The properties of a sample of 31 very powerful classical double radio galaxies with redshifts between zero and 1.8 are studied. The source velocities, beam powers, ambient gas densities, total lifetimes, and total outflow energies are presented and discussed. The rate of growth of each side of each source were obtained using a spectral aging analysis. The beam power and ambient gas density were obtained by applying the strong shock jump conditions to the ends of each side of the source. The total outflow lifetime was obtained by applying the power-law relationship between the beam power and the total source lifetime derived elsewhere for sources of this type, and the total outflow energy was obtained by combining the beam power and the total source lifetime. Composite profiles were constructed by combining results obtained from each side of each source. The composite profiles indicate that the ambient gas density falls with distance from the central engine. The source velocities, beam powers, total lifetimes, and total energies seem to be independent of radio source size. This is consistent with the standard model in which each source grows at a roughly constant rate during which time the central engine puts out a roughly constant beam power. The fact that the total source lifetimes and energies are independent of radio source size indicates that the sources are being sampled at random times during their lifetimes.
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