Well, the evidence Saxton presents casts doubt on his suggested figures, frankly, but yes, that scaling does as well. However, I think his scalings can be useful, even if they are less precise:Mike DiCenso wrote:I think a much more important point here is that it quite effectively casts serious doubt on the Saxtonian estimates for a 160 and 900 km DS1 and 2 respectively, if the upper limit for a DS1 can only be around 140 km.
-Mike
Let's go through his scalings, shall we?
Polar trench (Rebel diagram, onscreen numbers without units):
Highest distance indicator seen on a Rebel screen: 32600. This, he concludes, is less than 2/3 of the length of the Rebel's trip, which he claims must be 1/12th to 1/8th the circumference of the Death Star. His conclusion: 157.5 +/-27.5 km.
Reasons for doubt: That latter claim is not necessarily that well founded from what I see; it could easily be off somewhat. It is also not quite certain that the apparent "32600" figure is a measure in meters - or that the trench is a perfectly longitudinal shot up the Death Star, or that the Rebel diagram is exactly to scale.
Trench diameter (Rebel diagram)
On the basis of magnification sequences, Saxton concludes that the ratio of trench width is "at least" 1:2207. He takes the trench diameter to be 59 +/- 17 m based on the proportions seen in the Rebel diagram. His conclusion: 131 +/- 38 km.
Reasons for doubt: Again, the Rebel diagram may not be precisely to scale. Additionally, the magnification process is not assigned a margin of error (which is probably large enough to make a difference, even with the trench being so poorly measured).
Blueprints: 67.375 km, which he suggests really mean 222 km.
ICS: 160 km, which he suggests is low.
Bantha Tracks (interview with SFX): 164 km.
Now, there are two potential conundrums as far as how we should treat all these scalings. First, what's the appropriate margin of error to assign to the Rebel diagram in relation to the finished product - i.e., how accurate are its proportions expected to be? Second - if we are to consider the assorted EU and backstage figures - what margin of error should be assigned to stated "exact" figures?
Well, we actually do have a method - although I'll tell you bluntly this would be greatly improved through the use of higher resolution figures: Compare the dish size to the overall diameter.
So far as I can tell from the 800 px wide shots on SWTC, the portions of Dodonna's briefing leading up to all the information Saxton uses show a dish 10-15% too large so far as I can tell. (Pixel rounding and JPEG compression play heavily in the width of this margin, and a much more secure figure could be gotten by using high-resolution DVD screencaps.)
It is therefore reasonable to assume, that the transition from the Rebel briefing diagram to the actual Death Star gives us the features to only within a 15% MOE, that our four measurements from the film are, appropriately speaking (reporting too many significant figures for the sake of calculation, as usual for this sort of thing):
157.5 +/- 36.25 km (23% MOE)
131 +/- 42.75 km (33% MOE)
124.4 +/- 25.3 km (20% MOE)
135 +/- 21.3 km (16% MOE)
When we have figures with MOEs that vary this widely, it's appropriate to perform a weighted average. Traditionally, the weight chosen is proportional to the inverse square of the MOEs - which tell us that, considering all sources of errors, Saxton's measurements don't contribute
Taking all four measurements into account, the best guess is 134 km diameter (124 km height, 131 average dimension if we're approximating it as a sphere for whatever reason); the first pair alone would give 139 km, while the second pair gives 131 km.
Given the sort of MOEs we're talking about, this would strongly suggest the best value to report for the overall diameter of the Death Star is 130 km. Claiming anything more precise is silly, and we'd be pushing it if we claimed the measurements didn't allow for a possible (if less likely) 140 km or 120 km diameter.