"Before, however, I get to the actual quantities of propellants involved, I must acquaint you with some points of view which determine the structures of the vessels, and thus significantly affect the computations.
"You will have noted that the four maneuvers described do not involve surface landings, either on Earth or on Mars. This eliminates the determining factor for a surfacelaunched rocket ship, namely that the thrust must exceed the weight of the ship. We require thrust amounting to only fractions of the weights of the ships, by reason of their weights being constantly sustained by the centrifugal forces generated in their satellite orbits. We can get by with surprisingly small power plants, which will, however, be operated for relatively long periods during the initial maneuvers when large masses are still involved. These masses consist mainly of the propellants reserved for later maneuvers. We propose to use units of no more than 200 metric tons thrust, such as have long been employed in the top stages of Sirius-class vessels.
"Secondly: these Mars ships will always operate in a vacuum and that permits us to neglect all forms of streamlining, in contrast to our rocket ships, which must traverse the atmosphere. Nothing even remotely resembling the familiar hull is required. Propellant tankage will be supported in light, tubular, thin-skinned framing. Although the tankage volume, particularly for the first maneuvers, is very large, stresses are never very high, because the unvarying thrust of 200 tons cannot accelerate the ships rapidly when heavy. Therefore, all tanks can be of very light construction.
"In the third place, we shall be able to abandon the multi-stage principle. We shall rather jettison each tank, together with its supporting structure, as the propellants contained are exhausted.
"Fourthly: the tanks, as well as the crew spaces, will be made of thin-walled plastics.
This will mean that tank shells and supporting structure will weigh but one sevenhundredth of the weight of the contents. Such tanks are collapsible, and will be freighted up to the orbit of departure all ready for assembly despite their bulk. Operation techniques of this nature were developed for Lunetta, so they are familiar to us.
"Fifthly: our rocket motors will be more efficient owing to their operation in vacuum. They will be more economical of propellants than those working in denser atmospheric layers. This improvement is accounted for by the so-called expansion ratio, which is particularly favorable in vacuum. In vacuum, the gases of combustion do not have to drive out of the nozzles against the back-pressure of the atmosphere, thus we can convert a greater proportion of the energy liberated during combustion into kinetic energy of movement of the gases. Of course, this is also done in the top stages of our present ships, so that their power plants are designed for just these conditions and there's nothing novel about it. The figures used in computing our propellant requirements include an exhaust velocity of 2,800 meters per second. You might be interested in the fact that the first booster of a Sirius-class vessel, designed for low altitude, attains an exhaust velocity of 22,550 m/sec.
"And now, I'd like you to bear with me for a moment on the subject of mathematics. I'll cut it as short as I can.
"One of the basic formulas of rocketry states that the velocity increment of a rocket in vacuum and beyond gravity is the product of the exhaust velocity and the natural logarithm of the ratio of initial-to-terminal weight. That sounds a bit more complicated than it really is. It simply means that it is possible to compute directly the initial weight of a rocket vessel before a propulsive maneuver if the change of velocity, the exhaust velocity and the final weight are known. The difference between the weights, of course, represents the propellants expended during the maneuver.
"This allows us to compose in tabular form the propellant requirements of the four maneuvers already discussed. Since the only figure that we can accurately predetermine is the final weight of the ship after the last maneuver, namely 50.5 metric tons, our purpose is best served by commencing with that figure. I will explain later how we reached this figure. Please note that in the following an allowance is made for a velocity reserve of 10 % in each of the power maneuvers 2, 3 and 4. For maneuver 1 the computation of the required propellant weight is a bit more complicated because, in view of the extremely low accelerations, we have to take into consideration the climb against the Earth's gravitational field during the power maneuver proper. The velocity reserve for maneuver 1 amounts to but 3.5 %, roughly." Spencer turned to the blackboard and wrote upon it the following tabulation: -
"There it is," he said with a gesture at the board. 3,720 metric tons total initial weight, 3662.5 of which are propellants used in the four maneuvers, is required so that the ship may weigh 50.5 tons when it is all over. The volumetric content of the propellant tankage for the initial maneuver of exit from the orbit of departure must suffice for 2,814 tons.
Those tanks will be jettisoned before the second maneuver is undertaken, the latter requiring tankage for 492 tons. This will likewise be jettisoned before departure from the satellite orbit around Mars. 222 tons of propellants suffice for this departure and, when the corresponding tankage has again been disposed of, the final tankage for entering the terminal orbit around Earth need hold but 134.5 tons.
The above will give you a rough idea of the general dimensions of a space ship for a round trip to Mars."
"I have described only a part of the proposed journey, namely that between the two satellite orbits concerned. To effect safe and satisfactory landings on and departure from the surface of Mars poses an entirely novel set of problems. These cannot be solved by the vessels hitherto discussed. It would be worse than spendthrift to land all those propellants on the surface of Mars and then be faced with the tremendous power requirement for overcoming Martian gravity. Not only that, but the construction of the vessels utterly unsuits them to operate in any kind of atmosphere. They have no fuselages or hulls, nor are they winged, and their rocket motors wholly lack the power to lift them from the Martian surface. For that reason, we propose to make our landings in special craft which we shall call "landing boats," the space ships themselves continuing to orbit around Mars at the altitude of 1,000 kilometers. They will complete this orbit in about two hours and twenty six minutes at an orbital velocity of 3.14 km/sec.
"Now, the problem of descending from this orbit to the Martian surface is not dissimilar to that of descending from Lunetta to Earth. That is to say, the landing boat will decrease its velocity from that of its mother ship. This will throw it into an unpowered elliptical path touching the upper layers of the Martian atmosphere after one half of a revolution around the planet. Such a landing boat must of course be equipped with wings and controls permitting it to produce negative lift, in order to force it into a circular path within the atmosphere. The drag will then slow the boat down. The wings will eventually produce the positive lift required for a glide and a normal landing in airplane fashion.
"But a landing of this nature on Mars is accompanied by two novel problems when compared to its terrestrial counterpart. One is due to the Martian atmosphere being, at surface level at least, markedly less dense than that of Earth. This will diminish the following tabulation
"There it is," he said with a gesture at the board. 3,720 metric tons total initial weight, 3662.5 of which are propellants used in the four maneuvers, is required so that the ship may weigh 50.5 tons when it is all over. The volumetric content of the propellant tankage for the initial maneuver of exit from the orbit of departure must suffice for 2,814 tons.