Charles Talleyrand wrote:
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 same way on a BAE Hawk.

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?

Some years ago there was an Airbus A330 FBW fly by wire widebody that
ran out of fuel crossing the atlantic. It had to make an emergency
landing at (I thnk) the Azores I think from over 100km out without
fuel.

A leaking fuel delivery pipe in the engine pylon drained the aircrafts
fuel: the pilot didn't believe his instruments and thus kept
transfering fuel from the good side to the bad side rather than
shutdown the bad engine. He thus drained both wings.

When fuel cut out (I saw a dramatisation ogf the events) the ram air
turbine deployed and the pilots, after finally acknowledging their fuel
situation went through their checklist.

Lights and pressurisation was lost with the power.

Most pointedly they lost spoilers and flaps; they really only had a few
instruments, ailerons, tail surfaces and the undercarriage. As a
result of being without flaps the landing speed was very high and
becuase there were no spoilers they couldn't loose speed or altitude
and actually had to circle and zig zag to loose both speed an altitude.
This made the one chance of making the runway even harder as there
would be no go arounds.

To cap it all of the runway in the azores ends in a 300ft shear cliff.
They stopped a few dozen meters short with blown tyres.

Airbus changed their software and though the pilot was clearly not
making the best decisions that day it was easier to given him awards.

The ram air turbine provides very little power. I think the idea of
giving the APU its own reserve fuel supply is tempered by the fact that
it is perhaps better to keep the engine lit for a few seconds longer.

Perhaps a cartriedge or two of of rocket-gas generator turbine could be
used to provide pressure for flap and spoiler deployment