Is the plane you see/hear a C130? If so, it might be a test flight after repairs have been made at a Dothan, Alabama, repair facility. They overfly Dothan quite often. In fact, when I first saw these birds, I thought of ELINT or surveillance activities but later learned of the repair facility. It might also be some Air Force reservists getting in their flight time as well.
The C130 (SLUFFs - Slow Little Ugly Fat (uh - time for censorship) Fellows) family is by definition low and slow and flies circles often for training. Even out here in the prairie...