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A project team within my company is stuck on a conundrum and have asked me for some insights. They want to develop a driver model (mathematical or drawn) where input is the car's velocity profile, and the output is the braking (for deceleration) or throttling (for acceleration) applied by driver. The car can be assumed to be moving on straight level road. Should I approach this problem through constructing a differential equation based on Newton's 2nd Law? Is there a better alternative to the problem where I can relate the braking needed to the velocity profile? What factors must I consider in order to construct the differential equation? Any help will be greatly appreciated. PS - I am relatively new to this field

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    $\begingroup$ "Should I approach this problem through constructing a differential equation based on Newton's 2nd Law?" That's certainly part of the answer . "Is there a better alternative ?" Yes, because you'll end up with the way a robot would drive, not a human driver. You can research using the keywords driver model preview PI control, but Newton will still be the fundamental. $\endgroup$
    – Greg Locock
    Commented Aug 16, 2023 at 22:24

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There are different modes of braking, preplanned braking, and braking to avoid collision.

braking

For planned braking declarations of the order of 0.4g is acceptable. It should start with a short transition easing in part.

formulas for speed and distance are,

$$v = v_o + a t$$

  • v = speed
  • $\alpha$ = acceleration
  • d = distance $$d = v_o t + 0.5 a t^2 $$

Many cars have suspensions that accommodate higher deceleration comfortably.

Many adaptive cruise control radars will decelerate at a rate of $(-3 to -5m)/s^2$, about, $ 0.3 to 0.5g$. Hard braking starts at $0.55g.$

acceleration

For acceleration again it depends and the weight of the car, its suspension, and tire width. The acceleration of

$ 0\ to\ 60\ miles \ per\ hour \ in \quad 5\ seconds\ is\ = 0.55g.$ It is not comfortable.

Recommended acceleration is 0.25-0.3 g.

Below is a chart of the braking of some common cars! source

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typical car brake chart

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  • $\begingroup$ Did you really mean 60 miles in 5 seconds? re your part about acceleration or is there a unit error? $\endgroup$
    – Solar Mike
    Commented Aug 18, 2023 at 5:40
  • $\begingroup$ Yes, 0 to 60 miles per hour in 5 seconds. $\endgroup$
    – kamran
    Commented Aug 18, 2023 at 7:31
  • $\begingroup$ So you are missing the "per hour"... $\endgroup$
    – Solar Mike
    Commented Aug 18, 2023 at 9:10
  • $\begingroup$ I edited my answer to read more clearly! $\endgroup$
    – kamran
    Commented Aug 18, 2023 at 16:18

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