Estimating traversal time of car on a path

[fishingspree2]

Hello, I have defined a C2 continuous path using piecewise functions, and I want to estimate the time a car takes to go from the beginning to the end. There are many things left out, such as weight transfer. Here is the "pseudocode" of what I tried:

deltaT is set to 0.1 seconds
input: beginning, end, deltaT

t=0
v=0
a="some acceleration i choose"
position= beginning

while "end of path not reached" do

travelleddistance=$$v\Delta t+0.5a\Delta t^{2}$$
position="new position on the path, given the traveled distance"
t=$$t+\Delta t$$
$$v=\min \left(\sqrt{\frac{curveradius\cdot \mu_{s}\left(mass\cdot g+downforce)}{mass}},v+a\Delta t,\left(\textrm{maxspeed given power of car, bounded by air drag}\right)\right)$$
$$a=\min\left ( \sqrt{\textrm{formula derived from tractioncircle}},\frac{Power of car}{v\cdot mass} \right )$$​

end do
output: t

A few questions:
this basic algorithm assumes the car can always decelerates from speed v to the next maximum speed, for any delta T. Any ideas on how to take deceleration limits into account?

 

[Navin A S]

Yes, you can take the deceleration limits into account by introducing an upper limit on the acceleration that is applied. This can be done by making sure that the acceleration used in your equation is within a certain range. For example, if the maximum deceleration of the car is 5 m/s^2, you could set the acceleration used in the equation to be no higher than 5 m/s^2.