My immediate response? A quick scan to ensure everything else seems to be working and that the plane's still under control, a quick report to NorCal basically just saying I've lost my turn coordinator but I'm currently VMC so no big deal but I don't want any routing into IMC, then... not much, to be honest. It's VMC, I can see Oakland (the city, not the airport, at any rate) way up ahead, the rest of the panel is still there and working, and I'm now flying (manually) straight and level towards SUNOL after the brief turn. In IMC it'd be very different -- an immediate emergency -- but the first thing that comes to mind this time is "why do they make the TC flag so bloody innocuous? It ought to be a flashing annunciator somewhere up there with the others or on the unit itself", then "why didn't I hear the autopilot disconnect itself?" (probably because I was talking to the controller and missed it). But over the next few minutes I also can't stop thinking "this would be a major challenge in IMC...". On the 172s I prefer using the turn coordinator for keeping the wings level to using the AI, since it's easier to see the TC. Yes, this isn't true of the vast majority of planes, but that pathetic little AI in the 172s I fly just doesn't give you much to go on compared to, say, the PFD in the Cirrus 22. And yes, I have no trouble just using the AI -- it's a convenience thing mainly.
My other response? Amazement at just how quickly the turn coordinator went belly-up -- no warning signs, none of the usual bearing noises, nothing -- just a flagged TC in the space between scans. And this with a new TC that replaced the previous one that failed a few months ago. Yes, the TC still appears to be working -- well, it reflects turns correctly -- but it's sitting there effectively useless for real flying or for the autopilot. And distracting -- way too easy to see out of the corner of my eye. So I scrabble around in my flight bag for the covers, without much success. Another lesson -- keep the bloody covers truly handy, not just buried in your flight bag somewhere (I knew that!). An emergency wouldn't quite be the right time to be digging into your flight bag in the backseat looking for these things.
A sobering experience, for sure. It seems to be starting a tradition of sorts: a few years ago, on my second flight as PIC after getting my complex endorsement, I had a gear failure (a total non-event in the Arrow, thankfully -- the simple emergency gear mechanism works wonderfully compared to the contortions needed to crank the gear down in some other models...); the second time I fly IFR after getting my rating... well, I'm sitting here with a broken TC. One more memento mori for the collection.
And the rest of the fight? Scenic, relaxed, easy, enjoyable. But somehow I was still quite nervous beforehand -- my first completely solo IFR flight -- which (again) seems ludicrous, but there you are.
Another lesson in real-world IFR flying -- following John's lead I ask for direct BORED as I depart Monterey but get direct BUSHY instead after a minute or so, an even better deal (either will save more than 90 nautical miles compared to the standard routing over Panoche VOR (PXN)... I idly wonder what'll happen if I ask for the ultimate, "direct SUNOL", but decide not to push my luck). On the way down in the early stages of the NEUVO5.SHOEY departure from Oakland I get direct MUNSO (the ILS LOM at Monterey) from a little past San Francisco (KSFO), which seems a stretch -- why not direct Salinas VOR (SNS) which is a feeder route point for the LOC/DME 28L I'd just asked for? No big deal in 2SP, a /G, but just one of those ATC mysteries...
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Take a look at the Monterey LOC/DME 28L approach sometime. One of the reasons I did this flight was to try that approach in daylight VMC to get some practice with it before having to do it at night or in actual someday (Monterey's a popular destination for friends of mine, an easy hour's flying away from here, but a dreadful three hour drive). Terrain clearance is the issue here. Done visually, it's an eye-opener -- I was routed over a shallow saddle near some peaks at or above my altitude, then descended over sloping ground towards the airport. The ground slope basically mirrors your glideslope nearly all the way down, so you never seem to be more than 1,000' AGL at any point in the procedure, and you have rising terrain only a few thousand feet laterally. Not a difficult approach, but there's not a lot of room for lateral or vertical error on almost any part of the procedure (like the nearby Salinas ILS 31 approach, with that same range in the picture).
The Monterey ILS 10R is more likely in really bad weather, but it has a note that prohibits coupled approaches. I'm not sure what the thinking is here unless they're concerned about the unusability of the ILS after the middle marker (see the other approach note). Why the lack of reliable ILS after the MM? I'm not sure about that either, especially since in that direction terrain isn't a factor, and there don't seem to be any interesting buildings or reflective problems in the neighbourhood.