# Acceleration on a Rollercoaster (And Integration to Velocity)

• DLDude
In summary, the Rollercoaster's accelerometer is integrated with the Wiimote to track velocity. The issue is that the rollercoaster has loops and hills, and you need to take gravity into account when integrating the data.
DLDude
Hey everyone. I'm working on a project that will incorporate a wireless accelerometer on a model rollercoaster. My issue is that we wish to take the accelerometer data and integrate it to give us our velocity through any part of the ride. This in turn will help us determine losses, etc. My issue is that the rollercoaster has loops and hills. It would be easy to integrate the 'X' accelerometer data on a flat plane, however since the coaster will be angled up or down depending on the part of the ride, you'd have to consider the affect of gravity in the 'x' direction when the car is tilted. This can be done easily with vectors by hand, but we need to be able to integrate in real time using pure accelerometer data (which is in normal values such as 'x=1.00 y=.40'.

Attached is a photo explaining my axises.

I know the Wiimote does something like this. My guess is we'd need to determine the angle of the bank and then take out the gravity aspect. That could become hard because through a loop, the Y axis data will be very large (along the lines of 5-6G's), so you cannot just compare the X and Y data and do some math there.

Any ideas?

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• Accelprob.jpg
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The issue is that you need some known initial conditions so you know which direction gravity is relative to the accelerometer. Then you'd hope that your integration (perhaps numerical) is accurate enough so that the calculated results very close match the actual results.

Initial height could be pretty standard, plus it will begin horizontally. I have a hunch you mean there would have to be a pre-set track configuration to match the graphed results to.

DLDude said:
Initial height could be pretty standard, plus it will begin horizontally. I have a hunch you mean there would have to be a pre-set track configuration to match the graphed results to.
The configuration information isn't needed the accelerometer and integration techinque are accurate enough, but it would have to be very accurate.

Note that internal inertia based guideance systems were used on early long range missles, so high accuracy is possible, but I don't know how accurate your accelerometer is or the effect of accuracy versus distance or time varies versus accuracy.

## 1. What is acceleration on a rollercoaster?

Acceleration on a rollercoaster is the rate of change of velocity over time. It is the measurement of how quickly the rollercoaster's speed is changing.

## 2. How is acceleration calculated on a rollercoaster?

Acceleration on a rollercoaster can be calculated by dividing the change in velocity by the change in time. This can be represented by the equation a = (vf-vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## 3. How does acceleration affect the experience on a rollercoaster?

Acceleration plays a crucial role in the experience on a rollercoaster. It is responsible for the feeling of weightlessness, drops, twists, and turns. High acceleration can also cause feelings of excitement and fear.

## 4. What is the relationship between acceleration and velocity on a rollercoaster?

Acceleration and velocity on a rollercoaster have a direct relationship. This means that as acceleration increases, velocity also increases, and as acceleration decreases, velocity decreases. This relationship can be observed in the steepness of the rollercoaster's track and the speed of the train.

## 5. How is integration used to calculate velocity from acceleration on a rollercoaster?

Integration is the reverse process of differentiation and is used to calculate velocity from acceleration on a rollercoaster. This is because acceleration is the derivative of velocity. By integrating the acceleration function over time, we can find the velocity function. This can be represented by the equation v = ∫ a(t) dt, where v is velocity, a(t) is the acceleration function, and ∫ is the integration symbol.

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