Standard Atmosphere from 0 to 80Km

Values for calculation

$h$ $\mathrm{m}$
$φ$ $\mathrm{°}$
$r$ $\mathrm{m}$
$R$ $\mathrm{J\cdot K^{-1}\cdot kg^{-1}}$
$N_A$ $\mathrm{kmol^{-1}}$
$R^*$ $\mathrm{J\cdot K^{-1}\cdot kmol^{-1}}$
$σ$ $\mathrm{m}$
$M$ $\mathrm{kg\cdot kmol^{-1}}$
$κ$
$S$ $\mathrm{K}$
$β_s$ $\mathrm{kg\cdot m^{-1}\cdot s^{-1}\cdot K^{-1/2}}$

Calculation

Gravitational acceleration

$$g=\left(1+0.0053024\cdot (\sin{φ})^2-0.0000058\cdot (\sin{\left(2\cdot φ\right)})^2\right)\cdot 9.780318-0.000003085\cdot h$$

Geopotential altitude

$$H=\cfrac{r\cdot h}{r+h}$$

Temperature gradient $β$

$\text{if }\ H\geq 71000$
$$β=-2E-3$$
$\text{else if }\ H\geq 51000$
$$β=-2.8E-3$$
$\text{else if }\ H\geq 47000$
$$β=0$$
$\text{else if }\ H\geq 32000$
$$β=2.8E-3$$
$\text{else if }\ H\geq 20000$
$$β=1E-3$$
$\text{else if }\ H\geq 11000$
$$β=0$$
$\text{else}$
$$β=-6.5E-3$$

Lower limit temperature

$\text{if }\ H\geq 80000$
$$T_b=196.65$$
$\text{else if }\ H\geq 71000$
$$T_b=214.65$$
$\text{else if }\ H\geq 51000$
$$T_b=270.65$$
$\text{else if }\ H\geq 47000$
$$T_b=270.65$$
$\text{else if }\ H\geq 32000$
$$T_b=228.65$$
$\text{else if }\ H\geq 20000$
$$T_b=216.65$$
$\text{else if }\ H\geq 11000$
$$T_b=216.65$$
$\text{else}$
$$T_b=288.15$$

Lower limit geopotential altitude

$\text{if }\ H\geq 80000$
$$H_b=80000$$
$\text{else if }\ H\geq 71000$
$$H_b=71000$$
$\text{else if }\ H\geq 51000$
$$H_b=51000$$
$\text{else if }\ H\geq 47000$
$$H_b=47000$$
$\text{else if }\ H\geq 32000$
$$H_b=32000$$
$\text{else if }\ H\geq 20000$
$$H_b=20000$$
$\text{else if }\ H\geq 11000$
$$H_b=11000$$
$\text{else}$
$$H_b=0$$

Lower limit pressure

$\text{if }\ H\geq 71000$
$$p_b=3.9564$$
$\text{else if }\ H\geq 51000$
$$p_b=66.939$$
$\text{else if }\ H\geq 47000$
$$p_b=110.91$$
$\text{else if }\ H\geq 32000$
$$p_b=868.02$$
$\text{else if }\ H\geq 20000$
$$p_b=5474.9$$
$\text{else if }\ H\geq 11000$
$$p_b=22632$$
$\text{else}$
$$p_b=101325$$

Temperature $T$

$$T=T_b+β\cdot\left(H-H_b\right)$$

$$T\le 2273.15$$

Atmospheric pressure air

$\text{if }\ β=0$
$$p_{air}=p_b\cdot\exp\left[-\cfrac{g}{R\cdot T}\cdot\left(H-H_b\right)\right]$$
$\text{else}$
$$p_{air}=p_b\cdot\left[1+\cfrac{β}{T_b}\cdot\left(H-H_b\right)\right]^{-g/\left(β\cdot R\right)}$$

Density air

$$ρ_{air}=\cfrac{p_{air}}{R\cdot T}$$

Specific weight air

$$γ_{air}=ρ_{air}\cdot g$$

Pressure scale height

$$H_p=\cfrac{R\cdot T}{g}$$

Air number density

$$n=\cfrac{N_A\cdot p_{air}}{R^*\cdot T}$$

Mean air-particle speed

$$v̄=\sqrt{8\cdot π\cdot R\cdot T}$$

Mean free path of air particles

$$l=\cfrac{R^*}{\sqrt{2}\cdot π\cdot N_A\cdot σ^2}\cdot\cfrac{T}{p_{air}}$$

Air-particle collision frequency

$$ω=4\cdot σ^2\cdot N_A \cdot\sqrt{\cfrac{π}{R^*\cdot M}}\cdot\cfrac{p_{air}}{\sqrt{T}}$$

Speed of Sound

$$a=\sqrt{κ\cdot R\cdot T}$$

Dynamic viscosity

$$μ=β_s\cdot\cfrac{T^{3/2}}{T+S}$$

Kinematic viscosity

$$ν=\cfrac{μ}{ρ_{air}}$$

Thermal conductivity

$$λ=2.648E-3\cdot\cfrac{T^{3/2}}{T+245.4\cdot10^{-12/T}}$$