The physics of flipping

[IKE]

Some other factors to take into consideration:

Torque at the wheel. Larger torque on the rear wheels also adds to the moment of tipping. For the same traction force and acceleration, the larger the rear wheel will require larger torque and thus be more prone to tipping (works both ways including dynamic braking).

Another big factor is if you plan to go on the ramp. As you climb the incline, the normal force on the rear wheels will increase and thus have a higher traction potential. If you then apply a large torque to accelerate up the ramp, you can flip over as well. Tilt your Powerpoint model 15 degrees, and you will see how the gravity vector will now angle more rearward. http://www.chiefdelphi.com/media/papers/2321

Last but certainly not least, wheel and carpet compliance can be very big in flipping. The compliance in the carpet and your wheels/tires can act as a spring. When timed wrong, shifting back and forth can exercise those springs. The more compliant the wheel/tire (pneumatic), the more effect you can get. This can start to get complicated pretty quick.

A good "rule of thumb" for a drivetrain that you plan on having traction limited (gearing and motors powerful enough to spin the tires) is...
Assuming a Coefficient of friction of 1, then the acceleration and traction vector can be equal, and thus your CG needs to fall inside of 45 degree lines from your tire contact patches. Higher COF means a lower angle (though not much lower). Wanting to traverse inclines means reducing angle as well. Assuming the 15 degree ramp is a goal, keeping your CG below 30 degree lines should be fairly conservative. For a long robot with 8" wheels ((38-8)/2/sqrt(3)=8.67), this would be keeping the CG in the center below 9" and lower the more offset from center it becomes. For a wide bot with 8" wheels (((28-8)/2/sqrt(3)=5.78), would be keeping the CG lower than 6" (which can be tough with 8" wheels)...