## Definitions, units and conversions

### International Standard Atmosphere (ISA)

The ISA to be used for FAI matters is given in ICAO Document 7488 tables 3 and 4. It assumes a temperature and pressure at sea level of 15C and 760 mm of mercury (or 1013.25 mb/hPa).
Above sea level, it assumes a constant temperature lapse rate from sea level of 6.5C per 1000 m (1.98C/3.56F per 1000 ft) rise in height, up to an altitude of 11,000 m (-56.5C) . 11,000m is assumed to be the Tropopause, above which constant temperature (-56.5C) is assumed.
Pressure figures from this ISA are used in calibration of barographs, because although the real atmosphere varies from day to day, for calibration purposes a set of internationally agreed figures are needed so that all calibrations are to the same datum, whether or not such figures correspond to `true' height on a given day. A similar principle is used in calibrating pressure altimeters for aircraft, so that all aviation activities have a common standard of pressure height indication in the cockpit.

### WGS 84 - World Geodetic System 1984.

A co-ordinate system based on a mathematical model of the earth and including many variables such as gravity constants and coefficients, formulas for the Earth's angular velocity, a WGS84 ellipsoid and a WGS84 geoid, with associated constants, conversion factors and co-ordinate systems. For the purpose of GNSS, the ellipsoid model is important, and is the currently accepted best overall simple mathematical model for the earth's shape and upon which all IGC GNSS fixes and calculations are initially based. Fix position and distance calculations can then be transformed to any of over 200 other ellipsoids (local Geodetic Datums). Some similar systems to WGS84 include the International Terrestrial Reference Frame (ITRF, eg ITRF96) and the European Terrestrial Reference System (eg ETRS98) but lat/long differences between these systems are less than 1m with respect to co-ordinates based on WGS84.
WGS84 Ellipsoid.
The ellipsoid radii for WGS 84 are as follows:
Major Axis (the Equator), radius = 6378.1370 km
Minor axis (Polar), radius = 6356.7523 km (flattening 21.3847 km)
Orientation The minor axis is between the Earth's centre of mass and the Terrestrial Pole as defined by the Bureau Internationale de l'Heure (BIH). In approximate terms, this is the Earth's spin axis.
WGS84 Geoid.
The maximum differences between the WGS84 Geoid and the WGS84 Ellipsoid are +65m at 60N 030W (S of Iceland, geoid above the ellipsoid) and -102m on the equator at 080E (S of India, geoid below the ellipsoid). A table of WGS84 Geoid heights with respect to the WGS84 Ellipsoid is available in MS Excel format from FAI (via the GFAC Chairman).

### Distances on the earth's surface.

For FAI distance calculations, the surface of the earth is taken to be a sphere of radius 6371 km exactly. This is an approximation which FAI uses for ease of calculation and is a radius appropriate to a sphere of the same volume as the WGS 84 ellipsoid. The distance for FAI purposes shall be the length of the arc of the great circle joining given points defined by their geographical coordinates, using the same Geodetic Datum for each set of co-ordinates. A short paper titled “FAI Distance Calculations” giving the appropriate formulas and methodology, is available from the FAI Secretariat.

### FAI UNITS OF MEASUREMENT

Distances On and Above the Earth's Surface
 Long Distances (over 10 Km) Kilometre (km) Short distances (less than 10 Km) Metre (m) Very short distances Centimetres (cm) Altitude Metre (m) Horizontal speed Kilometre/hour (km/h) Vertical Speed Metre/second (m/s) Temperature Degrees Celsius (°C) Pressure Hectopascal (hpa) or Millibar (mb) Mass Kilogramme (kg) Time Hours, Minutes, Seconds UT (hr, min, sec)

### COMMON CONVERSION FACTORS

```DISTANCE
1 foot = 0.3048 metre
mile (nautical) = 1852.0000 metre
kilometre = 3280.8 feet
mile (statute) = 5280 feet
mile (statute) = 1.6093 kilometres
mile (nautical) = 1.1508 miles (statute)
centimetre = 5 kilometres (on 1:500,000 map)
inch = 4 miles (on 1:250,000 map)
degree = 111.1949 kilometres (Great Circle arc)
SPEED
1 foot/second = 0.3048 metres/second
metre/sec = 3.6 kilometres/hour
metre/sec = 1.9438 knots
metre/sec = 2.2369 miles/hour
mile/hour = 1.6093 kilometres/hour
knot = 1.8520 kilometres/hour
knot = 1.1508 miles/hour
knot = 101.2686 feet/minute
mile/hour = 1.4667 feet/second
PRESSURE
1 atü = 15 psi (for tire pressure)
psi = 6.8948 kilopascals
atmosphere = 101.325 kilopascals
inch Hg (0°C) = 33.8639 millibars (mb)
atmosphere = 29.9213 inches Hg (0°C)
atmosphere = 1013.3252 millibars
millibar = 0.7501 millimetres Hg
VOLUME
1 gallon (Imp) = 1.2009 gallons (US)
gallon (US) = 3.7854 litres
gallon (Imp) = 4.5459 litres
MISC.
1 gallon (Imp) = 10 lbs water (15°C)
as a rough approximation:
100 ft/min = 1 knot = 1/2 metre/sec
```

### Temperature Conversion Table

From To Fahrenheit To Celsius To Kelvin
Fahrenheit (F) F (F - 32) * 5/9 (F - 32) * 5/9 + 273.15
Celsius (C or o) (C * 9/5) + 32 C C + 273.15
Kelvin (K) (K - 273.15) * 9/5 + 32 K - 273.15 K

### Pressure and altitude

Pressure decreases with height in the first 10 kilometers above the earth's surface according to the formula P(z)=P(sea level)*exp(-z/H). P(z)= pressure at height z, P(sea level)= sea level pressure(~1013 millibars), z= height in meters, H= scale height( to keep the formula simple, we're using 7 kilometers for the scale height)
Pressure to altitude conversion:
h = 288.15/0.0065 * (1-(p/101325)^(0.0065*287.053/9.80665))
h - altitude (m)
p - pressure (Pa)