Topic
of interest: No. 19
Barrel
Length vs. Muzzle Velocity
It is a usually accepted fact that gun barrels of different lengths
will produce different muzzle velocities with the same load. Generally,
the longer the gun barrel, the higher the velocity...at least up to
a point. Only a few decades ago the common length of center fire rifle
barrels ranged from 26" to 30". These rifles were heavy and
unwieldy to carry around in the field all day. Today, the more common
lengths for sporting rifles are in the range of 22" to 24",
resulting in a lighter and more portable firearm. With this change many
shooters want to know just how much velocity is lost in switching to
the shorter barrels or how much velocity gain can be achieved in a longer
barrel.
It seems that little useful information can be gained by comparing
the muzzle velocities of two different rifles, of the same caliber,
but with different barrel lengths. Varying dimensions in the chamber,
throat and start of the rifling affect the velocity too much for a meaningful
comparison. The more obvious solution is to use a single rifle, cut
the barrel off, in given increments, and carefully measure the muzzle
velocity at each barrel length. Many experiments were performed using
this technique on both rifle and handgun. The problem was that the variation
in velocity, from shot to shot, with the same ammunition, was often
larger than any effect noted by shortening the barrel in 1" or
2" increments. However, if the data were plotted graphically to
smooth out the irregularities due to variations in velocity measurements
then a reasonable relationship between velocity and barrel length can
be shown.
Various mathematical equations were developed to relate muzzle velocity
to barrel length, but one of the simplest relationships was developed
by Homer S. Powley. He defined the relationship between muzzle velocity
and barrel length, as one giving muzzle velocity (v) as a function of
charge weight C, bullet weight B and expansion ratio (R). Here the expansion
ratio is defined as the ratio of the barrel volume plus cartridge volume
(total volume of the gun) to the cartridge volume. The equation relating
to these factors is represented by:
v

= K[C(1 R^.25)/ (B + C/3)]^.5 
Where, v is in f.p.s., C and B are in grains and K is a constant that
depends on chamber pressure and other factors in the gun. The expansion
ratio is dimensionless. From this equation, it can be seen that for
a given gun, with a given powder charge and bullet weight, the muzzle
velocity is dependent only on the expansion ratio. By cutting off the
barrel the barrel volume is reduced, thereby reducing the expansion
ratio. The relationship can be represented by:
F

= [(1R2^.25)/(1R1^.25)]^.5 
Where, F is the correction factor to correct the muzzle velocity at
expansion ratio R1 to that of the reduced expansion ratio R2 (shorter
barrel). For example, a rifle chambered for the .223 Rem. cartridge,
has a 24" barrel, and fires a 50 gr. bullet at 3,080 f.p.s. when
loaded with 25.1 gr. of IMR 3031 powder. The expansion ratio is 8.5.
What is the muzzle velocity if the barrel is shortened to 22"?
The new expansion ratio is 7.8. Plugging these values in the equation
we get:
F

= [(17.8^.25)/(18.5^.25)]^.5 

= 0.9846 
v

= 0.9846 X 3,080 

= 3,032 f.p.s. 
The new velocity for the 22" barrel is 3,032 f.p.s. The velocity
loss for removal of two inches of barrel is 48 f.p.s. (3,080  3,032).
The table below lists the velocity change for different barrel lengths
for several popular calibers.
Cartridge

Bullet Wt., grs.

Charge Wt., grs.

IMR Powder Type

M.V. in a 24” Barrel

Difference in velocity for a 2” change in barrel length,
f.p.s.

20”22”

22“24”

24”26”

26”28”

.223 Rem.

50

25.1

3031

3,080

46

48

42

38

.243 Win.

100

40.6

4350

2,920

56

50

45

32

7mm Rem. Mag.

154

66.8

7828

2,885

89

54

48

44

3030 Win.

150

32.4

3031

2,228

32

29

25

23

.308 Win.

150

40.5

4895

2,531

40

36

32

28

3006 Rem.

150

52.7

4320

2,770

50

44

39

35

.338 Win. Mag.

200

66.9

4831

2,684

52

38

41

37

.375 H&H Mag.

270

70.8

4320

2,460

39

41

35

28

.460 Weath. Mag.

500

96.0

4831

2,164

34

36

27

24

Note that the greater velocity increase, per inch of barrel length,
generally occurs in the shortest barrel length. As the barrel is lengthened
the velocity increase, per inch of barrel length, decreases. For instance,
the .223 Remington shows a 46 f.p.s. velocity increase by lengthening
the barrel from 20" to 22" This drops to 38 f.p.s. when the
barrel is increased from 26" to 28". Some of the magnum calibers
show more variation in velocity from barrel segment to barrel segment,
but the velocity change, per segment, is generally less as the barrel
is lengthened.
The powder charges and powder types shown in the table are for illustration
purposes only and are not to be used as load data. For details on loading
for a particular cartridge the reader should consult a good loading
manual or internal ballistics software program. The software program
offered at this web site will quickly calculate muzzle velocity for
any barrel length from 18" to 50".
Watch our web
site for the next topic of interest. Until then, shoot safely and
know where your bullets are going.
Sincerely,
The Ballistician
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