I know that the angle of incidence is the angle between the chord line of the wing and the longitudinal axis of the fuselage. I know that it doesn't change in flight because it is fixed.
And usually, there is a positive angle of incidence on airplanes, which means that the wing kinda looks like this:
credits: Naval Aviation Schools Command aerostudentguide(dot)pdf
My question is, why is there a need to incline the wing like that? Why is there a need for Angle of Incidence?
Strictly speaking, there is no need to set a particular angle of incidence- the wing will decide that for itself depending on the conditions (speed, weight, altitude etc.). What we are deciding is the The mounting angle, which is set for various reasons and is not variable in flight (except for some rare cases) including:
Mostly this is set so that the fuselage is (nearly) horizontal during cruise. This is especially important for airliners- DC-10, especially flew at a pronounced nose high attitude requiring the cabin crew to walk uphill.
Setting the wing at an incidence helps improve the visibility- this is important especially for carrier aircraft, where the pilot requires good visibility and also higher angle of attack (for keeping t/o and approach speeds low).
Setting the wing at an angle helps in keeping the drag low for the given lift. Having the wings at an angle and fuselage horizontal means that the drag is minimized, while the wing has the required angle of attack.
Though the angle of incidence is usually fixed, it can be varied in response to specific requirements. A good example is the Vought F-8 Crusader, which allowed the wings to be pivoted 7° out of the fuselage on takeoff and landing, resulting in a high angle of attack -- reducing the approach and take-off speed -- while keeping the fuselage level and giving the pilot a good forward field of view.
F-8 Crusader with the wing pivoted up during landing. By USN - U.S. DefenseImagery photo VIRIN: DN-SC-88-06695, Public Domain, Link
Another example is the Martin XB-51 which had a variable incidence wing to reduce the takeoff run.
The wing will pick the angle of attack that is appropriate for the given speed, air density and the needed lift. If it is too high, the aircraft will accelerate upwards which will reduce the angle of attack, and vice versa. The wing's angle of incidence will then define the angle at which the fuselage sits during flight. What a proper angle is depends on the aircraft:
The next important detail is the height of the tail surface relative to the wing's vortex sheet. If the tail is too far above, it will sink into the wing's wake during stall and become less effective. A deep stall stability condition might be the consequence. Only by defining the angle of incidence can the airplane be built and operated as designed.
My understanding is this. One of the design consideration of fuselage design is to avoid flow separation. And another important thing is that usual looking fuselage is not very efficient at providing lift because both above cases produce huge amount of drag.
So it is important to avoid the fuselage from separating flow and non-lifting/less lifting in normal configuration in cruse condition. To do so its important to keep the fuselage nearly horizontal
Secondly to produce max L/D or nearly max L/D wing has to operate in some positive AoA.
This can be achieved by introducing this incidence angle.
Let us denote $\delta_{wing}$ the incidence of the wing. For moderate values of the angle of attack of the airplane $AoA$ the lift coefficient of the wing has a linear behavior : $$Cl_{wing}=\frac{dCl_{wing}}{dAoA}(AoA+\delta_{wing}-AoA_0)$$ Where $AoA_{0}$ is the value of $AoA+\delta_{wing}$ for which the lift coefficient is zero. $AoA_0$ is a constant. Basically the incidence of the wing increases the effective angle of attack of the overall wing.
what we call THE angle of incidence of the plane is the angle between the velocity vector of the aircraft and the longitudinal axis of the aircraft. It is often denoted AoA The question clearly states angle of incidence ON airplanes not OF airplanes
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You understand that lift is generated by the action of the wing pushing air molecules down as it moves forward, requiring an angle of attack to the air passing under the wing? So if you don't tilt the wing with respect to the body of the aircraft, then to get the angle of attack required to generate lift, you would need to tilt the body as well, greatly increasing the (non-lift generating) surface area and so greatly increasing the drag.
Angle of incidence is required to generate lift if the roll axis is parallel to the airflow. Otherwise the fuselage would also be required to present AoA in order to generate lift. The wing's AoA = AoA of roll axis + angle of incidence and AoA is the primary creator of lift, not the shape of the wing, contrary to popular belief. Otherwise how could planes fly inverted?
