VFR, you ought to be able to revert to your map+compass at any point on the flight if you experience a multiple navaid failure.
IFR in IMC, you should immediately tell ATC of the failure and ask for assistance. They will quite happily vector you in these circumstances, I'm sure.
IFR in VMC is a slightly more tricky one, where it might be reasonable to expect the flight to continue VFR by reference to map+compass in some cases, but not all. The type of aircraft, the recency of the crew's experience of VFR flight, whether a VFR chart is being carried and the type of airspace the failure occurs in and the weather conditions on the day are all factors which immediately spring to mind.
Not sure I agree with the above cases, not least because they could all be legally done
OCAS and
non-radio. And we all know there is no ATS service OCAS in the UK, well not one that is likely to provide you with a radar service
And if you are talking to a radar unit already (e.g. LARS) then loss of nav isn't going to be a problem anyway. Unless of course it is a total electrical failure, in which case (take IMC) where is your handheld GPS?? Short of a global nuclear war, nothing is going to take out ground based navaids
and GPS.
In reality, backing up radio nav with dead reckoning means flying every leg with a map and a stopwatch, which few people (navigating using radio nav) will be doing.
Back to the subject, I don't see a problem with using DME alone as an aid to navigation. Often, on long distance flights OCAS, there is no navaid to hand to backup one's GPS. One may have to resort to using a TDME from somebody's ILS to get a position check. It's easy to use a
single DME in this way; take several readings. In fact I was told by a Concorde pilot (in the cockpit, after one of the last flights in 2003) that this is how the Concorde INS does its correction (a single DME, not triangulating two of them).
Printed charts are not mandatory (UK or USA) and it is a good question whether VFR charts are mandatory on IFR flights. They can hardly be so, since there are
no VFR charts for most of the world (start with Greece and work further along
). How many VFR charts would a long haul 747 flight need to carry? Approx 100.