Interpolating Airplane Performance

[highflight1985]

I'm attempting to write an application that is intended to predict airplane performance based on current atmospheric conditions and other conditions selected by the pilot (such as altitude, engine power setting, etc.). Another program already exists that does this (and more), and I'm attempting to recreate this for my own education. It's called CoPilot.

Luckily, the author explains his methods of calculating this data to include equations. My issue is that I don't understand the math involved.

If you look at the "Aircraft" page from the link on the left, and then click on "Cirrus SR22 Example", you'll see charts describing the performance numbers of an Cirrus SR22 aircraft (small, single-engine, personal aircraft). You can view more charts by clicking on the "Gen", "Climb", and "Cruise" links at the top. These charts assume certain conditions regarding weather and the idea is that CoPilot takes this data and calculates actual performance figures the pilot can expect for the actual/current weather conditons.

Now, if you look at the "Developers" link on the left, you'll see a page that talks about how the program works. On it is an article discussing the mathematics. In the article, Mr. Davis (the author) states that he used a quadratic least squares curve fit. An excerpt from the article:

A mathematical model of the cruise performance is determined by performing a least squares curve fit to produce a quadratic equation that describes the true airspeed (knots) and fuel flow (US gallons per hour) as a function of density altitude (feet). The quadratic coefficients for true airspeed (ta, tb, tc), and fuel flow (fa, fb, fc) are stored in the aircraft database.

The actual true airspeed (t) and fuel flow (f) at a particular density altitude
(y) can then be calculated as follows:
t = ta * y2 + tb * y + tc
f = fa * y2 + fb * y + fc

The full article can be viewed at his website.

To the point: I'm a bit confused as to what values I need to plug into the equations from the performance charts to get the actual performance data (in this case, true airspeed and fuel flow).

I have never studied quadratic least squares curves that I can remember, so this concept is new to me and some explaination would be helpful.

Thanks!