405 lines
12 KiB
Mathematica
405 lines
12 KiB
Mathematica
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function [rho,a,temp,press,kvisc,ZorH]=stdatmo(H_in,Toffset,Units,GeomFlag)
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% STDATMO Find gas properties in earth's atmosphere.
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% [rho,a,T,P,nu,ZorH]=STDATMO(H,dT,Units,GeomFlag)
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%
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% STDATMO by itself gives the atmospheric properties at sea level on a
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% standard day.
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%
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% STDATMO(H) returns the properties of the 1976 Standard Atmosphere at
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% geopotential altitude H (meters), where H is a scalar, vector, matrix,
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% or ND array.
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%
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% STDATMO(H,dT) returns properties when the temperature is dT degrees
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% offset from standand conditions. H and dT must be the same size or else
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% one must be a scalar.
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%
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% STDATMO(H,dT,Units) specifies units for the inputs outputs. Options are
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% SI (default) or US (a.k.a. Imperial, English). For SI, set Units to []
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% or 'SI'. For US, set Units to 'US'. Input and output units may be
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% different by passing a cell array of the form {Units_in Units_out},
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% e.g. {'US' 'SI'}. Keep in mind that dT is an offset, so when converting
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% between Celsius and Fahrenheit, use only the scaling factor (dC/dF =
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% dK/dR = 5/9). Units are as follows:
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% Input: SI (default) US
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% H: Altitude m ft
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% dT: Temp. offset <EFBFBD>C/<EFBFBD>K <EFBFBD>F/<EFBFBD>R
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% Output:
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% rho: Density kg/m^3 slug/ft^3
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% a: Speed of sound m/s ft/s
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% T: Temperature <EFBFBD>K <EFBFBD>R
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% P: Pressure Pa lbf/ft^2
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% nu: Kinem. viscosity m^2/s ft^2/s
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% ZorH: Height or altitude m ft
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%
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% STDATMO(H,dT,u), where u is a structure created by the UNITS function,
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% accepts variables of the DimensionedVariable class as inputs. Outputs
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% are of the DimensionedVariable class. If a DimensionedVariable is not
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% provided for an input, STDATMO assumes SI input.
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%
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% STDATMO(H,dT,Units,GeomFlag) with logical input GeomFlag returns
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% properties at geometric altitude input H instead of the normal
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% geopotential altitude.
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%
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% [rho,a,T,P,nu]=STDATMO(H,dT,...) returns atmospheric properties the
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% same size as H and/or dT (P does not vary with temperature offset and
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% is always the size of H)
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%
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% [rho,a,T,P,nu,ZorH]=STDATMO(H,...) returns either geometric height, Z,
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% (GeomFlag not set) or geopotential height, H, (GeomFlag set).
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%
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% Example 1: Find atmospheric properties at every 100 m of geometric
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% height for an off-standard atmosphere with temperature offset varying
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% +/- 25<EFBFBD>C sinusoidally with a period of 4 km.
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% Z = 0:100:86000;
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% [rho,a,T,P,nu,H]=stdatmo(Z,25*sin(pi*Z/2000),'',true);
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% semilogx(rho/stdatmo,H/1000)
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% title('Density variation with sinusoidal off-standard atmosphere')
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% xlabel('\sigma'); ylabel('Altitude (km)')
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%
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% Example 2: Create tables of atmospheric properties up to 30000 ft for a
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% cold (-15<EFBFBD>C), standard, and hot (+15<EFBFBD>C) day with columns
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% [h(ft) Z(ft) rho(slug/ft3) sigma a(ft/s) T(R) P(psf) <EFBFBD>(slug/ft-s) nu(ft2/s)]
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% using 3-dimensional array inputs.
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% [~,h,dT]=meshgrid(0,-5000:1000:30000,-15:15:15);
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% [rho,a,T,P,nu,Z]=stdatmo(h,dT*9/5,'US',0);
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% Table = [h Z rho rho/stdatmo(0,0,'US') T P nu.*rho nu];
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% format short e
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% ColdTable = Table(:,:,1)
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% StandardTable = Table(:,:,2)
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% HotTable = Table(:,:,3)
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%
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% Example 3: Use the unit consistency enforced by the DimensionedVariable
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% class to find the SI dynamic pressure, Mach number, Reynolds number, and
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% stagnation temperature of an aircraft flying at flight level FL500
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% (50000 ft) with speed 500 knots and characteristic length of 80 inches.
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% u = units;
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% V = 500*u.kts; c = 80*u.in;
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% [rho,a,T,P,nu]=stdatmo(50*u.kft,[],u);
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% Dyn_Press = 1/2*rho*V^2;
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% M = V/a;
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% Re = V*c/nu;
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% T0 = T*(1+(1.4-1)/2*M^2);
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%
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% This atmospheric model is not recommended for use at altitudes above
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% 86 km geometric height (84852 m/278386 ft geopotential) and returns NaN
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% for altitudes above 90 km geopotential.
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%
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% See also DENSITYALT, ATMOSISA, ATMOSNONSTD, DENSITYALT,
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% UNITS, DIMENSIONEDVARIABLE.
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% http://www.mathworks.com/matlabcentral/fileexchange/39325
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% http://www.mathworks.com/matlabcentral/fileexchange/38977
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%
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% [rho,a,T,P,nu,ZorH]=STDATMO(H,dT,Units,GeomFlag)
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% About:
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%{
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Author: Sky Sartorius
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www.mathworks.com/matlabcentral/fileexchange/authors/101715
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References: ESDU 77022
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www.pdas.com/atmos.html
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%}
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if nargin >= 3 && isstruct(Units)
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U = true;
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u = Units;
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if isa(H_in,'DimensionedVariable')
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H_in = H_in/u.m;
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end
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if isa(Toffset,'DimensionedVariable')
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Toffset = Toffset/u.K;
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end
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Units = 'si';
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else
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U = false;
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end
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if nargin == 0
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H_in = 0;
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end
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if nargin < 2 || isempty(Toffset)
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Toffset = 0;
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end
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if nargin <= 2 && all(H_in(:) <= 11000) %quick troposphere-only code
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TonTi=1-2.255769564462953e-005*H_in;
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press=101325*TonTi.^(5.255879812716677);
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temp = TonTi*288.15 + Toffset;
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rho = press./temp/287.05287;
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if nargout > 1
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a = sqrt(401.874018 * temp);
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if nargout >= 5
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kvisc = (1.458e-6 * temp.^1.5 ./ (temp + 110.4)) ./ rho;
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if nargout == 6 % Assume Geop in, find Z
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ZorH = 6356766*H_in./(6356766-H_in);
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end
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end
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end
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return
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end
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% index Lapse rate Base Temp Base Geopo Alt Base Pressure
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% i Ki (<EFBFBD>C/m) Ti (<EFBFBD>K) Hi (m) P (Pa)
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D =[1 -.0065 288.15 0 101325
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2 0 216.65 11000 22632.0400950078
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3 .001 216.65 20000 5474.87742428105
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4 .0028 228.65 32000 868.015776620216
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5 0 270.65 47000 110.90577336731
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6 -.0028 270.65 51000 66.9385281211797
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7 -.002 214.65 71000 3.9563921603966
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8 0 186.94590831019 84852.0458449057 0.373377173762337 ];
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% Constants
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R=287.05287; %N-m/kg-K; value from ESDU 77022
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% R=287.0531; %N-m/kg-K; value used by MATLAB aerospace toolbox ATMOSISA
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gamma=1.4;
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g0=9.80665; %m/sec^2
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RE=6356766; %Radius of the Earth, m
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Bs = 1.458e-6; %N-s/m2 K1/2
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S = 110.4; %K
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K=D(:,2); %<EFBFBD>K/m
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T=D(:,3); %<EFBFBD>K
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H=D(:,4); %m
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P=D(:,5); %Pa
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temp=zeros(size(H_in));
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press=temp;
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hmax = 90000;
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if nargin < 3 || isempty(Units)
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Uin = false;
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Uout = Uin;
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elseif isnumeric(Units) || islogical(Units)
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Uin = Units;
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Uout = Uin;
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else
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if ischar(Units) %input and output units the same
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Unitsin = Units; Unitsout = Unitsin;
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elseif iscell(Units) && length(Units) == 2
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Unitsin = Units{1}; Unitsout = Units{2};
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elseif iscell(Units) && length(Units) == 1
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Unitsin = Units{1}; Unitsout = Unitsin;
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else
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error('Incorrect Units definition. Units must be ''SI'', ''US'', or 2-element cell array')
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end
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if strcmpi(Unitsin,'si')
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Uin = false;
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elseif strcmpi(Unitsin,'us')
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Uin = true;
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else error('Units must be ''SI'' or ''US''')
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end
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if strcmpi(Unitsout,'si')
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Uout = false;
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elseif strcmpi(Unitsout,'us')
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Uout = true;
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else error('Units must be ''SI'' or ''US''')
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end
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end
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% Convert from imperial units, if necessary.
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if Uin
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H_in = H_in * 0.3048;
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Toffset = Toffset * 5/9;
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end
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% Convert from geometric altitude to geopotental altitude, if necessary.
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if nargin < 4
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GeomFlag = false;
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end
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if GeomFlag
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Hgeop=(RE*H_in)./(RE+H_in);
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else
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Hgeop=H_in;
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end
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n1=(Hgeop<=H(2));
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n2=(Hgeop<=H(3) & Hgeop>H(2));
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n3=(Hgeop<=H(4) & Hgeop>H(3));
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n4=(Hgeop<=H(5) & Hgeop>H(4));
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n5=(Hgeop<=H(6) & Hgeop>H(5));
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n6=(Hgeop<=H(7) & Hgeop>H(6));
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n7=(Hgeop<=H(8) & Hgeop>H(7));
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n8=(Hgeop<=hmax & Hgeop>H(8));
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n9=(Hgeop>hmax);
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% Troposphere
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if any(n1(:))
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i=1;
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TonTi=1+K(i)*(Hgeop(n1)-H(i))/T(i);
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temp(n1)=TonTi*T(i);
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PonPi=TonTi.^(-g0/(K(i)*R));
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press(n1)=P(i)*PonPi;
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end
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% Tropopause
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if any(n2(:))
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i=2;
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temp(n2)=T(i);
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PonPi=exp(-g0*(Hgeop(n2)-H(i))/(T(i)*R));
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press(n2)=P(i)*PonPi;
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end
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% Stratosphere 1
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if any(n3(:))
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i=3;
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TonTi=1+K(i)*(Hgeop(n3)-H(i))/T(i);
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temp(n3)=TonTi*T(i);
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PonPi=TonTi.^(-g0/(K(i)*R));
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press(n3)=P(i)*PonPi;
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end
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% Stratosphere 2
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if any(n4(:))
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i=4;
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TonTi=1+K(i)*(Hgeop(n4)-H(i))/T(i);
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temp(n4)=TonTi*T(i);
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PonPi=TonTi.^(-g0/(K(i)*R));
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press(n4)=P(i)*PonPi;
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end
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% Stratopause
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if any(n5(:))
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i=5;
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temp(n5)=T(i);
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PonPi=exp(-g0*(Hgeop(n5)-H(i))/(T(i)*R));
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press(n5)=P(i)*PonPi;
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end
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% Mesosphere 1
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if any(n6(:))
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i=6;
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TonTi=1+K(i)*(Hgeop(n6)-H(i))/T(i);
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temp(n6)=TonTi*T(i);
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PonPi=TonTi.^(-g0/(K(i)*R));
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press(n6)=P(i)*PonPi;
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end
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% Mesosphere 2
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if any(n7(:))
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i=7;
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TonTi=1+K(i)*(Hgeop(n7)-H(i))/T(i);
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temp(n7)=TonTi*T(i);
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PonPi=TonTi.^(-g0/(K(i)*R));
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press(n7)=P(i)*PonPi;
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end
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% Mesopause
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if any(n8(:))
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i=8;
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temp(n8)=T(i);
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PonPi=exp(-g0*(Hgeop(n8)-H(i))/(T(i)*R));
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press(n8)=P(i)*PonPi;
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end
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if any(n9(:))
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warning('One or more altitudes above upper limit.')
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temp(n9)=NaN;
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press(n9)=NaN;
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end
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temp = temp + Toffset;
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rho = press./temp/R;
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if nargout >= 2
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a = sqrt(gamma * R * temp);
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if nargout >= 5
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kvisc = (Bs * temp.^1.5 ./ (temp + S)) ./ rho; %m2/s
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if nargout == 6
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if GeomFlag % Geometric in, ZorH is geopotential altitude (H)
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ZorH = Hgeop;
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else % Geop in, find Z
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ZorH = RE*Hgeop./(RE-Hgeop);
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end
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end
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end
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end
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|
|||
|
|
if Uout %convert to imperial units if output in imperial units
|
|||
|
|
rho = rho / 515.3788;
|
|||
|
|
if nargout >= 2
|
|||
|
|
a = a / 0.3048;
|
|||
|
|
temp = temp * 1.8;
|
|||
|
|
press = press / 47.88026;
|
|||
|
|
if nargout >= 5
|
|||
|
|
kvisc = kvisc / 0.09290304;
|
|||
|
|
if nargout == 6
|
|||
|
|
ZorH = ZorH / 0.3048;
|
|||
|
|
end
|
|||
|
|
end
|
|||
|
|
end
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
if U
|
|||
|
|
rho = rho*u.kg/(u.m^3);
|
|||
|
|
if nargout >= 2
|
|||
|
|
a = a*u.m/u.s;
|
|||
|
|
temp = temp*u.K;
|
|||
|
|
press = press*u.Pa;
|
|||
|
|
if nargout >= 5
|
|||
|
|
kvisc = kvisc*u.m^2/u.s;
|
|||
|
|
if nargout == 6
|
|||
|
|
ZorH = ZorH*u.m;
|
|||
|
|
end
|
|||
|
|
end
|
|||
|
|
end
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
% Credit for elements of coding scheme:
|
|||
|
|
% cobweb.ecn.purdue.edu/~andrisan/Courses/AAE490A_S2001/Exp1/
|
|||
|
|
|
|||
|
|
% Revision history:
|
|||
|
|
%{
|
|||
|
|
V1.0 5 July 2010
|
|||
|
|
V1.1 8 July 2010
|
|||
|
|
Update to references and improved input handling
|
|||
|
|
V2.0 12 July 2010
|
|||
|
|
Changed input ImperialFlag to Units. Units must now be a string or cell
|
|||
|
|
array {Units_in Units_out}. Version 1 syntax works as before.
|
|||
|
|
Two examples added to help
|
|||
|
|
V2.1 15 July 2010
|
|||
|
|
Changed help formatting
|
|||
|
|
Sped up code - no longer caclulates a or nu if outputs not specified.
|
|||
|
|
Also used profiler to speed test against ATMOSISA, which is
|
|||
|
|
consistently about 5 times slower than STDATMO
|
|||
|
|
17 July 2010
|
|||
|
|
Cleaned up Example 1 setup using meshgrid
|
|||
|
|
26 July 2010
|
|||
|
|
Switched to logical indexing, which sped up running Example 1
|
|||
|
|
significantly(running [rho,a,T,P,nu,h]=stdatmo(Z,dT,'US',1) 1000 times:
|
|||
|
|
~.67s before, ~.51s after)
|
|||
|
|
V3.0 7 August 2010
|
|||
|
|
Consolodated some lines for succintness Changed Hgeop output to be
|
|||
|
|
either geopotential altitude or geometric altitude, depending on which
|
|||
|
|
was input. Updated help and examples accordingly.
|
|||
|
|
V3.1 27 August 2010
|
|||
|
|
Added a very quick, troposhere-only section
|
|||
|
|
V3.2 23 December 2010
|
|||
|
|
Minor changes, tested on R2010a, and sinusoidal example added
|
|||
|
|
V4.0 6 July 2011
|
|||
|
|
Imperial temp offset now <EFBFBD>F/<EFBFBD>R instead of <EFBFBD>C/<EFBFBD>K
|
|||
|
|
V4.1 12 Sep 2012
|
|||
|
|
Added ZorH output support for quick troposphere calculation
|
|||
|
|
uploaded
|
|||
|
|
V4.2
|
|||
|
|
tiny changes to help and input handling
|
|||
|
|
nov 2012: some :s added to make use of any() better
|
|||
|
|
added see alsos
|
|||
|
|
uploaded
|
|||
|
|
V5.0
|
|||
|
|
STDATMODIM wrapper created that takes DimensionedVariable input
|
|||
|
|
uploaded 5 Dec 2012
|
|||
|
|
V6.0
|
|||
|
|
STDATMODIM functionality integrated into STDATMO; example three changed
|
|||
|
|
for illustration.
|
|||
|
|
%}
|