Rocket each pound of fuel + oxidizer you burn a second gives produces a few hundred pounds of thrust. Call it 300.
Air breathing engine doesn't carry oxidizer. A rocket needs to carry ~3 lbs of oxidizer per lb of fuel. Using the 300 number above an air breathing engine would have an ISP of 900.
It gets worse of the rocket because prop and turbo-fan engines also use air for reaction mass[1]. Which boosts the calculated ISP even higher. Call it 5X higher. Now your ISP is 4500.
So yes you can use rockets for an aircraft. But it won't travel as far as one with a piston or turbofan.
1 Thrust is basically mass flow X deltaV. Where power is mass flow X deltaV squared. So it's more efficient to create thrust by accelerating a large mass flow a small amount (turbofans) than a a small amount of mass a large amount (rockets).
https://en.m.wikipedia.org/wiki/SABRE_%28rocket_engine%29
https://www.gov.uk/government/publications/synergetic-air-br...
The answer is "its too expensive, unsafe and basically unnecessary." Even Concorde (with conventional jets) proved to be uneconomical when luxury commercial aviation was lucrative, and US rocket powered X-Planes like the X-15 never made it out of prototypes.
Giant turbofans are good enough.
https://www.marssociety.ca/2021/01/07/rocket-physics-the-roc...
TL;DR Rockets on launchpads have about the same fuel weight/body weight ratio as a soda can, with the soda being the fuel. A rocket airplane would similarly need to be mostly fuel.
Couldn't you just like find a more efficient fuel/oxidizer mix? Or is this like fundamental chemical energy density? Does it make any difference if you just have to fly in atmosphere, and not escape Earth's gravity? Seems like it should be easier...so you could have more payload.
Precisely. Rockets use liquid oxygen and cryogenic, extremely weight efficient fuels (usually liquid hydrogen or liquid methane). They are pretty much at the edge of practical chemical energy density.
> Does it make any difference if you just have to fly in atmosphere, and not escape Earth's gravity?
But they have to fly for a much longer time, with atmospheric drag. If you look up examples like the Me 163 and the X15, you will see that their range is extremely short:
https://en.wikipedia.org/wiki/Messerschmitt_Me_163_Komet
https://en.wikipedia.org/wiki/North_American_X-15
The reasons rockets use rockets (and not jets) is because their flight time in the atmosphere is even shorter, and they need a ton of thrust in that short period, not because they are particularly efficient.
Read up on the German rocket fighters used in WW2. IIRC the rocket engine lasted about six minutes. They had no power available for landing, so had to glide to a close-by landing strip or crash.
Fast, they were. Useful, not so much. Dangerous to their pilots, also.
Also, starting at about .78 times the speed of sound, the energy needed to fight against air friction (drag) increases drastically, and air travel is energy-expensive enough below .78 times the speed of sound.