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The physical origin of the beam spread factor is different from any other efficiency dealt with in the energy flow model. Beam spreading consists generally of two pieces: (1) beam’s geometric divergence, and (2) non-uniform values of the jet’s particle speed. In some real engines, either may prevail. 4 Rocketship Dynamics in Field-Free Space 13 come in computing thrust; but only factor-2 has to be taken into account in calculating the jet’s kinetic power. Two different engines belonging to the same propulsion mode may exhibit significantly different spreads.

Zander, and H. Oberth, the author likes to recommend some papers and books—in alphabetical order—which though do not exhaust all the pioneering works in those years. At least to the author knowledge, the following 8 It was generalized to four dimensions in tensorial form [28], Eq. (31), involving any exhaust type. This is because energy conservation and momentum conservation give different pieces of propulsion information, in general. These ones coincide only in the one-space + one-time case. 10 1 Some General Rocket Features ones (which contain many other references inside) are particularly worth citing, reading and remembering: [1, 4, 6, 7, 10, 13, 15–18, 21], and [14].

For the conventional non-relativistic specific-impulse propulsion systems, the χ-terms are by far dominant so that ηm = ξ , namely, the fraction of the propellant accelerated up to the exhaust speed. On the other extreme, for photon rockets, both χ and ζ vanish, so the utilization efficiency results (ph) in ηm = ηb εk /εa ≤ ηb . 9) The effective jet speed may be rather lower than 1 in a rocket where the energy source releases some large amount of γ-rays and neutrinos. 8 This equation, in various equivalent forms, has been re-discovered independently by many authors (including this author) in the 20th century and in the first years of the 21th century too.