That video is the only one that I know of on YouTube that demonstrates the high position with a shotgun except that Paul Castle is doing it one handed. He briefly shows the 2 handed positin and refers to it as the"high position" at 36 and 42 seconds.
I kind of thought things were getting confusing so I took some pictures last night of me doing the CAR high position and roughly how my arm moved under recoil.
Picture 1
Notice I am bladed 45 degrees to the target. I don't cant the gun much because this is my natural hold and I have ghost rings sights that could injury my chest.
Picture 2
Here is a side view of that same position. Notice that the stock is not pinched between my arm and ribs but is held slightly out from my body like this picture below. My trigger hand forearm rests on the stock and because I am smaller (5'7", 168lbs) it only partially rests on it. I grip the gun firmly with both hands but allow my elbows and shoulders to move back and forth.
Picture 3
Picture 4
This picture shows where my arms are when fired and recoil is occurring. My arms rock back to absorb the recoil but I keep the muzzle level so I can fire a follow up shot if required. Note how the receiver rides back, comparing picture 2 and picture 4, with recoil in a line parallel to the ground and at chest height. It is important to stay on target by keeping it level.
Next time I am at the range I may try to take a video.
Remember I have not trained in CAR but this position really worked for me.
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