My bad. You're completely correct. Read the wrong numbers. :rolleyes:
Printable View
Hey Buddy,
I really enjoyed / enjoying this thread, almost to the point to take some classes. Seriously.
Dose anyone know the right answer?
Cold, I thought I was on to something there. I am not discouraged though still reading. Fascinating stuff, but we still cant put aluminum in the microwave.:lol:
:D I'm just glad people are really and actually thinking about it. The more people think for themselves, and don't just accept everything we hear, the better off we'll all be.
For my part, just as important as knowing the end result, is knowing the 'why'. :)
Yeah, but it takes a little bit of math. I'll keep it as simple as possible.
Let's ignore things like drag, turbulence, viscosity, etc and just look at displacement of water.
Newton's law of gravity says that there's a force between any two objects proportional to the product of their masses and inversely proportional to square of the distance between them:
F = (g x m1 x m2) / (d x d)
where g is the gravitational constant, M1 and M2 are the masses and d is the distance between there centers of gravity.
Since in what we're talking about, one of those masses is the earth itself, and the distance to the earth's center of gravity is always going to be more or less the same, we can simplify this to:
F = G x mb
(mb is the mass of the bead; all I did was make (g x m1)/(d x d) into a new constant that I'm calling G)
Newton's second law of motion says that force equals mass times acceleration:
F = m x A
If we combine the equations we get:
G x mb = mb x A
which reduces to G = A. In other words, it didn't matter what the mass of the bead was, in a vacuum all objects are going to accelerate at the same rate (which happens to be about 32 feet per second per second).
If we're dropping through a fluid, however, we're not just dropping the bead down, we're moving some of the fluid up. This upward movement obeys the same law of gravity, and now the total force on the bead is:
F = (mb x G) - (mf x G)
(mf is the mass of the fluid.)
But as we already know from Newton's 2nd law, the force on that bead is
F = mb x A
combining the last two equations we get:
mb x A = (mb x G) - (mf x G)
rearranging we get
A = G x (mb - mf) / mb
which is the rate that the bead will accelerate in the fluid.
Notice that if mb = mf then A = 0. In other words if the bead has the same mass as the fluid it displaces, it doesn't sink at all. This checks with what we already know about floating, so our math is probably right.
Now suppose we had two bead of equal mass, one of lead, and one of tungsten. The one of lead will be larger (since it has less mass) and will displace more of the fluid (and hence more mass of the fluid). If you look at the equation, if mf is bigger, then acceleration is smaller. It doesn't sink as fast. By the same light, if the two beads are the same size, mb is less for lead, and once again, A is smaller.
If the fluid happens to be air, the mass of air displaced is trivially small compared to either bead, and we could approximate it as zero. The lead bead and the tungsten bead appear to fall at the same rate. If the fluid happens to be water, the mass displaces is non-trivial and a tunsten bead sinks faster than a lead bead.
Before a physicist jumps in here, I know I'm using "accleration" to mean faster (when it really means it gets fast faster). I'm also ignoring friction, viscosity, compressabilty of the fluids, and a bunch of other stuff that are only second-order effects, but I'm trying to keep it simple.
Talked for while with an old friend last night.
He's a metals guy.
He has some tungsten.
Bottom line, it's way too hard and too expensive for the hobbiest to work with in it's solid form. Buying cones and beads ready made is cheaper, much cheaper. Even the never give up do it yourselfers like me would be better served working on sourcing ready made products that making them yourself.
The only place where he saw possibilities for those of us with the make it ourselves genes was in the area of combining tungsten powders into various epoxies and compounds. Apparently this is being done more and more.
Tungsten powder is still prettty pricey, though. It does tend to mix and suspend well in other materials. He felt that there could be a hot glue mix possible, which I'm keeping an eye out for. That would work very nicely in several different applications.
If any of this goes anywhere, I'll post it here. If any of you run accross tungsten powder at any kind of price, please let me know. I'm looking for some kind of baseline on it.
Thanks,
Buddy
Thanks redietz! That was the post I'd been hoping for since this discussion began. :)
I've got some tungsten putty (tungsten suspended in a polymer) that I'm pretty happy with on my leader. I now wondering whether I couldn't apply it directly to the hook before tying, hit it with some CA glue, wrap it well and have a nicely weighted underbody.
The extensive discussion concerning hydrodynamics and Newtonian physics was interesting but I would suggest looking at the specific gravities of some metals. What immediately comes to mind is that plain old copper wire is only 20% lighter than lead. It will be more difficult to wrap on a hook shank but you can just double up on the number of wraps of finer wire. Also, if you want to exactly match the density of lead, gold is nearly perfect.
Regarding lead dumbbell eyes I've used plain plated steel bead chain. Flies I've tied for Alaskan Silvers the bead chain versions have actually proved themselves with the added benefit of not getting hung up on the bottom as much.
Ray,
I get you. In fact, after reading all of this, I'm pretty sure that Tungsten is something I'm not going to play around with myself. If I need it, I'll just buy it ready made.
But the discussion has been fascinating, at least to me. I knew how to work with lead. I can turn brass, but brass beads and cones are so cheap it's not worth the effort or time. Now I know something else I didn't know.
Not a bad result for a couple of minutes reading in January. The level of experitise that shows here on a wide range of subjects is impressive.
Buddy