Is it safe to fly in a spinning hollow asteroid?

[DaveC426913]

TL;DR

Under what conditions (diameter, rotational speed) would it be safe/unsafe to have human-powered flight inside a hollow spinning stucture - specifically worst-case impact speed?

Say we have a hollow asteroid colony, spun up to provide gravity. The residents would be unable to resist making wings and flapping about in the zero-g near the axis. What is the worst possible case in terms of impact with the ground?

I'm actually working at it backwards: what radius and rotational rate would be the maximum, above which free flying without nets would have to be prohibited? (So, if I wanted them to be able to fly without zone restrictions or safety nets, how big could my colony be?)


I'll start with some arbitrary numbers and go from there.
Say it has a maximum radius of 2.5km.
Say it contains one atmosphere of air.
Say they decide they like a comfy .333g. at the maximum radius.
(There's all sorts of complicating factors here if the interior space is not a cylinder. A more realistic sphere or football shape will have varying distances to fall, shorter - and therefore less danger - near the poles).

SpinCalc tells me that a hollow structure 2.5km in radius at its widest point (normal to axial spin), producing .33g will require a spin rate of ~1/3rpm, and a tangential velocity of ~90m/s.

(I thought the simplest scenario would be to ignore the accerelating influence of the air. So a flyer near the axis, whose wings break, will fall and hit the outer shell with a velocity of ... not applicable. Without air, the flyer will not fall at all. They'll just float around with their initial velocity until they drift near the wall, which will be moving by at a rate of 90m/s.)

OK, so that's a bust. Guess we need the air. So now the falling ex-flyer gets spun up to rotational speed via drag.

John Varley's Titan series taught me that falling in a spinning space station diverts your motion tangentially, so that you will hit the ground at a very low angle.

I have no idea how to calculate or even estimate what speed that impact might be.



Alas, my gut is telling me that there is no safe speed to fall out of the sky. I will need to invoke
- designated areas where flying is allowed (perhaps near the poles, where fall potential is limited)
- parachutes
- safety nets.

Or, worse, flying might be limited to near the axis but in a cage.


(Context: No futuristic safety technology (think: steampunk). Also, set in a time when technology was idealistic and the world was not so litigious about a citizen spraining their ankle.)

Followup question: would the air pressure differential between axis and ground be substantial? Would simple breathing be noticeably impaired?

 

[Nugatory]

Who needs gravity? Check out "The Integral Trees" by Larry Niven.

 

[DaveC426913]

(Just for fun, I ran it through ChatGPT. I don't trust it but why not?)

It suggests - factoring in drag - the flyer would hit the ground at a 60 degree angle (from horizontal) at about 50mph (equivalent to a fall from 30-40 ft.) Although maybe more akin to jumping out of a moving car, since you have a chance to roll with it.

 

[DaveC426913]

Who needs gravity? Check out "The Integral Trees" by Larry Niven.

I have every Larry Niven book ever written.

Alas, there appears to be a paucity of neutron stars with smoke rings in our Solar System.

 

[ohwilleke]

To be clear, you mean impact with the ground inside the asteroid, not the asteroid impacting something else.

And, it seems that this question doesn't want to consider changes to human physiology that arise from living in space for prolonged period of time, but that probably isn't reasonable to ignore.

Also, to be clear, you aren't worried about the myriad other dangers of using a natural asteroid as a habitat (e.g., the asteroid breaking apart, the asteroid developing leaks that compromise the internal atmosphere, lack of protection from cosmic rays, the threat of an outside object impacting the asteroid and damaging it, the asteroid containing toxic materials that poison the people who live in it, the threat of recycling water and air imperfectly before it can be resupplied, the threat of food supplies failing, the threat of inbreeding, or the threat of a villainous dictatorship arising in the asteroid habitat's community).

So, down to some analysis.

First, before doing the physics, you need some reference points, that I've developed intuition about from practicing law and handling car accident and fall cases.

An impact at 100 km/hr or more (about 28 m/s) will very likely kill you if you hit a hard surface with little give, and the faster you're going, the worst off you are.

An impact at 50 km/hr (about 14 m/s) will still mess you up pretty badly on impact, but is survivable with a hospital visit.

An impact at 25 km/hr (about 7 m/s) will leave you injured similarly to being thrown from a horse or a bike at full speed or a fairly low speed impact between a car and a pedestrian, but has a good chance of not breaking your bones or causing serious permanent damage but would still require an urgent care center visit in many case.

On Earth, landing with a parachute typically gets you down to 5-6 m/s on impact which is jarring and requires you to fall in a correct way, but rarely causes serious injuries to someone who isn't too frail to start with.

An impact at 3-4 m/s is no big deal.

In reality, sustained periods at low G (multiple weeks or months) weakens you body if you aren't 100% virtuous about load bearing strength exercises, since your body isn't bearing loads as much, so you actually need lower impact speeds that pose comparable levels of harm. It's hard to know how much of a factor this is, but it isn't negligible and is more important than air pressure differences within the space.

It is reasonable to assume that, in an asteroid, assume 1 atmosphere of pressure more or less uniformly. While it would actually vary somewhat by location, it wouldn't vary that much because higher pressure air would quickly rush in to places where air pressure is low and the absolute scale is pretty modest.

On Earth, 2.5 km up would be the air pressure of ski resorts in Colorado and Europe v. sea level, which is important for cooking and furnace efficiency, and makes a noticeable but subtle difference that you can note if your an athlete or engaged in strenuous activity, but isn't all that much. So, while differences in air pressure throughout the space would exist, they'd be a second or third order consideration.

And, while you can probably safely ignore air pressure differences within the space, you absolutely can't ignore the impact of friction with the air, which in practice quickly becomes the predominant factor long before impact for a fall of this distance.

the terminal speed of a skydiver in a belly-to-earth (i.e., face down) free fall position is about 55 m/s (180 ft/s).

This speed is the asymptotic limiting value of the speed, and the forces acting on the body balance each other more and more closely as the terminal speed is approached. In this example, a speed of 50.0% of terminal speed is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99%, and so on.

From here.

But you can go three times as faster if you try to minimize air resistance (something that would only be done by suicidal people and by high school students who think that they are immortal).

You are at about 95% of terminal velocity at a height of 450 meters on Earth. 55 m/s is about 200 km/hr. The terminal velocity formula, from the link above is:

So, terminal velocity would be the square root of .33 relative to terminal velocity on Earth (i.e. about 57%) assuming that centrifugal force is entirely comparable to gravity (which it isn't, but it's not a bad first order approximation). This would give you terminal velocity of 31 m/s, which is easily reached from the center of the enclosure which is plenty fast enough to kill you.

So, you will need some safety tech, although it needn't be all that sophisticated.

The limitation of "futuristic technology", however, is a bit unclear. Are wing suits used by thrill seekers on Earth now to fly off cliffs futuristic? Are emergency parachutes futuristic? What about air bags to blunt impacts? What about gymnastics floor exercise level bouncy floors (basically weak trampolines)?

 

[DaveC426913]

To be clear, you mean impact with the ground inside the asteroid, not the asteroid impacting something else.

Yes. Thank you.

And, it seems that this question doesn't want to consider changes to human physiology that arise from living in space for prolonged period of time, but that probably isn't reasonable to ignore.

For another time.

Also, to be clear, you aren't worried about the myriad other dangers of using a natural asteroid as a habitat (e.g., the asteroid breaking apart, the asteroid developing leaks that compromise the internal atmosphere, lack of protection from cosmic rays, the threat of an outside object impacting the asteroid and damaging it, the asteroid containing toxic materials that poison the people who live in it, the threat of recycling water and air imperfectly before it can be resupplied, the threat of food supplies failing, the threat of inbreeding, or the threat of a villainous dictatorship arising in the asteroid habitat's community).

Correct. Not part of this analysis. If we got into that, I might move this to the Sci-Fi World-building forum.
This thread is strictly about the physics of flying.

So, down to some analysis.

First, before doing the physics, you need some reference points, that I've developed intuition about from practicing law and handling car accident and fall cases.

An impact at 100 km/hr or more (about 28 m/s) will very likely kill you if you hit a hard surface with little give, and the faster you're going, the worst off you are.

An impact at 50 km/hr (about 14 m/s) will still mess you up pretty badly on impact, but is survivable with a hospital visit.

These all assume a straight fall (90 degrees). On the other end of the spectrum is falling out of a moving car (essentially zero degrees). Survivable with some luck (I think).

If the clanker is to be trusted, the fall in a hollow space will be more akin to 60 degrees, which ameliorates at least some of the impact, and allows for some rollout.

Still, we're way past the safety level here.


< off-topic >

An impact at 25 km/hr (about 7 m/s) will leave you injured similarly to being thrown from a horse or a bike at full speed or a fairly low speed impact between a car and a pedestrian, but has a good chance of not breaking your bones or causing serious permanent damage but would still require an urgent care center visit in many case.

(Partly tongue-in-cheek): In Journey to the Centre of the Earth, Pat Boone was flung out of an erupting volcano into the valley below - and survived by landing in a tree. (Jules Verne is the style of this story).

I have a little latitude by hiding behind the blissful optimism of 19th century sci-fi writing. :)

The "landing in a tree" is dumb, but so is the ultra-realistic modern "I twisted my ankle and now I am sunig the highest court in the land for not psoting a big enoguh warning sign".

I only post this to show why I am choosing to ignore some very real, practical concerns about this physics problem. It's a fine line I have to walk with a tightrope.
< /off-topic >

On Earth, landing with a parachute typically gets you down to 5-6 m/s on impact which is jarring and requires you to fall in a correct way, but rarely causes serious injuries to someone who isn't too frail to start with.

An impact at 3-4 m/s is no big deal.

Parachutes would be an ideal solution.

< off-topic >

In reality, sustained periods at low G (multiple weeks or months) weakens you body if you aren't 100% virtuous about load bearing strength exercises, since your body isn't bearing loads as much, so you actually need lower impact speeds that pose comparable levels of harm. It's hard to know how much of a factor this is, but it isn't negligible and is more important than air pressure differences within the space.

Quite the opposite. Living in space isd eaiser on the body, It gets banged up less. And you actually live much longer!

Again, the wonders of a retro sci-fi style of writing. :)
< /off-topic >

It is reasonable to assume that, in an asteroid, assume 1 atmosphere of pressure more or less uniformly. While it would actually vary somewhat by location, it wouldn't vary that much because higher pressure air would quickly rush in to places where air pressure is low and the absolute scale is pretty modest.

On Earth, 2.5 km up would be the air pressure of ski resorts in Colorado and Europe v. sea level, which is important for cooking and furnace efficiency, and makes a noticeable but subtle difference that you can note if your an athlete or engaged in strenuous activity, but isn't all that much. So, while differences in air pressure throughout the space would exist, they'd be a second or third order consideration.

The clanker suggested the difference is akin to, say, 500m altitude. Measurable, but otherwise virtualt inconsequential.

And, while you can probably safely ignore air pressure differences within the space, you absolutely can't ignore the impact of friction with the air, which in practice quickly becomes the predominant factor long before impact for a fall of this distance.

Yes. This the reason this thread exists.

From here.

But you can go three times as faster if you try to minimize air resistance (something that would only be done by suicidal people and by high school students who think that they are immortal).

A scenario that, as writer, I am free to studiously ignore.

< off-topic >

So, you will need some safety tech, although it needn't be all that sophisticated.

The limitation of "futuristic technology", however, is a bit unclear. Are wing suits used by thrill seekers on Earth now to fly off cliffs futuristic? Are emergency parachutes futuristic? What about air bags to blunt impacts? What about gymnastics floor exercise level bouncy floors (basically weak trampolines)?

That fine line again. I hope to write about the eternal human dream of human-powered flight, which ideally will appear magical. It is an open question whether to write it without having to dilute the reader's experience with practical constraints such as safety devices, or whether that very careful thought into practical constraints can be made part of the story. Do I want a story of magic? Or a story of technical minutiae? TBD.

(But it's looking like the latter. 21st century readers will not be that forgiving.)
< /off-topic >

 

[ohwilleke]

Quite the opposite. Living in space isd eaiser on the body, It gets banged up less. And you actually live much longer!

Easier on the body, but it makes you more fragile, which could be a good local color plot point.

A scenario that, as writer, I am free to studiously ignore.

You can. But in the sci-fi/fantasy/adventure genre, really all of the way back to Icarus, in Greek mythology, all of the way to Star Wars, much more than a majority of the time, the literary choice when it comes to flying is to emphasize someone pushing the limits (and beyond) intentionally, either for the thrill, or out of despair, or because someone else messed with them. Some of the relevant tropes are explored here.

Someone who thinks they know their limits and then finds due to limits in their own ability or understanding, or something broken (intentionally or unintentionally) with their gear or the safety measures, or because their under pressure and tired or sleepy or injured or drugged, and then has to get out of the situation, usually makes a better story.

For example, suppose that they get tangled in their flying gear which reduces their surface area and have to increase it to reduce the rate at which they are falling with mere seconds to figure it out. The manage it, but just barely, with some serious bruising and a sprained ankle (or even momentary loss of consciousness). That's exciting.