Higher speed -> you reduce the angle of attack -> lower cross-section. The drag per unit of area increases, but the area decreases. Overall, you still have higher drag, but you get faster to where you need to get. It is not pre-ordained that you need to burn more fuel overall.
In fact, you can end up burning less, not more fuel.
Here's why: drag per se doesn't matter. What matters is the lift-to-drag ratio [1]. To keep the plane at a constant altitude, the lift needs to be equal to the gravitational force acting on the plane. To keep the plane at constant speed, the thrust needs to equal the drag. If the lift-to-drag ratio is 10, the thrust needs to be one tenth of the weight of the plane.
Now, the fuel consumption per second is roughly proportional to the thrust. If you double the speed and the lift-to-drag ratio gets cut in half, your overall fuel consumption is the same. But here's the thing: in supersonic regime, the lift-to-drag ratio does not get cut in half. The empirical lift-to-drag ratio is 4(v+3)/v, where v is expressed in Mach number. For example at Mach 3 you get LTD ratio = 8 and at Mach 6 you get 5.33.
Of course, things are not that rosy: on one hand the airplane needs to be sturdier, because it needs to withstand higher vibrations. On another hand, even if in cruise mode you may save fuel, it's difficult to optimize the plane in a very wide range of velocities. Concorde was horrible at low speeds, so it was burning a lot of fuel at take-off; it is quite obvious that a plane is the heaviest at take-off, so if you burn more fuel at that point, you really burn more fuel.
But design has made huge advances in 50 years. We may be able to optimize better an airplane now than we could when the fastest supercomputer was slower than the iPhone in your pocket.
Bottom line: it is not at all obvious that a supersonic plane needs to burn a lot of fuel, and it may be that it could actually burn less than a subsonic one.
Higher speed -> you reduce the angle of attack -> lower cross-section. The drag per unit of area increases, but the area decreases. Overall, you still have higher drag, but you get faster to where you need to get. It is not pre-ordained that you need to burn more fuel overall.
In fact, you can end up burning less, not more fuel.
Here's why: drag per se doesn't matter. What matters is the lift-to-drag ratio [1]. To keep the plane at a constant altitude, the lift needs to be equal to the gravitational force acting on the plane. To keep the plane at constant speed, the thrust needs to equal the drag. If the lift-to-drag ratio is 10, the thrust needs to be one tenth of the weight of the plane.
Now, the fuel consumption per second is roughly proportional to the thrust. If you double the speed and the lift-to-drag ratio gets cut in half, your overall fuel consumption is the same. But here's the thing: in supersonic regime, the lift-to-drag ratio does not get cut in half. The empirical lift-to-drag ratio is 4(v+3)/v, where v is expressed in Mach number. For example at Mach 3 you get LTD ratio = 8 and at Mach 6 you get 5.33.
Of course, things are not that rosy: on one hand the airplane needs to be sturdier, because it needs to withstand higher vibrations. On another hand, even if in cruise mode you may save fuel, it's difficult to optimize the plane in a very wide range of velocities. Concorde was horrible at low speeds, so it was burning a lot of fuel at take-off; it is quite obvious that a plane is the heaviest at take-off, so if you burn more fuel at that point, you really burn more fuel.
But design has made huge advances in 50 years. We may be able to optimize better an airplane now than we could when the fastest supercomputer was slower than the iPhone in your pocket.
Bottom line: it is not at all obvious that a supersonic plane needs to burn a lot of fuel, and it may be that it could actually burn less than a subsonic one.
[1]https://en.wikipedia.org/wiki/Lift-to-drag_ratio