How to Slow Down Faster: The Math behind Brakes. Part 2b: Stopping Distance

brake2

Part 1 is here.

Part 2 is here.

     Ok, now that we’ve established how to calculate the Brake Force, we can work with the whole car now.  For this step, we’re going to assume that there is NO weight transfer at all; the car’s weight is static throughout.  We’re also going to assume the tires have unlimited grip for this part. This is just an exercise for now, and we’ll expand this later by applying real-world physics (which will obviously complicate things).

The previous equation chart is here.

     Last time, we just caluclated the Brake Force for one corner.  We’ll be continuing with the Brake Force(lb) here and calculate the Stopping Distance of the car.  Remember that the front and rear brakes are usually different; with an emphasis on the front brakes.  We’ll get into that next time, but for now we’ll continue from the top, utilising the Brake Force we derived last time.  Remember from our first post, Mu and Vehicle Deceleration (Tires = Stopping?) can be used interchangebly.  And you can’t just multiply our previous Brake Force by 4, since again; the front and rear brakes are different.  Keep that in mind if you were to actually use these equations to tune your car’s brake system.

     Our next step:

mathbrake2

     To find out our total brake force, we just add the two front brake forces to the two rear ones.

     We then factor in the total vehicle weight (like we did with our single axle) to figure out our total car deceleration (again, we’re assuming the tires have limitless grip).

     Then can approximate our Stopping Distance by squaring the vehicle speed, and dividing that by the Vehicle Deceleration, and then dividing that by 29.9.

     Now, if we could use math to figure out a car’s stopping distance, then why do magazines and journalists still have to test the brakes in the real world?  Well We’ll talk about that in the next post.  Stay tuned.

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