```From: ahahma@utu.fi (Arno Hahma)
Subject: Re: Barrels and rapid fire
Organization: University of Turku, Finland

In article <1993Jun19.234436.25614@btree.uucp> btree!hale@UCSD.EDU (Bob
Hale) writes:

#Ok, then I have to ask: why does a barrel get red-hot just short of
#the muzzle when it is rapid fired?  Obviously the muzzle end gets

For at least two reasons. The barrel is usually thinnest close to the
muzzle - less material to heat up. The bullet is moving at its fastest
near the muzzle. A portion of the heat comes from friction, but the
gases also do heat the barrel a lot.

#is higher when the pressure is that much lower.  It is also hard for me
#to believe that the specific heat of the gas is high enough to cause
#much heating of the barrel.

You forget the gas is under a very high pressure. It has quite a high
density and it is flowing fast with a turbulent flow. All that makes
the heat transfer efficient, although the gas has a low heat capacity
per unit volume. However, per unit _mass_ it certainly has a higher
heat capacity than metals do. When you fire the gun, all of the gas is
inside the barrel, i.e. as many grams as there was powder in the
chamber.

Consider also the energies stored in the moving bullet and the powder.
A typical .30 cal rifle will fire its bullet at a muzzle energy of
about 3 kJ. For that purpose, you burn up about 3 grams of powder,
which contains about 12 kJ of thermal energy. Where does the rest go?
Answer: to heating the barrel and to residual heat of the muzzle gases.
There is much more thermal energy available from the gases than from
the bullet.

#On the other hand, the velocity of the bullet is greatest at the
#muzzle.  It looks like the heating at the muzzle is due mostly
#to the friction between bullet and barrel.

You are correct, the bullet friction also heats the barrel and its
effect is largest at the muzzle. At the same time, the heating effect
of the gas gets lower, as the gas cools down due to expansion and the
pressure drops making the heat transfer less efficient. The heating due
to the gases is largest near the chamber, where you get the peak
pressure. This is also the location, where the barrel heats a lot, a
few centimeters from the chamber you will find a hot place. However,
that is also where you have the thickest steel to absorbe the heat.

If you doubt a hot gas flow can heat metals inefficiently, then how
about trying to heat a piece of steel with an oxyacetylene flame? When
powder burns under pressure, it generates 2300..2800 K and the gases
are under pressure of a few thousand bar. In an acetylene flame you
have 3400 K at 1 bar pressure only and you can weld with that...

ArNO
2
```

```From: sfaber@ihlpb.att.com
Subject: Re: Barrels and rapid fire
Organization: AT&T

#From article <93Jun21.214142eet_dst.30554-1@utu.fi>, by ahahma@utu.fi (Arno Hahma):
# In article <1993Jun19.234436.25614@btree.uucp> btree!hale@UCSD.EDU (Bob Hale) writes:

...
#
# #On the other hand, the velocity of the bullet is greatest at the
# #muzzle.  It looks like the heating at the muzzle is due mostly
# #to the friction between bullet and barrel.
#
# You are correct, the bullet friction also heats the barrel and its
# effect is largest at the muzzle. At the same time, the heating effect
# of the gas gets lower, as the gas cools down due to expansion and the
# pressure drops making the heat transfer less efficient. The heating due
# to the gases is largest near the chamber, where you get the peak
# pressure. This is also the location, where the barrel heats a lot, a
# few centimeters from the chamber you will find a hot place. However,
# that is also where you have the thickest steel to absorbe the heat.
#

I wonder why the friction effect would be largest at the muzzle.
The greatest force on the rifling would be at the pressure peak, and
the longitudinal friction would be constant or greater at the pressure
peak also if normal force due to the squeezing of the bullet is a
significant effect.  The amount of heat per unit length of barrel
due to friction then would be lower at the muzzle than at the pressure
peak.  The heat per unit time would be greater at the muzzle, but that
would just affect the localized temperature between bullet and barrel.
If this localized temperature increases the coefficient of friction
a lot, then I could maybe see why, but I don't know if there is any
evidence for that.

Some more data points:  According to one reference ( Lowry )
he indicates the typical energy lost to the barrel of a rifle is
around 10%, and the energy due to friction is 4%.   He said
that for shotguns heat lost to the barrel is quite a bit more
due to the longer time in the barrel.  Another reference (Hunt)
gave the 4% as a  standard estimate of friction  in large guns.
In pistols I believe the friction becomes a more dominant percentage
of the charge energy.

An approximation in some internal ballistics equations in Hunt
is that the heat lost to the barrel is proportional to the shot
energy.

Steve

```

```From: sfaber@ihlpb.att.com
Subject: Re: Barrels and rapid fire
Organization: AT&T

From article <1993Jun20.043341.19018@ncsu.edu>, by hes@unity.ncsu.edu
(Henry E. Schaffer):

#   Another thought on this topic - the temperature rise of the barrel
# is limited by the heat capacity of the hot gas in the bore.  Here
# are a few simple numbers and calculations:
#
#   Specific heat (cal/gm) Steel - .11; Air - .25
#   Density (gm/cc) Steel 7.8;  Air .0013 (at 0 C - so this is high)
#
#   Assume: Diameter of bore - .3"; Dia of barrel 1" so material volume
#   of steel:air is 10:1.
#
#   Then 10 x (7.8 / .0013) x (.11/.25) = 26,400  which seems to
# be how many degrees the gas in the barrel has to cool to raise the
# steel barrel one degree. If the gas starts out at, say, 4000 degrees
# then one shot would (according to this calculation) raise the
# barrel temp by 1/6 degree.  (This calculation doesn't seem to be
# quite right - I'd appreciate people reviewing this.)
#
#   However if each time the gas cooled down, it was replaced by more
# hot gas (another shot) then the heating up of the barrel would go
# faster.  Therefore the firing rate should be important.  It would
# also be nice to know how fast the heat was transferred from the gas
# to the barrel.
# # ...

I think the above calulation pretty well illustrates how not much
heating of the barrel can occur from the gases left at atmospheric
pressure between shots, even if you substitute the greater heat
capacity given below.

According to my calculations on heat capacity of the powder gases
at around 2800 deg K, the Cv= 8.5 cal/gram , (Thermo of Firearms by
Robinson).  This is quite a bit higher than your .25 value for air.

Here is a calculation:

Lets figure 13% of the powder energy heats the barrel for a Springfield
rifle ( from the Thornhill approximation if I did it right) and another
4% is contributed by friction.

If we have a 45 grain charge * 178 ft lbs/grain gives 8010 ft lbs

So 17% of 8010 is 1362 ft lbs of heat to the barrel.
Using the 8.5 cal/gram heat capacity of the gases (45 grains) gives
a temp drop of 421 degrees K.

The barrel weighs 2.875 lbs  and the heat cap. of the steel is
.117 cal/gram or so from my Machinists handbook, so for 1362 ft lbs of
energy, this gives a 2.9 deg K rise in temp.

I know that after firing 10 slow fire standing, 10 rapid fire sitting
and then 10 rapid fire prone, the barrel gets hot enough to boil water
which it did the last match when we were rained out.

If the barrel starts at 25 deg C and goes to 100 C it would take
26 rounds according to our calculation not allowing for any cooling.

So we are probably in the right ball park anyway.

Steve Faber

```

```From: sfaber@ihlpb.att.com
Subject: Re: Barrels and rapid fire - specific heats
Organization: AT&T

From article <1993Jun24.141120.28780@ncsu.edu>, by hes@unity.ncsu.edu
(Henry E. Schaffer):

# In article <C93755.6uz@cbnewse.cb.att.com> sfaber@ihlpb.att.com writes:
# ##From article <1993Jun20.043341.19018@ncsu.edu>, by hes@unity.ncsu.edu (Henry E. Schaffer):
# ## In article <1993Jun19.024352.20037@ncsu.edu> hes@unity.ncsu.edu (Henry E. Schaffer) writes:
# ##  ...
# ##   Specific heat (cal/gm) Steel - .11; Air - .25
#
#   In the old days (i.e. back when the reference I used at home was
# new, specific heat referred to the relative heat capacity compared
# to water - I think).
#
Right, so specific heat should be unitless, but since
the heat capacity of water is 1 cal/(gram*K) it turns out
the specific heat and heat capacity are the same if those
units are used.

# ##  ...
# #According to my calculations on heat capacity of the powder gases
# #at around 2800 deg K, the Cv= 8.5 cal/gram , (Thermo of Firearms by
# #Robinson).  This is quite a bit higher than your .25 value for air.
#

Sorry, the Cv=8.5 cal/gram was wrong and should have read
Cv= 8.5 cal/(mole*K).  Converting the units we get:

Cv=.335 cal/(gram*K) which is a lot closer to your values.

Jim Burns pointed out that my previous calculation was
inconsistent and this is why.  I did do the conversion
when figuring the gas temp drop, so that should be OK.

#   I obtained that value late at night and with a book I have at home.
# Let me see what I can find in "Mark's Standard Handbook for Mechanical
# Engineers" 9th ed.  Table 4.2.20 is Specific Heat at Constant Pressure
# (kJ/kg.K) of Liquids and Gases [where the . should be midway up between
# the g and the K].  At 300K it shows values of 1.021 for Air, .845 for
# CO2 and 4.179 for "Water substance".  At 500K (the hottest temp. shown)
# the values are 1.035 for air, 1.014 for CO2 and .159 for Water substance.
# Table 4.2.5 Mean Specific Heats of Various Solids (32-212F, 273-373 K)
# has a value for c, kJ/(kg.K) for Nickel steel of .46.

The term "specific heat" must have been used loosely here,
since they give the heat capacity in kJ/(kg*K)

Converting:  1.035 kJ/(kg*K) for air at 500K is   0.247 cal/(g*K)

and .46 kJ/(kg*K) for steel is  = 0.110 cal/(g*K)

so everything is consistent.

Steve Faber

```