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National Advisory Committee for Aeronautics, Research Memorandum - A Study of Several Parameters Controlling the Trajectories of a Supersonic Antiaircraft Missile Powered with Solid or Liquid Fuel Rockets
The trajectories for a supersonic antiaircraft missile vera calcu- latea a step-by-step integration method for a nuzmer of different con- ditions. The effects of changing drag Initial thrust ratio (ratio of initial thrust to initial grogg weight), and weight ratio (ratio of Ini- tiaI grogs weight to weight after all fuel has burned), which are the principal variables controlling the tragectory for a fixed launching .1e, were investigated. The results of the analy sis Indicated that: (1 Dho rate of change of range and altitude of the missile would beccme increasingly favorable with reduction of drag; (2) In general, there would be an op±åmum Initial thrust ratio giving range or altitude; above this bptfmnm value the range and altituda would decrease because of the large ænount of energy expended in overcoming arag at low altitudes; and (3) Increase of the weight ratio of the missile, within the limits In- vestigatea, would Inprove the ran.ge and 8.1tituae obtainable with fuel of a given specific impulse.
The of a eupergonlc self-propelled miBBiIe presents many problems in the fields of aerodynamics and thermod.ynamics upon which very little work hag been done. AIX)ng these problems that of calculating the perfornznce of Bueh a miBB11e and haw it will be affectea by changes in the aerod.ynam.ic pover characteristics, This problem hae muy rem- Ifications, but its f0im 1B that of detenl.ining the zero-lift trajectory of the miBB11e when launched from the ground under a given set of initial conditions. Since, for missile of this type the degignec
1B chiefly Interested in the rate of climb, maximum altitude obtainable, and range, the determination of the trajectory can serve ae a guide to the pergormance of the missile In theee respects. it iB recogxlzea that lift forces will alter the perfomance of the missile, especially the range at low altitudes, the complexity of any analysis which includes lift forces becomes so great that for the preliminary study presented in this paper these forces have been neglected. The zero-lift trajectory of a missile dependent upon the drag of the mlBBi1e, the launching angle, the weight and the type of fuel carried, and the initial acceleration. Tho weight of the fuel can be conveniently by the ratio of Initial gross weight to the weight after all the mel has burned (weight ratio) . The initial acceleration lg given by the ratio of thrust to initial grogs weight (Initial thrust ratio) where the thrust 1B aetemlned by the thermodynamic properties of the fuel and the rate at which the fuel burns.