If an Aircraft has an empty weight of 12 tonnes and a zero fuel weight of 17 tonnes, what is the max payload it can carry?
Assuming that you mean "a maximum zero fuel weight of 17 tonnes" you don’t know, as the maximum P/L is the difference between the operational empty weight (OEW) and the MZFW (I’m industry W&B and stuck with MZFW, even though I appreciate the idea behind using the more correct MZFM). On top of the BEW you have the operational items (pilots, galley supplies, various fluids, ELTs and a number of other items) which are not payload.
As worded, you know that the payload is 17 tonnes minus the BEW and the weight of the operational items, or 17 tonnes minus the OEW, and nothing about the max P/L.
I would say 5 tonnes, zero fuel weight - empty weight. Is this right?
Sorry, no.
Then it says the maximum take off weight is 21 tonnes. So does this mean that the maximum fuel weight is 21-17 = 4 tonnes?
No. It means that if the aircraft is loaded up to the MZFW you can only fill it up with 4 tonnes of fuel. Most aircraft can be fuelled with quite a bit more than this – but you will not be able to use MZFW.
Because the question says calculate the lift generate by the aircraft in kN after the aircraft has used 22,000lbs of fuel.
(MTOW in kg – 22,000 lbs/2,205)*9,82
But 22,000lbs = 10 (metric) tonnes? How can it use this if the max fuel weight is 4 tonnes?
See above.
One solution to the problem of the BEW (which should have been OEW, making matters even worse) plus the fuel used exceeding the MTOW is that the maximum ramp weight can exceed the MTOW. In other words, you can weight more sitting on the ramp than taking off. This enables aircraft to take off at MTOW even after a long taxi. You also have a max taxi weight, which can be lower than the MRW, meaning you will have to burn fuel at the stand from MRW before being able to taxi.
Good luck!
Fred
Repeating parts of previous posts, but I figure a complete reply to the original question is often better than connecting patches of other replies.