The atmospheric conditions are found by knowing only the projectile's ight trajectory and its aerodynamic coef cients together with the initial atmospheric conditions on the ground. The test trajectories were generated as solutions of the modi ed point mass equationsof motion.The correct atmospheric conditionsfor the generated ight trajectory are obtained from data collected during a weather balloon ight. A nonlinear least squares method then was used to t the modi ed point mass equations to the test trajectory by varying the meteorological parameters. Density, temperature, and wind pro les agreed well.
Nomenclature= parameter to t the temperature gradient, K/km D = h a G V 1 h a V 2 , 1/s E = gun elevation, rad E = relative error in the tted air density G = gravity plus Coriolis acceleration, g C, m/s 2m/s 2 g = g , m/s 2 g = gravity acceleration, m/s 2 g 0 = g at sea level; U.S. Standard Atmosphere (STAT) value at 45 N latitude is 9 80665 m/s 2 H = geopotential altitude, m H A = value of H at the starting time of a tting interval, m H B = value of H at the bottom of a STAT altitude zone, m h aaxial moment of inertia, kgm 2 J = number of signi cant digits in the tted air density k 2 a = I x m 2 L = latitude at the launch point; for southern hemisphere rings, replace L by L, rad = reference length equal to diameter equal to caliber, m = molecular weight, kg/mol m = projectile mass, kg Q = constant in the STAT air density formula, g 0 K/km Presented as Paper 95-3437 at the R = effective radius of the Earth, 6,356,766 m = universal gas constant, J/(mol K) S = reference area, 2 4 m 2 T = temperature, K T = temperature gradient dT dH , K/km T A = temperature at the starting time of a tting interval, K T B = STAT temperature at altitude H B , K t = time, s t = nondimensionalizedtime, U 1b t t b U = X X projectile velocity with respect to the Earth, m/s U i = at-Earth system components of U, m/s V = V , m/s V = projectile velocity with respect to air, U W, m/s V s = speed of sound, m/s W = wind velocity with respect to the Earth, m/s W i = at Earth system components of W, m/s X = projectile position with respect to the Earth, m X i = at Earth components of X, right handed, m X 1 = downrange X 2 = height above sea level X 3= lateral x = nondimensional position variable, X 1 X 1b e = yaw of repose, rad = mass fraction of water vapor in the air = air density, kg/m 3 A = air density at the start of a tting interval, kg/m 3 B = STAT air density at H B , kg/m 3 = axial spin rate, rad/s = angular velocity of the Earth, rad/s = d dt