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elevation adjustable 1" scope rings for picatinny rail

I have a Benjamin Np2 .22. With regular rings and an optically centered scope it shoots about 4 inches low at 10 yards. I zeroed the scope using the turrets but the scope is almost maxed out on elevation and won't hold zero. I tried it first with a hawke sport hd ao 2-7x32 and then a centerpoint ao 4-16x40 with the same results. I tried googling barrel droop rings (the gun has a picatinny rail on it) and can't find any for a 1" scope tube. Any suggestions would help. I would prefer not to spend more than $50 but if I have to I will.

Thanks,
Adam 
 
You might be able to shim between the picatinny rail and the rifle, you should be able to shim between the picatinny rail and scope mount and I'm sure you can shim under the scope. All done at the rear of the scope. Keep in mind that the pellet is rising to meet the line of sight of the scope somewhere between 25 and 35 feet depending on velocity. The height will be the distance between the center of the rifle bore and the center of your scope - maybe 1.75" or more. So a rifle zeroed at 20 yards will have a POI lower at 10 yards. 4 inches at 10 yards is a lot.

You should have - and if you don't, go here; http://www.hawkeoptics.com/brc.html and down load the BRC & ChairGun http://www.hawkeoptics.com/chairgun.html Applications - it's free!

In the ChairGun app there is a utility under the Toolbox menu - Scope Mount Shims, that will calculate distance you need to tilt the scope to get your scope zeroed. Then go here and read all this thread http://airgunnation.dev/topic/scope-zeroing/ Adjust your scope back to the optical center and go to work. With a little creativeness you should be able to get your scope optically centered and zeroed at 26 yards or so.

I needed to shim a Weihrauch HW97 .015 between the rear of the scope and scope ring for the elevation and put a .020 shim between the scope mount and the dove tail for the windage to get a Bushnell 4500 Elite optically centered. It will take some messin around put it should be worth it when your done.
 
The Burris rings I ordered ended up being out of stock, so i stole the mount off my ar-15. It's a Nikon M-223 XR mount that has 20 moa of elevation built into it. I still had to shim the rear end of the scope to get it to shoot to where i wanted it. I sight in at 10 yards because that is all the farther I can shoot in my basement and it the distance to my bird feeders that the chipmunks won't leave alone. I did recenter the scope optically before remounting it in the new mount. I put about 50 shots through it and the scope seems to be holding poi now.