Global Optimized Isothermal and Nonlinear Models of Earth’s Standard Atmosphere

Both, a global isothermal temperature model and a nonlinear quadratic temperature model of the ISA was developed and presented here. Constrained optimization techniques in conjunction with the least-square-root approximations were used to design best-fit isothermal models for ISA pressure and density changes up to 47 geopotential km for NLPAM, and 86 orthometric km for ISOAM respectively. The mass of the dry atmosphere and the relevant fractional-mass scale heights have been computed utilizing the very accurate eight-point Gauss-Legendre numerical quadrature for both ISOAM and NLPAM. Both, the ISOAM and the NLPAM represent viable alternatives to ISA in many practical applications and specifically for drag calculations at high altitudes for trans-atmospheric flight vehicles. A particular advantage of ISOAM and NLPAM is that only single expressions for each: temperature, pressure, and density is used compared to multiple different expressions in multi-layered ISA formulation. A parabolic NLPAM is an especially accurate replacement for ISA up to 47 geopotential km and physically approximates well ISA temperature lapse rates. Fractional mass scale-heights have been calculated for both ISAOM and NLPAM and compared to ISA values. The agreement is especially good between ISA and NLPAM, as was expected. The ISOAM can also be extended into lower heterosphere for approximate pressure and density calculations. The parabolic vertical nonlinear temperature distribution can be extended to higher-order polynomials describing also mesospheric temperature profiles