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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

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

$$H=\cfrac{r\cdot h}{r+h}$$
$H=\cfrac{r\cdot h}{r+h}$
Equations in LaTeX code
H=\cfrac{r\cdot h}{r+h}

Temperature gradient $ β $

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

Lower limit temperature

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

Lower limit geopotential altitude

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

Lower limit pressure

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

Temperature $ T $

$$T=T_b+β\cdot\left(H-H_b\right)$$
$T=T_b+β\cdot\left(H-H_b\right)$
Equations in LaTeX code
T=T_b+β\cdot\left(H-H_b\right)
$$T\le 2273.15$$
$T\le 2273.15$
Equations in LaTeX code
T\le 2273.15

Atmospheric pressure air

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

$$ρ_{air}=\cfrac{p_{air}}{R\cdot T}$$
$ρ_{air}=\cfrac{p_{air}}{R\cdot T}$
Equations in LaTeX code
ρ_{air}=\cfrac{p_{air}}{R\cdot T}

Specific weight air

$$γ_{air}=ρ_{air}\cdot g$$
$γ_{air}=ρ_{air}\cdot g$
Equations in LaTeX code
γ_{air}=ρ_{air}\cdot g

Pressure scale height

$$H_p=\cfrac{R\cdot T}{g}$$
$H_p=\cfrac{R\cdot T}{g}$
Equations in LaTeX code
H_p=\cfrac{R\cdot T}{g}

Air number density

$$n=\cfrac{N_A\cdot p_{air}}{R^*\cdot T}$$
$n=\cfrac{N_A\cdot p_{air}}{R^*\cdot T}$
Equations in LaTeX code
n=\cfrac{N_A\cdot p_{air}}{R^*\cdot T}

Mean air-particle speed

$$v̄=\sqrt{8\cdot π\cdot R\cdot T} $$
$v̄=\sqrt{8\cdot π\cdot R\cdot T} $
Equations in LaTeX code
v̄=\sqrt{8\cdot π\cdot R\cdot T}

Mean free path of air particles

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

Air-particle collision frequency

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

Speed of Sound

$$a=\sqrt{κ\cdot R\cdot T}$$
$a=\sqrt{κ\cdot R\cdot T}$
Equations in LaTeX code
a=\sqrt{κ\cdot R\cdot T}

Dynamic viscosity

$$μ=β_s\cdot\cfrac{T^{3/2}}{T+S}$$
$μ=β_s\cdot\cfrac{T^{3/2}}{T+S}$
Equations in LaTeX code
μ=β_s\cdot\cfrac{T^{3/2}}{T+S}

Kinematic viscosity

$$ν=\cfrac{μ}{ρ_{air}}$$
$ν=\cfrac{μ}{ρ_{air}}$
Equations in LaTeX code
ν=\cfrac{μ}{ρ_{air}}

Thermal conductivity

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