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.The reason for doing this is that resulting equation looks like Newton' s Second Law, equation (5).If you replace with asymbol, I, the equation is identical in form:(10)Physicists like to find formal equivalences amongst equations because they can use the same mathematical techniques to solve all of them.The equivalences also hints atdeeper insights into similarities in the Universe.OK, if you haven't already guessed it,is the polar moment of inertia.Tocompute it for a given car, we take all the parts in the car, measure their masses and their distances from the CM, square, multiply and add.In practice, this is very difficult.I doubt if PIMs are measured very often, but when they are, it is probably doneexperimentally: by subjecting the car to known torques and measuring how quickly yaw angle accumulates.We can also see that, for a given rotational torque, the acceleration of yaw angle is inversely proportional to I.Thus, we have backed up, from first principles, our statement that cars with low PMI respond more quickly, by yawing, to transientcornering forces than do cars with large PMI.A car with a low PMI is designed so that the heavy parts - primarily the engine - are as close to the CM as possible.Moving the engine even a couple of inches closer to the CM can dramatically decrease the PMIbecause it varies as the square of the distance of parts from the CM.Since equation (10)is formally equivalent to Newton's Second Law, an analogous insight applies to that law.A car with low mass responds more quickly to forces with straight-line changes in motion just as a car with low PMI responds more quickly to torques with rotational changes in motion.Why would one design a car with a high PMI? Only to get a big, powerful engine into it that might have to be placed in the front or the rear, far from the CM.So, take your pick.Choose a car with a low PMI that yaws very quickly and give up on some engine power.Or, choose a car with colossal engine and give up on some handling quickness.55The Physics of Racing,Part 14: Why Smoothness?Brian Beckman PhD©Copyright April 2000I'm back after a hiatus of nine years.Time does fly, doesn't it? For those counting articles, the last one published was part 12; there is no Part 13.After such a long time away, it might be worthwhile to repeat the motivation and goals of this "Physics of Racing" series.I am a physicist (the "PhD" after my name is from my Union card).I'm also an active participant in motorsports.It would be almostimpossible for me not to use my professional training to analyse my hobby.So, I've been thinking for some time about the physics of racing cars.Part of the fun for me is to do totally original analyses.As such, they won't have the specifics of a hardcore engineering analysis.You can look that up in books by Fred Puhn, William Milliken, and Carrol Smith, amongst many others.I want to find thebare-bones physics behind the engineering--at the risk of bypassing some detail.In sum, I analyse things completely from scratch because:• I want the depth of understanding that can only come only from figuring thingsout from first principles,• "peeking at the answer" from someone else's work would spoil the fun for me,• I hope to give a somewhat fresh outlook on things.In 1990, one of my fellow autocrossers asked me to write a monthly column for theSCCA CalClub newsletter.After receiving lots of encouragement, I released thecolumns to the Internet via Team Dot Net.Back then, the Internet was really small, so I was just sharing the articles in a convenient way with other autocrossers.Since then, the Internet got big and my articles have acquired a life of their own.I have received thousands of happy-customer emails from all over the world, plus a few hate mails(mostly about article #4, in case you're wondering).So, here we go again.This month, I'd like to understand, from first principles, why it's so important to be smooth on the controls of a racing car.To me, "smooth" means avoiding jerkiness when applying or releasing the brakes, the gas, or steering.Most of the time, you want to roll on and off the gas, squeeze on and off the brakes, slither in and out of steering.It's just as important to avoid jerkiness at the end of a manoeuvre as at the beginning [ Pobierz całość w formacie PDF ]