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There has been a fair bit of previous discussion about how high mountains could get. I'm currently thinking about a different question: assuming the existence of a very tall mountain, how high would it be feasible to climb?

In all of this, I'm assuming gravity, atmospheric composition and sea-level atmospheric pressure are the same as on Earth.

I think it's trickier than it sounds. The limiting factor is oxygen supply. Everest, 8848 m, is already borderline in that regard: it is barely possible to climb without carrying an oxygen supply, but only at severe risk of permanent brain damage. Let's say anything over 10 km or thereabouts is flat-out impossible to climb without supplemental oxygen.

Okay, so you carry supplemental oxygen, right? But that runs you into a different problem: there is a limit to how much you can carry. The obvious solution is to set up additional camps at high altitude with stores of oxygen for further ascent, but this is an instance of the Jeep problem where the most important conclusion is

However, the amount of fuel required and the number of fuel dumps both increase exponentially with the distance to be traveled.

The key word in that sentence being 'exponentially'. That's going to set a theoretically soft but practically pretty tight upper limit. I don't know enough about mountaineering to know what the parameters would be, to estimate an actual maximum altitude. Maybe around 15 km?

It would be tempting to think okay, you need to cheat, bring in a helicopter. But helicopters have altitude limits, too. I don't think they can actually go much higher than mountaineers.

Airships can, but they cannot cope with strong winds... though now that I think about it, you could use an airship to drop supplies onto the high slopes. If the wind prevents the airship being precise about position, that's okay; the climbers can move to where the supplies are. Okay, so there is a technological cheat.

If one is unwilling to cheat, and everything has to be carried on the backs of climbers, what would be the practical altitude limit? Would anyone ever climb, say, a 20 km mountain?

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    $\begingroup$ What's the budget, Elon Musk or Joe from the hardware store? $\endgroup$ Commented Apr 9, 2022 at 4:02
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    $\begingroup$ An O2 pipe up the mountain would be OK? $\endgroup$ Commented Apr 9, 2022 at 5:37
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    $\begingroup$ @rwallace "actual mountain climbers" have used helicopters to hop from one 8000 base camp to another and beat records. $\endgroup$
    – L.Dutch
    Commented Apr 9, 2022 at 6:31
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    $\begingroup$ @Dragongeek "if one is unwilling to cheat, and everything has to be carried on the backs of climbers" is a fairly major constraint. Money might buy you a chunk of twitter, but it can't yet conjure up a superhuman. $\endgroup$ Commented Apr 9, 2022 at 20:03
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    $\begingroup$ @Dragongeek none of that will help. The problem is not one you can spend your way out of, because it is fundamentally limited by human physiology which can't be trivially fixed. Marching up everest on benzedrine will kill you, and the stuff you're carrying will probably be lost. This isn't a simple task like "fly a rocket into orbit". $\endgroup$ Commented Apr 9, 2022 at 21:01

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TL;DR: 12-15km Earth-equivalent altitude, because you start needing spacesuits and pressurized habitats instead of a nice warm coat and a tent.

You might be OK if you could launch rockets to drop pressurized accomodation for you at high altitude, but you might consider that cheating.


Firstly:

  • You need a low-gravity world to keep very high mountains.
  • Mountains on low-gravity worlds are easier to climb than mountains on high-gravity worlds (cos you can carry more, and jump higher)
  • Low-gravity worlds have a larger scale height so the air pressure drop (and hence oxygen partial pressure drop) is lower for the same altitude gain on a high-gravity world.

There's wiggle room in all those statements though, so they aren't strong arguments alone.

Okay, so you carry supplemental oxygen, right? But that runs you into a different problem: there is a limit to how much you can carry

The supplemental oxygen used by mountaineers is inhaled via an open-circuit respirator. This means that any oxygen that is not taken up by the body is exhaled into the atmosphere and effectively wasted. This means that they end up carrying a lot of oxygen but rather less of it is actually used in metabolism than you might initially expect.

There is a technological solution to this in the form of rebreathers. These are more commonly associated with diving, because they let users spend more time at depth without having to carry huge amounts of additional air. As a very brief summary: rebreathers scrub excess CO2 from exhaled air, and keep the oxygen partial pressure constant by trickling in oxygen from a tank as needed. This ensures that all the oxygen in the tank can be consumed by the user.

Using rebreathers for high altitude mountaineering isn't a new idea: The Use of Closed-Circuit Oxygen in the Himalayas

Two days before the first ascent of Mt. Everest in 1953, Tom Bourdillon and Charles Evans climbed to within 90 m of the summit at unprecedented speeds. By breathing pure oxygen from a closed circuit, the pair were able to obtain an enormous physiological advantage. Unfortunately, due to a malfunction in Evans's circuit, the pair abandoned their attempt on the South Summit. For many who used the circuit in the 1930s and 1950s, the device proved too heavy, uncomfortable, and tiring for mountaineering.

You will not be surprised to learn that rebreather technology has advanced considerably since 1950, and rebreathers used in low pressure air (rather than at high pressure under water) are a little simpler and safer than their conventional underwater cousins. A modern mountaineering rebreather would be much lighter and smaller and more reliable than their primitive 50s forebears, and would make oxygen supplies go much further. There would still be technological hurdles to overcome (because operating rebreathers at very low temperatures is probably not something that's done very often) but there's no reason they should be insurmountable.

(note that rebreathers form a part of the primary life support system of modern spacesuits, for an example of their use at low pressures)

You're still subject to exponential losses, but when the exponential term is small enough then your maximum altitude increases considerably. The practical gain from a rebreather might be a tenfold reduction in O2 consumption.

It would be tempting to think okay, you need to cheat, bring in a helicopter. But helicopters have altitude limits, too. I don't think they can actually go much higher than mountaineers.

This is true, but given your example of "Elon Musk" budget you can consider the use of a small rocket driven lander, assuming suitable sites can found to put it down. Maybe the thing could be dropped from a plane and glide to its destination using a parafoil, and use rockets at the end of the flight to fine tune its landing zone. It'll still be vulnerable to "weather windows", and making it robust enough to keep its cargo safe and in place during bad weather might be a problem too, but again: not necessarily an insurmountable one. And it is something that can be tested ahead of time and validated before any climb.

Would anyone ever climb, say, a 20 km mountain?

At a certain point, external pressure becomes low enough that simply being exposed to it is unhealthy even if you have a good supply of oxygen. On Earth, high-altitude pilots wear pressure suits:

The physiological-deficient zone extends from 3,600 m (12,000 ft) to about 15,000 m (50,000 ft). There is an increased risk of problems such as hypoxia, trapped-gas dysbarism (where gas trapped in the body expands), and evolved-gas dysbarism (where dissolved gases such as nitrogen may form in the tissues, i.e. decompression sickness). Above approximately 10,000 m (33,000 ft) oxygen-rich breathing mixture is required to approximate the oxygen available in the lower atmosphere, while above 12,000 m (40,000 ft) oxygen must be under positive pressure. Above 15,000 m (49,000 ft), respiration is not possible because the pressure at which the lungs excrete carbon dioxide (approximately 87 mmHg) exceeds outside air pressure. Above 19,000 m (62,000 ft), also known as the Armstrong limit, fluids in the throat and lungs will boil away.

That last one is worth a deeper look:

The Armstrong limit or Armstrong's line is a measure of altitude above which atmospheric pressure is sufficiently low that water boils at the normal temperature of the human body

This means that at some point between the altitude of the top of Everest and 15000m your climbers start needing spacesuits to provide counterpressure simply to let them breathe at all. At 20km they need a spacesuit to stop exposed fluids boiling away, which is likely to be an unpleasant way to die (unless their air supply was damaged in which case you just pass out in a few seconds).

More designs for mechanical counterpressure suits for use on Mars would probably do an excellent job, though I don't relish the idea of carrying a complete spacesuit up to the top of Everest and then having to put it on and climb another Everest and a half!

The need for a spacesuit, and a positive pressure respirator suggests that 12km altitude on Earth (or an equivalent atmospheric pressure on another planet with different gravity) might be as high as you'd reasonably want to climb because of the problem of eating and sleeping safely. You can have food-tubes in a space suit or pressure suit, and a clever vent system could allow you to pee and poop too. Damage to the suit might be very serious, and injuries are effectively untreatable unless you were able to bring a pressurized habitat with you (like a cross between a Gamow bag, a TransHab inflateable space station and a portaledge). This probably means that even if human mountaineering activity above 12-15km is possible, the fact that small accidents or kit failures can kill you in a quick and very expensive fashion probably limits climbing at that altitude (contrast with climbing 8000m peaks, where accidents kill you in a few hours in a merely expensive way, and sometime people get rescued).

edit: Here's a big problem: time.

Climbing is hard work, especially at high altitude, even with supplemental oxygen. It takes 11 hours to climb Everest from a base camp using supplemental oxygen, which is a rise of <3500m. The round-trip time to base camp was 18 hours. For higher peaks, you'll simply run out of time and energy and you're going to need to camp high on the mountain. No-one camps in the "death zone" at 8000m+ because the chances of you surviving your nap are slim. At 12000m peak basically demands a camp unless the climbers are superhuman. Napping in a pressure suit might work, and your oxygen demands are reduced, but those long and unproductive sleeps will cost you dearly in terms of the amount of food and oxygen you have to carry.

Permanent and pressurized high-camps would probably be needed... imagine the effort required to construct a sealed building at the summit of Everest and maintain life support systems up there. Imagine the fun you'd have providing power, given the low levels of oxygen to run combustion engines or fuel cells (and the effort required to refuel). Wind turbines and solar cells might have problems with the weather, to say the least, but might be the only practical options. This may also be considered cheating, but it is hard to see what you might do instead.

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  • $\begingroup$ I like the answer, there are lot of useful details. But it fails to take into account the temperature. The higher you go the thicker your clothes have to be to protect you from the cold. I doubt that reaching an altitude of 11KM would be feasible, already at 10Km you would have to carry the material with the movements impeded by bulky clothes. $\endgroup$
    – FluidCode
    Commented Apr 10, 2022 at 12:51
  • $\begingroup$ @FluidCode modern mountaineering gear is not nearly as inconvenient as you might imagine, and there's scope for improving insulation. The temperature is also surprisingly steady between the altitudes of 11000m and 20000m, and fairly similar to the sorts of ground level temperature that might be experienced on the antarctic plateau during the winter. Dealing with cold is much easier than dealing with a lack of air pressure. $\endgroup$ Commented Apr 11, 2022 at 11:43
  • $\begingroup$ Space technology could help a lot. A small solar powered unit to extract oxygen from the atmosphere and fill cylinders could be used. Such a unit could be automated and communicate with a base camp to ensure that the unit was fully charged before any climbers left. Technology is also available that could produce water from the tenuous atmosphere at extreme altitude. Of course this might be claimed to be cheating, but that begs the question of how well defined the original question really is. $\endgroup$
    – Slarty
    Commented Apr 11, 2022 at 17:35

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