Last summer I asked a professor if I can try my hand at doing research under him in his field of interest. As I was an undergrad student (I still am) taking taking summer courses and working (I wasn't getting paid for the research) at the time and lacked a lot of skills/creativity to help in with what he was doing, I feel like I was not very successful in being very helpful with putting together a proper research report.
This being said, nearly whole year has passed since then, with no plans this summer for courses, I have an idea I want to do original research that could be helpful to his field (I didn't find anything written on the matter, so I'm not 100% sure if it's a good one, but I sincerely think it should be tried if it hasn't to verify its validity for his field) and I in turn gain from his guidance, and possibly get a paid position with him.
Is it possible for me to get back to doing research with him after having a rough time last year? If so, how should I ask for it? Should I simply write an email asking if its possible for me to try doing research with him again or compose a formal research proposal and give email it to him to demonstrate interest in the field? The risk in turn of that would be that I would waste my time writing a proposal that would never be read or rejected where my efforts should be elsewhere.