This is the first in a two part post where I calculate the size and mass respectively of the Death Star in Episode IV (DS1). At the end of Part II I will discuss thoughts about the energy source of DS1.
Part I: Size of DS1
Conventional wisdom from multiple sources places the size of DS1 to about 100-160 km in diameter. Based on an analysis of the station’s plans acquired by the Rebels, I estimate that the diameter of DS1 is 60 kilometers, not 100 km to 160 km. To bolster the case, this scale is compared to other scales for self-consistency, such as the width of the trench leading to the exhaust port in the Battle of Yavin. Part II of the post will focus on the mass of DS1 using related methods.
To estimate the size of DS1, I will begin with the given length scale of the exhaust port w = 2 m. This information was provided in the briefing prior to the Battle of Yavin where the battle strategy and DS1 schematics are presented. This scale, when applied to Figure 1, is consistent with the accepted length of an x-wing L = 12.5 m. I assume that the x-wing has an equal wingspan (there does not seem to be consistent values available). I am also assuming that the “small, one-man fighter” referred to in the briefing is an x-wing, not a y-wing. The x-wing is a smaller, newer model than the y-wing and it is natural to take that as the template. The self-consistent length scales of w and L will establish the length calibration for the rest of the analysis.
From this, I extract the length of the smaller forward hole in Figure 1 to be approximately l = 10 m.
Using l as a calibration, this establishes the exhaust port chamber in Figure 2 to be approximately t = 186 m.
In Figure 3a and Figure 3b, circles of different radii were overlaid on the battle plans until a good match for the radius was established. Care was taken to have the sphere’s osculate the given curvature and to center the radial line down the exhaust conduit. From here, the size of the exhaust port chamber, of width t, was used as a calibration to approximate the diameter of DS1 as D = 60 km (red). Several other circles are show in Figure 3 to demonstrate that this estimation is sensible: 160 km (purple), 100 km (black), and 30 km (blue). It is clear that a diameter of 160 km is definitely not consistent with station’s schematics. A diameter of 100 km is not wildly off, but is clearly systematically large across the range over the given arc length. 30 km is clearly too small.
While a diameter of 60 km may seem modest in comparison to the previously estimated 100 km to 160 km range, an appropriately scaled image of New York City is overlaid in Figure 4 to illustrate the magnitude of this systems in real-world terms; even a sphere of 60 km (red) is an obscenely large space station, considering this is only the diameter — more than adequate to remain consistentwith existing canon. The size of the main ring of the LHC (8.6 km) is overlaid in light blue, also for scale.
As another check on self-consistency, the diameter D is then used to calibrate the successive zooms on the station schematics, as shown in Figures 5 and 6. The length B = 10 km is the width of the zoom patch from Figure 5, X = 4.7 km is the length of the trench run, and b = 134 m is the width of one trench sector. From Figure 6, the width of the trench is estimated to be b’ = 60 m, able to accommodate roughly five x-wing fighters lined wingtip-to-wingtip. This indicates that the zoom factor is about 1000x in the briefing.
Figure 7 is a busy plot. It overlays several accurately scaled images over the 60 m trench, shown with two parallel red lines, to reinforce plausibility. Starting from the top: an airport runway with a 737 ready for takeoff (wingspan 34 m); a 100 m-wide yellow calibration line; a 60 m-wide yellow calibration line; the widths of an x-wing (green, Wx = 12.5 m, where I’ve assumed the wingspan is about the same as the length — there does not seem to be a consensus online; I’ve seen the value quoted to be 10.9 m, but it isn’t well-sourced) and tie fighter (red, 6.34 m); and a scaled image from footage of two x-wings flying in formation, with a yellow 60 m calibration line as well as a calibrated green arrow placed over the nearer one to indicate 12.5 m. As predicted, about five x-wings could fit across based on the still image. Also from this, the depth of the trench is estimated to also be 60 m. The scales are all quite reasonable and consistent. It is worth noting that if the station were 100 km, the next possible sensible fit to the arc length in Figure 3, the width of the trench would be about 100 m, twice the current scale. This would not be consistent with either the visuals from the battle footage or the airport runway scales.
In short, while there is certainly worthy critique of this work, I argue that, after a reasonably careful analysis of the stolen plans for DS1, all scales paint a self-consistent picture that the diameter of DS1 is very close to 60 km.