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The relatively fragile nature of racing tires, coupled with the inevitable track debris which results from racing accidents, ensures that racing drivers will routinely experience conditions involving flat tire vehicle dynamics. We define flat tire vehicle dynamics as a situation which requires the driver to provide steering and/or braking and acceleration control while the vehicle is running on one or more tires which have dramatically reduced tire pressure. In the present work, we simulate the handling and braking vehicle dynamics which occur in the presence of a single flat tire on the vehicle. The flat tire was simulated via drastically reduced cornering stiffness, partially reduced limiting frictional capability and increased rolling resistance, and was alternatively simulated on both the front and rear axle. No simulations were conducted with more than a single flat tire because multiple tire failures which do not involve an actual accident contact and/or damage are rare.