The concept of altitude is fundamental to understanding physical location, representing an object’s vertical distance above a fixed point. Science and engineering utilize several distinct definitions depending on the application. Geometric altitude, or \(h\), is the most straightforward and physically real of these measurements, defining the true physical height above a specified zero-level reference surface. This distance is the basis for all other derived altitude calculations used in fields ranging from global navigation to atmospheric science.
Defining Geometric Altitude
Geometric altitude is the actual, physical distance measured along a straight line, known as the normal, from a point in space down to a defined reference surface. This measurement represents the true physical height of an object above the Earth’s surface or a mathematical model of it. Unlike other altitude types, geometric altitude is not influenced by fluctuating atmospheric conditions like air pressure or temperature.
Modern systems determine geometric altitude using satellite-based technology, such as the Global Positioning System (GPS) or other Global Navigation Satellite Systems (GNSS). These systems triangulate a position in three dimensions, providing a direct measurement of the vertical distance to the Earth’s mathematical model. This distance serves as the raw data for advanced mapping and positioning applications.
Geometric altitude does not inherently account for the variation of gravity across the Earth. It is a purely spatial measurement. When this measurement is used in complex atmospheric or orbital calculations, the changing force of gravity must be addressed through conversion to other altitude types.
The Importance of the Reference Surface
Geometric altitude requires a precisely defined reference point, or datum, from which the vertical distance is measured. The selection of this reference surface is important, as different datums can yield varying altitude values for the exact same point in space. Two primary surfaces establish a zero-level for geometric measurements: the Geodetic Ellipsoid and the Mean Sea Level (MSL), which relates to the geoid.
The Geodetic Ellipsoid is a smooth, mathematically defined, oblate spheroid that closely approximates the Earth’s true shape. Systems like GPS use a specific ellipsoid, such as WGS-84, as their default zero-altitude reference because it provides a standardized, globally consistent, and easily computable surface. Measuring altitude relative to this smooth model is called ellipsoidal height.
The other reference is the geoid, which is the equipotential surface corresponding to the global Mean Sea Level (MSL), extended continuously through the continents. The geoid is irregular because it is influenced by local variations in the Earth’s gravity field, unlike the smooth ellipsoid. Altitude measured relative to the geoid, often called orthometric height, is used for terrestrial height measurements, like elevations on topographical maps. The difference between the smooth ellipsoid and the irregular geoid surface is known as the geoid separation.
Comparing Altitude Measurements
Geometric altitude is often confused with two other widely used altitude types: geopotential altitude and pressure altitude, each serving a distinct purpose in science and aviation.
Geopotential Altitude
Geopotential altitude, or \(H\), is a mathematical adjustment of the geometric height that meteorologists and atmospheric scientists use to simplify calculations. This adjustment corrects the geometric height to account for the fact that the acceleration due to gravity decreases as one moves away from the Earth’s center.
The geopotential calculation assumes a constant standard value for gravity throughout the vertical column, which simplifies the hydrostatic equation used in atmospheric modeling. This adjusted altitude is useful for analyzing atmospheric data, as a constant difference in geopotential height always represents the same amount of potential energy, regardless of latitude.
Pressure Altitude
Pressure altitude, denoted as \(Z_p\), is the altitude indicated by an aircraft’s altimeter when calibrated to the standard atmospheric pressure of 1013.25 hectopascals (hPa). This measurement is purely a function of the local air pressure, assuming the conditions of the International Standard Atmosphere (ISA) model. Because it is derived from pressure rather than physical distance, pressure altitude is susceptible to variations caused by real-world weather systems, which can cause it to deviate from geometric altitude by hundreds of feet.
The primary application for pressure altitude is maintaining vertical separation between aircraft in flight, where it is used to define “Flight Levels” above a specific transition altitude. For example, a flight level of 330 represents a pressure altitude of 33,000 feet. Geometric altitude provides the true physical distance, geopotential altitude simplifies atmospheric physics, and pressure altitude ensures standardized air traffic control procedures.