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28 SMITHSONIAN ANNALS OF FLIGHT The velocity of the body falling freely from infinity to the moon would be Oao = 2370 m/sec The time used to go through the second phase can be calculated approximately by neglecting the moon's action which is entirely negligible during the total journey. It would be the same time as that taken by the body during a free fall from the moon to the point where we had stopped the engine: Third Phase t = 48 hr 30 min One must now decrease the speed by turning the body upside-down as said before, and by re-starting the motor. What will be the law of this slowing down? We would establish it in the same manner as we did for the earth; but the moon's attraction being much smaller, and as we do not at this stage seek a great precision, we will deduct from the acceleration due to the propulsor, half the acceleration due to the moon, and we will assume the motion uniformly slowed down under the action of this fictitious acceleration. We find that the body has to be turned upside-down at a distance from the moon's surface equal to d = 250,000 m approximately This point is so close to the moon, and the present calculations not being rigorous, the time necessary to reach the surface could be mistaken for the time necessary to reach the moon itself. The time of the slowing down will be t — 226 sec = 3 min 46 sec The total time for the whole process is approximately then: First phase 0 hr 24 min 9 sec Second phase 48 hr 30 min Third phase 0 hr 3 min 46 sec 48 hr 58 min approximately The return trip could be done by reversing the process and in the same time. It must be pointed out that, by this means, the propulsor is used only 28 min going and the same time coming back unless the earth's atmosphere is used for the slowing down process, in which case the 28 min used for the departure, and the time necessary to orient the body properly, would suffice. We will now consider the power actually needed to realize these minimum conditions and the resulting efficiency output of the motor with respect to the theoretical work given. If we consider a 1000 kg vehicle out of which 300 kg are consumable; and if the engine has to work 27 min +3.5 min and to have a sufficient flow margin 35 min
NUMBER 10 29 = 2100 sec, the rate will have to be and the fluid's expulsion velocity 300 = 0.143 kg/sec 2100 v = 65,300 m/sec Therefore, by providing per kilogram of fuel T = 217.2 X 10 6 kgm or 512 X 10 3 cal one sees that the mixture H 2 + O would contain 133 times too little energy and the most powerful explosives 360 times too little. On the other hand, 1 kg of radium would contain 5.670 times too much] The power of the motor necessary for our 1000 kg vehicle would be 300 X 217.2 X 10 6 = 414,000 HP 2100 X 75 We could also see that the efficiency of the jet engine is in our particular case quite bad. Since to remove a mass of 1 kg from the earth to °o, we have to apply to it 6,371,103 kgm and we have spent 217.2 X 10 6 , so that the efficiency is p = 0.0293 Moreover, to give a gas an ejection speed of 65,300 m/sec in vacuum, we would have to reach the fantastic temperature of 2.525 X 10 6 degrees. In air, it would be even worse, since added to this temperature one would need a pressure of about the same magnitude. IV As an indication, we could assume the body moving to infinity, and also that we have kept the motor working even after the critical speed is reached, so that it eventually acquires and conserves a speed near to 10 km/sec. The times necessary to reach the closest planets as they attain their conjunction with the Earth are respectively: For Venus 47 days 20 hr For Mars 90 days 15 hr These figures are merely mentioned for curiosity and we must also notice that the amount of work to cover this distance would not be much larger than the minimum necessary to remove the body from the earth. In fact, once the vehicle has reached a sufficient distance, it would keep on going due to its inertia without being slowed down by the earth's attraction which has become quite weak. In other words, the difficulty would be to overcome the earth's attraction; but if some day this difficulty would be overcome, it would hardly be more difficult to reach a very distant planet than a close one. Subject, of course, to a cramped and hermetically closed vehicle being inhabitable for a sufficient amount of time and to another difficulty that we will consider later on.
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FIGURE 4.—Presentation by Dr. Con
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Astrodynamics is defined in terms o
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NUMBER 10 83 But it should be recog
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NUMBER 10 85 were experimenting in
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Vladimir Mandl: Founding Writer on
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NUMBER 10 89 PATENTNl OftAD REPUBLI
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10 Developments in Rocket Engineeri
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NUMBER 10 93 FIGURE 2.—The first
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NUMBER 10 FIGURE 4.—The ORM-9 eng
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NUMBER 10 97 FIGURE 9.—ORM-50 eng
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NUMBER 10 99 Section along AA Firin
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NUMBER 10 101 FIGURE 13.—The expe
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11 A Historical Review of Developme
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NUMBER 10 105 FIGURE 5.—Lithergol
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NUMBER 10 that the possibility of a
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NUMBER 10 109 the contrary; we then
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NUMBER 10 111 rocket combustion cha
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12 On the GALCIT Rocket Research Pr
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NUMBER 10 115 The undertaking we ha
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NUMBER 10 117 advise on the support
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NUMBER 10 methyl-alcohol rocket mot
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NUMBER 10 121 5. "Rocket Performanc
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NUMBER 10 123 FIGURE 5.—Overall v
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NUMBER 10 on the possibility of usi
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NUMBER 10 33. Letters (note 14). 34
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15 Ludvik OcenaSek: Czech Rocket Ex
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NUMBER 10 159 FIGURE 2.—Ludvik Oc
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NUMBER 10 161 FIGURE 5.—Ludvik Oc
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NUMBER 10 163 FICURE 6.—a, Launch
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NUMBER 10 165 quarry near Prague. E
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168 SMITHSONIAN ANNALS OF FLIGHT re
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17 First Rocket and Aircraft Flight
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NUMBER 10 179 The rocket project wa
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NUMBER 10 181 FIGURE 2.—Second st
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NUMBER 10 FIGURE 3.—DM-2 ramjet e
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18 On Some Work Done in Rocket Tech
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NUMBER 10 187 FICURE 3.—Launching
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NUMBER 10 189 on the smoked tape. A
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NUMBER 10 191 FIGURE 9.—Indicatin
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NUMBER 10 193 FIGURE 13.—Control
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NUMBER 10 195 2000 rpm by rotating
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NUMBER 10 197 Lubricant ^ 9a' " FIG
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NUMBER 10 199 of radio signals to t
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NUMBER 10 201 1. Register of experi
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A^ -/••••••.\ D+ VE •
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240 diesel fuel and lox began on th
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242 14 May 1940: Reviewed layout fo
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248 SMITHSONIAN ANNALS OF FLIGHT th
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250 SMITHSONIAN ANNALS OF FLIGHT tl
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NUMBER 10 253 FIGURE 6.—a, Model
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NUMBER 10 255 FIGURE 9.—Winged ro
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NUMBER 10 257 6. Small gyroscopic a
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262 SMITHSONIAN ANNALS OF FLIGHT N?
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264 B C FIGURE 7.—Drawing from Sw
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266 SMITHSONIAN ANNALS OF FLIGHT in
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24 Some New Data on Early Work of t
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NUMBER 10 271 jy.. FIGURE 3. /# £
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NUMBER 10 273 conclusions, which we
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NUMBER 10 275 thrust engines. A for
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25 Early Developments in Rocket and
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NUMBER 10 279 Time reference 5 sec
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NUMBER 10 281 During measurement of
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NUMBER 10 283 First Personal Involv
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NUMBER 10 285 on the Wasserkuppe, o
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27 Annapolis Rocket Motor Developme
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NUMBER 10 297 I remember being so f
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NUMBER S P. (P»i) P, (psi) Po (psi
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NUMBER 10 301 Figure 6 shows these
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304 Frank-Kamenetskiy, D.A., 193 Fr
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306 SMITHSONIAN ANNALS OF FLIGHT Ro
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TUT10N NOIifUIISNt NVINOSHlitNS S3f
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