Still looking for the answer.

Here's what I know; There was dirt track called Capital City Speedway near Lansing, MI that ran from the 40's until about 1965, it is long gone. Lansing Speedway opened near Lansing, MI in 1956. The name was changed to Spartan Speedway in the 60's, and it remains open today. The movie was filmed at the still-open Petaluma Speedway in Northern Cali. Tucker DID do some testing (1947?) at Indianapolis Motor Speedway. I'm doubtful Tucker did any testing in Lansing, MI. I'm assuming Hollywood didn't (or couldn't) get the rights to use the Indy name in the movie, so they pulled "Lansing Speedway" out of a hat. Happy to hear anything new, or corrections!
