Astro, just to be clear on how these cutoff switches work. Say you were cruising at 35,000 ft. hand flying the airplane, and you moved one of these switches to "cutoff". Then waited 30 seconds, and moved it back. Would the engine flame out, spool down, then automatically relight and spool back up to the same power setting? Or would other adjustments have to be made?
The faster you go from “cut off“ back to “run“, the faster the engine will relight and spool back up.
So, in the case of this airplane, the engines have a “auto relight” feature. So do many types of engines. It’s pretty common. In fact, the CF-6 will auto-relight automatically while other types require cycling the switch.
Cycling the fuel control switches from run, to cut off, back to run, starts the relight.
30 seconds is a long time.
Without the pressure of combustion, the RPM on the engine drops pretty low. It depends on the airspeed & altitude of the aircraft, but it’s gonna get down below where it would normally idle.
In that case - the relight might take as long as two minutes. Might be quicker - again, it depends on a lot of factors.
Turbines take a while to get from low speed to operating speed. There is an aerodynamic balance between the high-pressure, and low pressure, spools. Those spools contain both the compressor section, and the turbine section, and they have to be kept in balance as they accelerate.
So there’s a limit on the rate of that acceleration, and therefore on the rate of restart.
Over 40 years ago, a Delta Airlines 767 accidentally shut down both engines while taking off from Los Angeles.
It happened at about 2000 feet, they quickly realized they had cycled (not really bumped) the fuel switches, which was the wrong thing to do, and they put them back in run. The engines re-lit, accelerated, and the airplane flew away.
I am pretty certain that incident caused Boeing to redesign the 767 fuel control system, and place the EEC switches on the overhead, but even back then, it was impossible to “bump“ the fuel control switch.
The crew was responding to a malfunction, and really messed it up.
https://asn.flightsafety.org/wikibase/147073