Air Density and Bullet Performance
By: Daniel Lilja
Primarily the concern of long-range riflemen, air density is a factor that affects all bullets. As soon as a bullet leaves the muzzle it starts to slow down in velocity and also begins to drop. The reason for the velocity loss is of course drag caused by the air and the drop, by gravity. Gravity is constant, but air drag varies with air density.
The density of the air into which we fire our bullets has a similar but opposite effect on airplanes. That is an airplane performs more efficiently in terms of lift in dense air. If it has a carburetor engine, it produces more horsepower in denser air. Bullets, on the other hand perform better in less dense air. The performance of both is predictable if the density of the air is known and the performance characteristics of the bullet or airplane are known under standard conditions.
The performance indicator of a bullet is its ballistic coefficient. Ballistic coefficient describes a bullet’s ability to resist drag caused by the air. If the ballistic coefficient and muzzle velocity, are known, the downrange bullet performance can be predicted by modifying the ballistic coefficient from standard air density conditions to those of the present air density.
The ballistic coefficient of a bullet for standard conditions is available from the bullet manufacturer. It can also be determined from actual firing tests using two chronographs. Ballistic tables based on G1 or Ingall’s tables use as standard conditions, 29.5275″ of pressure, 59 degrees F., and 78 percent humidity at sea level altitude, often referred to as Standard Metro. These are the standard conditions used by Sierra and Hornady bullets. Speer Bullets and Nosler Bullets have used the International Civil Aviation Organization, (ICAO), standards of 29.921″ of mercury, the same temperature of 59 degrees F., and zero percent humidity at sea level. The difference results in a minor change in ballistic coefficient of less than two percent.
Air density can be measured relatively easily. The factors that determine the density are barometric pressure, air temperature, and relative humidity. Using formulas that will be described later, the ballistic coefficient of the bullet will be modified to account for the changes in air density.
The effect of humidity is negligible and can for most practical applications be ignored. For example, an extreme change from one percent relative humidity to 100 percent changes the ballistic coefficient by only about one percent. The reason for this is probably that when the air is 100 percent saturated with water vapor it still contains only four percent water vapor. Absolute barometric pressure (including altitude changes) and to a lesser extent air temperature, on the other hand, can have a much greater effect.
Barometric pressure is measured in inches of mercury, or in the metric system, in millibars. As mentioned above, the ICAO recognizes 29.921 inches of pressure and 59 degrees Fahrenheit as standard conditions for sea level.
Barometric pressure is constantly varying with changes in weather systems. Absolute barometric pressure also varies with elevation. Our atmosphere can be looked on as a very tall column of air. This column behaves of course, as a gas and is compressible. For this reason the pressure must decrease with elevation. It is the most dense at sea level. An increase in 1000 feet elevation will decrease the pressure approximately one inch. The actual, uncorrected for altitude, standard pressure for 1000 feet above sea level would be about an inch less than sea level. Actually it is 28.67″. This is sometimes confusing because local weather stations always give the barometric pressure as if it were at sea level. That is, a value is added to the uncorrected pressure or absolute pressure, depending on the local altitude, to make the pressure reading comparable to sea level pressures. The value that is added is also dependant on humidity, day and night average temperature, and local anomalies.
As stated above, the standard temperature for sea level is 59 degrees Fahrenheit. Standard temperature also changes with elevation, decreasing as elevation increases.
A decrease in barometric pressure reduces the density of the air. A decrease in temperature though, has the opposite effect, increasing air density. The rate at which altitude change decreases the density of the air, is greater than the effect of colder temperatures increasing the density, with the same altitude changes. As a result, the overall air density decreases with altitude under standard conditions.
The instruments used to measure air density can be a standard thermometer and a barometer. If the shooter lives close to sea level a standard household barometer can be used to measure pressure changes. For someone living in mountainous country though, the standard barometers do not have enough range to measure the changes. There are two ways around this. One is to obtain a barometer that reads in absolute pressure, that is, uncorrected for altitude. The other is to use an altimeter which is actually a wide ranging aneroid barometer that reads in feet instead of inches of mercury.
As mentioned above there are formulas for modifying the ballistic coefficient of a bullet with changes in temperature, barometric pressure and altitude. The Sierra handloading manual has a good section on this subject and I will present their formula. It is: Ceq = Ft x Fp x Fa x Co Where: Ceq is the equivalent ballistic coefficient for the current conditions, Ft is the temperature correction factor and is found in the formula Ft = 1 + (T-Tstd)/(Tstd + 459.4)
Where: T is the actual temperature in degrees F. and Tstd is the standard temperature for that altitude.
Fp is the pressure correction factor and is found in the formula Fp = 1-(P-Pstd)/Pstd
Where: P is the actual pressure and Pstd is the standard pressure for that altitude.
Fa is the altitude correction factor and is found in the formula Fa = 1/(e^-hy)
Where: h = 3.158 x 10^-5 y = the altitude in feet
(This formula for Fa is not in the Sierra manual. They list a table of factors in 1000 feet elevation increments. The results are the same with this formula and it can be used for any altitude.)
Co is the ballistic coefficient for standard sea level conditions as given by the bullet manufacturer.
From this formula we can see that with all of the air density elements taken into consideration, the ballistic coefficient of a bullet will have a higher value for air of less density than standard, and a lesser value for air of greater density than standard.
If using these formulas to change the ballistic coefficient in conjunction with an exterior ballistics software program, the modified ballistic coefficient should be entered into the program and the altitude and temperature inputs left at standard sealevel conditions. An easy method of entering non standard local barometric pressure variations is to simply change the altitude being entered. Remember that an inch of pressure change is worth about 1000′. As pressure goes up, altitude goes down.
Using an altimeter is actually a much simpler method for measuring current barometric pressure. In determining long-range trajectories with most commonly available exterior ballistics software, two of the input variables are temperature and altitude. Both are easily measured.
Referring again to the similarities between airplanes and bullets, what we are really looking for is, in aviation jargon, density altitude. Density altitude is the altitude corrected for local barometric pressure and temperature.
How is density altitude computed? Again, it is a simple procedure. First we need to correct the altitude for local variations in barometric pressure. To do this, the pressure altitude is determined by setting the standard pressure of 29.92″ into the altimeter. That is you are “fooling” the altimeter into thinking that the current barometric pressure is standard as opposed to the actual pressure. The altimeter will then read the pressure altitude for those conditions. For those not familiar with altimeters, this may sound complicated, but it is really a very common and simple procedure used by all pilots. Now that we have accounted for local pressure, we need to consider the temperature effect.
This is also a simple calculation requiring the use of a flight computer. A flight computer is a handy slide rule type computer. It can determine a number of things for a pilot such as wind vectors, fuel remaining, time to destination, etc. For our application, though, we are interested only in the density altitude portion of the computer. In addition to slide rule type flight computers, small electronic pocket type calculators are available. They perform the same functions. In use the pressure altitude is entered into the computer along with the current temperature and the output is the density altitude.
As an example, let us say we are on a rock chuck hunt at an elevation of 4500 feet on a nice warm June day of 70 degrees F. We want to know the effects of the altitude and temperature on our bullet. First we need to determine the pressure altitude. There is a high pressure system developing over our area and the barometric pressure is going up. Because of this our pressure altitude is 4250 feet, determined as described above. Combined with a temperature of 70 degrees our density altitude is 5920 feet. That is to say the bullet would perform the same as if it were fired under the standard temperature and barometric pressure for 5920 feet elevation.
As an example of the difference in drop from an elevation change of 4500′ to 5920′, let’s take an 85 grain Sierra HP BT bullet with a ballistic coefficient of .279, from a 240 Weatherby cartridge at a muzzle velocity of 3500 fps. The difference in drop figures is not significant until the range is out to 1000 yards or so – about 17 inches difference. At that range and beyond however the difference becomes greater. With a bullet of higher ballistic coefficient, the effect would be less.
A solution to knowing the drop for the bullet at varying ranges, then, is to have available several drop charts calculated for different altitudes (at standard temperatures), for density altitudes that might be expected on the trip. For example on our rock chuck hunt we might have along drop charts for 4000, 4500, 5000, 5500, 6000, and 6500 feet. Using the altimeter, a thermometer and the flight computer, we would determine the density altitude. The bullet drop changes can then be read off of the correct chart for that density altitude.
Where can you get altimeters and flight computers? Take a trip down to the local airport and ask the fixed base operators what they have available. I talked to one FBO that said they had just recently sold at auction several altimeters for $20 apiece. Another had them for $50 to $75 on occasion and a salvage shop had overhauled and calibrated altimeters for $125. There are also non aviation altimeters available. I have a pocket size electronic altimeter that also reads the temperature and barometric pressure (both corrected and uncorrected pressures) called an Ultimeter. They run about $170 and are made by Peet Brothers Co., of Ocean, New Jersey. Any FBO that offers flying lessons will have flight computers. They range in price from about $25 to $75 for the electronic calculator type.
Predicting bullet drop at long range is really not as difficult as it may seem at first glance. The effects of air density changes become much more pronounced at long range. Using the methods described here, some of the guess work can be eliminated.
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