This week I got about what I expected to do. I had initially set myself the goal of calculating variable thrust curves, and if I completed that I would begin working on putting the Air Resistance Force in my equation. I didn’t get to the Air Resistance yet, but I’ve nearly completed the variable thrust curves. Initially I struggled with the variable thrust curves. Unfortunately, they aren’t given in the form of an equation. Instead, the variable thrust curves are given in the form of a series of data points on a graph (or in raw data if needed). The problem with this is that I can’t just slap a series of points into an equation and expect any meaningful result. This issue is one I’ve been grappling with since I first saw these varying thrust curves, and I believe I've finally found a solution.
The solution I developed for the problem is one that seems shockingly simple when you first look at it. All I’ve done is calculate the slope between each point (using the slope formula of (xf-xi)/(yf-yi), or the delta-x over delta-y) and used those as my equations. The slope is an estimation of the change in force during the time between those two points, which is a variable I’m already using to calculate Jerk. This means I can very easily plug in the slope between those two points into my jerk equation, get the Jerk variable, and use that. The difficulty or annoyance with this method is that I need to do this calculation between every point, however I have some ideas on how to fix that in two weeks. In addition, this estimation method may not be accurate enough, which I’ll test next time by using a set of test data I developed myself as a baseline.
The Spreadsheet I’m using to test the method (and where previous ideas were tested) can be seen here: https://docs.google.com/spreadsheets/d/11QFaIN5TggM2PF5hD-tJt4xdMaGEqkxeT7qj5tbi2hA/edit