# Units of 2D density

1. Nov 19, 2006

### tony873004

density is (mass / volume). But what is (mass / area)?

For example, if I wanted to know the mass of how much water would fill a jar, it would be mass = (volume of jar * density of water) = cubic length * (mass / cubic length.)

But imagine I knew how much a square meter of paint weighed, even if I did not know the thickness of a coat of paint. If I wanted to know the mass of how much paint it would take to cover a wall 10x10 meter wall, it would be mass = (area of wall * ??) = squared length * (mass / squared length).

mass / cubed length = density
mass / squared length = ??

Is there such a term?

2. Nov 19, 2006

### chroot

Staff Emeritus
I don't believe there's a name for the quantity.

- Warren

3. Nov 19, 2006

### Cyrus

If you know how much it weights for one square meter, then you know the thickness of your paint.

4. Nov 19, 2006

### Gokul43201

Staff Emeritus
If you want a name, go with "areal density".

5. Nov 19, 2006

### billiards

density per unit thickness? [M/L2]

I'd imagine it only has meaning where the thickness is known to be constant, not really a very natural phenomenon at macroscopic scales

6. Nov 19, 2006

### Chi Meson

"Area density" is the term used for this quantity. Sometimes it's (incorrectly) called "mass spread rate." Do a google of "area density" for plenty of examples.

7. Nov 19, 2006

### tony873004

Thanks, everyone for you answers. And thanks, Chi, that's exactly what I was looking for.

8. Nov 19, 2006

### SpaceTiger

Staff Emeritus
In astronomy, it's often called "surface density", though I'm sure that term isn't universal.

9. Nov 21, 2006

### tony873004

Thanks, ST. For my purposes, I think "area density" is the more proper term. As a challenge to our Astrobiology class, we were asked to consider whether or not a light sail might be a good idea for accelerating an interstellar spacecraft towards Alpha Centauri. The goal is to reach 10% the speed of light.

The area density of the sail seems to be very critical. For example, a mylar emergency camping blanket 56x84 inches and weighing 10 ounces, with an advertised reflectivity of 90%, has an area density of 0.093 kg/m2. This is WAY too heavy to accelerate even a 1 kilogram nano-bot to even solar escape velocity, let alone 10%c, even starting the journey from the surface of the Sun for maximum flux. But sails made of ficticious materials 1/1,000,000 the area density of an emergency mylar blanket can do the trick as long as they are HUGE (kilometers in diameter).

Here's a link to a calculator I made using my new knowledge of area density just to make the formula prettier. For small velocities (<~500 km/s) the answers it gives are a bit high as it ignores gravity. But for higher velocities where gravity becomes neglible, the answers are in nice agreement with my numerical model.

http://orbitsimulator.com/gravity/articles/sailformula.html

Sorry for getting a little off-topic, but I thought I'd show everyone why I needed to know this.