Easy to get - free play, Ariel Atom, 50 laps Indy Speedway. You should run out at 40+ laps - do not pit even if you have trashed your tires as it will fill the tank at the same time.
17 laps round la mans in s class
I have just recently got the run out of gas badge, and I did this buy using a fully upgraded Viper '13, which at stock has a 8.4L, as mine was upgraded it was 8.5L. The track I used was Indianapolis motor speedway, on the brickyard speedway, i did this on free play and set the laps to max of 50 laps but got the badge on lap 43.
To help you can fine the fuel gauge under the gears in the speedometer, it will start off as a solid white line and we slowly go.
For people who don’t understand, the bigger the engine the more fuel it can take, but will run out quicker, that’s why i went for the Viper '13 as it had the biggest engine for fuel at 8.4L, plus this is the biggest with out DLC, if you have DLC the Bugatti Veyron SS with a 8.0L but could be higher when upgraded.
Bear in mind i did this badge and write this comment at around 2am in the UK.
The Ariel Atom with a 3.0L V8 runs out at Indy Speedway in a similar number of laps. Engine capacity is not the only thing that determines when you run out of fuel.