'Modern' Lift Equation? Has it changed then?
The website does discuss the difference between old and new equations of lift.
Seriously [Pompeypaul], is your software project part of a student project, flight simulator, or project such as a video game involving aircraft where fidelity isn't particularly important?
Lots of clever people have worked very hard on computational fluid dynamics for simulating new aircraft designs, or on flight simulators for fun or serious training. It's a field where it's hard to contribute anything new, and meaning no disrespect it sounds as if you're starting from the beginning.
Look up 'blade element analysis' if you haven't already.