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.Likewise, when you unwind the wheel, you want to start and stop the unwinding smoothly.Thus, a complete steering manoeuvre consists of four gradual, slithery start-and-stop mini-manoeuvres.A complete braking event has four little mini-slithers: one each for the start and stop of the application and the releasing of the pedal.Same for the throttle.Ok, great, but why? At first blush, it seems one would be able to get back on the gas more quickly by snapping the throttle on or get into a corner more quickly by whipping the wheel.Furthermore, supposing we can justify smoothness, are there exceptions to the rule? Are there times when it is best to snap, whip, or jerk? And exactly how smooth 56should one be? Smoothing means slowing the control inputs down, in a particular way, so it's obviously possible to be too smooth, as in not quick enough, as in not getting as much out of the car as it's capable of delivering.Let's tackle "why", first.As usual, physics has technical meanings for everyday words.One of the "physically correct" meanings of "smooth" is sinusoidal.A sinusoid is a curve that looks like this:If we think of, say, steering-wheel winding angle as proportional to the vertical axis and time in seconds along the horizontal axis, then this picture describes a really smooth windup taking one second followed immediately by a really smooth unwinding takinganother second.In fact, you can easily see the four mini-slithers discussed above as the head-and-tail-sections of the bumps and valleys of the curves.So, the question "why", in technical terms, amounts to asking why such a curve represents better steering input than a curve like the following, "upside-down-hat" curve:Now, here's the reason: sinusoidal inputs are better because they match the natural response of the car! The suspension and tyres perform, approximately, as damped harmonic oscillators, or DHOs.A DHO can be in one of three conditions:underdamped, critically damped, or overdamped.In the underdamped condition, a DHO doesn't have a strong damper, which is another term for shock absorber.An underdamped DHO responds sinusoidally.We've all seen cars with broken shocks57bouncing up and down on the springs.In the critically damped and overdampedconditions, the car bounces just once, because the damper provides some friction to quiet down continued bouncing.However, even in these conditions, the one bounce has an approximate sinusoidal shape.The most important parameter of any DHO is its frequency.In the underdamped condition, the frequency corresponds to the number of bounces per second the DHOperforms.In the critically damped and overdamped conditions--as well as in theunderdamped condition, the frequency corresponds to the resonance frequency or natural frequency of the system! In other words, if you provide so many inputs per second, back and forth, as in a slalom, at the resonance frequency, the car will have maximal response.If the inputs are faster, they will be too fast for the DHO to catch up and rebound before you've reversed the inputs.If the inputs are slower, the DHO will have caught up and started either to bounce the other way or to settle, depending on condition, when the reverse input comes in.So here's the bottom line: to maximize the response of a car, you want to providesteering, braking, and throttle inputs with sinusoidal shapes at the resonance frequency of the DHOs that constitute the suspension and tyre systems.Inputs that are more jerky just dump high-frequency energy into the system that it must dissipate at lowerfrequencies.In other words, jerky inputs upset the car, which what drivers say all the time.By matching the shape and frequency of your control inputs to the car's natural response curve, you're telling the car to do something it can actually do.By giving the car an "instruction" like the upside-down hat, you're telling it to do something it can't physically do, so it responds by flopping and bouncing around some approximation of your input.Flopping and bouncing means not getting optimum traction; means wasting energy in suspension oscillation; means going slower.Now, there is an exception: if the front tyres are already sliding, a driver may benefit from quickly steering them into line, hoping to "catch" the car
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