To quote from
http://www.hq.nasa.gov/pao/History/SP-4026/noord12.html
"... If the v/c ratio becomes greater than 1 (the travel velocity exceeds the velocity of expulsion), the efficiency of the reaction is diminished again and, finally, for v/c=2 it again goes through zero and even becomes negative (at travel velocities more than twice as large as the velocity of expulsion).
The latter appears paradoxical at first glance because the vehicle gains a travel velocity as a result of expulsion and apparently gains a kinetic force as a result! Since the loss of energy, resulting through the separation of the expulsion mass loaded very heavily with a kinetic force due to the large travel velocity, now exceeds the energy gain realized by the expulsion, an energy loss nevertheless results for the vehicle from the entire process despite the velocity increase of the vehicle caused as a result. The energy loss is expressed mathematically by the negative sign of the efficiency. Nonetheless, these efficiencies resulting for large values of the v/c ratio have, in reality, only a more or less theoretical value.
It can, however, clearly and distinctly be seen from the table how advantageous and, therefore, important it is that the travel velocity approaches as much as possible that of the expulsion in order to achieve a good efficiency of reaction, but slight differences (even up to v=0.5 c and/or v=1.5 c) are, nevertheless, not too important because fluctuations of the efficiency near its maximum are fairly slight. Accordingly, it can be stated that the optimum travel velocity of a rocket vehicle is approximately between onehalf and one and onehalf times its velocity of expulsion."
Thus, v/c = 2 is not asserted as an absolute limit on rocket velocity. The exhaust velocity of LOX/LH rocket is approximately 15,000 mph and escape velocity of Earth is about 25,000 mph. So, achieving escape velocity is within v/c=2. From
http://www.nasa.gov/mission_pages/station/expeditions/expedition30/tryanny.html it is noted
" If the radius of our planet were larger, there could be a point at which an Earth escaping rocket could not be built. Let us assume that building a rocket at 96% propellant (4% rocket), currently the limit for just the Shuttle External Tank, is the practical limit for launch vehicle engineering. Let us also choose hydrogen-oxygen, the most energetic chemical propellant known and currently capable of use in a human rated rocket engine. By plugging these numbers into the rocket equation, we can transform the calculated escape velocity into its equivalent planetary radius. That radius would be about 9680 kilometers (Earth is 6670 km). If our planet was 50% larger in diameter, we would not be able to venture into space, at least using rockets for transport. "
Assuming a proportionate mass increase, escape velocity would increase to about 36,000 mph at r = 9680 km, which exceeds v/c = 2. I therefore concluded v/c = 2 was reasonably correct.
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