What is the speed at the end of each gear in a drag race?

[Chrisupra]

Hey guys,

I've been looking around online and only find formulae for car passing through a distance with an initial velocity but nothing to calculate the speed of an object starting from a stance and accelerating to complete a distance.

I have a car that has done a 1/4 mile (375m) and completes it in 7.671 seconds. I calculated the acceleration at 12.74m/s. Can anyone help me figure out the speed across the line?

I've tried .25/ (7.671/3600) and I get 117mph which is wrong..

 

[HallsofIvy]

I take it you are assuming a constant acceleration because you only give one value.

In that case speed= acceleration*time. If the car accelerated at 12.41 m/s^2 (NOT m/s) for 7.671 s then it speed at the end was (12.41 m/s^2)(7.671 s)= 95.19711 m/s.

 

[Chrisupra]

I know the car crossed the line at roughly 181mph. I got 12.74m/s^2 from the formula..

x = ut +1/2at^2 for each gear in the car as I know the seconds in which they shifted gear so I've calculated the acceleration and velocity per gear. I initially got 12.74m/s^2 by re-arranging that formula as I know x(375metres), t(7.671s) and then we have 1/2.
UT = 0 as there is no initial velocity..

 

[Gnosis]

Hey guys,

I've been looking around online and only find formulae for car passing through a distance with an initial velocity but nothing to calculate the speed of an object starting from a stance and accelerating to complete a distance.

I have a car that has done a 1/4 mile (375m) and completes it in 7.671 seconds. I calculated the acceleration at 12.74m/s. Can anyone help me figure out the speed across the line?

I've tried .25/ (7.671/3600) and I get 117mph which is wrong..

Firstly: A 1/4 mile is 1,320 feet, which is “402.336 meters” (not 375 meters).

Secondly: A car traversing a distance with a steady initial velocity (merely for clarity’s sake since you stated that you found this equation) is computed as follows:

v = d / t

Naturally, this equation is useless for accelerated motion.

Thirdly: A car that accelerates from its state of rest to its highest velocity (as in the 1/4 mile) will not experience “uniform acceleration” over the 1/4 mile distance, as air resistance will exponentially increase per increases in velocity thereby significantly reducing the car’s rate of acceleration as velocities increase.

Even if you attempted to employ a drag coefficient for air resistance as the car’s velocity increases, headwinds and tailwinds further alter its potential top speed and gearing changes via up-shifts to taller gearing further increase the time required for the engine to increase its RPM to achieve its power-band therefore, the car’s top speed cannot accurately be calculated via simplistic kinematics equations, which deal with “uniform acceleration”. These equations only work in physics scenarios where the acceleration of the car is accepted as exhibiting a “uniform rate of acceleration”.

Typically, two beams positioned very close together whereby one is positioned slightly before the finish line, the other at an equal distance after the finish line, can be used to calculate the top speed by dividing the difference of the distance that separates the upper and lower beams by the difference of the two trip times. This yields a fairly miniscule acceptable error in 1/4 mile speed.

v = (d2 – d1) / (t2 – t1)

For instance, if the beams were positioned 1 meter before and 1 meter after the finish line (a difference in distance between the two beams of 2 meters) and the difference between the two trip times was detected as being .024717 seconds, it would indicate that a speed of 181 MPH had been achieved across the finish line:

v = d / t

2 meters / .024717 seconds = 80.916 m/s (181 MPH)

Since each of the trip times are sampled at equal distances before and after the finish line, they are times per velocities that are slightly lesser and slightly greater than would be achieved at the finish line. Since the lesser velocity causes the first distance (beam 1 to finish line) to be traversed at a slightly slower velocity (hence a slightly longer time), but the greater velocity (achieved between the finish line and beam 2) causes the second distance to be traversed at a slightly greater velocity (hence a slightly shorter time), the difference between these two times effectively average themselves to reveal the velocity that will be achieved as the car crosses the finish line.

 

[netgypsy]

Is this a "book" problem or a real life problem?

 

[Chrisupra]

Ok I will be honest. It is for a game being designed for SmartPhones and I need to carry over these equations so we can be hypothetical. Wind and other ambient forces can be neglected. Anyone who helps, i'll be sure to pass on free download codes for the game. Also, thanks for any responses

I always thought there was 1500m in one mile, my bad! Let me explain what I have done. I used my kinematic equations to calculate the velocity and acceleration for each gear individually. What I would like to do with the physics is have speed determine the performance of the car which I decide on. So in each gear right now I have time and acceleration decided on, I can change the figure and I get a different result. It is very easy.

There are two ways I can do this. I can either determine the speed of each gear individually and get a finally result when it crosses the line or I can try determine a hypopthetical speed crossing the line. I am thinking of each gear.

Time is very important in this equation. Time for me = BHP, TQ and weight of the car. So acceleration and time will give a cars performance in a gear. If I implement these into the formula x=ut+1/2at^2 gives me a distance for each gear, do this for each gear and add them up till you cross the line and we should have a speed and total of the times...

If it helps I can tabulate the results I got for you guys.

 

[netgypsy]

Hmmmmm
Did you say how many gears

Lets make an assumption first that this virtual car has traction control and the track is uniform. Let's also assume that there is enough power to exceed the maximum force of friction the road can exert on the car's tires. Corrected - use a vacuum first because the forward force is limited by the tire gripping the road so a backward air resistance would reduce acceleration.

Now we have to deal with shifting. I would think this shifting would be so fast there would almost no speed loss. So this would be your absolutely top possible acceleration and maximum speed over the given track once you set your track friction. Of course you don't have to do this for a game but you could.

Now let's remove the traction control and let the operator determine the force applied for each gear and insert gaps for shifting if you wish, or not if you wish.

If you have a different force and different acceleration for each gear then you just calculate the final velocity for each section using that given distance and elapsed time, plug it in as the initial velocity for the next section, and repeat until you get to the finish line.

(With the acceleration constant for each segment you can use displacement or directed distance = average velocity, the sum of the initial and final velocities for that segment divided by two, times time, as was mentioned before, which will allow you to calculate the final velocity for each segment which would then be plugged in as the initial velocity for the next section until you reach the finish line, which is what you indicated you were going to do.)

I don't see how you can arrive at the final velocity at the finish line directly using one calculation unless you go to the traction control model which would have constant acceleration for the entire trip giving a max velocity which cannot be exceeded without different tires, different track etc.

so there are a lot of parameters you can play with. Have fun!

 

[Chrisupra]

What you have suggested is what I did exactly. I need to calculate the most perfect, vacuum run and then start implementing the flaws that occur in Drag racing like initial wheelspin, the shift times and deceleration. I have got results for the Velocity if the driver hits the limiter in each gear and also if he shifts when he should. I have calculated the distances in each gear and how long they spent in that gear.

For example I have a Velocity of 102 m/s as the car cross the line at 400metres and completed his shifting and the run in 7.671 seconds. There are 6 gears and the acceleration differs from gear to gear

I need to calculate the speeds at the end of each gear