In an emergency course reversal, passenger safety first priority, to avoid say, a column of ash from a new volcano, what it the most G a 747 can withstand with an average passenger complement?
It depends on how you define :withstand". China Airlines flight 006 experienced vertical load factors of up to 5.1 g on 19 February 1985. The aircraft could be landed safely and there were no fatalities, but there was considerable damage:
From the NTSB incident report:
The wings were bent or set permanently 2 to 3 inches upward at the wingtips; however, the set was within the manufacturer's allowable tolerances. The left aileron's upper surface panel was broken and the trailing edge wedge was cracked in several places.
The maximum load factor an aircraft can be subjected to is a function of time. Two cases are determined for civil aircraft:
- Limit load factor. For transport aircraft weighing more than 50,000 lb (22,680 kg) this load factor is equal to 2.5, while for lighter aircraft it is a function of the weight.
- Ultimate load factor = 1.5 times limit load factor, is the higher of the gust and the manoeuvre load factor.
The load factors are determined in accordance with the airworthiness regulations 14 CFR part 23.341 and 14 CFR Part 25.341. Damage tolerance of the airframe and the consequences of metal fatigue are stated in 14 CFR part 25.571.
The B747SP of the incident is an aeroplane that was designed and constructed in the 60s/70s, before Computer Aided Design and engineering were wide-spread, and the structures were designed with analytical mathematics and knowledge from experience, then tested for limit loads and ultimate loads. The more the design stresses can be modelled on a computer screen, the closer the wing ultimate load can be to 150% of limit load. Older aeroplanes did not have these modelling tools, and wings could end up to be stronger and heavier than they needed to be. Something that everybody applauds, but nobody wants to pay for with a higher ticket price.
A video of the B777 shows how the static testing for ultimate load is done: an actual wing is bent until it breaks. It is not a test of wing flex, it is a test of static strength.
The particular 747 of the incident had a wing designed for an MTOW of 378,000 kg, while actual MTOW of the 747SP was 320,000 kg: an extra load factor of 1.18. Fuel in the wing tanks provides extra bending relief, not for the ailerons though..
Civil aircraft certification requirements for airliners demand normal operations be possible up to 2.5g and down to -1g in clean configuration up to design manoeuvring speed, reducing above that speed. Googling EASA CS25 should show this for European-certified aircraft. The same design requirements furthermore specify that the structure must withstand loads in excess of these, but I am not quite sure as to the actual factors.
There have been accidents where design operational loads were exceeded which still ended with a safe landing.