What you have would work, and I can imagine any range turning you away for not having proper equipment. The rules IBS/NBRSA rules state that the rest must not be connected to the rear, and it must have sand under the rifle font and back, and that the bags must be able to deflect when pushed on by a finger, no mechanical rest under rear bag.
A bit of advise on what you have and possible improvements.
To start, can you add some weight to that rig? Even with a cast iron rest like a Sinclair/Hart it is easy to tip the rest , when you pin the rifle. Placing a few shot bags might help, or change out the wood to a steel plate, or an engine flywheel. In the rear I would change over your rear screw to something with a course threading to make it function like a "speed screw," also if you look at menards you may find knobs that are round, it would make rear adjustments a bit easier. This is the area your going to want to use over the up and down adjustment of the jack. I am going to assume that you took the bolts you have through the rest and pointed up the ends, so that they grip the bench. If not being light, and such it will slide all over the bench.
You may want to add a stop on the front of your rest. This way you know that you have your rifle at the same point and can get it back into battery quicker. simplest way would be to take a bolt and put a 45 degree bend in it, attach it to your wood block and have it angle up to contact the stock. You can get fancier, and place a bolt in the front of the wood block, and take a coupler and drill a hole in it so that it can slide up and down on the bolt, and place a screw in it to lock it down to the bolt.
You may want to screw side plates on the sides of your wood block so that you can support the sides of your bag. The simplest way would be take some of the same wood, and cut it off to the height of the bag, and screw it onto the wood, and then places a thin piece of steel or aluminum against the bag, and the wood block, then put a couple of screws to place tension onto the bag.
Last thing get ride of that rear bag, or if you feel that you have to use it put it under the trigger, and rest you hand on it. This is be the biggest downfall of the entire rest, as pictured. A good rear bag doesn't have to break you, I highly recommend protektor model. This is what most competitive shooters use. You can get a #13 bag for around $20 bucks. The bag will last you the rest of your life. If you have a bit of extra money I would recommend you also ditch the Caldwell front bag in favor of a protektor. Once you have it in your hand you will see why I say that. Here is protektor's web site. http://www.protektormodel.com/
Last the main thing is you want the rifle to slide, use baby powder with cornstarch. Powder up both bags. Take off all sling swivels. Pack both bags with good sand. I highly recommend you go to true value and buy a blasting product called black beauty. It is coal slag. It runs about $7 bucks for a 50 lbs bag, and works very well in sand bags, and is very heavy. Last off do not pack the front bag hard, you want it firm, but able to still move the sand around. Pack the rear bag tight. Good luck and hope this helps.
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