How Can We Calculate Energy Loss Due to Drag on Roller Coasters?

[adriaat]

I'm carrying on a research project in my school about roller coasters and I'm wondering if the following question is right.

I have a drag force which equation is $\frac{1}{2}\rho·v^{2}·C_{D}·A$ where $\rho$ is air density; $v^{2}$ is squared velocity, $C_{D}$ is drag coeficient and $A$ is effective area.

I want to know the energy loss due to drag, so the $W_{Fair}$ done by the air.
Is there any $\int$integral which I can use to calculate its area and so the energy loss? It will be like a free falling object as it doesn't have any source of extra-proportion of kinetic energy, like engines.

By the way, I'm looking for any formula which I can use to calculate the effects gain/loss of velocity due to wind (by calculating kinetic energy). Is there any? I found:
$E_{C}=\frac{1}{2}·(\rho·A·v·t)·v^{2}$

 

[jbsteele]

Is this the right formula?Yes, the equation you provided is correct for calculating the energy loss due to drag. To calculate the effects gain/loss of velocity due to wind, you can use the equation E_C = \frac{1}{2}·(\rho·A·v·t)·v^{2}, which takes into account the air density, effective area, velocity and time.