I understand higher speed, and higher drag mean higher adiabatic compression leading to heating up the air, and the plane as result. X-15 needed ablative coating to prevent overheating. On reentry of space vehicles heat shielding is the most critical problem. This is perfectly understandable as higher speed with constant or growing air density means higher drag - and this results in higher speed.
I'd like to know how are these values related though.
[for the purpose of this question, let's neglect the issues of engine efficiency. We have a magical rocket engine that weighs nothing and needs no air nor fuel to produce thrust. This is a purely an aerodynamics question.]
At given pressure, drag is directly proportional to lift (both being quadratically proportional to airspeed and linearly to air density). That means higher airspeed allows raising the altitude, lowering air density, and thus lowering drag until lift and gravity even out.
Let's maintain such a flight: We're constantly accelerating (slowly); and climbing, at such a rate, that lift remains constant, and evens out with gravity (minus a minimal delta to retain climb). The increase of lift coming from rising airspeed is being offset by decreasing air density as the craft climbs.
With constant lift, and drag being directly proportional to lift, drag remains constant too.
Maintaining constant drag through climb like that, air density is inversely proportional to square of airspeed.
How would heat creation behave in this situation though?