**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.
Some derived units
Density: Slug/ft^{3} = 515.4 kg/m^{3} (1
lb/ft3 = 16.02 kg/m^{3})
Force: Pound (lbf) = 4.448 N
Work: Slug ft^{2}/sec = 1.356 Nm
Power: Slug ft^{2}/sec^{3} = 1.356 Nm/s
Pressure: Slug/ft sec^{2} = 47.88 N/m^{2}
(1 lb./in^{2} (psi) = 6895 N/m^{2})
Gas Constant: ft lbf/slug°R = 0.1672 Nm/kg°K
Coef.of Viscosity: Slug/ft sec= 47.88 kg/ms
Kinematic Viscosity: ft^{2}/sec = 9.290 x 102 m^{2}/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/sec^{2} = 9.81 m/sec^{2}. 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/sec^{2}.
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/ft^{3} which is equivalent to
1.225 Kg/m^{3}).
[Note: gravitational acceleration at ground level
'g'(average) is 32.2 ft/sec^{2} 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/cm^{2}
(often quoted in millibars = 10 kN/m^{2}).
[Note: Standard Atmosphere (atm) is sometime quoted for
pressure measurements = 10.01325 bar = 101325 N/m^{2}].
*Imperial Gallon* (Imp gal): The volume of 10 pounds
of water at 62°F
= 277.4 in^{3} = 4.546 litre.
[Note: U.S.gallon (US gal) is a smaller volume than the
Imp.gallon equalling only 231 in^{3} = 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].
Conversions
(exact conversions can be found in British Standards
BS350/2856)
Multiply by To get
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 (ft^{2}) 9.290 x 10^{-2} square
metres
Cubic foot (ft^{3}) 28.317 litres
Cubic foot (ft^{3}) 2.832 x 10^{-2} cubic
metres
Cubic inch (m^{3}) 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/in^{2}) 6895 N/m^{2}
Pound/Sq. ft (lbf/ft^{2}) 47.88 N/m^{2}
Slug/cubic ft (slug/ft^{3}) 515.4 kg/m^{3}
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
Some useful constants (standard values)
Gravitational Force at SL = 9.80665 m/s^{2} =
32.174 ft/sec^{2}
Air pressure at SL p_{o} = 760 mm Hg = 29.92 m.Hg =
1.01325 x 105 N/m^{2}
= 2116.22 lb./ft^{2}
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/m^{3} = 0.002378
slug/ft^{3}
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 m^{2}/s
= 1.5723 x 10-4 ft^{2}/s
Specific gravity at 0°C (lb/ft^{3} / kg/m^{3}):-
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)
Historical footnote
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) |