If it is a public event and there is no expectation of privacy on the part of the driver then the picture is the property of the photographer whether he asked to take it or not. Since it was a competitive event the only person other than the photog who might have a claim to it is the event organizer depending on their policy.

That being said I don't know a single photographer who would object to seeing their image published. If it had been my image and you wanted to publish it I would simply ask for a credit in the publication and a copy once it is printed. Unless of course you are making money from the sale of the calender .... then I'd want my piece too =)