Angle, Cosine and the Airgun Hunter

Today is an amazing time to be an airgun hunter. With the availability of reasonably priced airguns (specifically Pre-Charged Pneumatics, or “PCP’s”) that are not only powerful but amazingly accurate, and a wide range of optics to choose from that have been purposely designed for airgun use, the last decade has seen the effective range of airguns basically double: Hearing an airgun hunter speak of a successful 110 yard shot is no longer uncommon! (and in some instances, even believable, lol). In consideration of these increased ranges, new challenges to accuracy must be understood and overcome by the airgunner in the field.

For airgunners that find themselves hunting in hilly country as I often do, shot angle can greatly affect the point of impact of our pellets at these new “modern” airgun hunting distances. With this in mind, an airgunner must understand that due to the relatively large, arcing path of our projectiles caused by the low projectile speeds generated by our favorite hunting arms, knowing your individual airgun’s performance, accurate range estimation and shot correction are all critical to success in the field. In fairly extreme cases of high-angle, long-range (for airgunning) shots, the pellets point of impact can be significantly affected.

As an example, where I hunt Jackrabbits in the Arizona desert it is not uncommon to be presented with the following shot: A Jackrabbit at 80 yards distance as measured by use of a traditional rangefinder, but is 27 yards BELOW the shooter in elevation (See fig. 1, below).




Let’s assume that for this shot, the airgun hunter in fig. 1 is shooting a .22 caliber airgun that is sending out a 14.3 grain pellet at 825 FPS (a “middle of the road” pre-charged pneumatic rifle, if you will). If our theoretical shooter aims for the jack’s head at the 80 yard shot as told to him by his trusty rangefinder, the pellet’s path will only horizontally cross 75.2 yards of the earth’s gravitational field, leaving it to hit +2.07″ above the point of aim, completely missing his intended target!

To resolve this issue (and make a clean, ethical shot) we need to not only know the angle of the shot (which in this example happens to be 20 degrees), but properly adjust for it. To do this, the airgun hunter needs the following three pieces of information:

  • The trajectory of his pellet,
  • The range to his intended target,
  • The angle of the shot, and it’s cosine.

Pellet Trajectory Knowing the point of impact of your pellet at various ranges is one of the most critical components of successful airgun hunting! In the not too distant past, to learn the trajectory of a given airgun shooting a certain pellet, an airgunner would have to shoot at multiple yardages (20, 30, 40, etc) and measure the point of impact at those yardages to “chart” the trajectory path of his pellet. Though this is still a very accurate method, it is very time consuming and therefore rarely employed by the average airgun hunter.

Airgunning, like many other sports and hobbies, has recently benefited from software applications that allow information to be available to the user that was at one time only available to ballistics engineers and top trainers. Hawke Sport Optics provides an incredible freeware program, ChairGun Pro (Click this link to download) that is highly useful to the airgunner for determining the path of his pellet. The use of this software is beyond the intent of this article, but a quick search of the Yellow Forum ( for “Chairgun” will return hundreds of useful threads regarding it’s use and application.

Range Estimation The ability to accurately and quickly estimate the range to an intended target is one of the most critical skills that an airgun hunter must master. Many optics manufacturers such as Nikon, Leupold, Leica and Bushnell offer electronic rangefinders in the $150-$750 range that work well for airgun hunting.

Author's antiquated, yet trusty mechanical "coincidence" rangefinder, a Ranging Model 200 popular in the early 1990's prior to the availability of affordable laser rangefinders. It's accurate, fast, easy to use and completely overlooked by the majority of airgun hunters as a cheap, yet effective ranging tool.

Laser rangefinders are surely the most popular in use, but the airgun hunter that does not actively use them to sharpen their own range estimating skills is missing out on an opportunity to become an even more efficient hunter.

Shot Angle There are several manufacturers of both angle and cosine indicators that will allow the shooter to have the proper information required to compensate for this rule of simple physics  ( Once the airgun hunter can determine the angle of the shot, the COS(angle) Chart (fig. 2, below), will quickly provide the necessary cosine to apply to the ranged yardage. In use, a hunter can quickly become comfortable making these adjustments and add it seamlessly to his standard pre-shot preparations.

FIGURE 2, COS(angle) Chart -Author's Note: all cosines are rounded to the nearest .01th for ease of calculation in the field.

(An important note to remember is that it does not matter if the shot is uphill or downhill, the effect on the pellet’s impact is identical -the point of impact will be higher than the point of aim: On either shot, uphill or downhill, the actual distance that the pellet travels as relative to the force of gravity will be shorter than the measured distance to the target, hence the higher point of impact and need to compensate to correct this.)

Now armed with his pellets trajectory path, the range to his intended target and both the angle of the shot and the the COS(angle) Chart provided in fig. 2 above, our airgun hunter can properly adjust for this extreme shot angle simply by multiplying the ranged yardage by the angle’s cosine as follows:



As illustrated in fig. 4 below, our airgun hunter used the simple formula above to correctly adjust for the extreme angle of his shot and shot for an adjusted distance of 75 yards rather the 80 yard shot as measured with his rangefinder.


As in the example above, an airgun hunter that puts the effort into not only knowing his rifles performance (exact point of impact at various yardages being key) and makes an effort to understand the mechanics that affect his pellet’s flight path will be rewarded with not only the regular satisfaction of properly placed shots, but also with increased opportunities to take game when confronted with more difficult shots.


About azairgunner

is an architectural designer living in Scottsdale, Arizona with a love of all things air powered and accurate. You can find him in the foothills of the Sonora Desert with a .25 caliber PCP slung on his shoulder, Nikon DLR hanging from his neck and a big smile on his face as he re-lives wandering the Apache-Sitgreaves forest with a Crosman 760 as young boy always wondering what adventure lied just over the next hill. J.K. Chlarson is also a contibuting writer at the free online magazine, readers can follow this link to visit:
This entry was posted in Airgun hunting, Chairgun Pro, Cosine, inclined fire, Uncategorized. Bookmark the permalink.

3 Responses to Angle, Cosine and the Airgun Hunter

  1. Chris__Colorado says:

    Cool article.
    Check this out tool which does the math for you to determine horizontal distance.

    • azairgunner says:

      Chris, there are a few of the laser rangefinders that calculate the angle cosine for you. I believe the Nikon bowhunter “Chuck Adams” signature model does out to a limit of 80 yards. Pretty handy.

  2. Pingback: Crosman Social Marketing Manager Hinting at BIG 2011 SHOTSHOW Product Release of NEW AIRGUN | azairgunner

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s