  I derive and discuss a simple semi-analytical model of the evolution of
powerful radio galaxies which is not based on assumptions of self-similar
growth, but rather implements some insights about the dynamics and energetics
of these systems derived from numerical simulations, and can be applied to
arbitrary pressure/density profiles of the host environment. The model can
qualitatively and quantitatively reproduce the source dynamics and synchrotron
light curves derived from numerical modelling. Approximate corrections for
radiative and adiabatic losses allow it to predict the evolution of radio
spectral index and of inverse-Compton emission both for active sources and for
`remnant' sources after the jet has turned off. Code to implement the model is
publicly available. Using a standard model with a light relativistic
(electron-positron) jet, sub-equipartition magnetic fields, and a range of
realistic group/cluster environments, I simulate populations of sources and
show that the model can reproduce the range of properties of powerful radio
sources as well as observed trends in the relationship between jet power and
radio luminosity, and predicts their dependence on redshift and environment. I
show that the distribution of source lifetimes has a significant effect on both
the source length distribution and the fraction of remnant sources expected in
observations, and so can in principle be constrained by observations. The
remnant fraction is expected to be low even at low redshift and low observing
frequency due to the rapid luminosity evolution of remnants, and to tend
rapidly to zero at high redshift due to inverse-Compton losses.
