2.1 Earth's Atmosphere and Standard Atmosphere Model

Earth's atmosphere is a complex system that plays a crucial role in aerospace engineering. Its composition, primarily nitrogen and oxygen, and layered structure from the troposphere to exosphere, affect aircraft and spacecraft operations in various ways.

The standard atmosphere model provides a mathematical representation of atmospheric properties at different altitudes. This model is essential for aircraft design, performance analysis, and flight planning, allowing engineers to calculate crucial factors like lift, drag, and engine performance in different atmospheric conditions.

Earth's Atmosphere

Composition of Earth's atmosphere

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• Nitrogen (N2) makes up the majority of the atmosphere at approximately 78%
• Oxygen (O2) is the second most abundant gas at approximately 21%, essential for life on Earth
• Argon (Ar) is an inert gas that comprises approximately 0.93% of the atmosphere
• Carbon dioxide (CO2) and other trace gases (methane, water vapor) collectively make up less than 1% of the atmosphere but play crucial roles in climate regulation and the greenhouse effect

Layers of Earth's atmosphere

• Troposphere extends from the surface to about 7-20 km, contains most of the atmosphere's water vapor (clouds, precipitation) and weather phenomena, temperature decreases with altitude at a rate of about 6.5℃/km (lapse rate)
• Stratosphere sits above the troposphere from about 20-50 km, contains the ozone layer which absorbs harmful ultraviolet radiation, temperature increases with altitude due to ozone absorption
• Mesosphere extends from about 50-85 km above the stratosphere, temperature decreases with altitude reaching the coldest point at the mesopause (about -90℃), meteors burn up in this layer
• Thermosphere extends from about 85 km to 500-1,000 km above the mesosphere, temperature increases with altitude due to absorption of solar radiation (up to 2,000℃), contains the ionosphere (region of ionized particles) which reflects radio waves enabling long-distance communication
• Exosphere is the uppermost layer extending from the top of the thermosphere to about 10,000 km, has very low density transitioning to interplanetary space, contains orbiting satellites

Standard Atmosphere Model

Standard atmosphere in aerospace engineering

• The standard atmosphere model provides a mathematical representation of the Earth's atmosphere as a reference for atmospheric properties (temperature, pressure, density) at various altitudes
• Allows for consistent and standardized calculations in aerospace engineering applications such as:
  1. Aircraft design and performance analysis - determining lift, drag, and thrust requirements and calculating engine performance at different altitudes
  2. Spacecraft and missile design - estimating atmospheric drag and heating during launch and reentry phases
  3. Aviation weather forecasting and flight planning - predicting atmospheric conditions for safe and efficient flight operations

Calculations with standard atmosphere model

• Temperature variation with altitude:
  • Troposphere: $T = T_0 - L_0 \times h$, where $T_0 = 288.15 K$ (15℃), $L_0 = 6.5 K/km$, and $h$ is altitude in km
  • Stratosphere: $T = 216.65 K$ (-56.5℃) for $11 \leq h \leq 20$ km
  • Upper stratosphere and mesosphere: $T = 216.65 + L_1 \times (h - 20)$, where $L_1 = 1 K/km$ for $20 < h \leq 32$ km, and $L_1 = 2.8 K/km$ for $32 < h \leq 47$ km
• Pressure variation with altitude calculated using the barometric formula: $p = p_0 \times (1 - \frac{L_0 \times h}{T_0})^{\frac{g_0 \times M}{R \times L_0}}$
  • $p_0 = 101,325 Pa$ (sea-level pressure), $g_0 = 9.80665 m/s²$ (gravitational acceleration), $M = 0.0289644 kg/mol$ (molar mass of dry air), $R = 8.31447 J/(mol·K)$ (universal gas constant)
• Density variation with altitude calculated using the ideal gas law: $\rho = \frac{p}{R_s \times T}$, where $R_s = 287.058 J/(kg·K)$ (specific gas constant for dry air)

Atmospheric effects on aircraft performance

• Density altitude is the altitude in the standard atmosphere corresponding to a particular air density, higher density altitude results in reduced aircraft performance:
  • Decreased engine power output due to lower air density and mass flow rate
  • Reduced lift and increased drag on wings and control surfaces
  • Longer takeoff and landing distances required
  • Reduced climb performance and service ceiling
• High temperatures lead to increased density altitude and reduced aircraft performance, while low temperatures have the opposite effect
• Lower atmospheric pressure results in reduced air density and aircraft lift, pressure changes with weather systems (high and low pressure areas) can affect aircraft performance and flight planning
• High humidity increases density altitude and reduces aircraft performance by displacing air molecules and reducing air density, also decreases engine power output due to reduced oxygen availability for combustion
• Wind effects:
  • Headwinds increase takeoff and landing distances, while tailwinds decrease them
  • Crosswinds can affect aircraft stability and control during takeoff and landing (drifting, tipping)
  • Wind shear (rapid changes in wind speed or direction) can cause sudden changes in airspeed and altitude, potentially leading to loss of control if not properly handled