So far we have been showing the bullet traveling in a straight path. We know that in reality it does not; gravity makes it take a curved path. We could ignore that in our calculations in previous articles because all our shots were at the same distance. We got our sights zeroed for 25 yards. What if we want to shoot at different distances? What if we do not know precisely the distance to a particular target? To solve these questions we need to understand:

- the bullet’s flight path – how gravity and air drag affect the POI at different distances;
- how the trajectory relates to our sighting system – how high our sights are above the bore;
- how flat a path we want the bullet to take within the bounds of its trajectory.

The combination of these three factors will tell us how best to adjust our sights.

# Trajectory

The expanding gas from combustion of the cartridge’s powder is the first force acting on the bullet, giving it forward motion which we measure as velocity at the muzzle. As soon as the bullet leaves the muzzle, there are two other forces that affect its path: gravity and air drag.

The general formula for air drag shown above says that drag is a function of bullet velocity, air density, the Drag Coefficient and the surface area of the bullet. Calculating the complex fluid dynamics of a bullet in flight is a challenge. Ballistics scholars developed a different approach known as the Ballistic Coefficient (BC) to replace the C_{d}A part of the formula. The ballistic coefficient takes into consideration the area, length, weight, and streamlining features of the bullet, and is based on empirical testing. It is further dependent on whether the bullet is supersonic or subsonic due to the effect of the acoustic shock wave. That wave is why supersonic .22LR ammo is usually less accurate beyond 50 yards than standard velocity. As the bullet transitions to sub-sonic speed, it passes through its own acoustic wave which upsets its stability slightly. The standard speed of sound (defined at sea level at a temperature of 15°C) is 1116 ft./sec.

The combination of drag and gravity gives the bullet a curved path. The picture below shows the trajectory of a .22LR bullet fired horizontally over 100 yards, as if the line of sight were parallel to the bore:

The acceleration of gravity is constant regardless of bullet mass or velocity. This means that all bullets fired horizontally from the same height will fall to the ground in the same amount of time. But a faster bullet will travel farther in that time than a slower one will. This is the basis of what we call a “flat-shooting” round – over a given distance, the faster bullet will drop less than the slower one because gravity has had less time to work on it. By “faster” we mean average velocity over the distance. A bullet with a higher ballistic coefficient will hold its velocity longer than a lighter or less streamlined bullet with the same muzzle velocity. In the chart below, the .22LR round with a BC of .13 and a muzzle velocity of 1070 fps covers 100 yards in 304 milliseconds. The .223 Remington (5.56mm x 45) with a BC of .27 and a muzzle velocity of 3240 fps covers the distance in 99 milliseconds. You can see how much flatter the .223 trajectory is.

The chart below shows the flatter trajectory of the CCI Minimag high velocity (1235 fps) round compared to the CCI Standard Velocity (1070 fps) round. At 100 yards, the Minimag drops 6.7” and the SV drops 9.2” from the 25-yard zero.

You can see that the trajectory is initially quite flat – within 1” from zero for the Minimag from 5 to 60 yards and the same for SV out to 50, but it drops rapidly farther out. At 150 yards the Minimag drops 21.8”, and at 200 a whopping 47.0” – nearly four feet. The .22LR bullet, with its low velocity and low BC, simply cannot shoot very flat much beyond about 50 yards.

There are several ballistics calculators available on the web which show charts and data as in the above picture. One of the most comprehensive and easiest to use is at http://gundata.org/ballistic-calculator/ and for consistency I have used its data throughout this article. Another good calculator is at www.shooterscalculator.com. In addition to graphs, the calculators provide data tables showing velocity, drop, energy and time for each distance within the total range. I left these out to save space.

Data on the ballistic coefficient of various bullets differ slightly among various sources. A few ammunition manufacturers provide ballistic coefficients for their products, but many do not. The manufacturer’s website for Federal Automatch gives a BC of .138. But Gundata shows a BC of .134 for this round. Practically, this is a trivial difference, resulting in a variance of bullet drop at 100 yards of less than 1/16”. I don’t know how accurate these databases are. Gundata shows a BC of .12 for CCI Standard Velocity and .13 for Minimags, although they are both the same weight and the SV has a more streamlined shape. It’s best not to get mired in the precision of internet specifications; you’re going to have to test your own ammo and rifle setup anyway. (Note: the difference in drop between BCs of .12 and .138 for the same velocity is less than ¼” at 100 yards.)

# Sight Height

If there were no gravity, and your sights were aligned parallel to the bore 1” above the bore’s centerline, your shots would impact 1” below the point of aim. To zero, you adjust the sights to raise the muzzle so that the path of the bullet would intersect the line of sight at your desired distance. Of course, if there no gravity, the bullet would never come back down.

The relevant sight height is the rear sight, because your eye pupil and the aperture of the rear sight are the two points that define your line of sight. The trajectory calculation uses the height of the rear sight and the distance from the muzzle to the target to calculate the angle of the bore. The Ruger OEM leaf sight is about .70” above the bore centerline. The Tech-Sights TSR 200 and the Nodak NDS-26 are about 1.3” above bore centerline. If you have a receiver sight or an optic you can measure the height of your sight above the top of the receiver (at the flat part, not where it curves downward toward the rear) and add .564” to get the sight height above your bore axis – at least according to the blueprint of the 10/22 that I have.

The basic variables in calculating trajectory are muzzle velocity, ballistic coefficient, sight height above the bore, and the zero distance. Additional variables can include wind speed and direction and elevation of the target relative to the rifle. (In this article, we ignore wind and target elevation.)

So we adjust the sights so that the muzzle is raised slightly relative to the line of sight. The chart below compares the Ruger OEM blade sight to the Tech-Sights TSR-200 using CCI Standard Velocity and a 50-yard zero. The bullet’s flight begins below the line of sight at an upward angle, and then comes down, as in the picture below:

The trajectory actually intersects your line of sight twice. We call these points the “near zero”, where the bullet is still rising, and the “far zero” where it is falling. In between these there is the top of the curve, called the “mid-range trajectory” (MRT) or “maximum ordinate”. These points describe how flat, or how curved, the trajectory is out to and slightly beyond the far zero range. Sight height slightly affects each of these points. The OEM sights shoot flatter out to about 50 yards, because the bullet starts out closer to the line of sight than with the Tech-Sights. But then, because the MRT is at a shorter distance, the bullet drops slightly faster.

The chart below shows the trajectories for the same round, same rifle, with sights adjusted for zeros at 25, 50 and 100 yards:

The charts, and the data tables behind them, give us some interesting insights:

- The 25-yd zero gives us a very flat trajectory within a moderate range. The POI is no more than 1.00” either way from zero (total spread 2”) between 4 yds and 52 yds. If you want to hit lollipops or make head shots on squirrels, you might want to know the window for a total spread of 1.00”, or .50” above or below POA: this range is 10 – 46 yds.
- The 50-yd zero extends that 2.00” window to 3 – 56 yds and the 1.00” window is 31 – 57 yds. The 1.00” window is narrower for the longer zero because the trajectory is more steeply curved.
- The 100-yd zero trajectory is not very flat, so you would have issues adjusting POA to hit closer targets.
- If you are shooting CMP Rimfire Sporter and zero at 50 yds, you will need to adjust your rear sight to lower POI by .40” to be in the x-ring at 25 yds. At 25 yds, that’s 1.6 MOA (.40 x 4) or two clicks on your TSR 200. If you are zeroed at 25 yds, you will hit .79” low at 50 yds (which is also 1.6 MOA), so you will raise the rear sight by two clicks. Whichever sights or optic you use, knowing the MOA value of its adjustments enables you to adjust for the desired distance easily.
- What is the flattest trajectory? Where the near and far zeros are the same. For this rifle/ammo setup with the sight height of 1.3”, that range is 29 yards. The 1” window from MRT is 3 – 52 yards, with all shots at or below point of aim. Drop at 100 yds will be 9.28”.

These calculations and their results are all based on the Gundata.org online calculator. Your own rifle will probably shoot slightly differently. Perhaps your muzzle velocity is a little faster or slower than what was used in the database. Or you may be shooting different ammo from what it is in the database. There is no substitute for testing your own rifle, with the ammo you use.

What should you take away from this article? First, knowing the ballistic performance of the .22LR round enables you to set up your sights appropriately for the kind of shooting you do. If you shoot targets at varied distances such as hunting or rimfire silhouette (with targets ranging from 44 to 110 yards), understanding the trajectory and your rifle’s setup will enable you to dial in the correct adjustments for your targets. You will know that if you are hunting small game with a 50-yard zero, you may have to aim below your intended POI for shorter-range shots, and above for longer ones (3/4” drop at 60 yds, 1.9” drop at 70 yds). Third, if you take the range time to make a disciplined test of your gear, and make notes as you shoot, you can build your own data book for how your rifle shoots with the ammo you like, so that you can zero it and make adjustments with greater precision and confidence.

Very helpful! Thanks!

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Thanks. Appreciate the reference to CMP. I hope to fire this course in competition and with the dual range of 50 and 25 yards this gives me an idea of the change in the site settings – or conversely the amount of hold to hit center when zeroed at one distance or the other.

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