Write a MATLAB program to generate Standard Atmosphere values for Troposphere and Stratosphere ( h = 0 km to h = 47 km) in steps 1 km and plot each of the quantities that listed below.

The output of your MATLAB program:

I. Standard Atmosphere Table should include calculated values: -

h - geopotential altitude in km -

hG - geometric altitude in km -

T - temperature in Kelvin -

- density in kg m3 -

p - pressure in N m2

II. Plots of Geopotential Altitude h (km) vs.:

- temperature T (K)

- density ( kg m3 )

- pressure p ( N m2 )

1. Gradient Layer The gradient layers exist from h = 0 km to h = 11km (troposphere) and from h = 25 km to h = 47 km (stratosphere).

Start at sea level ( h = 0 ) , where standard sea level values of temperature, density, and pressure, respectively, are TSL = 288.16 K , SL = 1.225 kg / m3 , pSL = 1.01325 105 N m2 , g0 = 9.80065 m /s2 , R = 287 J kgK .

Use the following equations, derived from the hydrostatic equation and the equation of state:

T = T1 + a(h h1)

(p/p1) =( T/T1) ^(-g/aR)

(/1) = (T/T1)^((- g/aR) 1 )

where a = dT/dh - the lapse rate for the gradient layer: a = 6.5 103 K m (troposphere) a = 3103 K m (stratosphere)

2. Isothermal Layer The isothermal (constant temperature) layer exists from h = 11 km to h = 25 km. Use the following equations, derived from the hydrostatic equation and the equation of state:

p/p1 = e^( g/RT)^(hh 1)

/1 = e^( g/RT)^(hh 1)

3. Geometric vs. Geopotential Altitude Geopotential altitude is a fictitious altitude, which is physically compatible with the assumption of a constant gravitational acceleration ( g = const = g0 ). Geometric altitude hG can be related to geopotential altitude h by:

hG = (hr E)/( r E h)

(where r E the radius of the Earth r E = 6371.0008 km