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Books using the equation, Lift=Weight, to calculate stall velocity or lift coefficient for cruise condition or something like that.

Problem is that, weight of aircraft is written by unit of lb. or kg which are actually mass. This makes me confusing since the equation Lift=Weight is not valid for mismatch of dimension; lift is in N, weight is in kg.

Can anyone explain about this?

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The other answers are correct in that they describe Lift and Weight as Forces -- that should be measured in Newtons or pounds-force (lbf).

Mass is not the same thing as force (and must not be confused). In an engineering context, we should use a consistent set of units. This means that mass is typically described in kilograms or slugs. People frequently use the pound-mass (lbm), but you must convert away from that when performing calculations.

What these two descriptions leave out is a definition of force and mass -- a lot of people unfortunately don't understand how they are different.

Force is an ability to change the momentum of an object. How much oomph.

Mass is the quantity of matter in an object. How much stuff is there.

As it turns out, objects resist changes in momentum in proportion to their mass. F=m*a. So a force is a measure of changing motion and mass is a measure of an object's tendency to resist its motion being changed.

When you understand how different these quantities are, it is a lot harder to confuse them. Force and mass are very different things.

There are other cases where we use similar (or the same) units to measure things that are very different -- for example work (units of force*distance, say N m or ft lbf) which has the same units of torque. Of course, work and torque are not the same thing.

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  • $\begingroup$ Thank you for your answer. I aware that mass is not force. What I've found is that density is written by slug/ft^3 so the equation L=W in lb holds with out multiplying coefficient of gravitational acceleration. I was confused because I'm usually dealing with SI unit. Maybe it is convention to write lbf just lb like 1g*kg = 9.8N = 1kgf so usually say 1kgf = 1kg in daily conversations. $\endgroup$
    – x xx
    Apr 23 at 12:35
  • $\begingroup$ While doing my degree in aerospace engineering in Germany, I don't think I've ever come across an actual usage of kilopond (kilogram-force), except for literature from before about 1970. When using kg, it is obvious that it's a mass, and you multiply by 9.81 m/s^2 to get the weight (on Earth) of that mass in N, and then use that value in those calculations that require an aircraft's weight. I'm not sure how other countries handle it, but I can't recall seeing it in France either. $\endgroup$
    – Raketenolli
    Apr 23 at 14:23
  • $\begingroup$ I agree that kgf is commonly used -- but never written out. It is not used in technical settings, but instead in ordinary life. 1kgf=1kg in daily use is the same thing as 1lbf=1lbm. When I do technical work, I try to avoid lbm -- but I still label lbf (not lb) wherever possible. The mass unit seems to be where the trouble always arises. If you're working lbf, in, s, then the consistent mass unit is sometimes called blob, slinch, slugette, or snail... Similarly, if you want to work in N, mm, s then mass is in tonne and density t/mm^3 $\endgroup$
    – Rob McDonald
    Apr 23 at 18:13
  • $\begingroup$ Thanks for mentioning slugs! $\endgroup$
    – Organic Marble
    Apr 24 at 22:00
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Weight is a force, and therefore should be measured in units of force. But, of course, humans have very little experience with environments that don't have 1g of gravity, and thus routinely conflate force and mass. This kind of thinking goes far beyond aviation; you can find it everywhere. For instance, spring-loaded bathroom scales measure force but will almost always display a result in kg (in metric countries). It's sloppy, but it works, and so there's little incentive to change it.

The pound is both a unit of mass and a unit of force. A one-pound mass will produce one pound of force in standard Earth gravity. If for some reason you need to specify which one you're talking about, you can use the terms "pound-mass" or "pound-force" to differentiate*.

There's less of an excuse for this in the metric system, which has separate units for force and mass, but that doesn't stop it from happening anyway. If need be (such as when reading a manual that uses kg as a unit of force), you have to think of "kg" as "newtons divided by 9.8", because that's pretty much the way they're being used.

*Of course, just about the only reason you'd need to differentiate is if the local gravity field is something other than 9.8 m/s/s, which would mean that you're dealing with space travel, which would mean that you're almost certainly using the metric system to begin with, and thus would have no need to use either pound-mass or pound-force for anything.

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  • $\begingroup$ Thank you for answer, now I understand uses of units here. $\endgroup$
    – x xx
    Apr 22 at 4:24
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    $\begingroup$ IMHO this answer further perpetuates that mass and force are the same thing -- kg is N/9.8. This is a terrible habit. Force and mass are not the same thing at all. And don't fool yourself that the aerospace industry works in the metric system. If you're going to work in aerospace, you need to be comfortable with a lot of strange combinations of units. $\endgroup$
    – Rob McDonald
    Apr 22 at 4:28
  • $\begingroup$ @RobMcDonald I did mention that confusing mass and force is sloppy, but it's what we have. You do have to think of kg as N/9.8, because that's what everyone else is doing, as illustrated by the OP's example. The choice is either to be pedantic or to be practical. While I do agree that using the proper units would be better, that's just not the world we live in. Also, I've never seen any aerospace company use anything other than SI since before the turn of the century. $\endgroup$
    – HiddenWindshield
    Apr 22 at 17:09
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    $\begingroup$ @hiddenWindshield I agree that society at large doesn't know the difference between mass and force -- and that we have to accept that units of pound-force, pound-mass, and frankly, kg-force exist. And when kg-force is used, the user usually doesn't know the difference and they drop the -force. I am not a theoretical zelot ignoring the real world. I just think the advice "If you get confused, just think of "kg" as "newtons divided by 9.8", because that's pretty much what they are." goes too far and in fact perpetuates the problem. $\endgroup$
    – Rob McDonald
    Apr 22 at 19:08
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    $\begingroup$ @RobMcDonald I wasn't intending to offer general advice, I was speaking specifically to the OP's original question. I've edited my answer slightly to make that a little more clear. $\endgroup$
    – HiddenWindshield
    Apr 22 at 19:49
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Properly speaking, weight is the force of gravity felt by an object, and units of force (pounds-force or newtons) should be used. Both colloquially and in engineering, weights are often given in kilograms-force, which is equal to the force a 1 kilogram object feels when it is in a $1g$ gravitational field.

The pound is legally a unit of mass (it is defined as an exact number of kilograms, not newtons), but the American system has no equivalent definition for force and "pound" is often used unqualified for both a force and a mass.

Theoretically, an airplane is ever-so-slightly lighter at a higher altitude and so requires less lift. In practice, this difference is so minor as to be negligible for everyday purposes- it's less than $1\%$ everywhere that planes regularly go.

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  • $\begingroup$ Thank you for answer, now I understand uses of units here. $\endgroup$
    – x xx
    Apr 22 at 4:24
  • $\begingroup$ The pound is a unit of mass, the pound-force is the unit of force. $\endgroup$
    – Bianfable
    Apr 22 at 10:07

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