Ballistic Effects of Altitude, Temperature, and Humidity
By: Daniel Lilja
At a match recently I overheard another competitor comment that the wind seemed to be blowing the bullets more than usual that day. He suggested that the humidity level must be high, that the air was “heavy”. I know that there have been days when it seemed to me that a little change in the wind caused a big change in the impact point of the bullet. Too often I noticed it on the record portion of my target. On other occasions I have fired a shot, only to look up and see that the wind flags were not in the position I thought they were when I pulled the trigger. Much to my delight though, when I looked through my scope the bullet went into the group.
The question then is, can changes in humidity or temperature or barometric pressure have an effect on the amount of bullet drift caused by the wind? The answer is yes. The measure of these three atmospheric conditions is known as relative air density.
How well a bullet will perform in the air is indicated by its ballistic coefficient and initial velocity. A typical 6mm, 68 grain bullet made on an .825″ length jacket with a 7 caliber tangent ogive has a ballistic coefficient of about .265.
Usually ballistic coefficients are based on the “Standard Metro” sea level atmosphere. This atmosphere has a barometric pressure level of 29.53″, a temperature of 59 degrees F. and the humidity is 78 percent. There is also another recognized standard atmosphere referred to as the “ICAO” International Civil Aviation Organization standard atmosphere. It also is at sea level but the barometric pressure level is 29.92″, the temperature is also 59 degrees and the humidity level is zero percent. As mentioned above though, most ballistic data is based on “Standard Metro”.
If any of the above components of air density are changed, the density and relative speed of sound will change as well. Fortunately we can simulate these changes and the resultant change in down range ballistics, by using a modified ballistic coefficient for the particular bullet.
For example a bullet with a ballistic coefficient of .265 could perform as though it had a ballistic coefficient higher than .265 under certain atmospheric conditions. That would mean that it would shoot flatter and be affected less by the wind.
Often this is exactly the case. When the temperature is above the standard of 59 degrees and the other conditions remain the same, the air density decreases. The same is true if the barometric pressure decreases or the elevation increases. We will get into more on barometric pressure and elevation later.
Contrary to popular opinion, an increase in the humidity level actually decreases the air density. That sticky, humid air is not really “heavy” air after all. Hard to believe? It is true and the reason is that the molecular weight of dry air is greater than that of water. This information can be found in the CRC HANDBOOK OF CHEMISTRY AND PHYSICS. The book is not hard to find, my small town library has it. There is also a brief explanation of this in the exterior ballistics section of the third edition of the Sierra reloading manual. As we will see later though, of all the air density components, a change in the humidity level has the least effect.
Though they are two different terms, barometric pressure and altitude are very closely related. As mentioned earlier, the standard pressure at sea level for “Standard Metro” is 29.53″. Any change in altitude will also cause a change in pressure. The function of an altimeter is based on this principal. The actual change in pressure is about one inch of pressure per thousand feet of elevation change. The pressure decreases as elevation increases.
This can be confusing, because if you live at 2000 feet elevation and you have a household barometer, it will usually read between 29.5″ and 30.5″. If the pressure level dropped as it should, then the barometer should read about 2″ less than that. In fact, it does. The true uncorrected barometric pressure would be 2″ less at that altitude. Increasing or “correcting” the pressure level by these 2″ allows local weather forecasters and others to compare a standard throughout the world. Reported pressures related to weather and aviation use the “ICAO” standard of 29.92″ but the difference between this and ‘Standard Metro’ is not very significant. It amounts to a difference in the ballistic coefficient of less than two percent.
In order of magnitude, a change in altitude has the most effect on ballistic coefficient, followed by temperature and then humidity. It is necessary to keep in mind though, that all of these components are inter-related. A change in one is almost always tied to a change in another. For example, if the temperature at the range goes up during the match it is probable that the humidity level will decrease. Barometric pressure changes occur more slowly, as a general rule, and an inch of change over several days means a major weather system is moving in or out of the area. Driving from one location to another in mountanous country can change the uncorrected barometric pressure very quickly.
To see how the effects of air density change the ballistic coefficient, I modified an equation that was in an article written by William C. Davis, Jr. in the March 1989 issue of the AMERICAN RIFLEMAN. There are also similar formulas in the Sierra handloading manual.
In the following examples, the sea level ballistic coefficient of .265 was used. Let’s see what the ballistic coefficient was during one afternoon at the 1990 NBRSA Nationals held at the Ben Avery range north of Phoenix. According to my AOPA airport directory, the elevation of the small airport 12 miles north of town is 1560′. For our example we will use the figure of 1500′ elevation for the range, not knowing exactly what it is. The temperature was around 95 degrees F. several days and the humidity was in the 20% range. Plugging these values into the formulas yields an equivalent ballistic coefficient of .301.
To see the effects of a humidity change, if the humidity level was actually 75% in Phoenix and the temperature stayed at 95 degrees, the ballistic coefficient would be .304. That is not a significant change, about 1%, but it is interesting to note that the ballistic coefficient increased with the more humid air.
Probably the most humid and hot conditions I have shot in were during the 1987 Nationals at Charlotte, North Carolina. The temperature was about 100 degrees and the humidity level not far behind, probably 90%. Charlotte has an elevation of about 750 feet. For these conditions the ballistic coefficient of that typical benchrest bullet would be .300, about the same as Phoenix. If we dropped the temperature in our simulation to 30 degrees at Charlotte and kept the humidity at 90%, the ballistic coefficient would be .256. This is a much more significant change, about 15%.
The range in Helena, Montana is just east of the continental divide at an elevation of about 5300 feet, just over a mile high. At a temperature of 70 degrees and humidity level of 25% the ballistic coefficient would be .330. That value is quite an increase over our sea level figure of .265, about a 25% improvement.
Interestingly, the temperature at this range would have to drop to 17 degrees below zero to bring the ballistic coefficient back to its original .265. Interesting except to those that live there, below-zero temperatures at this range are not uncommon during the winter months.
The Tacoma, Washington range is often very close to the standard sea level conditions of 59 degrees F. and high in humidity. Driving to the range, you drop down to within a few feet of Puget Sound. The ballistic coefficients here would not often be far off their standard values.
The obvious next question is, how much does a change in the ballistic coefficient have to be to alter bullet drop and wind drift? While both drop and drift are changed, in benchrest we are really only concerned with wind drift. If the 200 yard drop is affected, it is easy to change the elevation adjustment in the scope to compensate. Wind drift is not so easy to compensate for, though.
A bullet with a ballistic coefficient of .265 fired with a muzzle velocity of 3150 FPS, a reasonable figure from a 6PPC, would drift 1.05″ at 100 yards and 4.50″ at 200 yards in a 10 MPH wind.
In the same wind and with the same muzzle velocity a .300 ballistic coefficient bullet would drift .91″ at 100 yards and 3.93″ at 200 yards.
The .330 ballistic coefficient bullet would blow .81″ at 100 yards and 3.55″ at 200 yards with a 10 MPH wind and the same muzzle velocity.
Our cold Charlotte conditions and .256 ballistic coefficient would cause a drift of 1.09″ at 100 yards and 4.67″ at 200 yards.
In these examples, we can see that the same bullet under different atmospheric conditions would drift, at the most 1.09″ at 100 yards and 4.67″ at 200. This was Charlotte in the winter. Under the least dense air conditions in our examples, the bullet would drift .81″ at 100 yards and 3.55″ at 200 yards, Helena in the summer time. This is a difference of .28″ at 100 yards and
1.12″ at 200 yards.
The amount of wind drift a bullet undergoes is directly related to wind velocity. That is, if a 10 MPH wind will move a bullet one inch, a 20 MPH wind will move it two inches at the same target distance. Similarly a 5 MPH breeze would push it a half inch.
To summarize we have seen that changes in air density can have a somewhat significant change on the equivalent ballistic coefficient in extreme cases. A change in altitude will have the greatest influence followed by changes in temperature. Fluctuations in the humidity level will also change the air density and ballistic coefficient, but the amount is at most about one percent. Because humidity has such a small effect it can be ignored.
Increasing the temperature or altitude will increase the ballistic coefficient. Increasing the barometric pressure decreases the ballistic coefficient. It has the same effect as going down in elevation. Remember an inch of pressure is equivalent to 1000 feet of altitude.
Determining how much movement a particular condition is worth on the target is difficult at best. Firing a few shots on the sighter portion of the target during the “worst” wind can be helpful later in making a correct decision. Small groups can be the result of luck. Small aggregates however are the result of a good shooter properly shooting good equipment.