Yes, sectional density is important in ballistics. It is properly given in units of projectile mass divided by the cross-sectional area of its nose as seen from directly ahead. The sectional density of a large rocket or missile might well be specified in kilograms per square meter.

Certainly, sheets of paper are measured in "gsm" which stands for grams per square metre.

https://en.wikipedia.org/wiki/Area_density

Thank you @George, but I was thinking that paper does have thickness even if it is in microns, means third dimension is there, isn't?

Although not a standard, I guess that kg per square meter could be seen as a measure of pressure per unit surface.

Thank you @André Michaud,

that make sense, but what if the problem involves mass per unit area?

I agree with the answers given by George and Andre. kg/m2 is unit of pressure, where gsm (gram per sq meter) is a standard unit used in textile or paper industry.

The problem boils down to your specific requirement. If you can shed more information about your problem, maybe I can provide a better answer.

Thank you Gurjot Singh,

The problem is that in medical science BMI (Body mass index) is used as a proxy for health. The unit of BMI is Kg/m2, and it is not a unit of pressure but how much mass is there in person's body per square meter. I was thinking that it should be Kg/m3 instead? what are your thoughts?

Well, some units are industry specific, with GSM being 1 example (Refer to George's answer). Similarly, BMI can be kg/m2, if medical experts can explain why. I do understand your argument about kg/m3 (which is unit for density), but again, you need to refer to medical books on this topic.

Dear Bahadur,

It seems to me then that the BMI method would be meant to relate a person's weight to obesity via the ratio of body mass to skin surface area.

Ah, I see the problem.

BMI is an empirical relationship. It comes from statistical studies of life expectancy. For people who are perfectly healthy, you would expect someone taller to also weigh more, but not necessarily in relation to the cube of their height. An elephant needs leg bones much broader in relation to its height than an antelope.

Studies have shown that people with similar ratio of their weight to the square of their height have similar life expectancy and similar health problems if it is not optimum.

Dear André Michaud,

Thank you, you really gave me a different perspective.

Dear George Dishman,

Thank you for your enlightened answer and providing me the direction. I was actually trying to visualise the quantity expressed in BMI.

Bahadur,

Mass per unit area is emphatically not a pressure - and might be encountered if one is evaluating different construction materials for locally-plane structures (say, pressure vessels, etc.).

In the discussion of BMI, we should note that the skin area of the human is only tolerably-well predicted by the square of height.

I'm sure that there's a wikipedia page on that matter.

Yes, sectional density is important in ballistics. It is properly given in units of projectile mass divided by the cross-sectional area of its nose as seen from directly ahead. The sectional density of a large rocket or missile might well be specified in kilograms per square meter.

German engineers according to DIN 1304 have names for

kg/m: Massenbelag, Massenbehang

kg/m2: Massenbedeckung

kg/m3: Dichte

Obviously these notions imply idealisations as, taking into account the atomistic structure of matter, is already clear for the normal mass density (the one measured in Kg/m3).

With respect to the BMI the mental picture of having the body mass distributed as a layer one meter thick on some area is neither amusing nor usefull. Body mass/(Body length)2 is simply an construct which seems to correlate with the unsharp notion of 'normal constitution'. An interesting question is why this is a better indicator than the more natural guess Body mass/(Body length)3. My, so far rather unsubstantiated, guess for a better indicator is Body mass/(Body length)2.5.

Dear Mutze,

Thank you for your answer. Can you please elaborate more on why the power should be 2.5 rather than 3?

The reasons for trying somthing are not necessarily the reasons why something holds true. If 3 is a natural first guess and 2 is established but far from ideal (there are different BMI-recommendations for young and adult people) it is natural to look for something in between. Playing arround with tables on age-dependent BMI recommendations I made a few tests in which I found "BMI(2.5)" depending weaker on age than "BMI(2)". I don't remember the details and did not archive my notes. If you are interested in the matter try it yourself; perhaps something useful comes out.

density=mass/volume;

mass=density x volume = density x area x length;

mass/area = density x length .

Dear all,

In exterior ballistics the projectile is condsidered a point (with no dimension) with a given mass concentrated at the "center of mass"(not center of gravity).That, in fact, is the mass of projectile. The resistance of air depends on the projectile mass.

Since the point-mass has no sectional area, but the resistance of air depends as well on the sectional area of the projectile, at the differential equatio ithat describe the flight of projectle,t is adedd a multiplier coefficient (factor), called ballistic coefficient,

BC= i*d^2 * 1000/m

that takes into account both the influence of mass and sectional area of the projectile.

Thus, d^2/m (or m/d^2), is a derived factor and so is the corresponding unit in SI.

Formally, in the point-mass Math model, we just need to know BC, ignoring how it is derived (see formula). In fact, for any projectile, the BC is an experimentally found quantity.

GK

Dear George,

center of mass and center of gravity differ only for projectiles that are so large that the Earth's gravitational field should not be idealized as being constant over dimensions of the projectile. Does 'exterior ballistics' deal with such situations? Does the resistance of air depend on the projectile mass? I thought it is determined by geometry, with sectional area as the most influential factor, and by surface structure (all packed into the factor i of your BC-formula ?).

Dear Ulrich,

In fact there is an error stating that drag depends on "projectile mass" when in fact have intended to write "cross-sctional area" I apologize for that error.

In fact both centers are different, that is why we have projectile gyroscopic stability in motion.

I think Boatright can explain it better.

In fact we are talking for the point-mass model of projectile where the projectile is considered a non-rotating body flying in presence of drag in a standard atmosphere (mostly ICAO atmosphere) ; gravity is constant, the Earth is flat and not in rotation.; etc. etc.

That is an idealized model that gives very approimate results.