Research on transition corridor of distributed tilting power configuration

For a distributed tilt-power configuration aircraft, the transition corridor was studied based on limited conditions such as wing lift characteristics and propeller power requirement. By establishing the dynamic model of each component and balancing according to the balance equation, the boundary of the transition corridor of distributed tilting dynamic configuration is determined. The results show that the minimum forward flight speed required for a low Angle of attack is less than that for a high Angle of attack; the wing lift characteristic high-speed boundary and the propeller power limit boundary together form the high-speed boundary of the transition corridor.


Introduction
The tilting power configuration aircraft has the advantages of vertical take-off and landing and highspeed cruise, so it has become a research hotspot in the field of aviation.It can achieve multi-state flight through the tilting of the propeller, so the tilting transition of the aircraft is the most critical state in the whole flight process [1] .
It is necessary to adjust flight speed and propeller tilt angle in time to ensure the balance of aircraft force and torque.When transitioning from helicopter mode to fixed-wing mode, if the propeller Angle is too large or the airspeed is too low, it may pose a safety threat.At the same time, the rated power of the power system restricts the maximum flight speed in the current state [2] .Cao and Chen [3] proposed a method to determine the tilt-rotor transition corridor by using the particle model.Cheng et al. [4] established the balance equation of transition state based on Newton Euler method, and studied the method of determining the transition corridor of distributed propulsion VTOL fixed-wing aircraft under multiple constraints.
In this paper, an analytical method for determining the transition corridor of distributed tilting power configuration aircraft is proposed according to the characteristics of variable speed and variant in the transition state.The method is based on the reasonable matching of propeller and wing aerodynamic forces in the transition state, and then the transition corridor boundary is determined according to the lift characteristics of the wing and the available power of the propeller.

Transition corridor solution model
The distributed tilting power configuration aircraft studied in this paper mainly consists of the wing, flat tail and the distributed propeller system in front of it.In order to simplify the calculation and simplify the non-power system components of the aircraft, the calculation model is shown in Figure 1.
During the transition phase, the combined force and torque acting on the aircraft must be balanced, and it is mainly in the transformation of the longitudinal flight state, so this paper only studies the longitudinal motion dynamics of the aircraft.Figure 2 shows the external forces acting in the longitudinal symmetry plane of the system.In the figure, L, D and M represent the lift, drag and pitch moment of the wing respectively, T i (i=1, 2, 3, 4, 5, 6) is the pulling force of propeller 1~6 respectively, Q i (i=1, 2, 3, 4, 5, 6) are the torque of propeller 1~6 respectively, and G is the gravity of the system.
According to Figure 2, the dynamic relationship of the aircraft in the longitudinal plane is obtained: 0 where i=1, 2, 3, 4, 5, 6 represents the propeller number.
The distributed tilting power configuration has 6 propellers, and it is necessary to consider the aerodynamic interference between the propellers and the surrounding components, which can be roughly divided into parallel propellers and propeller/wing aerodynamic interference.There is a side-by-side effect between the left and right propellers.According to the XV-15 tiltrotor aircraft GTRS model [5] , the equation for calculating the mutual interference correction of the induced velocity of the left and right propellers is as follows: where X s is the parallel effect coefficient of the propeller, Ω is the propeller speed, R is the propeller radius, C T is the propeller thrust coefficient, and κ is the tip loss coefficient.
During flight, the propeller-induced airflow can change the angle of attack and relative velocity of the downstream wing.The wing is divided into two parts: one is affected by the propeller slipstream, its area size is A s , and the other is not affected by the slipstream area is A-A s .The area A s can be calculated by Equation (5).
where η s is the propeller slipstream correction factor, B is the propeller tilt Angle, c is the average chord length of the wing, μ max is the maximum advance ratio of the propeller wake deviated from the wing, a and b are 1.386 and 3.114 respectively [6] .In this paper, the aerodynamic coefficient is calculated by CFD.The aerodynamic force on the wing can be expressed as: where ρ is the air density, V and V T , C Lw and C Lh , and C Dw and C Dh are the wing incoming velocity, lift coefficient and drag coefficient in the freestream and slipstream regions, respectively.It can be obtained from the propeller aerodynamic model based on blade element momentum theory [7] .
where φ 0.7 is the reference twist angle of the blade, N is the number of propeller blades, k is the slope of the lift line of the blade, c 1 is the blade chord length, µ x and µ z are the dimensionless X-direction and Zdirection flow velocity, Δφ is the total blade twist angle, and ̅ is the inflow-induced velocity.The propeller power coefficient C P can be used in Equation (11) as follows [8] : where ̅ is the dimensionless inlet flow velocity perpendicular to the propeller disk, ̅ is the dimensionless propeller-induced velocity, K ind is the propeller-induced power correction factor, and σ is the propeller solid degree.The propeller thrust and power are calculated by Equations ( 12) and (13) [9] .

Boundary limiting condition
Within the boundary of the transition corridor, the distributed tilt-power configuration can achieve balanced flight at any flight speed and angle of the tilting propeller system.The realization of balanced flight is constrained by several constraints, including the limitations of wing lift characteristics and propeller power.

Wing lift characteristics limitation
It's necessary to fly in the safe angle of attack area when flying in the transition state, and the stall angle of attack and zero lift angle of attack of the wing correspond to the upper and lower limit boundaries of the lift characteristics of the wing respectively.The safe wing Angle of attack range can be determined by Equation (14).
where α stall is the stall angle of attack, α 0 is the zero-lift angle of attack, and ϕ is the wing installation angle.

Propeller power limit
Distributed tilting power configuration During tilting, the maximum flight speed is limited by the available power and dynamic stability of the distributed propeller system.The maximum forward flight speed corresponding to the conversion envelope is determined according to the available propeller power limit.The power limiting condition of the distributed tilting dynamic configuration is as follows: where P r is the power of a single propeller, and P e for the motor-rated power.

Example solution and analysis
The total weight of the configuration is 1000 kg, the plane wing chord length is 1 m, the propeller radius is 0.48 m, and the distributed propeller adopts synchronous tilting mode.

Calculation process
Figure 3 shows the calculation flow of the distributed tilt-power configuration transition corridor.The calculation process of the power limit boundary is as follows: the tilt angle and flight speed are set for the trim calculation to get the corresponding propeller power, and the propeller limit conditions are compared to get the propeller power limit boundary.The limiting boundary of wing lift characteristics is calculated as follows: given the angle of attack and flight speed of the wing, the aerodynamic force of the wing is calculated into the balance equation, and the limiting boundary of wing lift characteristics is obtained by using Newton method for trim calculation.

Results and analysis
Figure 4 shows the comparison between the calculated and test values of the built propeller model under hovering, and it can be seen that the accuracy of the propeller model meets the requirements.Figure 5 shows the variation of propeller tilt angle with flight speed under constant wing angle of attack in the safe angle of attack region of the wing.Under the same tilt angle, when the wing transitions from a large to a small angle of attack, the speed required by the aircraft increases, because the angle of attack of the wing is decreasing, and the flight speed required to provide the same lift is increasing.
Figure 6 shows the change curve of propeller power required with flight speed at different tilt angles, and the power limit of the motor.According to the power equality condition, the tilting angle-velocity power limit boundary can be calculated.Under forward flight conditions, the required propeller power first decreases and then increases with the increase of forward flight speed.This is because the forward flight speed gradually increases with the decrease of the tilt Angle, increasing waste resistance power.
Figure 7 shows the tilting envelope of the distributed tilting power configuration under various constraints.It can be seen that when the tilting angle is 90°, the maximum forward flight speed is 35 m/s, and the wing angle of attack is -6°.When the tilt angle is 0°, the minimum and maximum forward flight speeds are 33 m/s and 60 m/s, respectively.Meanwhile, the high-speed boundary of the distributed tilting power configuration tilting transition corridor is composed of the high-speed boundary of wing lift characteristics and the propeller power limit boundary.

Conclusion
In this paper, the transition curves of the distributed tilt-power configuration under different transition angles of attack are calculated.The curves corresponding to the zero angle of attack and stall angle of attack constitute the upper and lower boundary of the wing lift characteristics transition corridor, and the minimum forward flight speed of the safe transition is inversely proportional to the transition angle of attack.
For the distributed tilting dynamic configuration, the method adopted in this paper has a certain universality, on the basis of which the design parameters can be changed, the sensitivity analysis of the limiting boundary can be carried out, and the influencing factors of the configuration can be obtained.

Figure 2 .
Figure 2. Distributed tilt-power configuration system force representation.

Figure 5 .
Figure 5. Distributed tilt-power configuration system force representation.

Figure 6 .
Figure 6.Relationship between propeller power and flight speed at equal tilt angle.

Figure 7 .
Figure 7. Example configuration of the tilting transition corridor.