# Calculate an acceleratin in a racing (drag) application

• fastdude
In summary: Now I can be happy about the new titanium rods in my back without worrying about where they came from.In summary, the conversation revolved around calculating acceleration and determining top speeds in a racing application. The method discussed involved using distance and time to find average speed, and then using that to calculate speed at different points in the race. The concept of an acceleration curve was also mentioned, which could be affected by factors such as friction and shift points. The conversation ended with a joke about medical implants.

#### fastdude

I am trying to calculate an acceleratin in a racing (drag)application. I am an engineer at a medical implant manufacturing company so i know a bit about calulations but it has been a while for most (computers,,) Here is the scenario, we race from 150' to 300'. the quickest time determines the winner. I would like to know what type of speeds are achieved. an example would be 180 foot track with a time of 3.3 seconds from a dead stop. In most cases, the acceleration curve would continue past the 200 or 300ft if it would be continued. do you have any suggestions?

You can find the average speed by simply taking Distance/time. In your example, 180 ft/3.3 seconds = 54.5 f/s = 37.2 mph. Assuming you accelerated uniformly from 0, your speed at the 180 ft mark would be twice your average speed = 74.4 mph.

Hopefully some knowledgeable racing fan might be able to give you more practical advice about determining top speed in a real race.

erm i was thinking maybe if you knew the relation between the acceleration and time, then you could integrate and plot out the graph for the velocity.

fastdude said:
In most cases, the acceleration curve would continue past the 200 or 300ft if it would be continued.
What do you mean by acceleration curve? Using your data from before (180 ft in 3.3 seconds) you can calculate your average acceleration during that interval using:

$$a_{ave} = \frac{2d}{t^2}$$

This gives you an average acceleration of about 33 ft/s^2.

Again, assuming that your acceleration is constant from the start, you can calculate your speed at any point using:
$$v = \sqrt{2a_{ave}d}$$

Thus,
at 200 ft: v = 115 ft/s = 78 mph
at 300 ft: v = 141 ft/s = 96 mph

On the other hand, if the acceleration varies with time, you'd have to factor that into your calculation (as Oerg suggests). If you knew how it varied.

A racing car would initialy accelerate with aproximately constant acceleration (limited by friction), resulting in the covered distance:

v(t)=a*t

a=g*k (k is coefficient of friction)

After a time certain time the speed becomes large enough that the power of the engine becomes the limit:

a=P/(m*v) -> mv^2/2=P*(t-to)+W(to) ,

The second formula replaces the first one when the second acceleration becomes
smaller than the first one.

If you are interested in covered distance, then integrate v(t):

s(t)=Integral(v(t')dt') from 0 to t

fastdude said:
I am an engineer at a medical implant manufacturing company

I certainly hope that doesn't mean that there's a Hemi-powered colonoscope in my future.
However brief they might be, your acceleration curve will also be determined by your shift points. Even with a tweaked automatic, there'll be a tiny 'hiccup' for each gear.

what i meant by the acceleration curve would continue is that most cases acceleration does not plateau in the distance of the race. Thanks for all your replies, of course this if just a i wonder,,,,

oh, luckily we only make spine implants

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fastdude said:
oh, luckily we only make spine implants

:rofl:

## What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is a measure of how quickly the object's speed increases or decreases.

## How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is: a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## What is the unit for acceleration?

The standard unit for acceleration is meters per second squared (m/s²). This means that for every second an object is in motion, its speed changes by 1 meter per second.

## How is acceleration measured in a racing (drag) application?

In a racing (drag) application, acceleration is typically measured using a device called an accelerometer. This device uses sensors to measure changes in velocity and can provide precise measurements of acceleration during a race.

## What factors affect acceleration in a racing (drag) application?

The main factors that affect acceleration in a racing (drag) application are the power and torque of the vehicle's engine, the weight and aerodynamics of the vehicle, and the grip of the tires on the road. Other factors such as air resistance, track conditions, and driver skill can also play a role in acceleration.