British-American System of Units

Discussion

foot-pound-second

The foot-pound-second system is an attempt to make useful scientific units out of the mess that traditional English units evolved into. The foot is pretty good (since most people have two feet available for service). The second is very good (since it's an internationally recognized unit). But the pound, for lack of a better word, is bad. What is a pound? Is it a unit of mass or is it a unit of weight (and thus a unit of force)? To be precise, one should always indicate.

Start from the pound avoirdupois, the usual unit of mass and weight in the English system. SI dominates the world now and the English pound mass is now defined in terms of the kilogram.

pound mass = 0.45359237 kg

This value is exact by definition. It is not measured or calculated.

From here we move on to the first unit of force in the English system. Yes, you heard me right, the first. There are two — one in which the pound is a unit of weight and one in which it's a unit of mass. The pound force is defined as the weight of a pound mass in a standard gravitational field. Thus …

W  =  mg
pound force  =  (pound mass)(acceleration due to gravity)
pound force  =  (0.45359237 kg)(9.80665 m/s2)
pound force  =  4.44822162 … N

The corresponding unit of mass is the horribly named slug. The slug is the unit of mass when the pound is a unit of force. A mass of one slug will accelerate at one foot per second squared when pushed by a one pound force.

F  =  ma
1 pound force  =  (1 slug)(1 ft/s2)
(1 pound mass)(acceleration due to gravity)  =  (1 slug)(1 ft/s2)
(1 pound mass)(32.1740486 ft/s2)  =  (1 slug)(1 ft/s2)

Thus …

slug = 32.1740486 … pound mass

In SI units, this is approximately …

slug  =  (32.1740486 … lb)(0.45359237 kg/lb)
slug  =  14.5939029 … kg

And now for the second unit of force in the English system. The poundal is the unit of force when the pound is the unit of mass. A one pound mass will accelerate at one foot per second squared when pushed by a one poundal force.

F  =  ma
poundal  =  (1 pound mass)(1 ft/s2)
poundal  =  (1 pound force)(1 ft/s2)
(acceleration due to gravity)
poundal  =  (1 pound force)(1 ft/s2)
(32.1740486 ft/s2)
 poundal  =  0.03108095 … pound force

In SI units, this is exactly …

poundal  =  (1 pound mass) (1 ft/s2)
poundal  =  (0.45359237 kg) (0.3048 m/s2)
poundal  =  0.138254954376 N

Now that we've sort of resolved the whole mass-weight debacle let's get on with this subsystem of the English system of units.

quantity full name symbol
pound force pound mass
distance foot ft
time second s
speed   ft/s
acceleration   ft/s2
acceleration due to gravity   32.1740486 ft/s2
force pound force lb (also lbf)  
poundal   pdl (lb ft/s2)
mass slug slug (lb s2/ft)  
pound mass   lb (also lbm)
energy   ft lb ft pdl
power   ft lb/s ft pdl/s
moment of inertia   slug ft2 (lb ft s2) lb ft2
torque   ft lb ft pdl
area   ft2
volume   ft3
mass density   slug/ft3 lb/ft3
weight density   lb/ft3 pdl/ft3
volume flow rate   ft3/s
mass flow rate   slug/s lb/s
weight flow rate   lb/s pdl/s
pressure   lb/ft2 pdl/ft2
dynamic viscosity   lb s/ft2 (slug/ft s) pdl s/ft2 (lb/ft s)
kinematic viscosity   ft2/s
Units of the foot-pound-second systems

Base notes from the public domain Webster's Revised Unabridged Dictionary of 1913

some more units

Blah, blah, blah. So many, many units.

horsepower
A unit of power, used in stating the power required to drive machinery, and in estimating the capabilities of animals or steam engines and other prime movers for doing work. It is the power required for the performance of work at the rate of 33,000 English units of work per minute; hence, it is the power that must be exerted in lifting 33,000 pounds at the rate of one foot per minute, or 550 pounds at the rate of one foot per second, or 55 pounds at the rate of ten feet per second, etc.
btu
{Mechanical equivalent of heat} (Physics), originally defined as the number of units of work which the unit of heat can perform, equivalent to the mechanical energy which must be expended to raise the temperature of a pound of water one degree Fahrenheit; later this value was defined as one {British thermal unit} (B.t.u). Its value was found by Joule to be 772 foot pounds; later measurements give the value as 777.65 foot-pounds, equivalent to 107.5 kg-meters. This value was originally called Joule's equivalent, but the modern Joule is defined differently, being 10^{7} ergs. The B.t.u. is now given as 1,054.35 absolute Joules, and therefore 1 calorie (the amount of heat needed to raise one gram of water one degree centigrade) is equivalent to 4.186 Joules.
therm
100,000 btu
quad
quadrillion btu
candle
{Standard candle} (Photom.), a special form of candle employed as a standard in photometric measurements; usually, a candle of spermaceti so constructed as to burn at the rate of 120 grains, or 7.8 grams, per hour. {Candle power} (Photom.), illuminating power, as of a lamp, or gas flame, reckoned in terms of the light of a standard candle.
foot candle
The amount of illumination produced by a standard candle at a distance of one foot.
inches of mercury
 
fahrenheit
{Fahrenheit thermometer} is so graduated that the freezing point of water is at 32 degrees above the zero of its scale, and the boiling point at one atmosphere of pressure is 212 degrees. It is commonly used in the United States and in England.

212 ℉ = 100 ℃ and 32 ℉ = 0 ℃

T[℉] = (T[℃]*9/5 +32) or T[℃] = (T[℉] − 32)*5/9

rankine
 
knot
(a) A division of the log line, serving to measure the rate of the vessel's motion. Each knot on the line bears the same proportion to a mile that thirty seconds do to an hour. The number of knots which run off from the reel in half a minute, therefore, shows the number of miles the vessel sails in an hour. Hence: (b) A nautical mile, or 6080.27 feet; as, when a ship goes nautical eight miles an hour, her speed is said to be eight knots. [1913 Webster] a unit of length used in navigation; equivalent to the distance spanned by one minute of arc in latitude; 1,852 meters
reyn
Dynamic viscosity. 144 lb s/ft2

Anything else? Don't answer that question.