# Why is maximum zero fuel mass used in take off mass calculation?

In calculation we consider maximum takeoff weight , maximum landing weight and maximum zero fuel weight

we selected the lowest of below mentioned

1. Maximum Zero fuel weight + Take off fuel
2. Regulated take off mass
3. Regulated Landing mass + Trip fuel

"2" and "3" are related to structural limitations that if we cross we might damage the aircraft or runway while doing landing or takeoff . My understanding is since both Regulated take off weight and Maximum Zero fuel weight is related to structural limitation during take off so Maximum Zero fuel weight would be factor while calculating the Regulated take off weight itself. Then why does we consider Maximum Zero fuel weight separately while calculating take off mass?

The calculation that needs to be made is: when trip fuel is subtracted from the MTOW, is the Max Zero Fuel Weight exceeded? MZFW is a structural design limit as well. The weight difference between the MTOW/MLW and the MZFW may only be utilised for addition of fuel.

From Torenbeek, Synthesis of Subsonic Airplane Design:

The empty tank case can be a critical loading case in certain critical areas of the structure at positive load factors, as there is no relieving load due to the fuel mass. For some aircraft there may be a limit to the weight for initiating fuel transfer between tanks (Maximum Design Fuel Transfer Weight. MFTW) .

Picture above is also from Torenbeek page 269, and lists the components of the various weight groups. For instance Operational Empty Weight + Payload = Zero Fuel Weight, Zero Fuel Weight + Fuel At Takeoff = Takeoff Weight etc. All operational actual weights must be below the maximum values imposed by the aircraft manufacturer.

• Doesn't maximum take off weight include maximum payload and Max fuel on board ? Jan 10 at 8:23
• Not necessarily... Jan 10 at 8:29
• Then can you explain more about Maximum take-off weight Jan 10 at 8:40
• MTOW is a performance limitation, the total mass the engines have to push, and the wings have to lift. MZFW is strictly a structural limitation that limits the bending applied to the spars by the weight of the payload in the fuselage that has to be born by the wing spar roots. Load above MZFW can only be fuel in the wings that is not adding to that spar root bending load. Jan 10 at 13:58
• @JohnK I believe MTOW is a structural limitation and also a weight established by the manufacturer during the aircraft's certification process (must meet minimum required engine inop climb gradient). It does not vary with environmental conditions, runway length, obstacle climb performance requirements, etc. Max allowable or permissible takeoff weight is a performance limitation. Jan 10 at 14:41