Battle of Britain

What follows below is the version of the page as it existed on January 6, 2003.  I have created these back-ups for the sake of historical accuracy, since my site and its pages will continue to evolve long after StarDestroyer.Net's attempted "attack on [my] credibility" is forgotten.


Ewoks, Tree Trunks, and Imperial AT-STs


This brief look at the Imperial Ford Pinto was created using a high-quality 25fps vidcap of RoTJ. The brightness was lacking, however, so I have therefore brightened most of the images on this page, and the filenames are marked to reflect this when it occurs.


Quick Reference: AT-ST vs. Swinging Logs, AT-ST vs. Earth, AT-ST vs. Phaser Rifles, AT-ST vs. Gravity, and Concluding Remarks


AT-ST

In Return of the Jedi, we are treated to the combat skills of what the Emperor describes to Luke as "an entire legion of my best troops", during their crushing defeat at the hands of the Teddy Bear Horde. In use at Endor were small biped walker vehicles. In the non-canon, these are known as AT-STs, or "All-Terrain Scout Transport", a knock-off of the canon "All-Terrain Armored Transport" term from the TESB novel which refers to the huge four-legged AT-AT walkers. In spite of the non-canon denigration of the vehicles, AT-STs are evidently the premiere small combat vehicle of the Empire, not reconnaissance vehicles or transports (how does one do much transporting in a two-seater?). We have witnessed their frontline combat use at Hoth alongside the larger AT-ATs, and we see them serve as the primary fighting vehicle in the thick forests of the Endor moon. In the RoTJ novelisation, they are referred to as "war wagons", "armored vehicles", and "war-machines" . . . in the script, they are "giant", "mighty machines" . . . hardly terms befitting a mere scout. Indeed, the only scout/recon activity we see is performed on the speeder bikes which suit the role best. Nevertheless, I yield to the conventional designation of "AT-ST" (whatever it would more properly stand for), simply for the sake of easy identification.

In the midst of the Endor battle, the Ewoks begin employing their primitive, pre-industrial technology against the Imperial walkers. Some of these attempts were unsuccessful, such as those involved dropped or catapulted rocks. Other attempts were literally "smashing successes". One such effort involved two logs suspended in the air which, when released, swung into one another, crushing the AT-ST between them. This total destruction of the vehicle is an interesting event, worthy of further examination, since it lends itself well to analysis of Imperial armor.


The Log Smash

First, the basics.

A cropped and marked version of the frame above

The above image offers a nice opportunity to perform scaling to determine the size of the AT-ST. The commander's entire torso is visible, along with several easily measured areas which can serve as excellent size reference. In the image, the commander's height from belt to the top of the helmet is 39 pixels. The height of the chin gunwell is 45 pixels, width being 49 pixels. The upper, outer corners of the viewport "eyes" are 76 pixels apart. (Though the front face is angled in this view, it happens to measure 139 pixels from the bottom of the outer chin to the top of the forward face.)

Assuming a standard height of 1.8 meters for the commander (1.9 with helmet), a likely height from helmet to buckle should be about .8 meters, especially given the high-riding belts on those uniforms. However, we'll still give it .9 meters, since such overestimation shall prove conservative for later uses.

This allows us to get a rough meters per pixel figure at the commander's range. In this case, it is approximately 0.023 m/px. With that figure, we may estimate the chin gunwell to be 1.038 meters tall and 1.130 meters wide. The viewport line reads 1.754 meters. (The face is just under 3.2 meters tall in this image, suggesting a total height of just over nine meters. Given that the full-scale model of the AT-ST was built to a height of 8.13 meters, the aforementioned presumption of overestimation is correct.)

Now that we have a workable estimate for the size of the AT-ST crew cab, we can now perform scaling work with the logs which destroyed the AT-ST, determining all that is required to get an estimate of their kinetic energy.

The AT-ST and logs

The above image occurs about one frame before the impact of the left-hand log. The right-hand log has already begun colliding with the extension on the side. As you can see to the right, the width of the chin gunwell is 53.3 pixels ('Pythagorized' due to the angle). The top outer corners of the viewports measure 93.3 pixels. The angle of view evidently produces some distortion, since getting a meters per pixel figure from the chin gunwell gives us 0.0212 m/px, whereas the viewports give us a mere 0.0188 m/px. I shall use the larger figure in this instance, and given that the logs are a bit more distant, I shall bump that figure up slightly to 0.022 m/px. The diameter-line of the left trunk is at an angle, but is reached by two corners of a box 67px by 10px. Overestimating slightly, we arrive at 67.75px for the diameter of the log. At 0.022 m/px, that gives us a log diameter of 1.49 meters . . . 1.5 for short. Note, of course, that the log's end is much thicker than the remainder . . . but nevertheless, the full 1.5 meter figure will be used. Now to the length. Unfortunately, we never get a perfect shot of the entire log. But, we do see the lines which suspend it, and can make a reasonable guess. The distance from the rope to the edge of the trunk (before the point starts) is 94.7 pixels. At 0.022 m/px, that's a hair over 2 meters.

The log in flight,
image marked for measurement

The only clear shot of the entire log is in the frame above. I am assuming that the front and rear anchor points are the same distance from the edges of the logs, which not only appears to be the case, but also makes good sense under the circumstances. If so, then the length of the log is approximately four times the length from edge to rope. We'll give it 4.5 for safety's sake.

So, we arrive at a log which should be nine meters long. That, with the diameter, works out to a volume of 15.9 m3.

Now, to figure out the mass, all we need is the density. According to this PDF published by the United States Forest Service, a wood's maximum possible density would seem to be about 1,750 kg/m3. (The highest I've found mentioned elsewhere for wood that's still "green" (i.e. with high water content as opposed to the dried-out, lower-density wood as used for construction) is from another Forest Service publication, which had a particular species of oak in the 900 range.)

It should be noted, however, that the density could not have been extraordinarily high. The trees had to have been able to stand upright when living, of course, but we must also consider the fact that the Ewoks weren't exactly working with Kevlar rope. As seen below, a simple stone axe was sufficient to cut the main cable holding the logs in place, and it is likely that a similar material was used to suspend the logs. Unless a mind-boggling array of pulleys was being used, this could place some severe limits on the mass of the logs.

The release of the logs
   

A volume of 15.9 m3 at a density of 1,750 kg/m3 gives us a total mass of 27,825 kilograms . . . which we'll just round up to 28,000 kilograms for ease.

And now, for the kinetic energy, we need velocity . . . we have the mass.

First frame with left log visible


Impact, 11 frames later
This is gonna hurt.

The logs travelled 243 pixels over the course of 11 frames, for an average speed of just over 22 pixels per frame. At 0.022 m/px, that works out to .486 meters per frame. The video capture I have is at 25 frames per second, which gives us a speed of 12.15 meters per second. So:

KE = (1/2) m v^2
KE = .5 (28000) (12.15^2)
KE = 14000 (147.6225)
KE = 2,066,715 joules

That, friends and neighbors, is not even 2.1 megajoules, but we'll call it that for short. (Note: With a wood density of 1000 kg/m^3 (which would seem to be a more common high-end figure), the KE would drop to a mere 1.2 megajoules.) This is roughly equivalent to a 2300kg minivan (such as a Chevy Lumina minivan) crashing into the cab at 100 miles per hour.

And what was the effect of two such log collisions at once? One frame after the left log's impact, the AT-ST is seen bursting into flames. It should be noted that the full impact of the logs isn't even complete.

Then, the logs continue on their path, totally crushing the cab as they appear to meet in the middle:

"Look sir!  Chunky salsa!"

A few frames later, all that's left is a smashed cabin and burning, smoking debris.

Note also that the logs rebounded after impact. Apparently, some of the impact forces involved appeared to transfer across to the cab to the opposite logs in a bounce effect, in a manner not unlike the popular swinging ball desktop toy. Nevertheless, if we assume that the AT-ST's armor had managed to stop the logs entirely, then we can get a decent estimate of impact force on the armor. The hull was 83 pixels wide (we'll say 70 for ease and to account for squished metal and troops). At the aforementioned 0.022 meters per pixel, that's a stopping distance of 1.54 meters. We therefore end up with an impact force of 1,342,022.72 newtons. Let's say that the somewhat-pointed tips of the logs were squares a mere 10 centimeters wide, and assume for the moment that the point angle is far more acute (in bullet terms, a longer ogive . . . i.e. that the rest of the log's diameter wasn't about to hit, too).

This works out to a pressure of 134.2 megaPascals. If we go with the full size of the log, this pressure would drop to 596.5 kilopascals.

Though the armor was not visibly pierced by the logs, the armor was severely bent and mangled (along with the structure of the vehicle). Barring some exotic armor material that is extremely soft and malleable against logs yet unpiercable by conventional means, we can make a few comparisons.


AT-STs vs. Modern Earth

1. A .44 Magnum

According to ballistics testing and information websites, a .44 Magnum bullet weighs in at 15.55 grams. Common muzzle velocity is around 426 m/s. This works out to just under 1411 joules of kinetic energy. If the primary armor component of the AT-ST is a mere centimeter thick (for example), it would most likely penetrate. Why? Given the bullet's size (.429 inches, or 1.09cm), total frontal area should be 0.9331cm2. Thus, the pressure would be 151,208.7 N/cm2, or 1,512 megaPascals, over ten times the figure for the 10cm log of the same mass.

So how thick is the armor in reality? Unfortunately, we don't know. In the shot I used and marked to scale the log, we do see the viewport covers roughly edge-on, and they seem to be no more than 5 pixels thick. At 0.022 m/px, that's .11 meters, or 11 centimeters. Assuming that's common for the remainder of the vehicle, the impact force drops to 12,827 newtons, with the pressure dropping to about 13.7 kiloPascals. So, unless someone fires into the wide-open, window-less viewports of the AT-ST, the crew is almost certainly safe from handgun fire.

2. A M829A2 "Silver Bullet" Depleted Uranium anti-armor round

These are tank rounds, fired to excellent effect by M1A1 and A2 Abrams tanks during the Gulf War. According to this site: "... the current A2 version throws a slightly longer (30") but skinnier (.8") 10.85 pound dart at 5512 f/s."

10.85lb = 4.921kg
5512f/s = 1,680 m/s

KE = .5 m v^2
KE = 2.4605 (2822400)
KE = 6,944,515.2 joules

To stop that force in 11 centimeters, the armor of the AT-ST would have to withstand a force of 63,131,956.4 newtons. At .8 inches (2.032cm) dart diameter, that works out to a frontal area of 3.24 cm2, for a pressure of 19,485,171.7 N/cm2, or 194,851.7 megaPascals. I think it safe to say that the AT-ST will be nicely slain by such a round.

3. 30 mm GAU-8/A firing DU rounds

As per this and FAS.org, "Depleted uranium rounds are also fired by a 30-mm, seven-barrel gatling gun mounted in the nose of the A-10 Thunderbolt aircraft, the only U.S. military plane that employs depleted uranium rounds. Depleted uranium is the primary munition for the A-10 Thunderbolt for combat. Each 30-mm depleted uranium projectile contains approximately 0.3 kg (0.66 lb) of extruded depleted uranium metal alloyed with 0.75% titanium. The projectile is encased in a 0.8-mm-thick aluminum shell as the final depleted uranium round." A link from the FAS site offers a DU penetrator diameter of 15mm. At a reported speed of 3,300 feet per second, we have the following:

KE = .5 (.3) (1,005.8)^2
KE = 0.15 (1011633.64)
KE = 151,745 J

For 11cm armor, that translates to a force of 1,379,500.4 newtons. At 1.5cm DU penetrator diameter (ignoring the remainder of the bullet and mass for the time being), we thus end up with a pressure of 780,637.5 N/cm2, or 7,806.4 megaPascals. Let's not even mention the firing rate of the A-10's gun.

4. A red and black customized 1982 GMC van

Previously, I've half-jokingly speculated that based on eyeball estimates, the AT-ST was no more resilient than a minivan. Well, whether or not that's the case, it is interesting and amusing to note that if we were to assume that Mr. T's "helluva-tough", "helluva-fast" customized 1982 GMC Van only had the weight of a modern Chevy Lumina minivan (a little plastic thing weighing in at 2325 kilograms) and that it was travelling at 100 mph (160.9 km/h, or 44.7 m/s), it would have a kinetic energy of 2.3 megajoules, .2 megajoules more than an individual log, and impact would occur over a similar area. Of course, 2325kg is only the weight of Mr. T's gold chains, so your figures may vary.

And yes, he would likely hit the legs, which are probably somewhat tougher than the head. Some have suggested that the head would be very light for weight distribution, but this is not necessary. We bipeds carry a great deal of our weight above the legs, as do most living quadrupeds. It is not the most stable configuration possible, but it serves us quite well for mobility. Further, the slip and fall of the AT-ST on the logs demonstrates that stability is not exactly an AT-ST specialty. But, we'll come back to that shortly. For now, I'll simply point out that such a collision would almost certainly result in a knock-down.


AT-STs vs. Federation phaser rifles

Phasers are a funny thing. They can stun people, heat rocks, melt things, blow things up, and vaporize them without actually producing vapor. Nevertheless, we do have a canon statement regarding their power:

In "The Mind's Eye"[TNG], Data and Geordi are in Engineering testing a recovered phaser rifle. Though it turns out to be a copy of a Federation rifle and of Romulan origin, the following energy usage comment by Data illicits no apparent suspicion:

Data: "Energy cell usage remains constant at 1.05 megajoules per second. Curious . . . the efficiency reading on the discharge crystal is well above Starfleet specifications."

A few seconds later, Data mentions that the normal phaser discharge crystal fires with 86.5% efficiency, which (for example) could be taken to imply a firepower of .91 megajoules per second. According to DITL, the weapon is fired for a total of 51 seconds. We do not know if the stated draw is the maximum of the phaser rifle, nor are we told the actual output. On the other hand, we know that hand phasers can vaporize human beings. Just to vaporize a single kilogram of water at 37 degrees Celsius requires 2,764,600 joules (2.7 megajoules), so we know that the effective output of a phaser should be in this range, at least. In TOS, TNG, and Insurrection, we've seen phasers used to heat rocks to glowing or blow them apart, and we've been told of thousands-of-degrees temperatures being created by phasers. Even at .91 megajoules, though, and assuming a 3cm2 beam spread, we're still looking at 3000 newtons per centimeter, or 30 megaPascals as a possible phaser discharge level upon striking armor. This compares rather favorably to the AT-STs kinetic armor potential, though its armor may have energy dissipation abilities we don't know about. It is quite likely, however, that a phaser would be more than sufficient to defeat an AT-ST, especially when the more energetic phaser capabilities are considered.


The Fall

Of course, some have claimed that phasers are ineffective against any dense, tough materials. This claim, though absurd, is rather common in Warsie circles. Even if we were to benevolently grant the claim some validity, however, AT-ST armor is most decidedly not an uber-dense material. Behold the behavior of an AT-ST that merely falls over after slipping on a few logs:





Note that upon impact, the entire head section warps considerably before the entire vehicle explodes in flames. Even the guns, vertical in the last image above, have bent. This hardly constitutes proof of wondrously advanced or dense materials. Further, the designers evidently didn't even know that armor set at an angle gives an artificial but apparent thickness boost . . . all the armor is set in a nice flat box, right where it can be shot clean through, if shooting (as opposed to tripping, mentioned in the novel) were even required. (Angling one's armor is why modern tank turrets look like this.)


Concluding Remarks

In short, the AT-ST is, for all intents and purposes, the Galactic Empire's most embarrassing ground combat vehicle. They are, as the novel states, "clumsy armored vehicles", and extremely fragile ones at that. If we assume that the Emperor's best troops got his best equipment, then it becomes even more embarrassing.

It should also be noted that, as a matter of general principle, one's land-based combat vehicles are usually tougher targets than one's aircraft. Of course, in the repulsor-lift-capable Empire, this may not be so, but, if it is the case, then TIE fighters are tin cans of death.


Special thanks to T. Lee for corrections regarding modern military weapons.
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