How to handle vacuum and turn coordinator failure in IMC?
This isn't exactly your scenario but at my last instrument checkride the DPE asked me how I would descend from VFR-on-top through a solid cloud layer following complete electrical and vacuum failure (in a C172 or something similar). No avionics meant no help from ATC (vectors, or even a PAR approach) and we also assumed that I had no tablet, phone or other external systems that could help me.

The question came at the end of a discussion about aircraft systems and failures and the DPE didn't expect me to have a ready answer because it isn't something you train for. But he suggested this procedure:


Set up the aircraft on an east or west heading to minimize compass turning errors
Use the rudder only to fly a constant heading on the compass; once you have the aircraft going straight, do not move your feet again
Set power and trim for a stable descent at a little above Va and a little less than your usual descent rate, e.g. 300fpm
Sit back, cross your arms and wait to break out. Resist the temptation to touch the ailerons or power.


His reasoning was that by avoiding using the ailerons and power you can avoid going into a graveyard spiral quickly. You may still do it, but you'll do it a lot more gradually and hopefully by that point you'll have broken out anyway. I've never tried it myself, but I'll have to do it sometime with a safety pilot.

In real life, if you can't get to VMC easily then a tablet app with a portable AHRS unit would be a good backup. Although personally, if I ever lost the complete panel my first thought would be to get to VMC, not to shoot an approach. I suspect that for most people, landing in a field is likely to be the much better choice. But like all 'what if' scenarios, it depends.