Splicing is easy; draw your pattern on piece of paper, cut it out and glue it on your stave with white Elmer's lining up the pattern with a drawn center line on the billet, flatten the belly of your billet so it will run true through the bandsaw. I always have to add a handle piece after I flatten the belly for cutting the splice but that is no problem.
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I place my flattened billet on the bandsaw table and sight down it to see if I have the flattened belly cut so the billet will not be twisted on the glue-up. If I am trying to glue up to remove twist I look for the best position to accomplish this.
Cut just outside your lines and fit things together. Unless the stars are aligned you probably won't have a perfect fit. Hold your splice up to a light and look at where the impingement points are that are keeping it from sliding together and sand or file a little until everything fits, then glue up with three clamps. I put one clamp on the middle of the splice and adjust the billet center lines so they line up then finish clamping.
I am replacing a bad limb in this picture.
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Here is the finished repair with the added handle piece. The initial bow was made from spliced billets, the darker wood is from the earlier splice.