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Comment by perihelions | Hacker News Reader

It fascinates me that it's an exponential function—the engine that transports fuel, and consumes fuel proportional to distance traveled: its fuel cost grows exponentially. The precise laws of physics work out, just barely, that we can send fuel around the world by boat; or, as here, by airplane to a near-antipode of the world. It's physically possible to circumnavigate the world either way.

It'd only take a slight modification of several physical constants that planets would be too large to cross. An alternate universe with continents so vast, no machine, no amount of fuel, could allow any exploration of their deepest interior; secrets permanently concealed.

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That's the famous rocket equation (and with rockets, none of the solutions other replies mention, like depots or pipelines, are available). There's a thought experiment that for a planet only a bit heavier than Earth (something like 2x or 5x) it might be completely impractical to launch anything into orbit.

Long before there was the tyranny of the rocket equation, there was also the tyranny of the wagon equation [1] that limited how far per-industrialized armies could move with wagons and animals (though the equation wasn't formalized).

[1] https://maximumeffort.substack.com/p/the-tyranny-of-the-wago...

Breguet range equation for airplanes also predates rocketry though postdates wagons. Airplanes can already have a significant portion of their weight as fuel. It has a logarithm of the mass ratio as one of the terms.

And by "significant", half or more their take-off weight.

Boeing B-52 Stratofortress: dry weight 38.25 tonne, fuel capacity 141.6 tonne, ratio 3.7:1. Max takeoff weight: 221.3 tonne. If at max fuel, that's 63% fuel. In practice, this aircraft refuels, often multiple times, on missions, which may span the globe.

Boeing 747-8: dry weight 220 tonne, fuel capacity 238.6 tonne, ratio 1.08:1. Max takeoff weight: 447.1 tonne. If at max fuel, that's 53% fuel.

Much of the fuel burn is on take-off and climb, meaning that cruise portions of flight are already at significantly less than take-off weight, and further reduce with time. You'll occasionally see long-distance flight profiles in which the altitude of the aircraft increases over the flight (in 1,000 ft increments given air traffic regulations) as fuel load decreases and maximum efficient altitude increases.

I would tend to assume that the equation was formalized.

Logisticians were intimately aware of the concept but I’ve never seen an equation formally written down or mentioned anywhere in ancient or medieval texts. They would have used a simplified version for planning - counting days of food an army has and how far they can move from their bases on that food, plus how much they can forage for and how much they can take from the local population.

It looks more like a Civ5 game board than a neat equation like the ideal rocket equation.

>a bit heavier than Earth

A planet's mass doesn't matter so much as the density. If you look at a planet like Saturn, it is almost 100x heavier, but it's surface gravity is nearly identical to Earth's. What really matters for rockets though is the surface escape velocity, which scales like the square root of mass divided by radius. So for large radii it is slightly worse than density, which scales like mass divided by radius cubed. Ideally you would live on a small rocky planet (Mars ftw).

I tried to calculate a formula once, to convert increment of Earth's mass to increment of Earth's gravity for a planet of the same density, so not the same as escape velocity but sort of related. I'm not sure if it's actually correct but it was: x/x^(2/3) So i.e. for 5 Earth masses and the same density, it would be 1.71 of Earth's gravity on the surface, 10 masses -> 2.15 Earth's gravity.

Reasoning: Acceleration is GM/R^2 and planets R is like (x * Me / 4Pi / density)^1/3 . Directly proportional to M and inverse square root of radius, while the radius is directly proportional to (x)^(1/3)

Though the density for 2 planets made of the same stuff and different masses would probably be different due to differences in pressure in its internals? Just a guess.

A good stackexchange question on that https://space.stackexchange.com/questions/14383/how-much-big...

Pipelines solve this problem quite neatly. The transport cost of a pipeline is very small compared to the fuel transported.

Interestingly pipelines can have near perfect fuel efficiency (though few do) since it's possible to run the pumps with electricity. That means if the electricity that ran the pumps came from wind or solar no fuel was burned to move the product.

At this point in time the only other thing that might be able to work that way is electrified freight trains. I don't believe there are any here in the US, at least not significant distances.

In one of his books (I believe it's Collapse though possibly Guns, Germs, and Steel, Jared Diamond comments on how introduction of novel foodstuffs, in particular the potato or sweet potato, by Europeans, greatly changed military capabilities and hence power relations amongst indigenous Pacific islanders. Particularly in New Zealand if memory serves.

I'd had to be careful in noting that these were foods introduced by Europeans, but not European foods of themselves, in that potatoes (both varieties) are native to the Americas.

That's an interesting idea but a long series of fuel caches, though inefficient, could overcome this problem.

Q: What do all of these places have in common?

Aden

Bahamas

Bermuda

Bombay

Gibraltar

Halifax

Hong Kong

Jamaica

Malta

Singapore

Suez

Trincomalee

A: They are all former coaling stations in the British Empire

Look up US coaling stations as well. The Great White Fleet (circumnavigated the globe from 16 Dec. 1907 to 22 Feb 1909) was a demonstration that the US could send 16 battleships and support vessels on global missions.

Transition of navies from coal to oil (initiated by the British just prior to WWI) greatly simplified bunkering operations. Fuel was still required, but oil (even the extraordinarily viscous bunker oil used by ships) is far easier to manage both in fueling and subsequent rebunkering to maintain ship's trim than solid coal.

Among significant US refueling stations was the Saudi peninsula (though precisely where I'm not certain), which had a strong influence on subsequent US relationships and allegiances in the region, particularly notable after the discovery of vast oil reserves.

I'd be interested in a list of US coaling / fueling stations, though I'm not finding one immediately. Pearl Harbor (Hawaii) and Subic Bay (Philippines) / were all but certainly two of these.

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