Scaling the Death Stars

Quick Reference: 
Page 1:    DS1 Scaling, Falcon Yardstick, DS2 Scaling, Shuttle Yardstick, Saxton vs. Sarli
Page 2:    Alternatives, The Endor Issues, Conclusion

We are told the following in the prologue of the Return of the Jedi novelization, regarding the second Death Star (DS2):

"The Death Star was the Empire's armored battle station, nearly twice as big as its predecessor, which Rebel forces had destroyed so many years before—nearly twice as big, but more than twice as powerful. Yet it was only half complete."

In and of itself, this tells us little.  For instance, I could say that the Galaxy Class Enterprise-D, with a length of 642 meters, was over twice as big as the Constitution Class Enterprise-A, with a length of 305 meters.  Alternately, I could say that the Enterprise-D, with a volume of over 5.8 million cubic meters, is almost 25 times bigger than the Enterprise-A, which only has a volume of less than a quarter-million cubic meters.   

Fortunately, we can perform the requisite scaling work to determine just how large the two Death Stars may be, and even more fortunately, some of this work has been done already.

DS1 Scaling

Curtis Saxton has used the zoom-in on the polar trench from the Dodonna briefing screen schematics in ANH to derive a value of 93 - 169 kilometers for the first Death Star, though he does not give details on the methodology employed.   His other canon-based scaling effort regarding the DS1 involves a lower limit of 125 kilometers, based on the relative polar trench length on the Dodonna briefing screen, with the assumption that the fighter computers were showing distance in meters.   However, the briefing schematic was rather dissimilar to the actual Death Star: the most eggregious error gives us the superlaser dish centered on the equator.   Further, the assumption that the Rebel fighter indicators showed a range in meters does not hold . . . the fighters would've had to have been travelling at better than 2.5 kilometers per second, which is flatly contradicted by the exterior visuals.

Lacking methodology and false assumptions aside, however, those efforts with the canon make a fair starting point.  The alternative would be to use the lesser-canon AoTC novelization statement that the Death Star is a "planet-sized" battlestation, which is ludicrous even by eyeball estimates of the film material.

So really, what is needed is a fresh start.

The Falcon as Yardstick

Perhaps the best thing to do would be to scale the docking bay the Falcon was tractored into in ANH, and work backward based on the scenes of the Falcon's capture.

First, some caveats.  Any estimate which is based on taking a small object and using it to scale a very large object is going to have its potential pitfalls . . . perspective distortions, pixel resolution, unavoidable rounding errors, and so on.  Uncertainty regarding the small object can blow up into increasingly large uncertainties regarding the large object.  Nevertheless, there are ways to mitigate these effects to the best of one's ability, and I shall employ them as much as possible below. 

Second, the pixel-counts described below are from the files themselves.  For aesthetic reasons, the presentation of images has them scaled to 800 pixels in width.  If you wish to follow along in the scaling, then, you'll want to copy the image files (e.g. right-click and save-as), instead of copying the images as presented.

With that out of the way . . . 

Based on assorted debates regarding the size of the Millennium Falcon at the old STrek-v-SWars.Net and StarfleetJedi.Net forums, the width of the Falcon is approximately 22.5 meters.

The DVD scene above shows a docking bay height of 309 pixels, compared to the ~396 of the Falcon's width.  That suggests a bay entrance height of 17.55 meters.  The two images below, in reverse order from how they are in the film, carry us outward from the docking bay, so we can see more of the trench itself.

It is easy to determine which bay the Falcon was flying toward, based on the shots above.

In this brightened key to the second image, it is the one circled in deep blue.   The more distant (circled) bays within the submerged dock area the Falcon flies into appear to be of equal height to the Falcon's intended bay, which allows us to scale the height of the entire submerged dock area (note the farthest wall). 

Now, let's zoom in a bit to get the full detail of the HD version of the film:


The farthest section of the nearest left-side bay . . . in other words, the bay wall closest to the column . . . measures 20 pixels.  The nearest section of the farthest left-side bay measures 18 pixels.  Assuming that 17.55 meters equals 19 pixels, then the height of the column between the two bays, measuring 497 pixels, is 459.1 meters.  Since the submerged dock area is apparently rectangular, this means that the outermost section of the submerged area is about 460 meters tall.

If you look to the left and below the Falcon, you can also see (circled) what seems to be another submerged dock area further along the trench, which appears to be the same height as the closer one.  It is marked by the yellow ellipse.  At that dock area's closest point, it measures 191 pixels in height.  The large column extending above and below the dock area (split in two by that area) measures 512 pixels in height, giving a value of 1,230.6 meters for the entire height of the column.   Judging by the lack of any other visible features, that value holds for the entire trench.

Thus, we can conclude that the height of the equatorial trench of the first Death Star measures just over 1.23 kilometers.

Last, but not least . . .

The trench is receiving some direct lighting of the interior in this shot, which could complicate scaling a bit.  However, we can see on the left-most side that the trench is at least 7 pixels in height.   The Death Star itself is 660 pixels in height.   Thus the entire Death Star, here some 660 pixels tall, is thus 116,027.9 meters tall in this image . . . or 116 kilometers.

However, there are two issues here that it would behoove us to make note of.

First, the image above shows us a Death Star that is not perfectly spherical.  Using a brightened image, one finds that the Death Star as shown above would be some 715 pixels in width, giving us a Death Star width . . . not height . . . of 125,696.9 meters, or 125.7 kilometers.

Checking against the DVD version of the image above and past literature, we find that this is not simply an artifact of the HD broadcast available in North America.  715 divided by 660 gives us an 8.33% greater width. 

In the shot above from the DVD, measurement brings us a difference of about 7.2%, which is very close.  A reprint of a shot of the Death Star model that Saxton provides in comments on Revenge of the Sith is very near this value, at 7.67%.

Happily this issue is largely irrelevant up until this point, since we've exclusively been measuring height, and not mixing measurements of height and width.  The one exception was from the first image wherein we measured the Falcon's width, but that image came from the DVD anyway. 

Assuming the DVD to be preferred for the purpose of finding the Death Star's width, then using the percentage increase in width from the DVD for the DS wide shot we would want to adjust the Death Star width to 124.4 kilometers.

Second, the measurement above involves us being forced to measure a small number of pixels at one point, as we measure the trench versus the entire Death Star.  With only seven pixels for the trench, a difference of even one pixel can produce vastly different results.   For instance, had we measured six pixels for the trench (forcing each pixel to cover over 200 meters of height), then the height of the Death Star would've come out to (1230.6/6)*660, or 135 kilometers.

On the other hand, one wishes to make as few 'hops' as possible in such a scaling, since the opportunity for small errors of rounding or pixel count increase with each step in the procedure.

Thus, it would be preferable to confirm ourselves via another step or two between the trench and the whole Death Star, just to check out those 7 pixels.

The best thing available for use would be the brighter band that runs along the trench.  While it is not perfectly invariable in its height, choosing the same location (if possible) can mitigate this to near-zero.   For instance, let's take the shot of the Falcon being tractored in from the DVD:

As you can see, I've rotated the frame so that the area beneath the superlaser is approximately level.   Why pick the spot below the superlaser, and not a closer location where we would have more pixels?   The reason is quite simple, really.  If you look at the white longitudinal (i.e. up & down) bands on the southern hemisphere of the Death Star, you'll note they are reversed in the image above compared to the wide shot.  Thus it's safer to go directly below the superlaser rather than risk additional problems.

So, beneath the superlaser we have a brighter latitudinal "waistband" of 129 pixels height, compared to a trench height along the same line of 16 pixels.  16 isn't great, but it's still much better than 7.  With these measurements, the band comes out to 9,921.7 meters.

In the wide shot, then, we have a band height of 52 pixels compared to 660 for the Death Star's height.   This gives us a total height of 125,929.3 meters, or 125.9 kilometers.  The Death Star width, using the DVD difference, would be 135 kilometers.

Splitting the difference between the two different methods to get the final height (which gave us 116 and 126 kilometers, respectively), we can estimate the Death Star to be some 120 kilometers in height, and 130 kilometers in width.

(The 120km figure, pleasantly enough, is the commonly accepted value, and fits within the scaling efforts of Saxton that were canon-based.  Also, not incidentally, that makes the superlaser dish about 36.25 kilometers in diameter.)

DS2 Scaling

A second Death Star of "nearly twice" that size would be either (a) somewhat smaller than 240-260 kilometers in diameter, based on a near-doubling of the diameter, or (b) up to nearly 160 kilometers in diameter, based on a near-doubling of the volume.  Given the specific reference to the second Death Star's incompleteness, there would be a bit of a fudge factor involved . . . in other words, DS2 could perhaps be somewhat larger than 250 or 160 kilometers and be within the bounds of reason.

Curtis Saxton has made use of canon and non-canon images and estimates of the size of the Imperial shuttle, using it to scale DS2 in a manner similar to the DS1 Falcon scaling above.   He arrived at a value of 270 kilometers for the station diameter (which, in the original version of this page, I accepted and employed).   Such a value would fall roughly within the diameter-doubling option.  However, fellow EU author and Star Wars researcher Gary M. Sarli has claimed a fatal flaw in Saxton's work, one based on a confusion of the docking bays of the second Death Star.   His scaling efforts place the second Death Star in the neighborhood of 160 kilometers, or nicely in line with the volume-doubling option.

So, which is it?   Ought we double the volume, or double the diameter?   As with the first Death Star, it seems to me that the best way to decide would be to take it from the top.

Imperial Shuttles as Yardstick

As noted, it's possible to derive DS2 scaling based on the Imperial shuttle, with a method akin to the one used earlier with the Falcon.   What is first needed, however, is data on the shuttle.  Both Saxton and Sarli use a width figure for the Imperial shuttle (in landed configuration) of 12.56 meters, a figure obtained from EU blueprints.  However, it is always best to work from the films themselves, so let's double-check that figure.

The shot below (which, incidentally, is one of my favorites and which I've been waiting to use in anything for ages) shows Darth Vader, identified in the first chapter of the ANH novelization as being two meters tall, just stepping off of the ramp of his shuttle in RoTJ.   His height is approximately 54 pixels in this view, with the shuttle's main hull/lower deck also being 54 pixels tall at the closest edge on the right side.   This suggests that the wide section of the main hull (i.e. the one with the wing hinges) is two meters tall.

Thus, in the wider-angle shot below of Vader's arrival at the beginning of RoTJ (which is a more perspective-free front view), the main hull's 19 pixels of height and 115px width give us a main hull width of 12.1 meters, comfortably inside the 12.5 meter value of the total shuttle (including the raised wings that jut out ever so slightly) that Saxton and Sarli employ.

For simplicity's sake, we shall also use the 12.5 meter figure for total shuttle width, including wings when raised.

Upon Vader's arrival at the second Death Star, his shuttle approaches and lands at one of the docking bays seen below.   Thanks to the pattern of the DS2's incompleteness, we can also say with certainty that the later landing of the Emperor and the escape of Luke at the end of the film also involve these "VIP bays".

Vader's approach is photographically well-documented, and shows unquestionably that he lands in the smallest visible bay above, which can be seen just off of the upper right corner of the largest visible bay.  The interior of that bay is seen below, at the end of Vader's arrival sequence:

The shuttle has quite clearly crossed into the bay aperture, and, depending on its precise height from the floor, appears to have its fore-aft centerline over the glowing threshold.   The shuttle main hull width in the image is 40 pixels, the total shuttle 44 pixels, with the entire aperture measuring 244 pixels at the inner rim at a height similar to that of the shuttle's.   Given estimates of a 12.1 meter main hull and a 12.5 meter wide shuttle, this means that the aperture is roughly 69.3 - 73.8 meters wide, and the reflection would appear to suggest a bay height on the order of 35-45 meters.

When the Emperor arrives at the battlestation later in the film, he uses the very large docking bay, as seen below.

(It would be lovely if the Emperor's shuttle or even the troops standing near were sufficiently large and visible in this image to allow for direct scaling . . . hopefully the Original Trilogy DVDs will make life easier in that regard.)

This tighter shot allows for a better view of the VIP bays.  The bay in which Vader landed is visible in the scene as the 24 by 16 pixel bay directly to the right of the various upperworks of the largest bay.  Given an average estimated width of 71.55 meters, this suggests a height of 47.7 meters.  This seems a little on the high side given the reflected image from the floor of Vader's bay, but then Imperial docking bay floors do not seem to be a good source of accurate reflections.  In the image below, note the aperture glow's reflection on the floor, with its odd stopping, angle changes, and other peculiar errata visible in the Emperor's bay . . . Vader's floor shows the same peculiarities once the shuttle has landed.  

In any case, we now have a good external point from which to scale the battlestation.   First, we'll use the tight shot to get a firm estimate for the largest bay.   We can then use the wider shots which feature the large bay to measure other, larger features.

With the above, we can determine from the 71.55 meter bay employed by Vader (marked in red) that the Emperor's bay (marked in green) is almost 373 meters in width, and almost 170 meters tall.

By employing the wider shot from Vader's arrival, we can thus scale the entire trench.

The Emperor's bay within the VIP bay inset is 52 pixels in width.  The outermost part of the VIP bays' inset structure is 96.5px tall.  There is a depth difference involved of at least a couple of hundred meters distance due to the inset.  However, with the upper left inner corner not visible, the best we can do is to estimate based on the angles . . . "level to eyeline" in this case is just a few dozen meters above the VIP bay inset's 'ceiling'.  My estimate of 90px is in light blue.  

The inner trench wall reads 181 pixels, suggesting a total trench height of 1,210 meters.  As seen in the two images below, the lighter-colored waistband is a little variable in its height . . . but if we take the rightmost section (which seems to be the least variable), we can get a total waistband height of approximately 3.83 kilometers.

And, finally, the image below shows the right-hand side of the waistband as being 12 pixels tall compared to the station width of 488 pixels. 

Thus, working out from the trench using various wider shots of the DS2 as was done with the DS1 Falcon estimate, we arrive at a final value for the entire station of 155 kilometers.  

The above is not a dead-firm figure by any means . . . the true figure might swing a dozen or more kilometers in either direction.   However, it does seem to suggest that the volume-based doubling is the way to go.  Interestingly, it also happens to correspond with the commonly accepted value for the second Death Star of 160 kilometers.   (That value, rather entertainingly, serves as a rough midpoint between my 155 kilometer result and Sarli's 166 kilometer result.)  

As before with the first Death Star, I'll make use of the common figure of 160km for the sake of simplicity.

Saxton vs. Sarli

Having engaged in the above, we now have the context with which to understand the dispute.

Saxton engages in a canon-based scaling of the bays and the equatorial trench and derives a value for the entire station of about 270 kilometers.   (Regarding his final conclusion of 900 kilometers, see here.)

However, as part of a page debunking Saxton's "Endor Holocaust" theory, Sarli argues that Saxton erred in regards to the docking bays, mismatching which were being shown.

The issue revolves around the scenes of Luke's escape from DS2:

Saxton assumes that the docking bay from which Luke escapes is the same smallest one that Vader entered at the start of the film, and takes these closer exterior views of the shuttle and bay as a source of scaling information.   Using one of his shuttle height figures of 22.25 meters and an estimate of the height of the bay, he arrives at a height of 64 meters, and scales the rest of the exterior shots according to this height.

Sarli argues, however, that Saxton made no effort to verify this assumption that the bay in which Vader landed and the bay which Luke escaped from were the same bay, and he is quite correct.   His argument can be restated as follows:

Remember, the external view of the bay Vader landed in showed quite clearly that the bay was 24 by 16 pixels.  Even assuming some pixel counting error, that puts the bay somewhere in the neighborhood of 1.5 times as wide as it is tall.   Since we got that clear view of the shuttle entering when Vader landed, we can take the scaled width and the known width/height ratio and say that the bay has to be between 45 and 50 meters tall . . . or perhaps 40 - 55 meters tall at the outer limits of reason. 

Saxton, however, argues for a 64 meter bay height.  This figure is not only out of bounds, but is also wrong by itself. Using my middle image above, we can see that the shuttle is 80 pixels and the visible part of the bay at that location . . . ignoring that which we cannot see . . . is 235 pixels.  If we assumed Saxton's 22.25 meter value were valid, then just that part of the bay aperture we can see is over 65 meters tall . . . in other words, we've not even acknowledged the full height of the bay and we're already above his figure.   (The reason behind the peculiarity of his figure is that is that he used an image of the shuttle after it had already exited the bay, and was well toward the left of the screen.  Distortion of the results thus occurred due to the perspective and distance issues I mentioned as potential pitfalls previously.)

We can extrapolate the location of the invisible top portion of the bay, and derive a better estimate based on the shuttle's approximate moment of bay exit:

Measuring accordingly, one can find that the shuttle height is 80 pixels . . . the bay at that point is over 260 pixels.  Like Saxton, we can extrapolate an additional 5 pixels of shuttle height for the landing gear.   Thus, the bay height must be just barely under 70 meters, minimum, using Saxton's shuttle height value.

Now, let's go back to that close shot of the bays we get when the Emperor lands, and let's try zooming in a little this time:

Despite the more readily visible pixellation, you can see that the Vader landing bay (marked in red) has a width roughly equal to the height of the right side bay (marked in yellow).  Recall, if you will, that the Vader landing bay was some 69-73 meters in width, as noted earlier.   

It would seem, then, that the only bay Luke could possibly have escaped from is the right-hand bay.   The results are not precisely in agreement . . . my average 71.55m value for the tiny bay's width based on different canon possibilities of shuttle width would give the right-hand bay a height of over 75 meters, not 70.   However, given that Saxton's values for the shuttle height (and hence the ~70 meter height for the bay) are based on the non-canon, whereas my own values are based on the canon, I don't have a problem with the difference.

As a result, Saxton's scaling of the tiny bay to a height of 64 meters, followed by his scaling of the trench by that erroneous bay height, means that his 270 kilometer figure for the diameter of the second Death Star is flawed and unsupportable by the canon.

(Hey, we all make mistakes.  I ran with the 270km figure, too, after all.)

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