Thanks for your posts!
Canadaelk: When I look at the PWM circuits, they seem to be good for speed controls which would essentially be a thrust adjustment. If so, I didn't mention the other problem with the rheostat and other "thrust adjustment" methods in my original post. At the long end of the required time (above, say, 9 sec), a weird thing happens. The amount of thrust required to move the vehicle at all (i.e. overcome the static friction of the car) will then move the car way to fast to reach the required time. Conversely, the setting of the Rheostat that will provide the precise amount of thrust needed would then require a slight nudge of the car (a big violation) to get it moving. Therefore, we abandoned the thrust-adjustment methods.
Cowboybob: That looks good. As I said, I'm a little green when it comes to transistor theory. The graphs got me thinking though. The top graph in the second picture would basically translate to complete silence for 15 s after the judges shout "GO". I'm not sure the judges would consider the car as having been "started" if it sits there initially as if it is completely turned off. I wonder if, instead of a square wave where Vcc is suddenly present after a period, if there could be an initial, slow ramping up of the voltage. That way, the propellers would immediately start turning (indicating to the judges that we have started) but not go anywhere until the voltage gets to the required level.
Thanks again for your posts!