Barrel Lengths & Velocities for the 50 BMG
By: Daniel Lilja
Bullet velocity is a very important ingredient of successful long-range shooting. This is especially true if that bullet also has a high ballistic coefficient. The higher the velocity, the flatter the bullet will shoot, with less wind drift, more energy when it reaches the target, and an extended maximum range. With a given case and bullet, there are just two ways to increase
velocity. One is to burn more powder, but exceeding safe pressures soon puts the brakes on that. The other option is to use a longer barrel (having no effect on chamber pressure), utilizing more of the powder gases. Adding barrel length is kind of like shifting a car into overdrive: more velocity for the same input.
There are a few drawbacks to choosing an extra long barrel, however. In the #1, 1994 issue of VERY HIGH POWER we looked at how barrel stiffness decreases with length, and as a result potential accuracy possibly degrades too. Also, the amount the rifle recoils while the bullet is still in the barrel increases. This can lead to poorer accuracy, because it becomes more difficult to consistently shoot the rifle with greater recoil movement. The presence of a muzzle brake has no effect on this recoil. And as barrel length increases, muzzle pressures decrease. Normally this would not be undesirable, but muzzle brakes become less effective with lower pressures.
Setting the negative aspects of longer barrels aside, I wondered how much velocity gain could be expected with longer barrels. Specifically, how much of an increase could be expected with each additional inch of barrel? To answer this question, I used two different internal ballistics programs that predict velocity as a function of barrel length. One of them utilizes LeDuc’s equation and was provided by Bill Davis of Tioga Engineering. His program also calculates muzzle pressure, and barrel time in milliseconds. The values for these two numbers in the accompaning chart are from this program.
For those not familiar with LeDuc’s equation, I’ll go into a little detail, but not enough to bore, I hope. A Captain LeDuc developed this formula just prior to the turn of the century, based on the simple theory that as a bullet travels down a barrel, its velocity increases and the amount of pressure behind it decreases, both exponentially. Some articles in other magazines have been published over the years about the equations. Most recently there was some good coverage of it in the January/February, 1994 issue of HANDLOADER magazine. LeDuc’s contribution to internal ballistics has been found by a number of authorities to be quite accurate in predicting velocities, often within a few feet per second. My own experience has shown it to be a reliable indicator, too.
The second internal ballistics program I wrote was based on an article written by Bill Davis which appeared in the NRA book, Handloading. The velocity calculations from these formulas apply only to IMR series powders. Bill Davis adapted Homer Powley’s slide rule type “Computer for Handloaders” into an equation workable with other applications. To be able to use this program with the 50 BMG case I extrapolated some information for IMR 5010 powder. Anyone interested in looking at all of the formulas and data may look up that article as well.
In actual practice both by myself and others, the data produced by both programs has proven to be an accurate predictor of velocities. In fact these programs are probably more accurate in predicting changes between barrel lengths, as opposed to actual muzzle velocities. To say that the numbers are exact would be foolish. But, to say that they are close would not be. However, anyone loading for a barrel the same length as one of those shown in the chart should not take these velocities to be the norm and try to reproduce them. Every rifle is a rule unto itself, and the common pressure indicators should be watched for closely whenever a new load is being developed. The inputs for both programs were the same, with a little juggling to get the initial velocity the same.
So now, looking at what I found, the greatest velocity change per inch came with the shorter lengths. Using a 28″ long barrel as a practical minimum length, I found that if we increased the length by one inch, on average we could expect a 19 – 21 fps gain in velocity. From the chart we can see that for barrels up to 34″ we can expect at least a 15 fps gain per inch. As barrel length increases , the rate decreases. (I ran the numbers for barrels up to 4 feet long.) At the longer lengths, each additional inch is worth 8-10 fps.
If we compare a 48″ barrel to the 28″ shorty however, we have increased our predicted velocity by at least 250 fps. When launching a high ballistic coefficient bullet of 750 grains or so, that extra velocity translates into big increases in downrange energy and big decreases in drop and drift. For example, if we compare the 750 grain Hornady A-Max bullet with a 2700 fps muzzle velocity from a 28″ barrel to the same bullet at 2950 fps from a 4 footer, we see some big changes.
To illustrate my point, I ran those velocities through an external ballistics program that computes drop, drift, remaining velocities, and energies. I used a C7 ballistic coefficient of .520 for this bullet. I prefer to use the C7 BC with the VLD type bullets as opposed to the traditional C1 BC because it was developed for long-pointed boattail bullets. As a result, the
ballistic coefficient changes much less with velocity than the C1 BC. When shooting at 1000 yards and farther, changes in a C1 BC due to decreased velocities down range can cause significant errors. The .520 C7 is roughly equivalent to a C1 of 1.05 at these velocities. We will compare the figures for both velocities at 1000, 1500, 2000, and 2500 yards. For this model I’ll use the standard sea-level atmosphere and a temperature of 59 degrees F. Most shooters are going to be firing at higher altitudes, but this compares apples to apples.
I’ve chosen 2500 yards as the maximum effective range, as that is about the range at which this bullet drops below the speed of sound. (The speed of sound is about 1120 fps at sea-level and 59 degrees F. It changes about 1 fps per degree, with the direction of the temperature change.) Other bullets with lower ballistic coefficients will be effective from about 1500 to 2000 yards.
When the velocity of a bullet drops below the sound barrier, accuracy is often wild. So it is generally accepted this this is the practical maximum effective range for any bullet.
If we compare the Hornady bullet at these two muzzle velocities, we find that the 2700 fps bullet will drop below the sound barrier at just past 2200 yards. The 250 fps faster bullet will remain supersonic out to a full 2500 yards. Almost 300 yards of effective range was added to the bullet because of the higher muzzle velocity. At 1000 yards, either load has plenty of energy, and actual drop isn’t as important as wind drift, in my opinion. The 2700 fps load will drift 37.7 inches at 1000 yards, but the 2950 fps bullet will drift about 33 inches, or 4.7 inches less. At 1500 yards the drift figures are 93.8 inches and 81 inches respectively. Converting drop figures (100 yard zero) to true MOA, we find that the slower bullet requires 45.3 minutes of correction. The faster bullet needs 36.8 minutes of up adjustment. Other comparisons can be made referring to the chart.
Using two proven internal ballistics programs, we’ve shown the amount of velocity increase that can be expected from longer barrels. Depending on where that length is added, we can expect from 10 to 20 fps per inch. Then using an external ballistics program, we were able to show quantitively what that increased velocity meant to downrange performance, including decreased bullet drop, less wind drift, and higher velocity and energy. A high ballistic coefficient bullet combined with high muzzle velocities can result in some very impressive downrange ballistics. And that is what long-range shooting is all about.
Velocity Changes Per Inch of Barrel Increase
NOTE: This chart shows the expected change in velocity for a change in barrel length of one inch. The first column represents the barrel length changing from the two lengths shown. The second column is the expected change per inch as computed using LeDuc’s equation. The third column represents the change as computed using formulas derived by Homer Powley and adapted for small arms internal ballistics by Bill Davis. The fourth column is the time it takes the bullet to travel to the shorter of the two lengths shown in the first column in milliseconds. The last column is the muzzle pressure for the shorter length.
Comparison of Hornady A-Max Bullet at 2700 FPS and 2950 FPS
Note: The drop figures are for a 100 yard zero and the adjustments are for a true MOA correction. Meaning that 1 MOA is equal to 1.047 inches at 100 yards. Not all scopes are calibrated for true MOA. The figure under the wind drift column is inches of horizontal movement.