Arthur C. Clarke wrote some absolutely classic space-travel stories in the late 1940s and early 1950s, which were amongst the first to give a “real life” account of space-travel and its challenges. Some were novels – “Prelude to Space“, “Islands in the Sky” and “The Sands of Mars“ – while others were short stories, like “The Sentinel”, “Earthlight” and “Breaking Strain”. The last story I mentioned was collected in “The Sentinel” – a gorgeously illustrated collection of shorts from 1981 spanning across his career, from “Rescue Party” (Arthur’s first serious sale) to “Songs of Distant Earth” (the movie outline version.)
“Breaking Strain” seems like an odd pick in the selection because it doesn’t involve alien contact, just two spacemen condemned to a slow death by an emptied oxygen tank on their way to Venus. Their vessel, “Star Queen“, is a nuclear powered cargo ship – two spheres separated by a 100 metre boom, a prototype of the “Discovery” from “2001: A Space Odyssey“. Their orbit is a low energy Hohmann transfer orbit which, to Venus, is only 145 days long – much less than the equivalent 258 day trip to Mars. With just 30 days to go the oxygen liquefaction system, which keeps their stored air liquid by cooling it in the ship’s shadow, is punctured by a meteoroid. Their air purifier system is imperfectly able to scrub the ship’s air, but with 10% losses on each cycle through. Thus they have air for 20 days, for the two of them. Thus the conflict that makes a story.
In the course of the telling Arthur mentions that passenger ships make the same crossing to Venus in a third the time for 10 times the propellant expenditure. So what does that involve? To work it out I assumed the passenger ships were on an orbit with the same semi-major axis, a, which simplified the search for an orbital solution. What changed with each new orbit tried was the perihelion (closest point to the Sun) and the aphelion (furthermost point from the Sun.) The assumed starting orbit was Low Earth Orbit at 1,000 km and the destination was a 1,000 km orbit around Venus – and Earth was assumed to be at 1 AU and Venus at 0.7233311 AU. The results don’t vary much with slight variations to these figures. A perihelion of 0.5833311 AU and an aphelion of 1.14 AU gives an angle of 36.25 degrees to the (assumed circular) orbits of the Earth and Venus, and a total velocity change of 46.13 km/s. The Hohmann orbit, for comparison, has an angle of zero at both by definition, and a total delta vee of 13.59 km/s. To get a ten-fold propellant increase between the two means the exhaust velocity is 22.5 km/s – a figure only extractable via iteration.
I’ve no idea if Arthur ever computed the orbits in as much detail. As president of the British Interplanetary Society he would have discussed these sorts of issues over and over again. Probably over beer at the “White Hart”. Whether he remembered the exact figures – if such ever existed – is unknowable now he has left us, but the challenge of describing realistic space-travel will remain with us. Until we actually do it, of course. But no one will seriously contemplate Hohmann transfers, except for robotic vessels. The time penalty is hefty and leaving any crew in space to soak in cosmic rays is detrimental to all. Oxygen recyclers are also somewhat more efficient now, so we may never have a “Breaking Strain” scenario…