I know this might be a dumb question but I've never known why a foot-pound is larger than a newton. Never made any sense as a kid, still doesn't now that I'm back fiddling with the math again after having returned to the hobby. A meter is longer than a foot, a kilo is heavier than a pound, so why does it take roughly 4.4 newtons to equal a foot-pound? Am I being a dyslexic or have I missed something really basic?
1 pound of force (lb-f or lbf) equals 4.45 Newtons of force
2.2 pounds of force equals 9.8 Newtons (9.8/2.2=4.45)
These are relationships of force.
A foot-pound can be a unit of work (ie, energy) or a unit of torque. A force of one pound applied to push an object one foot accomplishes one foot-pound of work and expends one foot-pound of energy.
Metric equivalents would be Newton-meters. One foot-pound of work equals
4.45*12/39.39 Newton-meters. (1.36Nm)
A force of one pound applied at a right angle to a crank one foot from the axis results in a foot-pound of torque.
Basically, the difference between work and torque is that for work, the force is applied in the direct of the distance (foot) while for torque, the force is applied at that distance from the axis.
Metric equivalents are again Newton-meters. There are many others. With R/C servos, you will frequently see ounce-inches of torque.
Rocket motor impulse is measured in pound-seconds (pounds force) or Newton-seconds. Perhaps you were getting these mixed up with the others?
1 lb-sec equals 4.45 Newton-seconds.
2.2 lb-secs is 9.8 N-secs
You will sometimes see N/s. This is a grammatical construct abbreviating Newton-seconds, but to a rocket scientist/engineer/physicist/mathematician, it means Newtons-divided-by-seconds and makes no sense.
I assume you are talking about thrust measurements so you aren't converting foot-pounds to newton-meters; you're converting pounds-force to newtons.
Pound-force , as it's name implies, is a unit of force while newton is a unit of mass. To convert between the two you have to assume a gravitational acceleration ( 9.8 m/s^2). Also 1 kg weighs ~2.2 pounds. Thus:
(1 kg X 9.8 m/s^2) / 2.2 lbs = ~4.45 N / lb
It's been awhile since I've thought about this stuff so someone correct me if I'm wrong.
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Show me an international agreement defining a slug.
Bet you can't.
Show me the official, exact definition of a slug. Can't even do that.
There was, of course, an international agreement in 1959 which defined the pound as 0.45359237 kg exactly. But there is no international agreement which gets you from there to either a pound force or a slug. For that you need some "standard" acceleration of free fall. We often borrow the one which is official for defining kilograms force,
9.80665 m/s², but other values are used as well, such as 32.16 ft/s². No international or national or professional organization has ever officially chosen a value for the purpose of defining either pounds force or slugs.
Not "about." The yard is defined by the same international agreement as exactly 0.9144 m. Divide that by three and you get the exact definition of a foot.
Sorry, was using numbers off the top of my head. Yes, a foot is exactly .3048 meters.
By "international agreement", I simply mean that most countries abide by the standards set by BIPM or NIST or whomever the discipline considers to be the authoritative standard, ie, there are standards which are common amongst nations with different units in use. Not necessarily treaties.
I'll check on the slug, I believed the lbf was defined as the equation I gave. Yes, you can do free fall tests, but now days the instruments are so sensitive that you have to cite the geoid you are using, leading to other measurement qualifications as well.
Indeed, the slug seems to be less than exact in definition in the traditional systems. As you say, however, it can be derived (if not defined) by the above procedure. Regardless of the precision of measured constants (g) the mathematical relationships hold in a classical (practical) world. (F=ma) There may not be an official international agreement, but if you have a lbm (above) and a g (however imprecise) a lbf falls (sic) right out and a slug is not far behind.
You get the lbf = slug * ft/s^2 equation, a slug being simply [(coefficient of g) * lbm]. It may not be official, but its exact. :)
But the BIPM doesn't deal with English units, and the best NIST can do for the pound force is to give us a qualified definition, with a big "if" based on the choice of a standard acceleration of free fall, since there isn't an official one for this purpose.
That is the way it sits for pounds defined as units of mass. This was a 1959 international agreement among the national standards laboratories of the United States, Canada, the United Kingdom, South Africa, Australia, and New Zealand. It wasn't a treaty, so not necessarily self-implementing. In the United Kingdom, this was implemented by statute in the Weights and Measures Act of 1963. In Australia, it is by regulation in the Weights and Measures Regulations. In Canada, it is the Weights and Measures Act of
1953--note that Canada had already defined both the pound and the yard this way six years before the rest of the world adopted their definition. In the United States, Congress had already delegated this power to what was then the National Bureau of Standards (now NIST), so all that was needed to make this the official, legal definition in the United States was an official publishing of the regulatory action taken in the Federal Register of 1 July 1959,
Announcement. Effective July 1, 1959, all calibrations in the U.S. customary system of weights and measures carried out by the National Bureau of Standards will continue to be based upon metric measurement standards and except for the U.S. Coast and Geodetic Survey as noted below, will be made in terms of the following exact equivalences and appropriate multiples and submultiples: 1 yard = 0.9144 meter 1 pound (avoirdupois) = 0.453 592 37 kilogram Currently, the units defined by these same equivalences, which have been designated as the International Yard and the International Pound, respectively, will be used by the National Standards Laboratories of Australia, Canada, New Zealand, South Africa, and United Kingdom; thus there will be brought about international accord on the yard and pound by the English-speaking nations of the world, in precise measurements involving these basic units.
This document also discusses the earlier U.S. definition of the pound as a slightly different exact fraction of a kilogram, from the late
But the specific geoid used has nothing to do with the somewhat arbitrary choice of a "standard" to use in defining gravitational units of force such as the pound force or the obsolete but still seen kilogram force based on a pound or a kilogram. That just has to be somewhere between the extremes found on Earth. THe one which officially defines the kilogram (9.80665 m/s^2), for example, is considerably higher than the average sea level acceleration on Earth (around 9.79 m/s^2, better values on my dead computer), and a little higher than midlatitude values.
Yes, the relationship of a slug to a pound force is exact. It's just that neither of those units has an official definition in the first place. (Any definitions in actual use probably differ by less than 1 part in 800, and the most commonly used definitions only differ by about 1 in 2300, however.)
My mathematics teacher, who was the only authority that mattered at the time, defined 1 poundal as the force needed to produce an acceleration of 1ft/s^2 (the foot and second being already defined exactly) on a mass of 1 pound, as defined from the Kg. No gravitational constant needed.
Well, 1 lbf is the weight of 1 pound mass in a gravity of 1.000 g (where g is the standard gravitational constant... the exact gravity at any spot on earth might vary slightly from that, so use the standardized nominal value as the definition.) This means that there's a conversion factor between lbf and newtons that's as exact as the standardized value of "g". (Is the root of your "circular reasoning" complaint that the standard value of "g" isn't as "exact" as the standard ratio of lbm to kg?)
Heck, for speculative engineering purposes, I just round "g" to "10" or "32" (depending on whether I'm using metric or American units at the moment) to facilite mental calculation...
The problem was due to Newton making a distinction between mass and force. Before him no one even had a clue that there Was a difference. One of the units (mass in this case) has to be derived from the other two (force and acceleration). If you decide that a kilogram is the fundamental unit of mass and m/s^2 is unit acceleration, then the force falls out (newtons in this case). It's all arbitrary at some level. Traditional units have at least generally had the benefit of accessibility to standards (e.g. feet) - not highly accurate standards, I'll grant you, but standards nonetheless, and few things required high accuracy at the time. The meter was first defined in revolutionary France as 1/10,000,000 of the distance on the Earth's surface from the equator to the pole. How accessible is that? They didn't know it very accurately at the time, and screwed up their attempt to measure it to some degree. We can still use it to design things that work (or not work, as the case may be).
Units are just tools that are shaped according to our purposes and allow us to make the math relevant.