# How is the Max Zero Fuel Weight used in calculating weight and balance?

In some weight and balance apps there is an option to "Use Max Zero Fuel Weight". Having never seen this in any of the aircraft I have experience flying, I am curious how this value is typically used in the calculation of an aircraft's weight and balance.

Can someone give me an example of how this value is used in a weight and balance calculation?

Maximum Zero Fuel Weight is an operating limitation intended to protect the wing spar structure by limiting the concentration of load, relative to all up weight, borne by the wings in the middle of the span. In other words it limits spar bending loads at the wing roots imposed by the mass in the fuselage because any additional weight must be in the wing tanks where the additional load doesn't add to root bending.

Generically, Zero Fuel Weight can just mean all up weight minus usable fuel. However, when an instruction says to use "Max Zero Fuel Weight" it's saying to apply a published MZFW value that is an operating limitation. In your case you would enter the Max ZFW value from the airplane's Operating Limitations in the AFM into the app.

• I think your answer would be stronger if you reworded to say that the MZFW is one of the structural design weights.
– JZYL
Commented Apr 10, 2020 at 1:35
• For pilot purposes, it's an operating limitation. Commented Apr 10, 2020 at 2:43
• I would tend to agree with this answer. The Learjet 35 has tip tanks. It does not have a published max zero fuel weight but instead a max zero wing and tip fuel weight. Learjet calculates the weight of the fuselage fuel as part of the latter just for the reason stated above. Commented Apr 10, 2020 at 13:33
• "In other words it limits spar bending loads at the wing roots imposed by the mass in the fuselage..." In what situation this spar bending moment is more pronounced? In the air or when an aircraft is on the ground? Or perhaps both? Commented Aug 24, 2023 at 19:02
• In the air, either from pulling G, or from a gust load. The more probable case is gust loads, say from flying too close to a thunderstorm cell. There is a "turbulent air penetration speed" and if you respect that and the loading limitations, you can't, in theory, overstress the airplane. Commented Aug 24, 2023 at 19:35

Zero Fuel Weight is the weight of the aircraft with everything loaded for that flight, minus useable fuel (Takeoff Weight minus weight of useable fuel).

The Zero Fuel Weight in your weight and balance calculations are just a reference mark. It is not used for much if anything in most flight applications since you should never get to within 30 minutes of your empty status. This reference is useful in calculating other reference points. One of which is your maneuvering speed (Va). If you know your Va at your takeoff weighting your Va at your Zero, it gives you an envelope to remain within when it is necessary to slow down to Va. Slowing down to your Landing Weight Va speed during turbulence is your best option.

Your Center of Gravity calculation is just as important. Keeping Takeoff, Landing, and Zero Fuel CoGs in the envelope ensures best performance for things such as spin recovery and stability during all phases of flight.

– Ralph J
Commented Apr 10, 2020 at 3:38
• Also, ZFW is used plenty for everything than shows fuel remaining in lbs or kg. Add current (or projected landing) fuel to your ZFW to get current GW or projected landing weight. About anything with an FMC has that functionality.
– Ralph J
Commented Apr 10, 2020 at 3:48

There could be two interpretations of this - Do we want to know (i) the Maximum ZFW for the particular flight, or do we want to know (ii) the calculations based on the MZFW certification, let's call it 'DESIGN' Limitation?

Here are figures for a large existing airplane:

MAX DESIGN WEIGHTS based (TONS)

DESIGN TAKEOFF - 351.5

DESIGN LANDING - 251.2

DESIGN ZFW - 237.7

The above weights must not be exceeded.

Typical DOW^^ - 175.0

^^ DOW - The Operator publishes the Dry Operating Weight. This is the basic/empty weight of the airplane alongwith standard furnishings, crew complement with their luggage, pantry load, etc. - generally any regular load that is not fuel and not payload. DOW is arrived at by calculating the sum of all components of the airplane, as well as actually weighing the airplane.

Example for interpretation (ii) above:

Using MAX DESIGN ZFW

MAX Payload (DESIGN) = 237.7 - 175.0 = 62.7 TONS

MAX DESIGN ZFW, limits Fuel to to 351.5 - 237.7 = 113.8 TONS

The Fuel tank capacity is about 145.0 TONS, so we lose a possible 31.2 TONS of Fuel/about 4hours of flight if we carry MAX DESIGN Payload.

An example of interpretation (i):

Based on Route, forecast winds, weights (!) etc. and available RWY at a particular point in time at a particular airfield, the dispatcher/Pilot calculations yield the following numbers:

RTOW = 342.0 TONS, REGULATED TOW, calculated for actual conditions

MINIMUM FUEL = 119.4 TONS, by calculation under actual conditions

RTOW - MINIMUM FUEL = MAXZFW = 222.6 TONS (= a loss of 15.1TONS) i.e. only 47.6 TONS OF Payload compared to the MAX 'DESIGN' value of 62.7 TONS.

SOME ARITHMETIC

The Take Off Weight is the sum of the following three weights:

DOW (as described earlier at ^^)

PAYLOAD - The Commercial Dept. are the ones who know how much Payload there is for the flight. We assume, in general, that they always want to load the flight to the fullest.

FUEL - The Dispatcher and Pilot are the ones who calculate how much Fuel is required to despatch the flight.They also calculate the performance limited MaxTOW for the flight (aka Regulated TOW, RTOW).

Take Off Weight, TOW = DOW + Payload + Fuel

When we add Payload to the DOW we get the Zero Fuel Weight:

DOW + Payload = ZFW, this should not exceed the Max DESIGN ZFW Limitation in any eventuality.

Substituting ZFW for DOW + Payload:

TOW = ZFW + FUEL.

As mentioned earlier, the Dispatch and Pilot calculate the Minimum Fuel and the Maximum TOW (RTOW)for the flight. The Pilot may choose to carry more than the Min fuel if the preflight briefing indicates a need for more fuel (marginal weather, last minute technical issues, etc.), last minute issues can also reduce the RTOW (RWY change eg). So the allowable load for the day is:

RTOW - Fuel = Max ZFW for the flight.