C# Multithreading Synchronisation

Hey guys. I wouldnt usually post asking for help with assignments on here, but I feel like im going round in circles with this one.
Basically clicking on each "Hanger" spawns an aeroplane, current represented by coloured squares, they then follow the runway round to the takeoff section. The assignment spec is very vague, but you get the idea.

I'm having problems with race conditions that appear when two planes are queueing for the same section of tarmac. They keep running out of sync and overwriting eachothers data. I'm hoping for a few tips/pointers, maybe a good way of queueing them so that one isnt left waiting indefinetly?


The VS 2005 project file, source code, and assignment spec can be found here.

Thanks in advance :)