Just ask. Write up a nice sponsor letter and drop it by some day. If they so no, your now worse off, if they say yes. Great!.
Offer to them to come out to bbq feed on Friday nigth at one of your contests. Then you can show them what your doing and they can really see how competition bbq really is.
Also, don't ask for a bunch of money. Start low, like in the hundreds low, and work up from there. After all, it's your hobby not theirs.
Check out my website on how I have included the sponsors so far.
Smokehouse 72 Competition Cooking team
Visit our Facebook page - Smokehouse72
Whole Hog Smoker