Please check this, somebody! - 04/02/03
In answer to an inquiry on "Ask Ken Howell," I wrote the posts copied below. The original poster isn't interested to this extent, but I still want to know whether my equation is sound -- so would appreciate confirmation or correction from someone who knows how to figure such things. STIA
-------------------------------------------
Pure lead weighs (nominally) 0.4096 pound per cubic inch. That's 0.4096 � 7,000 = 2,867.2 grains.
But your bullets -- cast or jacketed -- aren't all lead, so the workable weight per cubic inch is something less -- and I can't guess how much less. There's an equation for finding the weight of an alloy or heterogeneous bullet relative to the weight of the same volume of water -- by weighing the bullet suspended (by an essentially weightless thread or wire) in the air, then in water. Some of the better scales used to have a double hook on the beam and a beaker platform on the base for making these two weight measurements.
But I haven't seen that equation in decades, don't remember it, and don't know where to find it or how to derive it. I'm sure that some of the better educated guys here can supply or derive it and will post it here. (I hope so -- I've wanted to recover that equation, for lo! these many years!) If I find it, I'll post it. It may be more dependable than hardness for comparing cast-bullet alloys for their relative consistency.
-------------------------------------------
Well, FWIW, I think I've fingered it out. I'll give my reasoning, and somebody can check it for us.
Old Archimedes first figured-out that an object in a liquid is buoyed-up, supported, or "lightened" by a force equal to the weight of the liquid that it displaces. A bullet suspended in water, therefore, must weigh its weight in air minus the weight of the water that it displaces. Its relative density -- its weight in air divided by the weight of the water it displaces -- is therefore its weight in air divided by the difference in its two test weights.
If I'm right, then the "lost" equation is
x = a/(a-b)
if
a = weight of the bullet suspended in air
b = weight of the bullet suspended in water
x = specific gravity
The weight of the bullet per cubic inch, then, is the weight of a cubic inch of water (about 0.0361 lb or about 252 to 253 grains) times the bullet's specific gravity as determined above.
-------------------------------------------
Pure lead weighs (nominally) 0.4096 pound per cubic inch. That's 0.4096 � 7,000 = 2,867.2 grains.
But your bullets -- cast or jacketed -- aren't all lead, so the workable weight per cubic inch is something less -- and I can't guess how much less. There's an equation for finding the weight of an alloy or heterogeneous bullet relative to the weight of the same volume of water -- by weighing the bullet suspended (by an essentially weightless thread or wire) in the air, then in water. Some of the better scales used to have a double hook on the beam and a beaker platform on the base for making these two weight measurements.
But I haven't seen that equation in decades, don't remember it, and don't know where to find it or how to derive it. I'm sure that some of the better educated guys here can supply or derive it and will post it here. (I hope so -- I've wanted to recover that equation, for lo! these many years!) If I find it, I'll post it. It may be more dependable than hardness for comparing cast-bullet alloys for their relative consistency.
-------------------------------------------
Well, FWIW, I think I've fingered it out. I'll give my reasoning, and somebody can check it for us.
Old Archimedes first figured-out that an object in a liquid is buoyed-up, supported, or "lightened" by a force equal to the weight of the liquid that it displaces. A bullet suspended in water, therefore, must weigh its weight in air minus the weight of the water that it displaces. Its relative density -- its weight in air divided by the weight of the water it displaces -- is therefore its weight in air divided by the difference in its two test weights.
If I'm right, then the "lost" equation is
x = a/(a-b)
if
a = weight of the bullet suspended in air
b = weight of the bullet suspended in water
x = specific gravity
The weight of the bullet per cubic inch, then, is the weight of a cubic inch of water (about 0.0361 lb or about 252 to 253 grains) times the bullet's specific gravity as determined above.