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This question got me thinking. I remembered that Ivanova once said (I think it was in S02E23)

Ivanova: "He's almost weightless but the ground rotates at 60 miles per hour."

In that scene they were standing on the inside of the cylinder, meaning on the "uppermost" deck. If we assume earth gravity on that deck and then calculate the radius via centripetal force:

F = m * v² / r

G = m * g

F = G

g = v² / r

r = v² / g

r = (60 mph)² / 9.81 m/s² ~ (26.8 m/s)² / 9.81 m/s² = 73.3 m

That would be rather narrow considering the total length of 5 miles / 8 km (a 50 : 1 ratio length to diameter). So the station would have hydroponics and the innermost decks still at a lower force. Also the outermost decks will have higher gravity (they rotate at the same angular velocity, so every meter outwards increases the artifical gravity).

So what diameter has the station and what ist the gravity level inside Babylon 5 on the inner and outermost decks? Or is Ivanova's sense of speed just plain off?

Edlothiad
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Adwaenyth
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2 Answers2

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TLDR: Ivanova's statement is consistent both with believable gravity and with the pictures of the garden. The gardens do NOT span the length of the station

The quote is correct and can be viewed here:

The calculation is also true, in that Earth-gravity in the park in B5 green sector would imply an inner radius of 73 meters. We can also calculate the station angular velocity to be:

w = v/r = 1316 rotations per hour or 22.05 per minute.

Check: acceleration = w^2 * r = (22.05 per minute)^2*73m = 9.86m/s^2

However, The B5 station is stated to have an outer radius of 420 metres. If the park is at Earth gravity, this implies from the above formula that gravity near the hull would be 5 times earth gravity.
We know from other episodes that humans have no problem walking around normally at the lower levels, hence this must be false.

If we instead assume that the outermost levels have at most 1.5 times Earth gravity, we have:
1.5g = w^2 * 420m which give us a new value for w = 11.3 rotations per minute.

Knowing that the park rotates at 60mph and using the relationship v =w*r, we find that the inner radius of the green sector is:

60mph / (11.3 per minute) = 142 metres.

That is, a third of the radius of green sector is made up of open air. This seems consistent with the pictures of the garden "sky" as taking up much of the station. Note that the "garden cylinder" is contained in the green sector and so is a lot shorter than the 8 km length of the station, which the question refers to.

The "gravitational" acceleration felt in the park is:

(60mph)^2/142m = 5 m/s^2

This is lower than Earth gravity, but higher than the surface gravity of say Mars, which is at 3.7 m/s^2.

Ivanova's statement is thus consistent both with the visuals and with acceptable gravity in the garden.

And people say you'll never need that algebra you learned in school..

TheLethalCarrot
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Abulafia
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    You know, at 5.5 seconds per rotation, the exterior shots of B5 should have been much more visually busy. I wonder if the various decks don't rotate rigidly together... – Eric Towers Oct 20 '17 at 17:45
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    @eric-towers: Good point. Maybe someone would study exterior shots of the station to estimate the rotation rate(s) – Abulafia Oct 20 '17 at 17:57
  • 11.3 rotations per minute is very fast. If B5 rotated that quickly, a large majority of the visitors to the station would be feeling constantly nauseous. Besides, I do recall somebody having measured the rotation rate from one scene or another, and JMS having confirmed that the measured rate was the intentional, canonical rotation rate of the station. Now, if I could just find the quote... – Jules Oct 21 '17 at 01:20
  • @Jules most SF rotating habitats are just too small to have the gravity they do at a reasonable rate of rotation – hobbs Oct 21 '17 at 21:32
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    @hobbs - true, but B5 appears to have been designed with the commonly accepted figures at time of publication in mind, which were that 2 RPM would be considered roughly the fasted rate acceptable by most people (more recent studies have revised that upwards to about 3RPM). At 1.5 RPM and 840m, the resulting acceleration in the outermost decks is approximately 1G; at 2RPM it would be somewhat higher due to the quadratic factor. Obviously it would vary in different areas, so having a range would be good. Which suggests to me that about 2RPM would be the correct rate. – Jules Oct 22 '17 at 03:13
  • Yes, a lot of station designs are too small. B5 was consciously modelled on the O'Neill cylinder design, however, which was produced by a NASA study and is considered plausible (albeit a little conservative, largely because at the time of publication we believed that 1 RPM would be the fastest acceptable rotation rate). B5 is a little smaller than the O'Neill cylinder - half the diameter and about two thirds the length - which is a reasonable change for our more modern understanding. – Jules Oct 22 '17 at 03:15
  • Another question would be, when you do not see the exterior and have no external reference of the rotation (like in all of the middle decks) would you even notice that you are rotating at all? – Adwaenyth Oct 23 '17 at 06:00
  • @Jules: This is interesting. If the rotation is canonically 2 rotations per minute, the speed will be 60 mph at a radius of 800 metres. With the station having an outer radius of 420m, this means that the rotation rate cannot be reconciled with Ivanova's statement. – Abulafia Oct 23 '17 at 09:03
  • @Adwaenyth - yes. At a speed of 1-2 RPM there are noticeable coriolis force related effects. Things won't fall in a straight line, and your sense of balance will noticeably change according to the angle you're facing versus the direction of rotation. – Jules Oct 23 '17 at 13:01
  • @Abulafia - I'm convinced that no significance should be attached to the precise number in Ivanova's statement. She came up with it on the spur of the moment in a stressful situation, and it's not likely to be something that she knows off the top of her head: she probably just did an order of magnitude assessment and came to the conclusion that speed would be fast enough to be dangerous, and left it at that. – Jules Oct 23 '17 at 13:03
  • @Jules I'd expect of a commanding officer of such a space station, that she would be well aware of how fast the station must rotate to produce sufficient gravity. Not down to the exact number, but she shouldn't be further off than rounding that number to the nearest 10s. Also as senior military officer and trained fighter pilot she would specifically be trained to keep her calm even in very tense and stressful situations. – Adwaenyth Oct 23 '17 at 13:12
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So here states that the diameter is 840 M. There is an official sizing chart here

B5 sizing chart

It certainly doesn't look like a 50:1 ratio. So it is likely that the stated speed is off.

Jeremy French
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