Need help constructing simple model of paintball "flight"...

[cledford]

In a thread about barrel accuracy davidb suggested a great way to demonstrate paintball (in)accurac to people - drop a spherical piece of something that resembles the relationship of the mass and aerodynamic qualities of a paintball (to air) into water and watch what happens.

Is there anyone who can suggest the appropriate material, size and reasonable volume of water (to be easily transported) to *show* people how this works?

I'm invisioning a a tallish, plexiglass type tube that could be lugged around to public places.

http://www.automags.org/forums/showthread.php?s=&postid=1242830#post1242830

-Calvin

[SlartyBartFast]

Cool idea.

I figure some marbles and a tall fish tank might be appropriate.

To remove the effect of 'splash-down' and simulate the effect of the barrel, place a completely submerged vertical tube through which the marbles can be released.

[cledford]

I'm hoping some of our "closet-physicists" will be able to help us determine the exact size and weight for the "simulated" paintball and volume of "simulated air" as well as provide the math - so it can be posted for all to try at home :)

-Calvin

[SlartyBartFast]

Actually, I wonder if it would really matter whether it was an exact match.

Try it without proper numbers and see what the acuracy of marbles in water is.

You could even simulate firing the marble out of the tube with a weighted plunger.

But, good numbers would help. The whole thread on paintball spin dynamics lists a number of sources for reynolds numbers and so forth. That would give you the size/speed figures.

[AGD]

You have to match the reynolds numbers for the size of the ball and the speed of the flow. I think Black can do it.

AGD

[SlartyBartFast]

Originally posted by AGD
You have to match the reynolds numbers for the size of the ball and the speed of the flow.

But that's one of the problems with the proposed experiment. The 'ball' would be accelerating due to gravity the whole time.

The next big problem is getting anyone in the general paintball public to care. Even if they understand the demonstration as a general validation of the inaccuracy of a sphere in a fluid, they'll argue it's not going as fast, isn't spinning, isn't leaving from a specific barrel whose fairies impart magical powers on the ball...

[fallout11]

It's physics, Jim!

I copied this post over from the original thread, since the discussion has moved over here.....


At "room temperature" (25 deg C, or 77 deg F):
1) The density of water is 0.997070 grams/mL.
2) The density of "air" is .001239 grams/mL.
Note that 1 mL = 1 cubic centimeter
This means water is roughly 804 times as dense as air.

A paintball weighs 0.116 oz, or 3.228545 grams.
An average size paintball is 0.689 inches in diameter, or 1.75006 cm diameter.
The volume of a shere is 4/3*Pi*Radius cubed.
Thus, a paintball has a volume of 2.806451 cubic centimeters (or mL).

Thus, a paintball's density is: 3.228545 grams/2.806451 mL =
1.150401 grams/ml.
This is 929 times as dense as air, and 1.15 times as dense as water.
A paintball should sink slowly in water....and they do.

Hope that helps some.

Now, what was the original question?

To be an analogy to moving a paintball through the air at 300 fps, you'd need something that was 929 times as dense as water, roughly the same size as a paintball, and then move it though the water at 1/800th the same speed, or 22 feet per MINUTE. Very heavy, very small, and very slow.
Ideas?

[fallout11]

Lead, a cheap, readily available, and easily maleable material, has a density of 11340 kg/cubic meter, or 1134 grams/cubic mL (cc).

This is 1137 times the density of water, so it is "too dense" for a perfect analogy. It's close, but.....

A slightly less dense material is needed, for a paintball-sized (exactly same shape and volume) test object.

Carbonized steels (such as C-1020) have a density of 785 g/ml. This is a bit too "light" for a perfect match.

Unfortunately, I don't have ready access here at work to much in between. Any ideas I might investigate?

[cledford]

How a about determining the correct size (lead) sphere to be made to simulate the aerodynamic relationship between the PB and air in the water, then make the sphere. Then determine how over weight it is and remove (drill or otherwise excise) the correct volume to get things right weight wise, then fill said hole with wax or plastic - reducing the weight, but retaining the proper shape/flow characteristics?

Or, we could use something denser then water - like a heavy weight oil.

-Calvin

[fallout11]

Oil floats, generally.
It's actually less dense than water.

But I like your idea of working over the lead sphere.

Anyway, steel-alloyed ball bearings through water would be my suggestion for a pretty close match for paintballs through air. You can get them in precision sizes, they have almost the right density, and have a nice, smooth, round "shell".

Now the question becomes one of fluid force interaction.
Speed, drag, coefficients of surface friction, fluid viscosity, and the way vortexes are generated and dissipated in the air versus in the water.
This is pretty heady, computational-wise, and some assumptions may/will have to be made.

[SlartyBartFast]

Originally posted by fallout11
Oil floats, generally.
It's actually less dense than water.

But it's more viscous. More resistance to an object moving though it.

[fallout11]

At the low speeds (subsonic) and with small surface areas we are talking about, viscosity is the lesser of the two forces.
Fluid density is the driving force.

Plus, oils are lubricants. They may be "thicker" (impeding the ball, through viscosity), but at the same time they are also "slipperier" (aiding the ball, through low coefficient of surface friction).

[cledford]

Oil floats! Doh, I was assuming that it was heavier due to the viscosity!

-Calvin

[fallout11]

:)

[SlartyBartFast]

Good Reynolds Number calculator can be found here:

http://www.efunda.com/formulae/fluids/calc_reynolds.cfm#calc

But, the bloody thing's a subscription service.

Great video of cylinders in a flow:

http://www.flometrics.com/services/cylinder/cylfast.mov

http://www.flometrics.com/services/cylinder/cylsplit.mov

Think of a sphere as identical but with all the flow nastiness happening in 3d.

The one with the baffle shows that you don't need specially shaped fins, just anything to damp the flow. On the same site, the video with the damping provided by a second cylinder is interesting.