  We present investigations of the interaction between the relativistic,
precessing jets of the microquasar SS433 with the surrounding, expanding
Supernova Remnant (SNR) shell W50, and the consequent evolution in the
inhomogeneous Interstellar Medium (ISM). We model their evolution using the
hydrodynamic FLASH code, which uses adaptive mesh refinement. We show that the
peculiar morphology of the entire nebula can be reproduced to a good
approximation, due to the combined effects of: (i) the evolution of the SNR
shell from the free-expansion phase through the Sedov blast wave in an
exponential density profile from the Milky Way disc, and (ii) the subsequent
interaction of the relativistic, precessing jets of SS 433. Our simulations
reveal: (1) Independent measurement of the Galaxy scale-height and density
local to SS433 (as n_0 = 0.2 cm^{-3}, Z_d = 40 pc), with this scale-height
being in excellent agreement with the work of Dehnen & Binney. (2) A new
mechanism for hydrodynamic refocusing of conical jets. (3) The current jet
precession characteristics do not simply extrapolate back to produce the lobes
of W50 but a history of episodic jet activity having at least 3 different
outbursts with different precession characteristics would be sufficient to
produce the W50 nebula. A history of intermittent episodes of jet activity from
SS433 is also suggested in a kinematic study of W50 detailed in a companion
paper (Goodall et al, MNRAS submitted). (4) An estimate of the age of W50, and
equivalently the age of SS433's black hole created during the supernova
explosion, in the range of 17,000 - 21,000 years.
