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Explain the physics behind the hold? Springer shooting bench vs off hand

I was out shooting my fwb 124 today, despite the stay at home orders I haven't been shooting as much as I'd like. My 124 is mainly my "under 20 yards" rifle and I'm debating putting the beeman peep back on but for now I'm using a scope. Benched/rested I am getting single hole 10 shot groups pretty easily at 20 and under so I'm trying to practice my off hand more now. I'm managing 1 inch groups from a seated and kneeling position but my big question is this: my benchrest groups are about an inch higher than my offhand/seated/kneeling groups. Why? I know springers are "sensitive to hold" but this one doesn't seem to care if I'm holding it like a deer rifle or using the absolute lightest artillery hold. The only thing that changes impact is if it's shot off the bench or when I'm holding it and I'm just curious to know what causes this to happen?



Second question: any of you "older" shooters who have/need corrective lenses still using a peep sight? I really want to be able to use it as the rifle without a scope is so nice and light but I really can't see much past 15 yards without at least some magnification. I'm currently using a sightron 4x12 scope.
 
Howdy, I recently bought a used diana 54 that came with a very nice williams peep sight and interchangeable front inserts. I'm 49 and wear glasses with progressive lenses (so I can say that my vision is poor at distance and now up close too). This is my first time owning a gun with peeps and I have had an absolute blast shooting with them. I find a 2 inch target a good challenge in the 20-ish yard range. Here's a target where I was changing between a post front sight and aperture front sight (gun was rested).

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And here's roughly what it looks like:

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Oh, I should also give you a better pic of what I'm aiming at so you have some context. It's a typical bullet box:

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I can usually get a springer to hit the same place from the bench as sitting by fiddling with the front rest position. I don't know if there are any rules to this, but usually somewhere near the balance point just in front of the trigger guard is what turns out to be best. I also don't use a rear bag. As for the physics involved, it probably has something to do with the fact that the recoil thrust is not aligned with either the vertical center of gravity or the point of contact on the butt pad. So there is a rotational component to recoil that may not be resisted the same way when held or rested.

Theoretically, aging eyes can use iron sights as well as younger eyes as long as your eyeglass prescription allows you to focus clearly on the front sight. Having the front sight mounted at the end of a long barrel helps with this. There are also fancy rear aperatures that allow you to adjust your focus point if your eyeglasses alone can't quite bring the front sight into focus. And of course the use of a properly sized peep aperture helps sharpen both front sight and target. The fancy rear apertures I mentioned also allow that adjustment. Personally, I find that an aperture of 0.050" to 0.060" works well enough for me. I just buy the Williams 0.050" and drill it out a bit if I need to. So no excuses due to those aging eyes!
 
Springers are extremely hold sensitive so as others have said hold them differently you will get a POI or accuracy change for sure. The gun shakes before the pellet leaves the barrel so holding it in the same place you keep the vibration the same and the pellet leaves the barrel at the same moment in it's harmonic cycle. 

My eyes are a bit old so I use one of these Merit aperture units on my shooting glasses when I am using any open sighted gun. It's astounding how much better my sight and target acquisition is with the Merit. Of course I shoot better with it as well especially at longer ranges.

http://meritcorporation.com/
 
I don't know that the outer diameter matters that much. I suppose the idea is that the larger OD blocks out distractions and helps you focus on the sight picture. The smaller OD would help you pick up and track game when hunting. For informal target use the 1/2" size is a good compromise. I would buy two of the 0.050" ID, leave one as is and drill the second to 0.060" (#53 drill) or 0.063" (1/16" drill). One or the other might work better for you depending on the light conditions. I never found the "twilight" feature to be of much use, at least for target shooting. In fact I found the shiny brass ring to decrease contrast and clarity of the sight picture.

With open or aperture sights you have to train your eyes to focus on the front sight. It helps to align the sights outside of the bull, focus on the front sight, then swing the front sight to the bull while maintaining focus on the front sight. When aiming at a standard black bull, I find the ring type front sight to be easier to align with the bull than a post, especially vertically.
 
Well my 80year old eyes do very well with peep sights. Recently, I've removed optics from ten airguns, rifles and pistols and replaced with peeps on the rifles and notch on the pistols. I wear try-focal glasses and do just fine. The only two guns I had to really think about for peep sights were the P-rod and yesterday, my TX200. Those two the rear sight was easy, but the front sight took some thinking about. It's actually been kind of fun shooting guns without optics.