To orbit without rockets

I saw, on the BBC in the late 1990s, a marvelous series of programs on our knowledge of the solar system. My personal high-point of the series was the guy who went up to the highest thinnest bits of what might loosely be described as our planet's atmosphere and was the first man to look out at space first hand. He'd left the earth by balloon: he returned – via what must be the most breath-taking sky-dive possible – by parachute. This inspired me to think about how one might get the rest of the way to space.


The problem

Rocketry-based space travel seems to need the economic scale of a government, a (fairly large) corporation or some collaboration between such. It also has the distressing problem that you spend most of your fuel on lifting the fuel to spend on lifting you and the rest of your fuel the rest of the way, which tends to mean the mass of fuel you need is something like 20 times the mass of your payload. So that pretty much takes rockets out of any citizen-driven space program. But hey, once clear of the atmosphere one can do solar sailing, which sounds like it shouldn't require such huge bugetry. On its own, that would still involve buying passage on some large organisation's rocketry; which would expand the budget somewhat. Still, it'd be a fun half-way house to explore …

Alternatively, one can try to find some other way out of the Earth's gravity well. We need to get to the point where a solar sail is enough to take us the rest of the way; rocketry would put the sailing vessel into a low Earth orbit from which, by careful sailing, one should be able to escape; replacing the rockets would involve getting clear of the atmosphere and getting up a huge amount of sideways momentum (so as to stay in orbit, rather than falling back down again). It's a pretty safe bet that any replacement for rocketry is going to have trouble with both halves of that; though a space elevator would greatly reduce the orbital momentum problem by (somehow) delivering the energy to get all the way clear to geostationary orbit, out where one doesn't need much sideways velocity at all. Somewhere in there, there's a pay-off between brute lifting and building up sideways momentum; and a lower orbit has a lower total energy, making a strong case for low orbit.

Of course, once someone builds a space elevator, we can expect to see passenger services to space before very long. It remains that, althoug plenty of folks who understand the matter have stopped laughing at the suggestion, our fifty years aren't yet up: we haven't yet actually built one, although progress in the right direction is happening. Until that happy day, we want some other way to explore space.

As far as getting clear of the atmosphere goes, it begins with the troposphere – the dense bit at the bottom, with all the weather in it. Getting through the troposphere, into the low stratosphere, is easy: a big slack back of a helium balloon is reasonably affordable and can lift a fair old pay-load. After that, we come to the stratosphere: which is much thinner than the air we're used to – certainly not breathable, indeed thin enough one can see the stars against a black sky even when the sun is in sight. All the same, it'll be too dense for our solar sail, I suspect – at least at the altitutes one can reach by balloon.

Slack bags of helium

A slack bag balloon has (near enough – its skin is necessarily under some tension, if it's supporting a pay-load, which shall produce some inward pressure) the same pressure inside as out, so it expands as the ambient pressure drops; and its density drops accordingly. For a slack bag helium balloon (in contrast to a hot air balloon), the internal and external temperatures are the same: it works because Helium is lighter than air. The weight of the gas in the balloon doesn't change; nor does the weight of the body of air it displaces; and the ratio of these two weights is just the ratio of the densities of the gasses.

The densities of (near enough ideal) gasses are, at given pressure and temperature, proportional to their relative molecular masses (RMMs). The atmosphere is made up mostly of Nitrogen (80%, with atomic mass number 14) and Oxygen (20% with atomic mass number 16), both in diatomic molecular form, so has RMM equal to about 2×(14×0.8 +16×0.2) = 4×7.2 = 28.8. Helium is a monatomic gas, with mass number 4, so air is 7.2 times as dense as Helium. The buoyancy of a slack bag Helium balloon is just the weight of the air it displaces minus its own weight, which is thus 7.2−1 = 6.2 times the weight of the Helium. To support a given mass of payload, you thus need 1/6.2 of that mass of Helium; to lift it, you need a bit more. (If you do the arithmetic taking into account more details than here, the factor is 6.1974; but 6.2 is close enough).

So a hundred kilo (or so) of human plus about five times as much in supporting materials (oxygen supply, space suit, scientific instruments, big wicker basket and the slack bag itself) can be lifted by about 100 kg of Helium; and it'll keep on lifting up the atmosphere as long as the ambient RMM is more than 4, or until the minor pressure difference between outside and in starts to matter. While I can guess that the atmosphere probably does have less of its heavier components higher up, I doubt its RMM gets that low before you can say you've run out of atmosphere. However, the balloon is going to expand as the pressure drops, so your slack bag shall run out of slack eventually; after that, the Helium shall be under greater pressure than the air; its density stops increasing and it gets less effective at lifting.

To put it another way, I've treated the mass of the bag as negligible; but, if you intend to go far enough up for the pressure to drop by some factor 1/r3, the volume of the bag shall increase by r3; the filled portion's spatial dimensions shall grow by r and its surface area by r2; the mass of the bag thus needs to be r2 times as big as that of a bag that would have sufficed to hold the Helium initially; which starts to get significant once r is big enough. To drop atmospheric pressure to 46 millionths of a millionth of that at launch (see next section), you need a slack bag with linear dimensions 2800 times what would have sufficed to hold the Helium initially; and it'll weigh about 8 million times as much as such an initially-sufficient bag. At that point, it becomes a significant contributor to the mass you're having to lift !

Solar sailing

Johannes Kepler noticed comet tails blown by the solar wind and dreamed up the idea of sailing round the solar system on this solar wind; more recently, science fiction writers have had fun with the idea, throwing in sunlight's pressure as a further force. Combine these with the gravitational field, your momentum and the angle of your sail to get some fairly rich possibilities for controlled motion. Gravity pulls towards the sun or other massive body closer to hand. Depending on the angle of your sail, the sunlight pressure pushes at least partly away from the sun but possibly quite a lot orbit-ways (i.e. circumferentially). The solar wind has a large orbit-ways component (largely because it's made of charged particles, and The Sun has a significant magnetic dipole) as well as its outwards rush: and it pushes the sail at least partly down-wind but optionally quite a lot cross-wind. You need a very big reflective sail; but you can make that of mylar.

The total radiant power of The Sun, as observed outside the atmosphere (which, once you're up in your helium balloon, is pretty much where you are) is 1.4 kW/m2; divide this by the speed of light to get the momentum flux carried by sunlight, 5 micro-Pascals or about 46 pico-Atmospheres (pico is a millionth of a millionth). You can get up to a factor of two better than that, as force on your sail, depending on angle. The atmosphere is going to offer wind resistance to your sail that'll dwarf that as long as its ambient pressure is bigger than that; and (see aside at end of last section) getting to atmosphere that thin would involve your slack bag either significantly reducing the pay-load you can carry or running out of slack before you get there. So I don't think a Helium balloon is going to get you far enough up to exploit the photon pressure of sunlight.

If you can get far enough up the atmosphere – by whatever means – to exploit the solar photon pressure, you'll have the ionosphere to play with: this is where the solar wind is channelled by Earth's magnetic field, with interesting resulting dynamics that you can probably exploit. Once you get that far, you're pretty much on your way to wherever you want to go; but you also need fairly good radiation shielding to get through the ionosphere, so you'll need a proper space capsule.

Dawn will see you flying towards the Sun, dusk flying away; and, as you pick up speed, the intervals between them shall get shorter. At dawn you can turn forward momentum into lift, at dusk you can snatch some of each. While you are above the day-light world, the sun is shining downwards: but your sail can be angled to pull you in any direction out to right-angles with it. This allows you to get lift until late morning – though, in doing this, you slow yourself down. In the afternoon, with your sail now ahead of you along your orbit, you can get both lift and propulsion out of the sun. That's the direction of the photon pressure on your sail: as for the solar wind and last vestiges of atmosphere, I can say nothing of their direction, speed or variability through the day; you'll start where the mix is mostly atmosphere and work your way up into the ionosphere, which is mostly solar wind.

Atmospheric sailing

So, go up in a Helium balloon, go way up. You'll still have the tenuous threads of Earth's upper atmosphere around you: the balloon only works by virtue of the Helium having a lower RMM than, but the same pressure as, the ambient atmosphere. That'll give you a wind, albeit not the solar wind, which will be mostly sideways to gravity. You'll have sun-light shining on you, but it's too weak to matter, so you can't exploit differences between its direction and that of the wind, as you would for solar sailing. However, the stratosphere is stratified, with different horizontal wind-velocities (in particular, different wind directions) in different strata, so kites in different strata could pull in different horizontal directions, but all upwards, on a central pay-load. This might be ludicrously impractical, but warrants investigation. Kites are effectively sails without the usual rigid attachment to what they're pulling: and folk have indeed used them to propel surf-boards, even taking off at times.

That should make it possible to get lifted further than the slack-bag Helium balloon can take you; how much further is an open question. It's not going to get you much sideways velocity, beyond that resulting from the Earth's spin (about a thousand miles per hour, or just under half a km/s, at the equator; at other lattitudes, it decreases in proportion to distance from the Earth's spin axis), but it should be able to get you some. At first you'll still be riding in your balloon, with (relatively) small kites flying in the (relatively) thick near-vacuum of the stratosphere. As you move up you'll need bigger kites (to make the most of the steadily thinning air) but you'll be able to use kites of flimsier construction (i.e. lighter per unit area). Your (no longer slack) Helium balloon shall provide some marginal assistance to begin with but you'll only succeed if you can go far enough up to make it irrelevant.

This probably means you want to rendezvous with a previous balloon that's lifted up the equipment to lift you further (and the payload you want to take further up – Oxygen, food, scientific equipment and some kind of a capsule), under remote or robotic control (probably a mixture); move from your balloon's basket to the next stage craft and send the balloons on their return journey to meet your friends who'll be using them next. To do that, they'll need to pump out much of the helium from their slack bags into pressure vessels, to lose the buoyancy they needed to lift you or the next stage, plus a bit more to ensure they descend. Alternatively, you might rendezvous with the next stage craft used by someone else, after they've moved on to the stage beyond that and sent it down to meet you; then you'd only need to send one balloon down again. The next stage might even have a returning passenger on board, with whom you can exchange places. You may need several stages of such transitions; which shall imply a population of (hopefully automated) vessels plying the upper atmosphere, picking payloads (including passengers) up and transporting them up and down. They'll need solar panels and batteries; and their (occasional) passengers shall need radiation shielding, so I think they'll look more like space capsules than anything else we're used to.

Once you're up as far as kites can carry you, I must suppose the atmosphere is thin enough to let you start exploiting solar photon pressure; and the atmosphere has faded through to being the ionosphere, where you have quite high particle speeds that you should be able to exploit to get yourself moving sideways, on your way to reaching orbital speed. It may take some time but, from here on out, even the sky's not a limit.

A successful ascent to high orbit using balloon, kites and sun-sails would be a grand achievement. Infinitely more beautiful – clean and green – than all that thundering rocket fuel. If it can work, it provides excellent potential for ordinary folk to be able to visit space.

Atmospheric Intensity

If we imagine the atmosphere to be a perfect gas, we can anticipate that its pressure depends on its temperature according to the perfect case law:

in which n is the number of particles of gas, k is Boltzmann's constant (defined by this equation), P is the pressure, V is the volume and T the temperature; of course, we're considering the atmosphere, within which (to some degree (that I'll largely ignore) m,) P and T vary; but this equation applies sensibly to any given volume of the atomosphere; so should properly be phrased as

with n/V thought of as the number-density of the particles making up the gas, rather than total number divided by total volume of some macroscopic body of gas. If the atmosphere's mean molecular mass is m, then its density will be ρ = n.m/V, giving us the strictly local equation

Now, m is a mass per particle and k is an energy per particle per unit of temperature. We could equally have used a molar mass in place of m as long as we used the molar gas constant, R, in place of k; but what matters is their ratio, relative molecular mass (i.e. actual molecular mass divided by one twelfth of that of atomic 12C) divided by Boltzmann's constant. Now, in a gravitational field of strength g, pressure (P) varies with height (h) as dP/dh = ρ.g, so we can infer

in which T.k/m/g is a length. Near Earth's surface, T.k/m = P / ρ is roughly the square of 291 m/s; dividing it by the local gravitational field strength, g, gives roughly 9 km as the value of T.k/m/g. In so far as the atmosphere's temperature is roughly constant, we can thus expect its pressure to diminish by a factor of e = 2.718 with every 9 km of altitutde gain, so it halves roughly every 6 km. In fact, the atmosphere's temperature varies with altitude – but if it didn't, we could anticipate that its pressure and density would decrease by a factor of ten in each 20 kilometres of ascent. Since temperature does vary with altitude, we must accept that reality deviates from this; but temperature does not vary so hugely in the first few dozen kilometres as to make this prediction depart hugely from reality. None the less, the atmospheric pressure won't get below the solar photon pressure, even on this model, until about 12×20 = 240 km up.

If we divide the atomic mass unit (one twelfth of the mass of a 12C atom's mass) by Boltzmann's contant, we get a temperature divided by the square of a velocity; if we multiply this by the square of the speed of light, we get 10.8 tera Kelvin. But a speed of sound is likely more apt than that of light, here.

Helium-filled inflatable wings

JP Aerospace had a plan to put a big blimp 30 km up in the stratosphere, using blimps to ascend the atmosphere and rendezvous with it and blimps with ion-drive propulsion to go up from it to orbit, at costs (according to something I read in c. 2004, but neglected to record where) of order $/US ton/mile. The US ton is about 907 kg, orbit is about 100 miles up, so a dollar (or Euro) will get you about 9kg of pay-load into orbit (if those numbers actually pan out).

Once helium blimps are far enough up the stratosphere to stop rising by buoyancy, the stratosphere's so thin they don't have much air resistance, despite their size, so they can be accelerated gradually up to orbital speed. Make them reasonably wing-shaped and their forward movement will generate lift to a degree commensurate with such drag as they do incur. In so far as there's atmosphere present to offer resistance, it can't help but supply lift; by the time it's thin enough not to, your propulsion system's efforts have got you up to a high enough speed to stay up without the atmosphere's help.

Their plan is to have propeller-driven atmospheric airships that go up to 140,000 feet (42.672 km, a seventh of a light millisecond), where they rendezvous with a suborbital space station (how cool is that ?), also known as a Dark Sky Station (DSS), parked up at that altitude, permanently crewwed, with facilities for docking both the atmospheric airships and the orbital craft. It'll also be, initially, where the orbital craft are built. The orbital craft are huge airships using ion drives, once they've exhausted what buoyancy will do for them, to lift to orbit; the initial test vehicle they plan to make is 6000 ft long (1.82 km, 6.1 light micro-seconds); one can guess the production versions shall be bigger ! They reckon on being able to get to 200,000 feet (61 km, a fifth of a light millisecond) by buoyancy alone, then taking five (or so) days to reach orbital velocity. From there on out, as above, the sky's no longer a limit.

Everything can be re-used, nothing ever has to make a destructive re-entry, no fragile expensive equipment needs to be placed on top of a gigantic pile of explosives, nothing has to endure being accelerated at several g or being shaken violently. The energy expenditure per unit mass of material that reaches space is about as low as one can hope to make it – and way lower than for rocketry. The atmospheric airships and dark sky stations have practical uses independent of the space-bound portion of the journey (for example, mobile 'phone base stations can be put on them), which makes it possible for the project to pay for itself.

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