It seems that ranges of 4-500m are entirely possible with this largely being the maximum for any given machine...
Experiments by Schramm produced the followings results:
Two-cubit arrow-shooting catapult 370 metres
Three-span arrow-shooting catapult (based on the remains found at Ampurias) 305 metres
Small stone-thrower (with 1 1/2-mina stone) 184 metres
Small stone-thrower (with 1lb. lead shot) over 300 metres
Smaller onager over 200 metres
Larger onager over 300 metres
However:
"I acknowledge with admiration Schramm’s notable achievements. I am certain,
however, that it is possible to improve upon his ranges substantially for the following reasons.
Payne-Gallwey constructed an onager which hurled an eight-pound
shot about 500 yards, and this impressive superiority in performance over
Schramm’s one-armed stone-thrower was due, as I have suggested elsewhere,
to the much greater angle through which the arm and the spring
were allowed to operate. In his two-armed, arrow-shooting, euthytone
catapults, too, Schramm only seems to have given the arms an angle of
37 1/2 degrees through which to recoil.
This is approximately correct for a Mark IIIa or IV a arrow-firer,
but the arms of a Vitruvian euthytone can work through an angle exceeding 45 degrees,
and this must produce a significant increase in performance. Also, Schramm’s interpretation of.
the design for the hole-carrier of a palintone stone-thrower
only allows the arms movement through about 45 degrees,
whereas it should be possible to produce an angle of 50 degrees.
This will again lead to a significantly greater output of power. Incidentally, Schramm’s two
armed stone-thrower was a very small one by any standards, and small
models usually fail to match the performance of larger originals."
Source: Greek and Roman Artillery: Historical Development E.W Marsden 1969 Oxford Pg86
Ancient Sources for Artillery(German/Greek):
https://archive.org/details/philonsbelopoiik00philuoft
https://archive.org/details/heronsbelopoiika00hero