TexasMac's Web Site
By Wayne McLerran
Updated 4/12/20

Before I get to the main subject of this article the reader should understand the
difference between firearm accuracy and precision.  When shooting and
measuring the resulting group spread most shooters including myself tend to
incorrectly refer to a small group size as an indication of accuracy, i.e., it’s a
very accurate bullet or load.  What we correctly mean is it’s a very precise bullet
or load.  Simply put, the ability to hit the intended target is a measure of
accuracy.  The group size is a measure of precision.  I.e., in terms of hitting a
bull's-eye, accurately hitting the target means all the hits are grouped around the
bull’s-eye.  Precisely hitting a target means all the hits are tightly grouped even
if they are far from the bull’s-eye.

So now with the above understanding let’s get to the main subject, barrel
vibration, which directly affects shooting precision not accuracy.  If you’ve been
shooting and reading shooting articles any length of time you’ve no doubt run
across the term “barrel harmonics”.  Similar to when a guitar string is plucked;
when a rifle is fired the barrel vibrates along its length due to standing waves
collectively known as barrel harmonics.  There are many standing waves that will
fit in a rifle barrel.  The longest wave that fits is called the fundamental or 1st
harmonic. The next longest wave that fits is the 2nd harmonic and so on.
Notice that to “fit”, the wave length of the 2nd harmonic must be half the length
of the first harmonic. The wave length of the third harmonic must be a third the
length of the first harmonic, and so on.  The trick is to find the barrel locations
where most or all the standing waves cancel themselves out, referred to as
“sweet spots” for this article.  By the way, several techniques are used to
minimize the effects of barrel harmonics on the bullet as it exits the barrel
including changing the load configuration, “free floating” the forearm from the
barrel, using an adjustable weight at the end of the barrel (Browning Boss
system), etc.  But don’t confuse the term “sweet spot” in this article with finding
the sweet spot when “tuning” a rifle or a load for a specific rifle.

Update 4/12/20
The example above, known as a closed boundary system, is not technically
correct.  A rifle barrel is better described as an open boundary system with one
open end so any standing waves end at the muzzle in an antinode rather than a
node.  Here’s a good short YouTube video correctly illustrating how it works:

Cross sticks are used in BPCR matches to rest the forward portion of the rifle
when firing.  Although a good argument can be made for resting a true free-
floating forearm on the sticks nearly everyone rests the barrel on cross sticks
since many BPC rifle forearms cannot easily be free floated.  Also, due to the
barrel weight of typical BPC rifles, resting the forearm on the sticks would put
the balance point at or in front of the sticks and negatively affect the stability of
the hold.  With the barrel resting on cross sticks a vibrating barrel will tend to
bounce off the sticks unless the barrel is resting at one of the sweet spots.  
Watch the barrels at a match when some of the rifles are shot.  Some will
bounce a good bit up off the sticks while others will only slide back.  When
you’re shooting ask your “spotter” or someone close to watch your barrel.  
Although the barrel deflection may be the same from shot-to-shot, a bouncing
barrel can only have a negative effect on shot precision.  The goal is to
determine and mark the sweet spot or resting point so the rifle only slides back
due to recoil.  So how does one determine the sweet spot?  There are several
techniques.  Depending on your rifle and barrel configuration, some may work
better than others.

Remember, barrel harmonics as earlier defined consists of various standing
waves.  The rifle can be fired or we can induce the standing waves and use the
results to identify the sweet spot.  By the way, since none of my rifles have a
full octagon barrel I have not verified that the talcum powder technique below
will work.
• Talcum powder:
If the rifle has a full octagon barrel, sprinkle talcum powder along the top flat
and fire the rifle off hand.  Look at the powder pattern, it should be lined up like
this >>>>>>>>>><<<<<<<<<<.  The spot where the powder lines reverse is the
sweet spot.  Of course very light or no winds are necessary for this method to
• Measuring the barrel:
If the barrel has no taper and is either uniformly round or octagonal; measure the
distance from the front of the action to the muzzle, divide by 4.  The result
indicates approximately how far back the sweet spot is from the muzzle.  This
definitely worked on my Stevens 44 with a uniform round barrel which is used
for 22 BPCRA.  The same location was confirmed using the dancing wire and
stethoscope methods.
• Dancing wires:
Clamp the receiver in a vice, padded of course, with the barrel horizontal (level)
and hanging out in space.  Find a source of thin, bare wire and cut it into pieces
about 5" or 6" long.  The thinnest wire you can find that is lightweight but will
hold its shape when bent.  A good source is the copper wire out of four-
conductor telephone cable; the stuff that’s stung throughout your house to all
your telephones.

Bend the lengths of wire into U-shapes (like a fence staple) with long legs.  The
U-shape should be slightly wider than the barrel so the legs are not tight on the
barrel but long enough that they hang down and have no tendency to roll off the
barrel.  Place the wires along the barrel about every inch.

Now start tapping the barrel just in front of the forearm to set up the vibrations,
just hard enough to make the wires start to dance.  As they dance they will
move up and down the barrel.  After a good bit of tapping they should have
collected into two or more groups.  These are the vibration dead spots (sweet
spots) of the barrel and theoretically should be the best places to rest the barrel
on the sticks.

I expected this technique to be the most accurate but based on the results it was
not.  I tried it on 3 rifles as displayed in the following photos.  It worked fine
and agreed with the other techniques used on the Stevens 44.  The location
results were ¾” off the stethoscope method on the Sharps and off by 2” on the
Browning.  And for some reason the Browning sweet spot locations were less
conclusive using this technique.
• Feeling the vibrations:
Hold the rifle vertical by the stock wrist with the barrel hanging down.  Using a
wooden mallet, piece of dowel rod, or a wooden hammer handle; tap along the
length of the barrel.  You should be able to feel the vibrations.  The point of
minimum vibrations is the sweet spot.  This works but does not identify the
sweet spot as accurately as the following technique.
• Stethoscope method:
If you have a stethoscope handy or can borrow one, the following is a version of
the previous technique and is the easiest and by far best method in my opinion.  
Clamp the receiver in a vice and place the stethoscope on a portion of the barrel
above the forearm.  Using a wooden mallet, piece of dowel rod, or a wooden
hammer handle, lightly tap along the length of the barrel.  You will easily hear
the pitch of the ringing change from a hollow sound to a lower frequency or dull
thud which identifies the sweet spot.  Leveling the barrel is not necessary.
Here’s a good video on the technique in which the presenter used a microphone
taped to the barrel rather than a stethoscope:

A less accurate version of this technique is to place the stethoscope against the
end of the muzzle while lightly holding the rifle vertical by the front sight or
muzzle with the butt stock resting on your foot or carpeted floor.  Lightly tap
along the barrel to identify the sweet spot.

If you’re unsure if the method you choose has correctly located the sweet spot,
try another.  They should approximately agree.  If not I’ve found that the
stethoscope method is the most accurate.  Once the sweet spot is identified,
mark it by placing a piece of tape at the location and test it under actual match
firing conditions with the help of someone watching the barrel.  If the barrel still
tends to jump a bit off the cross sticks adjust the resting location slightly
forward or rearward of the tape location.  Once the location is firmly identified,
measure and note the distance to the muzzle since the tape will tend to wear off
or come off with cleaning solvents and oil.  Using masking tape I’ve painted a
ring around the barrel of my rifles using paint impervious to cleaning solutions.

Wishing you great shooting,