[opensores]

It gets orbital speed and kinetic energy from the aircraft.

Being dropped from a 747 the kinetic energy is far smaller than the potential energy. The 747 goes perhaps mach 0.8-something with a ceiling over 40,000 ft; say roughly 14 km.

That potential energy is equivalent to about 530 m/s.

(So, in terms of energy, you are comparing a bit under Mach 1 with a bit over Mach 1.5.) sqrt(2 g h) if you want to do the arithmetic: g=10m/s/s and h=14km.

So added together we are talking about Mach 2.5 equivalent launch speed from the aircraft stage, from an airliner like a 747 or 707. This is significant. Remember you're also doing the equivalent of accelerating the propellant that would be needed to accelerate the rocket up to this energy.

Now if you launch it from something like a military craft (Mig 31 or Tu-160) then you can ballpark add another Mach 1, so we're in the ballpark Mach 3.5 region. Probably exceeding Mach 4 for the Mig 31, but of course it only could launch a small orbital rocket.

Now Kerbal is an interesting way to get very crude approximations. And the reason usually that my above simple calculation ends up not impressing as much as it should is that the orbital rocket needs to transition from a horizontal flight path to something much steeper, or it will take a very long path through the upper atmosphere. This long path ends up creating a huge amount of friction eating into much of your gains imparted by the air launch.

Even though the atmosphere ~30 km high is incredibly thin, it will burn your vehicle that is racing though it at speeds that are ballpark Mach 10 (possibly considerably higher). In other words, massive amounts of friction.

A ground launched vehicle can take almost the shortest way, and pierce the atmophere with minimal friction---almost a vertical path through. That is ground launch's biggest advantage. It will pierce the thickest part of the atmosphere vertically and gracefully and optimally arc into a horizontal path near its peak (the height of the orbit).

[opensores]

oops, correction first sentence should read:

The rocket achieves orbit from the potential energy plus the kinetic energy. (Both kinetic and potential energy factor need to be a taken into account at the time the air drop.)