(1 M M。znt Stuhlinger!ll introduced a"characteristic velocity. 2nt whose meaning from the definition of a is that, if the powerplant mass above were to be accelerated by converting all of the electrical energy generated during t, it ould then reach the velocity vch Since other masses are also present v must clearly represent an upper limit to the achievable mission Av and is in any case a convenient yardstick for both Av and Figure 1 shows the shape of the curves of M+M versus c/with△V/asa M parameter. The existence of an optimum c in each case is apparent from the figure. This optimum c is seen to be near v, hence greater than Av. If -is taken to be a small quantity, expansion of the exponentials in(5)allows an approximate analytical expression for the optimum c (7) Figure 1 also shows that as anticipated the maximum Av for which a positive payload can be carried(with negligible M)is of the order of 0.8V. Even at this high AV, Equation (7)is seen to still hold fairly well. To the same order of approximation the mass breakdown for the optimum c is as shown in Figure 2. The effects of (constant)efficiency, powerplant specific mass and mission time are all lumped into the parameter vh. Equation (7)then shows that a high specific impulse In =c/gis indicated when the powerplant is light and/or the mission is allowed a long duration Figure 2 then shows that for a fixed av, these same attributes tend to give a high payload fraction and small (and comparable) structural and fuel fractions Of course the same breakdown trends can be realized by reducing Av for a fixed V This regime was called quite graphically the"trucking"regime by loh [ 2. At the opposite end(short mission, heavy powerplant) we have a low vh, hence low optimum specific impulse, and from Figure 2, small payload and large fuel fractions. This is then the sports car"regime References Ref.[1]:Stuhlinger,E.lon Propulsion For Space Flight. New York: Mc Graw-Hill Book Co., 1964. Ref. [2 W.H. Jet, Rocket, Nuclear, Ion and Electric Propulsion Theory and Design. New York: g,1968 16.522, Space Propulsion Prof. manuel martinez-Sanchez Page 2 of 1916.522, Space Propulsion Lecture 2 Prof. Manuel Martinez-Sanchez Page 2 of 19 ( ) 2 L - Vc - Vc so o o M M c =e - - 1-e M M 2t ∆ ∆ α η (5) Stuhlinger[1] introduced a “characteristic velocity” ch 2 t v = η α (6) whose meaning, from the definition of α is that, if the powerplant mass above were to be accelerated by converting all of the electrical energy generated during t, it would then reach the velocity vch . Since other masses are also present, vchmust clearly represent an upper limit to the achievable mission ∆ V and is in any case a convenient yardstick for both ∆ V and c. Figure 1 shows the shape of the curves of L so o M +M M versus ch c/v with ∆V vch as a parameter. The existence of an optimum c in each case is apparent from the figure. This optimum c is seen to be near vch hence greater than ∆V. If V c ∆ is taken to be a small quantity, expansion of the exponentials in (5) allows an approximate analytical expression for the optimum c: 2 OPT ch ch 1 1V c v - V- 2 24 v ∆ ≅ ∆ (7) Figure 1 also shows that, as anticipated, the maximum ∆V for which a positive payload can be carried (with negligible Mso ) is of the order of 0.8 vch . Even at this high∆ V, Equation (7) is seen to still hold fairly well. To the same order of approximation, the mass breakdown for the optimum c is as shown in Figure 2. The effects of (constant) efficiency, powerplant specific mass and mission time are all lumped into the parameter vch . Equation (7) then shows that a high specific impulse sp I = c gis indicated when the powerplant is light and/or the mission is allowed a long duration. Figure 2 then shows that, for a fixed ∆V, these same attributes tend to give a high payload fraction and small (and comparable) structural and fuel fractions. Of course the same breakdown trends can be realized by reducing ∆ V for a fixed vch . This regime was called quite graphically the “trucking” regime by Loh [2]. At the opposite end (short mission, heavy powerplant) we have a low vch , hence low optimum specific impulse, and, from Figure 2, small payload and large fuel fractions. This is then the “sports car” regime [2]. References: Ref. [1]: Stuhlinger, E. Ion Propulsion For Space Flight. New York: Mc Graw-Hill Book Co., 1964. Ref. [2]: Loh, W. H. Jet, Rocket, Nuclear, Ion and Electric Propulsion Theory and Design. New York: Springer-Verlag, 1968