Surface Area Methodology...?

Question

I need a methodology for measuring the surface area of an oddly shaped object whose density is unknown (and, in any case, isn't uniform). Any ideas?

Answer 1

That is a famously tricky problem because there is no relationship between the volume and the surface area (think of a marble and a sheet of paper).



Various "planimeters" have been designed, that are complex and expensive.



See http://www.leinweb.com/snackbar/planimtr/index.htm for a description of a clever mechanical device over 100 years old.

Answer 2

An electrostatic coating may work better than paint. You can regulate the thickness more tightly and get a better reading with material.



Another way would be to rotate the item (say in a lathe) Place a follower on the surface that comes down vertically until it touches. The height of the follower could be recorded by a computer. Rotate the item recording the height of the follower and slowly move the follower from one end to the other end of the item.

For example say the item is a ball. The follower will start out with zero height at the very edge of the ball, As the follower moves down the ball it will go up increasing the signal into the computer, as the follower hits the middle of the ball the signal maxes out then begins to decrease to zero again. The curve recorded by the computer would be the instantaneous radius of the item at every point recorded.

For simplicity say you placed the follower on the ball's surface twenty times and rotated one turn at each placement. You now know the geometry of the ball in 20 slices. Need more accuracy place it 50 times on the ball or make a device to move the follower as the item rotates.

My name goes first on the patent application!

Answer 3

I think the paint idea has merit.



If you take a cube with a similar surface finish (rough vs. smooth) and dip it into a known amount of paint, rotate it around so you get a consistent thickness then do the same for your mystery object you can use the ratio as described above. To get a more precise measure of paint used weigh it on a sensitive scale (maybe sneak into a University chemistry lab). If you use thinner paint the thickness will be more precise but it will be harder to measure the amount used. (It seems like a macroscopic version of the Heisenberg uncertainty principle.)



If this doesn't work for you it is possible to "map" the object in 3D with CNC equipment touching it with a probe. The machine will touch a sensitive probe to your object at regular intervals to create a virtual map based on X,Y,Z coordinates. A program like Inventor or Solidworks (3D modeling) could import the information and create a virtual version of it. At that point the software could calculate the surface area. Precision will be directly related to money invested and time taken.

Answer 4

Step 1: Find some paint.

Step 2: Find an object with a surface area that is known.

Step 3: Paint the known object and measure the amount of paint required.

Step 4: Paint the unknown object and measure the amount of paint required.



The surface areas of the two objects will have approximately the same proportion as the amount of paint used to paint them. For example, if the unknown object requires 1.3 times as much paint, then the surface area of the unknown object is 1.3 times the surface area of the known object.

Answer 5

u should give somewhat estimate of the length and then only we can tell u that which type of devices u can use.

Answer 6

Where's Will Hunting when you need him!? I want to show up and just see this solved...

It wasn't me, I promise!