Data E : Units and Conversion Factors

In many college courses and industries, aeronautical calculations will be conducted in SI units (Systeme International d'Unites). This system has the basic units of kilogram, metre, second, Kelvin, and derived units of Newton, Joule, Pascal, Watt etc.. Unfortunately, not all aeronautical work is done in SI units. Some companies and some older reports will be in the old British System. For example U.S. industries mainly use the old British System of foot, pound force, second and Rankin. Also, some European industries still use the Old Metric System (not to be confused with the SI system) metre, kilogram force, second and Kelvin. To work as an aeronautical engineer you will need to understand all these systems of measurement. Unfortunately, it is common practice for a variety of different units to be used in most types of aircraft analysis. It is therefore necessary to understand, and be familiar with using and converting between any system of units.

Coupled to the confusion that can arise from converting between different system of units are the "special" units used in the aircraft industries. These special units include the aptly named SLUG and the use of nautical terms for speed (KNOT) and distance (Nautical mile). Operational (e.g. air traffic control (ATC) and some flight instrument) parameters are often required when interpreting or confirming flight data. (e.g., altitude is often quoted in feet (or thousands of feet, e.g. 33), rates of climb in feet per minute (or metres per minute), weights in pounds (or kilograms force), engine thrust in pounds, speed in nautical miles per hour (or kilometres per hour) and pressure in millibars.

The following data has been compiled to help you to understand some of these terms and to provide assistance in converting to and from different systems of measurement. We start by defining units derived from the basic British System.

Density: Slug/ft³ = 515.4 kg/m³ (1 lb/ft3 = 16.02 kg/m³)

Force: Pound (lbf) = 4.448 N

Work: Slug ft²/sec = 1.356 Nm

Power: Slug ft²/sec³ = 1.356 Nm/s

Pressure: Slug/ft sec² = 47.88 N/m² (1 lb./in² (psi) = 6895 N/m²)

Gas Constant: ft lbf/slug°R = 0.1672 Nm/kg°K

Coef.of Viscosity: Slug/ft sec= 47.88 kg/ms

Kinematic Viscosity: ft²/sec = 9.290 x 102 m²/s

Specific fuel consump:(jet a/c) lb/hr. lb thrust = 0.283 x 10-4 kg/Ns

Funny units

Nautical mile (nm): The international nautical mile is 1852m exactly. The British nautical mile is 6080 feet but aviators and other navigators have sometimes used 6000 ft (2000 yards) as a crude approximation.

Knot (kt): is (nm/hour) = 0.514 m/s = 1.852 km/hr = 1.688 ft/sec = 1.1508 mph.

G [gee] (g): is the gravitational acceleration at ground level (average)

= 32.2 ft/sec² = 9.81 m/sec². Gee is used to divide aircraft accelerations to relate them to steady flight conditions (i.e. the aircraft is pulling 6g).

Slug: is a contrived unit used in the old British system devised to avoid multiplying by gravitational acceleration. It is a mass unit which provides a force of 1 pound when it is subjected to an acceleration of 1 ft/sec². It is often used for specifying air density in aerodynamic equations in ft:lb:sec units (e.g.air at SL.ISA,

ro= 0.002378 slug/ft³ which is equivalent to 1.225 Kg/m³).

[Note: gravitational acceleration at ground level 'g'(average) is 32.2 ft/sec² in British Imperial units, so a slug is effectively 32.2 pounds mass!]

British Thermal Unit (BTU): The heat required to raise the temperature of one pound of water through 1°F. [Note, 1BTU = 1055 Joule]

Horsepower (hp): An artificial measure of power = 550 ft.lb/s =3300 ft lb/min. = 746 watts

Bar (bar): An measurement of pressure = 106 dyne/cm² (often quoted in millibars = 10 kN/m²).

[Note: Standard Atmosphere (atm) is sometime quoted for pressure measurements = 10.01325 bar = 101325 N/m²].

Imperial Gallon (Imp gal): The volume of 10 pounds of water at 62°F

= 277.4 in³ = 4.546 litre.

[Note: U.S.gallon (US gal) is a smaller volume than the Imp.gallon equalling only 231 in³ = 3.785 litre. 1 US gal = 0.83267 Imp gal. (Be careful when interpreting aircraft fuel burn and tankage volumes from unspecified gallons)]

Ton: A measure of weight = 2240 pounds = 1016 kg (f) (approx. 1000 kg.)

[Note: A short ton (tonne) = 2000 lb. is sometimes used in US data]

Thou: One thousandth of an inch = 0.001in. [1mm = 40 thou.approx.]

Flight Level: is a derived unit of altitude used in air traffic control. One hundred feet altitude is the basic unit therefore flight level 330 is in practice at a height of 33000 ft.

Drag Count: is used as a crude measure for the change in drag coefficient (C_D) = 0.0001 [note, drag count is not a direct measure of drag as it is associated with a reference area, it is only valid for use as a relative assessment of change].

(exact conversions can be found in British Standards BS350/2856)

Inch (in) 25.40 millimetres

Feet (ft) 0.3048 metres

Feet(ft) 3.048 x 10^-4 kilometres

Statute mile(mi) 1.609 kilometres

Nautical mile (nm) 1.852 kilometres

Nautical mile (nm) 1.1508 statute miles

Square foot (ft²) 9.290 x 10^-2 square metres

Cubic foot (ft³) 28.317 litres

Cubic foot (ft³) 2.832 x 10^-2 cubic metres

Cubic inch (m³) 1.639 x 10^-5 cubic metres

U.S.gallon (US gal) 3.78542 litres

Imp.Gallon (Imp gal) 4.546 litres

Foot/second (ft/sec) 0.3048 m/s

(ft/sec) 1.097 km/h

(ft/sec) 0.6818 mph

Knot [nm/hr] (kt) 1.689 ft/sec

(kt) 1.151 mph

(kt) 1.852 km/h

(kt) 0.5151 m/s

Mile/hour (mph) 1.467 ft/sec

(mph) 1.609 km/h

(mph) 0.8684 kt

(mph) 0.4471 m/s

Slug (slug) 14.59 kg

Pound (lbf) 4.448 N

Pound/Sq. in (lbf/in²) 6895 N/m²

Pound/Sq. ft (lbf/ft²) 47.88 N/m²

Slug/cubic ft (slug/ft³) 515.4 kg/m³

Foot Pound (ft.lbf) 1.356 Nm (Joules)

Foot lb./sec (ft.lb/sec) 1.356 Joules/s (watts)

Horsepower (hp) 550 ft.lb/sec

(hp) 33000 ft.lb/min

(hp) 745.7 watts

Gravitational Force at SL = 9.80665 m/s² = 32.174 ft/sec²

Air pressure at SL p_o = 760 mm Hg = 29.92 m.Hg = 1.01325 x 105 N/m²

= 2116.22 lb./ft²

Air temperature at SL T_o = 15.0° C (conversions ß )

= 288.15° K (°K = °C + 273.19)

= 59.0° F° (°C = (°F - 32) (5/9))

= 518.67° R (°R = °F + 459.7)

Air density at SL ro = 1.22492 Kg/m³ = 0.002378 slug/ft³

Air coef.of viscosity SL mo = 1.7894 x 10-5 kg/ms = 1.2024 x 10-5 lb/ft s

Air Kinematic viscosity SL no = 1.4607 x 10-5 m²/s = 1.5723 x 10-4 ft²/s

Specific gravity at 0°C (lb/ft³ / kg/m³):-

Water =1.000 (62.43 /1000) Sea water = 1.025 (63.99 / 1025)

Jet Fuel JP1 = 0.800 (49.9 / 800) JP3 = 0.775 (48.4 / 775)

JP4 = 0.785 (49.0 / 785) JP5 = 0.817 (51.0 / 817)

Kerosine = 0.820 (51.2 / 820) Gasoline = 0.720 (44.9 / 720)

Alcohol = 0.801 (50.0 / 801)

Various units are named after eminent scientists and engineers

(source D.Stinton, Data 6, ref. 5.4):-

Celsius: Swedish astronomer, Ander Celsius (1701-1744)

Hertz: German physicist, H.R. Hertz (1857-1894)

Joule: English physicist, J.P. Joule (1818-1889)

Kelvin: Scottish physicist, Lord W.T. Kelvin (1827-1907)

Newton: English mathematician, Sir I. Newton (1642-1727)

Pascal: French Scientist, Blaise Pascal (1623-1662)

Rankin: Scottish engineer, W.G.M Rankin (1820-1872)

Reynolds: British engineer, Prof.Osborne Reynolds (1842-1912)

Watt: Scottish engineer, James Watt (1736-1819)