Standard Atmosphere Calculator (ISA 1976)

📋 Input Settings

System Units: SI Metric (m, K, Pa, kg/m³)

Altitude ($z$ or Flight Level)

Adjust Altitude Slider 0 m

Temperature Deviation ($\Delta T_{ISA}$)

Offsets the standard local temperature to evaluate non-standard conditions (Density Altitude, actual density, etc.).

🚀 Core Parameters

• Geopotential Height ($h$): 0.00 m

• Local standard Temp ($T_{std}$): 15.00 °C

• Pressure Altitude ($z_p$): 0.00 m

• Density Altitude ($z_d$): 0.00 m

📊 Calculated Air Properties

Actual Temperature ($T$) 288.15 K

Actual Pressure ($P$) 101,325 Pa

Air Density ($\rho$) 1.2250 kg/m³

Speed of Sound ($a$) 340.29 m/s

Property Name	Symbol	SI Metric Value	Imperial Value
Geometric Altitude	z	-	-
Geopotential Altitude	h	-	-
Temperature (Standard)	T_std	-	-
Temperature (Actual)	T	-	-
Atmospheric Pressure	P	-	-
Density of Air	ρ	-	-
Speed of Sound	a	-	-
Dynamic Viscosity	μ	-	-
Kinematic Viscosity	ν	-	-
Thermal Conductivity	k	-	-
Mean Free Path	λ	-	-
Local Gravity Acceleration	g	-	-
Pressure Altitude	z_p	-	-
Density Altitude	z_d	-	-
Pressure Ratio	δ	-
Temperature Ratio	θ	-
Density Ratio	σ	-

📘 Standard Atmosphere Mathematical Models

1. Geopotential Height & Gravity

The standard model integrates hydrostatic balance on a geopotential height $h$ to simplify the gravity variation $g(z)$ at geometric altitude $z$:

$$h = \frac{r_e \cdot z}{r_e + z}$$ $$g(z) = g_0 \cdot \left(\frac{r_e}{r_e + z}\right)^2$$

Where the nominal Earth radius is $r_e = 6,356,766\text{ m}$, and gravity at sea level is $g_0 = 9.80665\text{ m/s}^2$.

2. Thermal Profile & Pressure

Within any atmospheric layer $b$ characterized by a constant temperature lapse rate $L_b = \frac{dT_{std}}{dh}$:

If $L_b \neq 0$ (Linear lapse rate): $$T_{std} = T_b + L_b(h - h_b)$$ $$P = P_b \cdot \left[1 + \frac{L_b(h - h_b)}{T_b}\right]^{-\frac{g_0 M}{R^* L_b}}$$
If $L_b = 0$ (Isothermal layer): $$T_{std} = T_b$$ $$P = P_b \cdot \exp\left[-\frac{g_0 M (h - h_b)}{R^* T_b}\right]$$

Where $M = 0.0289644\text{ kg/mol}$ is the molecular weight of air, and $R^* = 8.31432\text{ J/(mol K)}$ is the universal gas constant.

3. Transport & Kinetic Properties

Standard viscosity is governed by Sutherland's law, and thermal conductivity utilizes an empirical formulation:

$$\mu = 1.458 \times 10^{-6} \cdot \frac{T^{1.5}}{T + 110.4}$$ $$k = \frac{2.64638 \times 10^{-3} \cdot T^{1.5}}{T + 245.4 \times 10^{-12 / T}}$$

The mean free path $\lambda$ (average distance traveled between molecular collisions) is computed based on effective collision diameter $d = 3.65\text{ Å}$:

$$\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P} \approx \frac{2.33228 \times 10^{-5} \cdot T}{P}$$

✈️ Standard Atmosphere Calculator (ISA 1976)