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It was proved by Pirl in 1969 the most optimal packing of 9 circles in a larger one https://en.wikipedia.org/wiki/Circle_packing_in_a_circle. The radius of the larger circle should be ≈ 3.613r (r is the radius of the smaller circle). The Merlin 1D has a radius of 1.25/2 = 0.625 meters (according to English Wikipedia figures). So the diameter of the larger circle should be at least 2 x (3.613 x 0.625) = 4.51625 meters. The Diameter of the Falcon 9 FT is 3.7 meters.

Additionally, how are they able to gimbal when they’re so close to each other? You can also add details on the gimbal range and direction and how it affects the diameter of the first stage.

Edit: English WP updated the diameter to 0.92 meters. So 0.46 meters radius.

Further edit: https://en.wikipedia.org/w/index.php?title=SpaceX_Merlin&oldid=966006133 shows the diameter to be 1.25 meters even in July of 2020

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  • $\begingroup$ The engines are not packed as close as possible, see wikipedia. $\endgroup$
    – Uwe
    Mar 3 '19 at 18:51
  • $\begingroup$ +1 for mathematics :-) $\endgroup$
    – uhoh
    Nov 7 '20 at 6:33
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Your radius number for the Merlin is too large. By measuring photos, people have estimated the diameter to be about 0.9 m.

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  • $\begingroup$ Oh that was your comment on that thread I presume. I got my figures from EN.WP. A diameter of 93.5 cm will require a minimum larger diameter of ≈ 3.378 meters. So I guess that could work. But what about the gimbal range? I'm assuming even a gimbal of 4° for all the 9 engines could put the diameter past 4 meters. That's just my assumption. I've not worked out the numbers to back that. $\endgroup$ Mar 3 '19 at 19:15
  • $\begingroup$ It was Wikipedia's number through July 2020 as well $\endgroup$
    – uhoh
    Nov 7 '20 at 6:34
  • $\begingroup$ @KevinMuhuri old thread, but.. On the falcon 9 , the outer ring of Merlins gimbal along one axis only. And when they do gimbal they need to act together, to avoid touching each other. (mostly) just for roll control. The central Merlin has 2-axis gimbal, and unrestricted space to do so. $\endgroup$ Jul 16 at 18:42

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