Distant powerful radio sources would provide a useful cosmological tool if an intrinsic length or luminosity could be estimated from the observations in a way that is independent of the coordinate distance to the source. A model for the propagation of the radio lobes of powerful extended radio sources is presented here; the model is written in terms of fundamental physical variables such as the luminosity in directed kinetic energy and the ambient gas density, rather than observables such as the radio power. It is shown that the fundamental physical variables may be estimated from observed quantities. The model parameter beta that relates the characteristic time the central engine is producing a collimated outflow to the luminosity in directed kinetic energy is constrained by low-redshift observations and extrapolated to high redshift. The application of the model to powerful extended radio sources allows an estimate of the characteristic source sizes that is nearly independent of the coordinate distance to the source, and thus is basically independent of the de/acceleration parameter q0. The characteristic source sizes estimated in the context of the model may be compared with the observed median source sizes, where each source size is determined directly from the angular extent of the source, the source redshift, and the coordinate distance to the source. The comparison of the intrinsic source sizes estimated using the model, which are nearly independent of q0, with the median source sizes estimated using the angular sizes of the sources, which depend on q0, constrains the allowed range of q0. The basic model and method is presented and discussed and is applied to one published data set consisting of 10 radio galaxies. Taken at face value, the data favor a low value of q0; a low value of q0 implies that either space curvature or a cosmological constant is important at the present epoch. Note that Doppler boosting and beaming of radio emission are unlikely to be important in these systems since the relevant flow velocities are small compared with the speed of light. This analysis has broad implications for the environments of powerful extended radio sources and for models for extracting the luminosity in directed kinetic energy from the central compact object.
