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/s^{2}) |
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/s^{2}) |
(1 pound mass)(acceleration due to gravity) | = | (1 slug)(1 ft/s^{2}) |
(1 pound mass)(32.1740486 ft/s^{2}) | = | (1 slug)(1 ft/s^{2}) |
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/s^{2}) |
poundal | = | (1 pound force)(1 ft/s^{2}) |
(acceleration due to gravity) | ||
poundal | = | (1 pound force)(1 ft/s^{2}) |
(32.1740486 ft/s^{2}) | ||
poundal | = | 0.03108095 … pound force |
In SI units, this is exactly …
poundal | = | (1 pound mass) | (1 ft/s^{2}) |
poundal | = | (0.45359237 kg) | (0.3048 m/s^{2}) |
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/s^{2} | ||
acceleration due to gravity | 32.1740486 ft/s^{2} | ||
force | pound force | lb (also lbf) | |
poundal | pdl (lb ft/s^{2}) | ||
mass | slug | slug (lb s^{2}/ft) | |
pound mass | lb (also lbm) | ||
energy | ft lb | ft pdl | |
power | ft lb/s | ft pdl/s | |
moment of inertia | slug ft^{2} (lb ft s^{2}) | lb ft^{2} | |
torque | ft lb | ft pdl | |
area | ft^{2} | ||
volume | ft^{3} | ||
mass density | slug/ft^{3} | lb/ft^{3} | |
weight density | lb/ft^{3} | pdl/ft^{3} | |
volume flow rate | ft^{3}/s | ||
mass flow rate | slug/s | lb/s | |
weight flow rate | lb/s | pdl/s | |
pressure | lb/ft^{2} | pdl/ft^{2} | |
dynamic viscosity | lb s/ft^{2} (slug/ft s) | pdl s/ft^{2} (lb/ft s) | |
kinematic viscosity | ft^{2}/s |
Base notes from the public domain Webster's Revised Unabridged Dictionary of 1913
Blah, blah, blah. So many, many units.
212 ℉ = 100 ℃ and 32 ℉ = 0 ℃
T[℉] = (T[℃]*9/5 +32) or T[℃] = (T[℉] − 32)*5/9
Anything else? Don't answer that question.