Thereâ€™s a certain misunderstanding common in aerospace that rockets are horribly inefficient and that long term we need air breathing ramjets or scramjets to efficiently launch things, with the idea that we can thus avoid accelerating oxygen to flight speed, which is considered wasted energy. â€œAirbreathing hypersonics are five times as efficient as rocketsâ€ they say. This, however, is not so.
The misunderstanding comes in part by considering oxygen as just as costly as fuel. Oxygen is not. It can be condensed out of the atmosphere with little energy and is available by the truckload at $100/ton or less. A dedicated production plant can produce it for as low as $10/ton. That compares to $1200 to $3500 per ton for industrial liquid hydrogen which is often the fuel being compared to.
A stoichiometric rocket burns 8 times as much oxygen as it does hydrogen. So if an airbreather consumes a factor of 5 times less propellant than a rocket, that means it consumes nearly twice the hydrogen!
Hydrogen requires the vast bulk of the energy to produce compared to oxygen, a couple orders of magnitude more energy. So for our purposes we can ignore the energy needed to produce liquid oxygen.
Letâ€™s look at LAPCAT II, and airbreathing hypersonic airline concept capable of traveling to the antipodes of the world at Mach 8.
As a percentage of its gross takeoff weight, 45% is hydrogen fuel and 15% is payload: http://www.icas.org/ICAS_ARCHIVE/ICAS2014/data/papers/2014_0428_paper.pdf
That means each kg of payload requires 3 kg of liquid hydrogen, which has an energy density of 142MJ/kg, giving an energy cost of 426MJ per kilogram of payload.
Hydrogen with variable mixture from oxygen rich to near stoichiometric would be the best fuel to compare with and the most efficient for rockets, but I will use SpaceXâ€™s ITS from 2016 as a comparison point even though itâ€™s less energy efficient.
ITS has a payload to LEO of 300 tons (more for the tanker variant), and uses a total of 6700 tons of propellant for the first stage and 1950 tons for the second stage ship (both including landing propellant). Given a O:F weight mixture ratio of 3.9, and a specific energy of 55.5MJ/kg for methane, the cost per kg of payload to orbit is just 330MJ, actually less than the hypersonic airliner in spite of using less efficient methane.
You might as well use rockets for long distance transport at high Mach numbers.
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