Why have a Max Zero Fuel Mass?
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I am seeing all these remarks zipping around and people keep reposting the definition of MZFW. The whole point of me adding to this thread and livening it up again was the attachment I found which explains centre tank fuel being used in reducing operational payload and what exactly is happening with wingroot/spar forces. Information that had not been alluded to before in the thread. Yes we all know ZFW doesn't include fuel, but that was probably invented before aircraft were designed that had centre tanks!
Chu Chu, yes correct, as per the attachment I put up in my post.
Chu Chu, yes correct, as per the attachment I put up in my post.
Just to explain my thinking a little more rigorously (and consistent with DeltaT's attachment), it's true that any weight added to the wing, considered by itself, creates a downward bending moment about the wing root. But if you think about it, weight added to the fuselage, considered by itself, creates only a downward force on the fuselage and has no effect on wing bending.
But any weight added anywhere on the aircraft (assuming level flight, symmetrical loading, etc) requires an equal increase in lift. The increase in lift acts through the center of lift on each wing and (considered by itself) creates an increase in upward bending moment about the wing root.
If the the weight is added to the fuselage, the upward bending caused by the additional lift is the end of the story. But if it's added to the wing, the the downward force from the weight must be considered.
If the weight is added inboard of the center of lift, it acts on a shorter moment arm than the lift, and partially offsets the upward moment. The net result is an increase in bending moment about the wing root, but smaller than if the additional weight were in the fuselage. Weight added at the center of lift acts on the same moment arm, and exactly offsets the upward bending from the lift. And weight added outboard of the center of lift acts on a longer arm and more than offsets the upward moment from the added lift, resulting in a net decrease in upward bending moment.
But any weight added anywhere on the aircraft (assuming level flight, symmetrical loading, etc) requires an equal increase in lift. The increase in lift acts through the center of lift on each wing and (considered by itself) creates an increase in upward bending moment about the wing root.
If the the weight is added to the fuselage, the upward bending caused by the additional lift is the end of the story. But if it's added to the wing, the the downward force from the weight must be considered.
If the weight is added inboard of the center of lift, it acts on a shorter moment arm than the lift, and partially offsets the upward moment. The net result is an increase in bending moment about the wing root, but smaller than if the additional weight were in the fuselage. Weight added at the center of lift acts on the same moment arm, and exactly offsets the upward bending from the lift. And weight added outboard of the center of lift acts on a longer arm and more than offsets the upward moment from the added lift, resulting in a net decrease in upward bending moment.
Aileron Upset
As an afterthought, is it fair to say that we've discussed wing bending on the basis of the simple case where the centre of lift always has the same moment-arm about the wing root? On swept-wing a/c it will change with speed, IIRC, but the structures men presumably allow for that. We've also talked about the merits of keeping the wing CG as far out as practicable for so-called wing-bending relief, which also and importantly reduces the stress on the wing root. Apart from design considerations such as the positioning of any engine mountings and the fuel tanks this can be achieved by the common practice of using fuel from the outer tanks last.
But a less-used, temporary method of wing-bending relief is to move the centre of lift towards the fuselage. On the Vickers/BAC VC10, for example, this was employed at high weights in the climb below F/L 240 by angling the ailerons, which were in the traditional position near the wing tips, slightly upwards. The system was known as aileron upset. With all its engines mounted on the fuselage, plus a centre-section fuel tank, the resulting deep wing root of the VC10 was a big design issue in terms of drag and weight. Consequently the VC10 and Super VC10 were less efficient in the cruise than their long-haul rivals, such as the B707-320B/C, which also enjoyed the twin advantages of a higher MZFW and lower APS weight.
But a less-used, temporary method of wing-bending relief is to move the centre of lift towards the fuselage. On the Vickers/BAC VC10, for example, this was employed at high weights in the climb below F/L 240 by angling the ailerons, which were in the traditional position near the wing tips, slightly upwards. The system was known as aileron upset. With all its engines mounted on the fuselage, plus a centre-section fuel tank, the resulting deep wing root of the VC10 was a big design issue in terms of drag and weight. Consequently the VC10 and Super VC10 were less efficient in the cruise than their long-haul rivals, such as the B707-320B/C, which also enjoyed the twin advantages of a higher MZFW and lower APS weight.
AfricanSkies says:
Strange?!!!! Impossible more like! Unless the fuel has a negative mass. You learn it all here.
Once the wings are fuelled, they provide a balance to the central fuselage mass, in effect lifting it, with the gear being the pivot, and the total load on all the gear is less. Sounds strange...
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I think the rule is to add centre tank fuel to the ZFW (or reduce the MZFW) if there is fuel in the centre tank with wing tanks less than full.
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Airframe manufacturers seem to have a much better understanding of avoiding fatigue cracks in wing structures now.
I remember the Trident wing crack problems in 1977 https://www.flightglobal.com/FlightP...20-%202406.PDF
Extra metal straps fitted under the wing and wing lift redistribution with less lift outboard (ailerons rigged upwards) and more lift inboard (flaps rigged slightly extended) in an attempt to extend the fatigue life.
Weight not carried in the wings will result in extra wing flexing / bending / stressing somewhere.
I remember the Trident wing crack problems in 1977 https://www.flightglobal.com/FlightP...20-%202406.PDF
Extra metal straps fitted under the wing and wing lift redistribution with less lift outboard (ailerons rigged upwards) and more lift inboard (flaps rigged slightly extended) in an attempt to extend the fatigue life.
Weight not carried in the wings will result in extra wing flexing / bending / stressing somewhere.
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With no fuel in the wings, certain aircraft can only take so much weight on the gear. Once the wings are fuelled, they provide a balance to the central fuselage mass, in effect lifting it, with the gear being the pivot, and the total load on all the gear is less. Sounds strange but once the wings are fuelled, more payload may be loaded. MZFW is a structural limit.
MZFW is a SUM of maximum payload added to aircraft that has or has not any fuel.
Period.
How will you load the fuel is another subject,
that can limit Max Fuel if wings are not full, but will not limit the MZFW.
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Practical use of MZFM limit
However, it's not the formula that bothers me, rather the practical use of MZFM. A/C can be limited either on take off by MTOM or on landing by MLM, but what a MZFM limitation on take-off represents? Ensuring wings won't bend in scenario we lose all fuel in flight? I wonder 2 things:
- How often MZFM limited MTOM happen in a real world? How often have you had to reduce your TOM due to MZFL limit?
- Is it a limit load, or the safety factor is reduced? In other words, if such a scenario zero-fuel in flight happens, and we're at the MZFM, does the limit ensure the wing won't bend permanently, or they will bend but not fail completely?
