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I am trying to calculate the critical loading conditions for Flaps (in order use them inside my Finite Element Analysis to, determine if the Flaps will be able to bear these critical loads) during the design phase of a civil aircraft. Below shows the generic V-N diagram for most of the civil aircrafts.

Now, I have the CFD results available for multiple combinations of angles of attack of the aircraft, with the deflection angle of the flap. I have to choose a couple, to input into my structural analysis of the flaps. How to determine the most critical loading conditions (Aircraft's angle of attack and Flaps' deflection at that angle of attack) for the flaps?

Now what is understood is that the greater the flap extension, the more overall Cl of the wing/aircraft (for the same angle of attack), and this will cause flaps to take more load during the flight (assuming that the extra load due to increase in Cl in just coming from Flaps only, and not from the actual wing).

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Therefore, when the flaps are deployed to full extension, that is when the flaps should take the maximum load. How should I determine and calculate the load factor at this maximum flaps deflection, and also maximum flaps extended speed for this case? If these both are known, then the angle of attack of the aircaft can be found, and hence that specific CFD result can be implemented in my structural analysis of the flap.

Is there a limit on the load factor that beyond which the flaps cannot be deployed (or fully deployed) during flight? Is it possible for the flaps to be deployed fully when the aircraft is undergoing limiting load i.e. 4.4g and -1.8g (as shown in the V-N diagram above)? Or a completely new and different V-N diagram should be built for the aircraft, where flaps are completely deployed?

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  • $\begingroup$ I think you are approaching this backwards. One computes the loads (and adds the desired safety margin) to determine the envelope boundaries. I.e you would use the FE analysis to determine the structural integrity and from that you set the envelope. The flaps will therefore be able to bear the critical loads because you’ve set them such that they will. $\endgroup$
    – Jim
    Nov 26, 2021 at 23:12
  • $\begingroup$ But that is the problem. For which loading conditions should I conduct my FEA? I mean there are hundreds of combinations of A.o.A of the aircraft with the flap deflection, and there might be a chance that some might even not be possible during the aircraft's life, so if I choose them and size my flaps in accordance with these, then I am essentially over-sizing the flaps. $\endgroup$ Nov 27, 2021 at 6:27
  • $\begingroup$ Everthing can become alot easier to work with if I know what is the maximum load factor that can be used with the flaps fully extended, then I already know the max/min Cl of the aircraft (when flaps fully extended) and I can then know the max/min velocity of the aircraft when flaps fully extended. $\endgroup$ Nov 27, 2021 at 6:27
  • $\begingroup$ Flap size is determined by performance goals for takeoff and landing, not by structural limits. The structure is designed to take the load required. $\endgroup$
    – Jim
    Nov 27, 2021 at 6:30
  • $\begingroup$ I think you are misunderstanding me. I never said that I need to size the flap (as in I need to size the surface area, span and chorlength of the flaps). What I meant is the thickness. If you are a bit familiar with the structures, then you would know that the thickness of structures will vary the stresses that the structure is undergoing, when subjected to transverse loading (as like lift). $\endgroup$ Nov 27, 2021 at 6:35

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The red zone in the graph is for high speed & load factor combinations, it is the zone where structural failure will occur. Trailing edge flap deflection is only allowed at limited airspeed, and the flap structural support is designed for those particular airspeeds only, with the usual structural safety margin of 1.5 of passenger aeroplanes (also mentioned in this question).

An example, from the B737 technical site:, Trailing Edge Flaps

Trivia: Although the flap placard limit speeds are different for each 737NG variant, the structural limit speed for the flaps is equal to the placard speeds (175k – F30, 162k – F40) for the heaviest variant (737-800/900). The Flap Load Relief trigger speeds (176k – F30, 163k – F40) are set to allow all variants to fly to the structural limit speed without system activation. Setting lower flap placard speeds for the –600 and –700 variants allows for greater service life of flap components due to the larger margins to the structural design speed.

So this is the Structural Limit Speed with extended trailing edge flaps.

  • From the V-N diagram, the maximum load factor at this speed will follow.
  • Maximum $C_L$ indeed follows from the lift curves, with the stall AoA taken as maximum. Leading edge devices need to be considered as well, since they allow for higher AoA, refer to the graph below from Torenbeek's Synthesis of Subsonic Airplane Design.

enter image description here

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