# Disturbance to velocity

1. Sep 13, 2006

### klyau

Dear All,

Hope you guys can help on this. I would like to measure how stable is an object moving at a spped, let's call it the stability metric.

For instance, an object is moving at a certain speed, but through the object history, we know that it changes its velocity with a certain amount, let's call it disturbance. The lower the disturbance, the higher the stability metric, which means more stable.

And, I would like calculate stability metric which is a function of velocity and disturbance.

Thanks.

2. Sep 13, 2006

### Staff: Mentor

This thing you are calling "disurbance" (change in velocity) already has a name: acceleration. And the resistance to acceleration is "inertia". The equation for finding inertia (mass) given acceleration is m=f/a.

3. Sep 13, 2006

### SGT

When you mention disturbance, I suppose you refer to random accelerations acting on the object, making the velocityto fluctuate around an equilibrium value.
A measure of this disturbance can be the rms of the difference between the actual velocity and the reference value.
If $$V_{ref}$$ is the reference value and $$V_{act}$$ the actual value you can have the disturbance at moment $$k$$
$$dist[k] = \left(V_{act}[k] - V_{ref}[k]\right)^2$$
If you want the value for n time instants you have the rms value:
$$dist = \frac{1}{n}\sum_{k=1}^n\left(V_{act}[k] - V_{ref}[k]\right)^2$$

4. Sep 13, 2006

### klyau

Thanks for your prompt replies. However, I still have some doubts in getting the stability metric.

As for SGT method, it requires the V reference to be known.

Let me refine my question.

Suppose, there are 5 cars moving around and I am in one of the car. To get the stability metric of how stable am I compared to the others, I first get the average velocity of all the cars and compare how close is my velocity to the average velocity.

However, disturbance (acceleration and variance in acceleration) does occur. Therefore, we need to take account of disturbance to show my real stability metric compared to others.

Specifically, how can I get derive my stabililty metric? Thanks.

5. Sep 14, 2006

### rcgldr

You could sum up all the absolute value of the all the work done on the car via the absolute values of acceleration x speed x mass x time.