Why does temperature increase with altitude in the stratosphere?

Because the ozone layer in the stratosphere (about 15-35 km) absorbs solar ultraviolet radiation (UV-B and UV-C) and heats the air. In the troposphere, temperature decreases by about 6.5°C per kilometer, but in the stratosphere it increases with altitude. This makes the stratosphere a stable layer where convection is suppressed.

Why do passenger aircraft cruise around 10 km altitude?

At 10-12 km, lower pressure reduces aerodynamic drag and improves fuel economy, while the lower stratosphere is relatively stable. Lower ambient temperature also improves jet-engine thermal efficiency, especially the turbine inlet temperature margin. This altitude range is where those trade-offs are optimized.

What is the Kármán line?

The Kármán line is the internationally common convention for the boundary between the atmosphere and outer space, at 100 km altitude. At this altitude, aerodynamic flight would require roughly orbital velocity (about 7.9 km/s). The FAI uses it as the spaceflight definition, while some organizations such as the U.S. Air Force use 80 km, so definitions vary.

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Atmospheric Science

Atmosphere Layers Simulator

Q: What is the International Standard Atmosphere (ISA)?

It is the standard set by ICAO for temperature, pressure, and density as functions of altitude. It starts from sea-level pressure of 101325 Pa, temperature of 15°C (288.15 K), and a lapse rate of 6.5 K/km, with different formulas for each atmospheric layer. It is used worldwide for aircraft performance calculations, altimeter calibration, and meteorological reference data.

Compute pressure, temperature, density and speed of sound at any altitude using the International Standard Atmosphere (ISA) model. Compare troposphere, stratosphere, mesosphere and thermosphere on interactive charts.

Rising Probe Simulation

Altitude h (scrub)

Ascent rate

km/s (visual)

Preset altitudes

Troposphere (0-11 km)

Pressure

—

hPa

Live results

Altitude

— km

Current layer

—

Temperature

— °C

Density ρ

— kg/m³

Speed of sound a

— m/s

Surface ratio (pressure)

— %

Kinematic viscosity ν

— m²/s

Mean free path

— nm

Probe rising through the atmosphere

Temperature profile (ISA)

Pressure & density profile

Theory & Key Formulas

Troposphere (0-11 km, lapse rate $L=-6.5$ K/km):
$T = 288.15 - 6.5\,h$ [K], $\;p = 101325\left(\frac{T}{288.15}\right)^{-g/(RL)}$ [Pa]

Lower-stratosphere isothermal layer (11-20 km): $T = 216.65$ K, $\;p = p_{11}\,e^{-g(h-h_{11})/(RT)}$

Density and sound speed: $\rho = p/(RT)$, $\;a = \sqrt{\gamma RT}$. Here $R=287$ J/(kg·K), $g=9.80665$ m/s², $\gamma=1.4$.

🎓 Learn the Structure of the Atmosphere Through Conversation

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It gets colder when you climb a mountain. If higher altitude is closer to the Sun, why does it get colder instead of warmer?

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Good question. The distance from Earth to the Sun is about 150 million km, while even the highest mountains are only about 8.8 km tall. That height difference is negligible relative to the Sun. The atmosphere is warmed mainly because it absorbs infrared radiation emitted from the ground. At higher altitude, you are farther from that heated surface and the air is less dense, so less radiation is absorbed. That is why the lower troposphere is warmer.

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But you said temperature increases with altitude in the stratosphere. Is that because of the ozone layer? What is the mechanism?

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Yes. Ozone (O3) directly absorbs high-energy ultraviolet radiation (UV-B: 280-315 nm and UV-C: 100-280 nm) and converts it to heat. This absorption layer is concentrated around 15-35 km, so temperature rises there. Near the stratopause around 50 km, temperature recovers to roughly -3°C. Because the ozone layer acts as a heat source, the stratosphere becomes a warm cap that limits upward transport of tropospheric water vapor and clouds.

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Passenger aircraft often fly at 10-12 km, near the lower stratosphere. Why do they fly that high?

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Mainly for fuel efficiency. Lower air density reduces drag; at 10 km, density is about 34% of the surface value and pressure is about 26%. Drag scales strongly with density, so resistance falls greatly. Lift also decreases, so aircraft must fly faster, but the overall fuel economy is still better. The lower stratosphere also has less turbulence and more stable flight. Jet engines also benefit thermally from low ambient temperatures near -50°C.

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How is this atmosphere model used in CAE?

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It is essential in aerospace CFD. For aircraft aerodynamic analysis, ISA pressure, temperature, and density at the target altitude are used as CFD boundary conditions. It is also used for engine performance calculations, wing Reynolds-number estimates, and reentry capsule heating analysis where upper-atmosphere density matters. Because the speed of sound in air ($a=\sqrt{\gamma RT}$) changes with temperature, the model is especially important for transonic and supersonic simulations.

Frequently Asked Questions

What is the International Standard Atmosphere (ISA)?

It is a standard model of altitude, temperature, pressure, and density defined by ICAO (International Civil Aviation Organization). Reference values at sea level: pressure 101325 Pa, temperature 288.15 K (15°C), density 1.225 kg/m³. It is defined in multiple layers: the troposphere (0–11 km) where temperature decreases at 6.5 K/km, the lower stratosphere (11–20 km) is isothermal at 216.65 K, and the upper stratosphere (20–32 km) where temperature increases at 1 K/km, etc.

What is the atmospheric pressure at 8848 m (Mount Everest)?

According to the ISA model, it is about 314 hPa (about 31% of sea level pressure), and the temperature is about −42°C. The partial pressure of oxygen is also about 31% of sea level, making it extremely difficult to summit without supplemental oxygen. Hillary and Tenzing used oxygen cylinders when they first climbed in 1953. ISA is an average for a standard year, so actual values vary with season and latitude.

How does the speed of sound change with altitude?

The speed of sound is given by $a = \sqrt{\gamma RT}$ and depends only on temperature (γ=1.4, R=287 J/kgK), not directly on pressure or density. In the troposphere, as altitude increases, temperature decreases and the speed of sound also decreases. Sea level: 340 m/s → lower stratosphere (T=216.65 K): about 295 m/s. The Mach number of a high-speed aircraft is the ratio of its speed to this local speed of sound, so at the same flight speed, the Mach number is higher at higher altitudes.

What are the characteristics of the mesosphere and thermosphere?

The mesosphere (50–80 km) sees temperature drop again, reaching the lowest atmospheric temperature (about −90°C) near 80 km. It is also the layer where meteors burn up. The thermosphere (above 80 km) absorbs extreme ultraviolet (EUV) from the sun and can reach over 1000°C, but the air is so thin that the heat content is low. The ISS flies in the thermosphere (around 400 km altitude).

How to use the ISA model for aircraft CFD analysis?

In aircraft CFD, ISA values at the flight altitude (pressure p, temperature T, density ρ, dynamic viscosity μ) are set as far-field boundary conditions. Dynamic viscosity is calculated using Sutherland's formula: $\mu = \mu_0(T/T_0)^{3/2}(T_0+S)/(T+S)$. The boundary conditions for compressible flow, determined by Mach number M = V/a, also change with altitude. In OpenFOAM, this can be set with the freestream boundary condition; in Ansys Fluent, pressure correction for altitude can be done under 'Operating Conditions'.

What is Atmosphere Layers Simulator?

Atmosphere Layers Simulator is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.

By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.

Physical Model & Key Equations

The simulator is based on the governing equations behind Atmosphere Layers Simulator. Understanding these equations is key to interpreting the results correctly.

Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.

Real-World Applications

Engineering Design: The concepts behind Atmosphere Layers Simulator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.

Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.

CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.

Common Misconceptions and Points of Caution

Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.

Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.

Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.

How to Use

Altitude range is 0-80 km, and both the slider and numeric input use 0.5 km steps.
Layer boundaries follow getLayerInfo: troposphere 0-11 km, stratosphere 11-47 km, stratopause 47-51 km, and mesosphere 51-80 km.
Displayed units are hPa, °C, kg/m³ and m/s.

Example

At 5 km, T=255.65 K (-17.5°C) and p=54,020 Pa (540.2 hPa). At 47 km near the stratopause, T=270.65 K (-2.5°C) and p≈110.9 Pa (about 1.11 hPa), so the air is extremely thin.

Practical Notes

Troposphere (0–11 km): primary weather layer; use for aircraft performance, wind load analysis, and meteorological input to CFD models
Stratosphere (11–47 km): temperature inversion; critical for high-altitude aerospace design, satellite drag estimation, and upper-atmosphere acoustics
Mesosphere (47–85 km): coldest layer (min 186 K); used in meteor ablation studies and near-space vehicle trajectories
Thermosphere (>85 km): exponential density decay; required for satellite orbital decay calculations and ionospheric coupling analysis