 625 terajoules, or about 20 times my calculated figure.

Then, he talks about the ramming of the Odyssey. After assuming that a downloaded clip of the special effects of that episode was representing the total time of the battle (hence his silly claim that the ship was destroyed after a battle of "less than 30 seconds"), he gives the Jem'Hadar fighter an estimated size and estimated mass. What goes unmentioned is that the density he uses for the Jem'Hadar fighter is 50 kg/m³, or 5% of water's density! He does make up for this a bit by "generously" tripling the actual speed of the Jem'Hadar fighter. However, even having neutered the Jem'Hadar ship's mass, he still managed to end up within an order of magnitude of my conservative calculated figure.

By monkeying with the numbers, it's easy to end up with the ISD taking a hit with 125 times more kinetic energy than the Odyssey ramming. However, such figures are unsupportably wrong.