1976 U.S. Standard Atmosphere Model Implementation

A Python implementation of the 1976 U.S. Standard Atmosphere model for calculating atmospheric properties (temperature, pressure, density) and drag forces at different altitudes.

Overview

This implementation:

• Calculates temperature as a function of geopotential altitude using a fitted 4th-degree polynomial
• Computes atmospheric pressure via numerical integration
• Determines air density using the ideal gas law
• Calculates drag forces on objects at various altitudes
• Valid for altitudes between -1,524 m and 76,200 m

Features

• Temperature calculation using fitted polynomial model
• Pressure calculation using numerical integration
• Density computation from ideal gas law
• Drag force calculations
• Supports Earth-Centered Earth-Fixed (ECEF) coordinates

Installation

1. Clone this repository:

git clone [repository-url]

2. Required dependencies:

pip install numpy scipy matplotlib

Usage

Basic Usage

from main import Atmosphere

# Create atmosphere model instance
atm_model = Atmosphere()

# Calculate properties at a given altitude (in meters)
h = 10000
temperature = atm_model.T(h)
pressure = atm_model.P(h)
density = atm_model.ρ(h)

# Calculate drag force
drag_force = atm_model.drag_force(
    Cd=1,           # drag coefficient
    A=100,          # cross-sectional area (m²)
    vh=20,          # vertical velocity (m/s)
    vx=100,         # x velocity (m/s)
    vy=3000,        # y velocity (m/s)
    h=10000         # altitude (m)
)

Model Details

Atmosphere Class

The main class implementing the atmospheric model.

Parameters

• h0 (float): Geopotential altitude at sea level (-1,524 m default)
• P0 (float): Pressure at sea level (101,325 Pa default)
• R (float): Specific gas constant for dry air (287.052874 J/(kg⋅K) default)

Methods

• T(h): Calculate temperature at given altitude
• P(h): Calculate pressure at given altitude
• ρ(h): Calculate density at given altitude
• drag_force(Cd, A, vh, vx, vy, h): Calculate drag force

Physical Model

The implementation is based on three key equations:

1. Vertical pressure variation:

dP/dh = -ρg

2. Ideal gas law:

P = ρRT

3. Drag force:

Fd = (1/2)ρv²CdA

Where:

• P is pressure
• ρ is density
• g is gravitational acceleration (-9.81 m/s²)
• R is the specific gas constant for dry air
• T is temperature
• v is velocity
• Cd is drag coefficient
• A is cross-sectional area

Limitations

• Valid only for altitudes between -1,524 m and 76,200 m
• Uses constant gravitational acceleration (g = -9.81 m/s²)
• Temperature model uses polynomial fit which may not have physical meaning
• Only considers dry air

Contributing

Feel free to open issues or submit pull requests for:

• Bug fixes
• Documentation improvements
• Model enhancements
• Additional features

License

MIT License

Copyright (c) 2024 Kamyar Modjtahedzadeh

This code was developed to implement the 1976 U.S. Standard Atmosphere model.

References

1. U.S. Standard Atmosphere, 1976 (NOAA/NASA/USAF)
2. The Engineering ToolBox - Standard Atmosphere properties
3. Public Domain Aeronautical Software - Geopotential & Geometric Altitude