Sight in a scope
You get a new rifle (or pistol), you get a new scope, now how do you sight it in? Sighting in a scope means adjusting it in many ways so you can shoot accurately.
Make sure your gun is not loaded or cocked! If you are not sure, walk up to a backstop, aim the gun at the backstop and pull the trigger.
Selecting a scope
You probably have a scope already selected, so I won't spend too much time on this topic. If you have a piston gun, make sure the scope is rated for one! Otherwise, you can destroy a perfectly good scope not intended for airguns after a few shots. Also, it is not always the bigger and more magnification the better. Only you can tell what range of magnification is needed for your purposes. Last, but not least, because airguns tend to have a short effective range, try to get a scope with adjustable objective (AO). This, essentially, lets you focus your scope to objects at different distances. However, it also helps to eliminate parallax, and therefore improve accuracy.
Centering a scope
If you have a scope that has a flat objective aperture (no built-in sun hood), then it is very easy! Find a well illuminated area, then place a flat mirror right in front of the objective lens of the scope. The objective aperture of your scope should be contact the mirror. Dial the scope to minimum magnification and set the distance to infinity. Look through the scope. If you see nothing because it is all dark, then you need more background lighting.
If you see two cross-hairs, use the elevation and windage adjustment turrets to realign the cross-hairs so they become one. That's it!
This steps set up the scope so that it is optically centered. It is not aligned to the barrel of your gun by any means!
Mounting a scope
First, secure the gun so it won't fall over. You can use a gun vise or shooting bags. Once the gun is supported in its up right position, you are ready for the next step.
Install the lower half of the scope rings onto the scope rail of your gun. Most airguns use the 11mm dovetail standard, but manufacturers increasingly use the weaver standard that is more commonly found in powder burners. Make sure your rings are designed for the rail on your gun!
Once the lower half of the scope rings are installed, gently rest the scope on the half rings. Put the top part of the rings on, and evenly and loosely turn all the screws. You can turn each screw a little until you feel resistance. Make sure the scope can still slide with little push/pull effort.
Next, shoulder your rifle and check the scope picture. You may need to adjust the scope and somethings the rings so that the scope picture has maximum view. Try this at different magnification powers. Many scopes have varying eye relief (the distance between the eye piece and your eye) distances depending on magnification power.
After you find the best placement, tighten the ring screws to secure mounting on the rail, but do not tighten the screws to hold the scope itself down, not yet!
Unless you have a dot sight or a scope that only has a single target dot, it is important to align the lines of a cross hair so you can level the gun when you aim. This is where a tool may be helpful. In general, you want to align a scope so the top of the receiver of a gun is parallel to the horizontal line in the scope sight. Note that some guns may not have a flat receiver top. In that case, you can use the lines of the scope rings for alignment purposes.
After you are satisfied with the alignment, check it again! When a scope is not aligned with the vertical axis of a gun, it is called "canting". Canting can introduce errors that seem difficult to diagnose. It is best to avoid canting by aligning a scope with the receiver of a gun correctly.
When you think the scope is at the right distance and is leveled, tighten the scope ring screws. Turn each screw a little in turns. This ensures a even pressure applied to the scope. While you want the scope to be firmly mounted, you do not want to overtighten the ring screws. If you have using a typical Allen wrench, put your thumb on the part that inserts into the screw, and use only one finger to exert torque about 2 to 3 inches out on the wrench. There is no need to turn until it is impossible to turn the wrench!
Overtightening a scope ring is a quick way to destroy a scope! If your scope ring is not tight enough, you can always retighten later on.
Measure scope height
Once your scope is mounted, you can measure scope height. Scope height is measured from the center of your scope (or the scope axis) to the center of the bore. On some guns, this is easy to measure. On others, it can be a little tricky.
If you are savvy with photo/image editing tools like Photoshop or the GIMP, you can take a picture of your gun/scope from a distance (and maximize the focal length) with a length reference included. Then, analyze the photograph to find out the axes of both the scope and the gun, and proceed to measure the distance between them. The key is to prop up the gun so that you are taking picture of the side of the whole set up and make it as perpendicular as possible.
If you are the low tech kind, there are other ways.
Putting your shots "on paper"
After the scope is firmly attached to your gun, it is time to do the dangerous part: putting your first few shots on paper. You should consider doing this at a gun range like DGS Airgun Range so that missing the "paper" will not hit someone or something valuable because there is a large size backstop. It is not uncommon for a rifle-scope combination to miss a letter-size paper target all together the first time!
Use a piece of paper that is as large as the backstop so you can see where the pellets land. If you are doing this at a range, you can consider spending a little bit of money and get a large cardboard.
Most scopes have a minimum focusing distance of 10 yards, although some can focus as close as 3 yards. Start at about 5 yards using the least magnification and closest focus on the scope. If you can see the target clearly, you can choose to use a smaller target dot. However, if your scope has high magnification power and cannot focus closely, you may not get a good sight picture at 5 yards. In that case, paint a relative large target (like a filled circle with a 2-inch diameter). While you may not be able to see the target, at least you can aim for the center of the fuzzy circle.
Adjust windage (left-right) to center the pellets horizontally. Remember, the caption on turret applies to the point-of-image (POI). Knowing the distance to target and how much your pellets are off, you can calculate the number of clicks needed to correct the error. For example, if you are off by 1 inch at 10 yards, and your scope has 1 click per 1/4" at 100 yards, then you first multiply the error by 10 (so it is expressed in error at 100 yards). That makes 10 inches of error at 100 yards. Next, divide the error (10 inches) by the click value (1/4"). In this example, the number comes out to be 40 clicks.
Elevation adjustment is a little more tricky, as you do not want to center elevation to the target at 5 yards.
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