The fact that you are able to pay full tuition without any aid is going to help you for the less competitive engineering schools. You are unlikely to get into the most selective schools, but I don’t think so much so that you shouldn’t put in applications, especially since finances aren’t an issue. You still have time to throw in a few more applications. Consider adding RPI - they have great mech engineering, the car clubs take freshmen, and they’ll love that you’re full pay. Also look at U Colorado at Boulder, UT Austin, Embry-Riddle in Daytona (location), Worcester Polytech, Texas A&M, Virginia tech, Ohio State, Penn State.
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