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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.