Charles Talleyrand schrieb:

Suppose a smaller airplane with it's fly-by-wire controls goes runs out
of fuel. All the engines quit. On a larger jet a ram air turbine
would drop into the airstream and power the controls. How does it work
on smaller planes like the Dassault Falcon or the F-16?

The Panavia 200 Tornado has a EPS battery (one shot battery) that in
case of double engine out situations supplies a few instruments and an
electric pump to have some hydraulic pressure. This allows maintaining
control over the a/c for ~5-7 (max 10) minutes.

Alternatively, I've always wondered if one could not keep a special
reserve tank for the APU. When the engines quit, the APU
automatically starts to power the controls. Would such a system be
safe and would it be certifiable? Would it weigh less than the
existing system?

I a lot of airplanes the APUs (resp. their intakes and exhausts) are
mounted in a way that they can't be used inflight. Besides that, if
there still is fuel in the tanks it's better served for keeping the
engine alive than just the APU...

Benjamin