# Walking around the ring on a spinning space station

When moving around a circular spinning space station (doughnut shaped) Is there any difference in the direction one goes? Is the energy expenditure the same or different?
Would one ever feel like one is climbing?

My gut feeling says no, as the person walking has the angular momentum matching the station. Yet I second guess myself....

berkeman
Mentor
I think the main difference would be what happens when you throw an object straight up and then try to catch it...

https://en.wikipedia.org/wiki/Coriolis_force

Is there any difference in the direction one goes?...
Would one ever feel like one is climbing?
Yes, there is difference but climbing - no.
Depending on the direction you walk your weight will be lower or higher (so is the energy spent). If the radius of the station is too small this (and some other issues) may cause some problems.

Ps.: an early experiment:

So, with small radius it's possible to create artificial gravity by running - kind of.
To turn this around, if the radius is small it's possible to negate artificial gravity by running.

AllanR
Ah I think I see. I would calculate the walking speeds acceleration the same way as I calculate it for the station a = 4 π² r n². So if I manage to run against the spin at the same rate of the spin I would stand still and have no gravity?

DaveC426913
Gold Member
if I manage to run against the spin at the same rate of the spin I would stand still and have no gravity?
Not quite. That would be true in a vacuum, but in the presence of air, you will be carried along, ultimately coming up to rotational speed.

Would one ever feel like one is climbing?
Ish.

Running spinward, you will feel a force that seems to be pushing you into the ground.
You could interpret this as the ground rising in front of you and you having to ascend it.

AllanR
If the radius is large, say a kilometre, or 6k circumference, and spinning at 1rpm to give about a g.
How could I calculate how much energy difference to walk all around it in either direction?

DaveC426913
Gold Member
If the radius is large, say a kilometre, or 6k circumference, and spinning at 1rpm to give about a g.
How could I calculate how much energy difference to walk all around it in either direction?
It will be negligible. Certainly below human sensitivity.
How many zeroes accuracy do you need?

I suppose if one were sprinting, one might detect a difference between sprinting spinward and antispinward.

Do this as a ballpark estimate:
Choose your g-requirement (do you want one-G?).
Calculate the rotation rate required to accomplish that.
What linear velocity does that equate to for a person standing "still" in the station?
Average sprint for a human is about 24km/h.
What ratio is that to the station rotation rate?
Double that (because it's antispinward to stationary + stationary to spinward).

That factor is how much difference a sprinter will feel running in the two different directions.

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AllanR
DaveC426913
Gold Member
Maybe for marathons it matters? Like how bike racers shave the hair off legs. (they can save a minute or more on a 40k race)
Sure. OK. So you're not merely interested in the human perception of it.
You want to know actual effort.

You're going to run into trouble because there's no easy way to determine how much extra energy it requires to run in an unusual posture spinward (you'll be preoccupied trying not to stumble), or how hard it is to run antispinward when you feel lighter.

(PS, I added some more instructions to the above post, including a link to a useful calculator)

AllanR
DaveC426913
Gold Member
Using calculator I mentioned, a 1km radius station with 1g gravity has a tangential velocity of 356km/h.
An average marathon runner might run at 10km/h.
So, running spinward is 366km/h and antispinward is 346km/h.
That's a total of about 5.5% difference.

I think that approximates to apparent weight. i.e. A 80kg person will weigh ~82kg spinward and ~78kg antispinward.

Huh. Losing 4kg of weight between one run and the next? I guess that's pretty perceptible.

(Someone check my math!)

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AllanR and BvU
Using calculator I mentioned
<laugh> I just posted SpinCalc as well, @DaveC426913, then saw I was treading in your footsteps. It's a handy URL that I've used a few times in stories, it takes the pain out of artificial gravity considerations when you're using centripetal acceleration to mimic it.

BvU
Homework Helper
Thing to do is rotate once per 24 hours, or else you get seasick looking out the window...
But to get 1g you then need a radius of 73 million kilometers. And that with current steel prices !

(someone check my math ... )

I wonder how the Star trek Enterprise crew get their gravity ... or do they simply accelerate upwards with 1 g without telling us ?

##\ ##

Filip Larsen
Gold Member
(Someone check my math!)
Your relative change in weight seems too big. The relationship is ##a r = v^2## and using that I get around half what you get, i.e. an 80 kg person running 10 km/h in that rotating ring feels a change in weight at around ##\pm 1## kg.

Filip Larsen
Gold Member
Thing to do is rotate once per 24 hours, or else you get seasick looking out the window...
But to get 1g you then need a radius of 73 million kilometers. And that with current steel prices !
In Ringworld the ring had a diameter of approximately 1 AU and a tad under 1g so here the rotation period is 9 days. Calculating the inhabitable area of that particular ring to be around 3 million Earth surfaces made my head spin back when I first read it.

DaveC426913
hutchphd
Homework Helper
Your relative change in weight seems too big. The relationship is ar=v2 and using that I get around half what you get, i.e. an 80 kg person running 10 km/h in that rotating ring feels a change in weight at around ±1 kg.
I get for fixed r $$\frac {\Delta a} a =2\frac {\Delta v} v$$ and $$a\to a(1\pm20/356)$$ so the kg weight changes ##\pm4kg##

AllanR
Filip Larsen
Gold Member
I pressed the square root and not the square button on the damn windows calculator
Using the right button I also get ##\pm 4 kg##. Guess my point about ##\pm 2kg## not being correct was at least correct

hutchphd
DaveC426913
Gold Member
Your relative change in weight seems too big. The relationship is ##a r = v^2## and using that I get around half what you get, i.e. an 80 kg person running 10 km/h in that rotating ring feels a change in weight at around ##\pm 1## kg.
OK, is that a change from 0 to 10km/h?
Or is that the total change -10km/h to +10km/h?

Filip Larsen
Gold Member
OK, is that a change from 0 to 10km/h?
Or is that the total change -10km/h to +10km/h?
With a speed of ##\pm 10## km/h the person would feel his weigh change ##\pm 4## kg. Or combined, when changing running direction the total 20 km/h change would feel as a change in 8 kg.

AllanR and hutchphd
DaveC426913
Gold Member
Calculating the inhabitable area of that particular ring to be around 3 million Earth surfaces made my head spin back when I first read it.
There are full scale maps of both Earth and Mars as islands in one of the Great Oceans. There are very difficult to spot on a map of the Ringworld. Blink and you'll miss them.

Filip Larsen
Would one ever feel like one is climbing?
Just to throw in another stone here: since for any such stations the floor will visibly bend upward, it's expected to have this kind of 'climbing upward' illusion all the time, but it is actually unrelated to the direction of walking.

On the other hand, if you straighten the floor locally to trick your vision then - depending on the radius - through your feet you might feel like it's curving downward.

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