How do these three forces: Drag, Lift and Downforce. Affect a formula one racing car?
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drag is the wind resistance (force) that acts against the car as it is moving forward. Less drag means higher speeds, more drag means lower speeds.
Lift and downforce are the exact same things, but acting in opposite directions. On a race car downforce is good because it is a force created through aerodynamics that pushes that car in a vertical direction towards the race track. This allows the car to have more traction, its having the positive effects of adding weight to the car (creates traction), without the negative effects of actually adding the extra mass.
Lift is just the opposite. Its the vertical force acting on the car, again created by aerodynamics, that is trying to lift the car off the ground. This is an incredibly negative effect not only for traction, but for safety.
Remember that downforce is good, but drag is a byproduct of downforce which is bad. The idea in racing is to balance your drag and downforce levels to be the most efficient given drivers driving style, area of the track (corner, straight away), speed, and a myriad of other factors.
Lift needs to be taken out of the car as much as possible. The drivers life usually depends on it.