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I would bet that your broadhead diameter is larger than the diameter of your arrow. Go buy some broadheads that are the same diameter and you will not tell the difference between them or your field tips.
Just happened to me this year- I tried new broadheads and they were a larger diameter. The arrows do not fly straight and there is no possibility of consistency.
Was having the exact same issue with my set up. Stopped by the bow shop to try some slick tricks thinking my broadheads were causing the issue. Ends up last year when the shop had put a new rest on for me that they didn't paper tune it, but they told me they had, and I took their word for it. We checked some stuff out and shot paper - and sure enough, my rest needed moved. Did that and then aligned the blades with the vanes and problem solved, consistant hits out to 60 with broadheads/ field points.
if u paper tune your bow u shouldnt have a issue with different impact, with field tips and broad heads.....u need to always check ur timing of bus cabels, string stretch.