TexasMac's Web Site
MEASURING & USING THE SPECIFIC GRAVITY OF
LEAD TIN ALLOYS
By Wayne McLerran
Technique Using the Wire Fixture to Measure SG
1.        Assuming the scale is warmed up and calibrated, install the
fixture and zeroing out the tare weight.
2.        Suspend the bullet on the hook using sewing thread or thin
monofilament line.  If everything is working correctly; the bullet should
weigh the same as when it’s placed directly on the scale platen.
3.        The bullet is then suspended in water by simply raising the cup
of water under the bullet until it’s fully submerged.  Make a mental
note of the “wet weight” reading while holding the cup steady and
ensuring the bullet does not contact the inside of the cup and nothing
touches the fixture.
4.        Using the dry and wet weights, determine the SG of the bullet
alloy.  Formula B applies for this procedure.  Using a dry weight of 427
grains and a wet weight of 389.3 grains, SG = 427.1 ÷ (427.1 – 389.3) =
427.1 ÷ 37.8 = 11.2989; rounded to 11.30.

Conclusion
Identical results were achieved by either technique.  No doubt
measuring the SG of very small or lightweight objects with a high
resolution scale would benefit from the increased stability when using
the wire fixture and water cup platform, but there’s no obvious
advantage to using the technique for bullet casting and lead alloy
applications.  Therefore the simpler procedure displayed in Figure 2
is the preferred technique.

Using SGs to Derive Alloy Weights & Mix
Using bullets from the two batches of alloy, 10 measurements were
made of each batch.  After tossing out the high and low values the
remaining 8 were averaged.  The alloy I had mixed turned out to have a
SG of 11.09, which equates to 22.8:1 with 4.2% tin, slightly off the goal
of 20:1.  The alloy that was reported to be 25:1 had a SG of 11.30,
equating to a lead/tin ratio of 136:1 and containing only 0.73% tin.  
Hence, my friends alloy was way off the mark of 25:1.  Using the
correct SG values and 427 grains for the 136:1 alloy bullet, the 22.8:1
alloy should cast a bullet of 427 (11.09 ÷ 11.30) = 419.06 grains; close
enough for government work to the 420 grains I had posted on the
forum.
Note - There is an excellent software-based casting alloy calculator
available that I highly recommend.  It offers several features including
the ability to compute the percentage of lead and tin in the alloy based
on SGs.  For more details on the calculator go to
http://tmtpages.
com/Alloy/alloycalc.htm.  I used it to quickly derive the lead/tin ratios
from the measured SGs.

For another example, let’s determine what a bullet will weigh if the
same mould is used but the alloy is changed.  So what will a 545 grain
bullet cast from 20:1 alloy weigh if cast with 30:1 alloy?  First calculate
the SG of the alloys using 11.345 for the SG of lead and 7.337 for the
SG of Tin.  By the way, it’s a common misconception that SGs of an
alloy can be accurately calculated by multiplying the weight or units of
the alloy elements by their densities or SGs; add the results and divide
by the total weight or units.  The correct formula is more complex and
is based on the reciprocals of the weights or units and densities or SGs.  
For example:
SG of 20:1 = 1 ÷ [20 ÷ (21 x 11.345) + 1 ÷ (21 x 7.337)] = 11.0574
SG of 30:1 = 1 ÷ [30 ÷ (31 x 11.345) + 1 ÷ (31 x 7.337)] = 11.1485
Notes - Depending on the source, published SGs of elements and alloys
will vary slightly but will be well within the accuracy required for bullet
casting.  And when solving the formulas above, remember to follow the
mathematical “Order of Operations” hierarchy, i.e. do things in
parentheses first, multiply or divide before adding or subtracting and
always go from left to right.

Knowing that a bullet cast with 30:1 will weigh more than one cast
with 20:1, the next step is to multiply the bullet weight by the correct
ratio of the SGs.  Therefore 545 (11.1485 ÷ 11.0574) = 549.49.  Hence
a 545 grain 20:1 alloy bullet will weigh approximately 549.5 grains if
cast with 30:1 alloy from the same mould and under the same casting
conditions.

Describing Lead/tin Alloys
Prior to closing this tutorial, I should mention there are several formats
used to describe lead/tin alloys.  Some shooters use all the formats
interchangeably which is incorrect.  Depending on the format used,
there is a difference in the alloy mix although it’s not large. The
following examples should help clarify the differences.

20/1, 20-1, 1/20, 1-20 or 1 in 20 implies 95.0% lead, 5.0% tin
19 units of lead + 1 unit of tin = 20 units of alloy
9.5 units of lead + 0.5 units of tin = 10 units of alloy

30/1, 30-1, 1/30, 1-30 or 1 in 30 implies 96.67% lead, 3.33% tin
29 units of lead + 1 unit of tin = 30 units of alloy
14.5 units of lead + 0.5 units of tin = 15 units of alloy

1:30, 30:1 or 30 to 1 implies 96.77% lead, 3.23% tin
30 units of lead + 1 unit of tin = 31 units of alloy
15 units of lead + 0.5 units of tin = 15.5 units of alloy

1:40, 40:1 or 40 to 1 implies 97.56% lead, 2.44% tin
40 units of lead + 1 unit of tin = 41 units of alloy
20 units of lead + 0.5 units of tin = 20.5 units of alloy

3/24/17 Update Information:
After experimenting with weight variations in cast bullets it became
clear that unseen voids in bullets have a direct affect on measurements
of specific gravity (SG).  As noted earlier, Archimedes’ principal, which
is the bases for SG measurements, states that “Any object, wholly or
partially immersed in a fluid, is buoyed up by a force equal to the
weight of the fluid displaced by the object”.  Therefore, since a bullet
will displace the same volume of water regardless of the size of
internal voids, SG measurements are inversely proportional to the size
of the void.  I.e. when using the air versus water weight technique, the
SG of a bullet with a large void will be lower than the SG of an
identical bullet with a small void.  Hence, the large void bullet
measurement will imply a smaller lead/tin ratio.  E.g. using a 530gr
bullet cast with 20:1 alloy, if another bullet from the same batch
weighs 529gr due to a 1.0gr void, the SG of the 529gr bullet will
suggest the alloy ratio is 18.6:1.  Therefore, when measuring SG to
determine the lead/tin ratio of an alloy, it’s wise to use bullets that
fall within the upper end of the weight spread, indicating minimum
voids.

Wishing you great shooting,
Wayne
Updated 3/24/17

The original article was published in the Summer 2014 edition (Issue
#86) of the Black Powder Cartridge magazine and is posted with
permission from SPG, Inc.  Please read the update information at
the bottom of the article prior to using this technique to determine
the lead/tin ratio of your bullets and alloy.

But before getting into the article and as a reference, listed below are
the specific gravity (SG) values of several well known bullet casting
alloys.  If you don’t have access to an alloy calculator such as the one
referenced in the article, once the SG is measured you should be able
to make a rough estimate of the lead/tin percentage from the
following values.

SG of pure lead is 11.3450
SG of 30:1 (lead/tin) is 11.1485
SG of 25:1 (lead/tin) is 11.1115
SG of 20:1 (lead/tin) is 11.0574
SG of 16:1 (lead/tin) is 10.9918
SG of pure tin is 7.337

Note - If there are elements in the alloy other than lead or tin the
above SGs do not apply.  Therefore the values cannot be used for
wheelweight alloys that contain antimony, arsenic or other stuff.  For
alloys containing only lead, tin & antimony here’s a link to an article
containing an excellent chart of SGs:
http://www.castpics.
net/subsite2/Classics/Determining%20Alloy%20composition.pdf

By the way, although I used a digital scale for the article, with a little
ingenuity a beam balance scale will also work
****************************************************************

You may be wondering what lead alloys and Specific Gravity have in
common and expecting you to remember back to your high school or
college general physics or chemistry class is probably a stretch,
especially for us older “codgers”.  So allow me to refresh your
memory.  Specific Gravity (SG), also known as Relative Density, is the
ratio of the density of any substance to the density of a standard
substance, water being the standard for liquids and solids.  To be
precise, the SG of a solid or liquid is usually measured at a temperature
of 20°C and compared to the density of distilled water at 4°C.  
Therefore a substance with a SG less than 1 will float on water, and
will sink if the SG is greater than 1.  We have the Greek
mathematician Archimedes to thank for discovering SG around 212 B.
C.  So what does SG has to do with lead alloys and bullet casting?

In many cases, using SG, the identity of an unknown element or simple
alloy components can be determined.  Examples are alloys of lead and
tin.  I was reintroduced to SG recently after posting on a well known
BPCR forum that a .40 caliber bullet cast from 20:1 (lead/tin) alloy
weighed 420 grains and the same bullet weighed 427 grains when cast
from 25:1 alloy.  Reading my post, an astute shooter and experimenter
with an engineering background took exception to the alloy mix versus
bullet weights and provided a convincing argument, using a simple SG
formula, that the increase in weight should be much smaller, only 1.35
grains to be precise.

For some time I’d considered purchasing or making a SG measuring
setup to confirm the purity of the lead and tin purchased and the mix
percentage of lead/tin alloys.  Until recently all my bullet alloys were
mixed from reportedly pure lead and tin, therefore a tester was not
essential.  Now the contents of two alloys were in question and SGs
were required in order to determine the actual lead/tin
concentrations.  Having mixed one batch from pure lead and tin I was
confident it was close to 20:1.  The other batch, reported to be 25:1
but now in question, was from a friend.  To determine the actual mix a
SG measuring setup was needed.

SG Measuring Techniques
Archimedes’ principal states that “Any object, wholly or partially
immersed in a fluid, is buoyed up by a force equal to the weight of
the fluid displaced by the object”.
 Therefore, depending on the
measurement technique detailed here, two formulas are applicable.  
Formula A: SG = weight of object in air ÷ weight of object in water.  
Formula B: SG = weight of object in air ÷ (weight of object in air -
weight of object in water).  To simplify the formulas the weight of the
object in air will be referred to as the “dry weight” and the weight of
the object in water will be the “wet weight”.  Hence, to obtain the
necessary values for the calculations, the object is 1st weighed in air
then weighed again while suspended in water, referred to as
hydrostatic weighing.  In theory this seemed easy enough but a digital
scale is required.  Ideally the scale should be capable of a resolution of
0.01 grains, but 0.1 grains is sufficient if a careful measurement
technique is used as explained later.

SG measuring setups are available from numerous laboratory
equipment manufacturers.  An example of one setup is shown in Figure
1.  But even simpler solutions will suffice for the bullet caster.  After
additional research I realized the platform shown in Figure 1 to hold
the cup of water is not absolutely necessary.  In fact a reasonably
accurate measurement can be made without the wire frame fixture to
hold the bullet or object.
Very Simple SG Measurement Technique
The simplest procedure uses a small container of water placed directly
on the scale platen.  The container should be as lightweight as
possible but large enough to hold a submerged bullet without the
bullet coming in contact with the container.  I used a prescription pill
container.  Figure 2 illustrates the 3-step measurement procedure.
1.        Assuming the scale is warmed up and calibrated, place the
bullet on the platen.  Measure and record the dry weight.
2.        Place the container of water on the platen and zero out the
tare weight.
Note - If the scale does not have a zeroing or tare weight feature, the
measurements can still be made but the scale must be capable of
accurately measuring the total weight of the container of water and
bullet to an accuracy of 0.1 grains minimum.  In this case the weight
of the container of water must be measured and subtracted from the
wet measurements.
3.        Using sewing thread or thin monofilament line, suspend the
bullet fully submerged.  Note the “wet weight” reading while ensuring
the bullet does not contact the inside of the container.
4.        Using the dry and wet weights, determine the SG of the bullet
alloy.  Formula A applies in this case.  Using a dry weight of 427 grains
and a wet weight of 37.8 grains, SG = 427 ÷ 37.8 = 11.2963; rounded
to 11.30.
Note - Although the test sample and faucet water will be at room
temperature, the resulting accuracy of the procedure will be sufficient
for our needs assuming the scale has a resolution of at least 0.1 grains,
several careful measurements are made and the results averaged,.  
Out of curiosity I did try very cold distilled water and there was no
measurable difference within the resolution of the RCBS scale.

Constructing a Test Fixture
Although the very simple procedure seemed to work fine, I wondered if
the wire fixture on the commercial setup shown in Figure 1 offered an
advantage.  Using it as a model, the fixture displayed in Figure 3 was
constructed.  It had to be sufficiently lightweight to allow zeroing out
its “tare weight”.  The fixture consists of a small cork, four pieces of
thin wire, a thin plastic disk from a compact disk container and a
lightweight plastic cap off an aerosol can.  The cap is slightly larger in
diameter than the scale platen.  It was cut down to the thickness of
the top of the platen and glued to the disk.  Although not absolutely
necessary, the cap centers the fixture and keeps it from sliding off the
platen.  The fixture is tall enough (8”) to insert a small handheld cup
of water under the bullet without spilling the water or touching
anything.  The space between the main support wires is sufficient to
allow entry of my hands while holding the cup.  The fixture weighs a
little less than 400 grains.