For the past month I have focused on problem finding. The goal was to define what the problem exactly is. Only after defining the exact problem, I want to solve it.
Here are some of the things that I found out so far:
John Cochrane makes a good effort, but is not perfect
John Cochrane, who published several papers based on a dynamic programming approach to contest flying, makes a very good effort at solving the problem. He assumes that we don’t know the exact weather circumstances (using a live internet connection, I do) and instead makes an educated guess about the circumstances. He models this as the probability to find a thermal of at least a certain strength (let’s say 2m/s) per kilometer traveled.
What I really like about his efforts is that he takes a step back from what I did in 2020: trying to specify exactly where to circle and where to glide. Instead, he outputs the most optimal MacCready setting for each location, which you can use to answer the question “should I take this thermal?”. I think this is a step up from my 2020 approach, because it gives you the optimal strategy regardless if the predicted thermals are actually present. He takes a step back from the ultimate uncertainty that I tried to reach with my 2020 approach, and provides more general answers to the same problem.
I do see one mistake in Cochrane’s papers though: he does not take the wind into account. Despite the fact that MacCready settings are valid regardless of the wind, your glide ratio with respect to the ground is different with headwind than with tailwind. This affects the amount thermals that you can expect to find before you run out of altitude. All of this means: you probably can fly with a higher MacCready setting with tailwind than with headwind, if you want to keep the range constant. This might cancel out the practice of flying a slightly higher MacCready value into wind, but it might not.
Another thing I miss in Cochrane’s papers is that he doesn’t consider flying in the wrong direction to make it home. Let’s suppose you are low on final glide and have just passed the last thermals you can expect. If you continue the glide, you will land out. But if you turn around, you could still climb and make it home.
What to optimize for?
I find it somewhat difficult to pick a mathematical goal to optimize towards. I find myself going back-and-forth between optimizing for competitions and leisure flights.
For competitions the rules are very clear and well-defined. One would optimize for the most competition points, and score potential outlandings accordingly. You neglect the consequences outside of the competition, which I’m not sure you would want.
For leisure flying, landing at home appears to be the most important goal. This naturally leads towards staying as high as possible, since that is the best guarantee against landing out (assuming the day is infinite). We can value outlandings according to the expected time it takes to reach home, which is probably quite long compared to slowly flying home. Landing on a remote airfield might speed things up a bit, as you have some help with disassembling the glider. Landing in rural areas or on water would be scored very high, since you might not survive this.