As I understand it, a ramjet has no moving parts. Compression is supplied by the speed of the aircraft carrying it. Since a ramjet is basically a tube, I’d guess that the aircraft’s speed must be great enough to ‘ram’ enough air into the front of the engine to counteract the pressure from the combustion of the fuel/air mixture.

How fast must a ramjet engine be moved through the air in order to operate?

I assume that an aircraft would need a turbine engine to attain ramjet operating speed. If so, does the turbine ‘shut down’ when the ramjet takes over? What about drag? If it doesn’t shut down, then how do they protect against overspeed? I imagine a rocket, contained within the fuselage, would solve the issue of drag; but I can think of very few aircraft that used rockets as the sole propulsion to leave a runway.

Given the need for an engine to get the aircraft up to ramjet operating speed, what is the advantage of a ramjet?

Tell me about the SR-71 engines. Are they some sort of turbine/ramjet hybrid? If so, how do they work?

The SR-71 used Pratt & Whitney J58 Turboramjets. As the name implies, the J58 is a hybrid design that functions as a turbojet and a ramjet.

IIRC, Ramjets start working at around Mach 1 or so, and become really efficient at around Mach 3. The J58 used a system of bypass flaps to switch from turbojet to ramjet mode. Basically, once moving fast enough for the ramjet to work, the bypass flaps close over the turbojet inlet, directing air around it and directly into the fuel injectors. Picture a big ramjet with a turbojet nestled inside of it, the bypass flaps are located at the end of the huge inlet cones and right in front of the actual intake of the turbojet engine.

LeDuc operated a ramjet at high subsonic speeds in the '50s. Nobody today would consider really operating one there - it’s got no real advantages.

You’ve already hit one of the biggest advantages of the ramjet/scramjet - no moving parts. In a turbojet keeping the compressors and turbines alive is one issue at high speeds - pressures and temperatures get quite high. Keeping rapidly rotating machinery at tight tolerances at high temperatures gets rough. In the ramjet you can largely separate the structural and high temperature resistant components of the engine. There are also fairly high losses through the compressors at high speeds. As a result of this (and other factors), at speeds above 2.5 times the speed of sound or so a ramjet has a higher specific impulse (is more fuel efficient) than a turbojet.

You are also ignoring the other alternative to ramjets - rockets. By using atmospheric oxygen ramjets get much better fuel economy (propellant economy?) than rockets. So perhaps if you are launching a missile from an already supersonic or high subsonic plane it makes more sense than a rocket if longer range interests you. Or if you are trying to extend the range of a munition fired from a gun.

There are two “combined cycle” engines that get played with a lot. Rocket based combined cycle, or RBCC, and turbine based combined cycle, or TBCC. They use rockets and turbojets respectively to reach ram speeds. Relatively lower speed apps (cruise missiles, etc) tend to be based on TBCC.

The RBCC typically has rockets integral to the flowpath of the engine (with or without the inlet initially being blocked off). The idea is you start flowing fuel and oxidizer to get moving. Once you are moving and injesting air you can run your rocket fuel rich to take advantage of atmospheric oxygen (this is an “ejector ramjet”). Once you are in comfortable ramjet territory speed wise, cut off the oxidizer and run as a ramjet. If you fancy a little more speed transition to scramjet mode at higher speeds (Mach 6 will do nicely). If you want to go to orbit just pop the rocket/oxidizer back on at some point between Mach 8 and Mach 25 and there you have it, a lovely little single stage to orbit spaceplane. You get to carry a lot less fuel but require significantly more structure than a pure rocket.

A TBCC may have two internal flowpaths - physically switching between the two. Depending on your application you might or might not turn the turbine off.