Day 2 was a busy day– by this point, I was settled into the apartment and was able to navigate around through Manhattan fairly well. We spent the morning in the classroom talking about various types of approaches, primarily ILS and VOR approaches.
There are two basic types of instrument approaches: precision and non-precision. The method of navigation for the approach determines how precise an approach you can fly. Some approaches give you guidance on whether you’re left or right of the runway centerline (lateral guidance), but you have to figure out your own vertical position. Others give you both lateral and vertical guidance. For example, an LNAV approach gives lateral guidance but no vertical guidance, while an ILS approach gives lateral and vertical guidance. A precision approach is one where vertical guidance is provided by a ground reference, e.g. the glideslope signal transmitted by an ILS. A non-precision approach can still include vertical guidance, but it’s either calculated or measured by something aboard the airplane. For example, my onboard GPS can use barometric pressure differences to calculate the current altitude, and it knows where the airplane is along the approach course. The diagram for each approach includes a profile view that shows what your vertical profile should look like on approach, such as this profile from the ILS to runway 17 at the Montpelier, Vermont airport:

The underline beneath those numbers has a simple meaning: don’t go lower than that altitude at that point in the approach or you might die.
Let’s say that the GPS sees I am between the REGGI and JIPDO waypoints. It knows that I can descend a maximum of 600′ between the two. By using either GPS altitude data (VNAV) or altitude data derived from the current altimeter setting (Baro-VNAV), it can give me a visual indication of how much I should climb or descend to follow a smooth path along the approach course.
After all that, it was time to go flying in the ancient simulator. This particular sim doesn’t have a GPS but that wasn’t a problem given what we were doing. I (mostly) tamed the roll axis sensitivity and flew pretty well; we flew a couple of approaches and then took a break for lunch at a nearby Mexican place, thence to the airport. Our planned route was pretty interesting: Manhattan-Salina-Newton-Emporia-Manhattan. It makes a pretty square, as you can see below:
We flew one approach at each airport; I forgot to note exactly which ones, but I’d guess (based on the approach plate history in my iPad) the ILS 35 at Salina, the VOR/DME-A at Newton, and one of the GPS approaches at Emporia, plus the GPS at Manhattan. 3 in the sim and 2.6 PIC in the airplane made for another fun-filled day!
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