# Research on Separation and Emission Reduction of Regional Airliner Based on Wake Encounter Response Model

Authors: Weijun Pan; Hao Wang; Yuming Luo; Jingkai Wang; Shuai Han
Journal: Journal of Advanced Transportation
 (2022)

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## Abstract

To ensure the safety of aircraft operation, the current regional passenger aircraft maintains a large distance from the preceding aircraft in actual operation, which result in reducing the operation efficiency of airports and airspace, and increasing pollutant emissions. To address these issues, in this paper, two aircraft types are selected in which the CRJ-900 encounters the trailing wake vortices of the A380 in front. An improved strip model is developed to build the CRJ-900 overall response wake encounter value. First, the safety of the CRJ-900 longitudinal and lateral wake encounters in different flight stages is analyzed. Second, we calculate the critical safety separation and its impact on air transport efficiency. Third, we use the LTO model to measure the reduction of aircraft fuel consumption and pollutant emissions. The results demonstrated that the medium-sized aircraft CRJ-900 has the potential to reduce the wake separation when following the super-heavy A380 aircraft. In terms of the critical safety separation calculated by the safety index, the operating efficiency of airports and airspace could be effectively improved, allowing the reduction of pollutant emissions during aircraft take-off and landing. During the takeoff, level flight, and landing phase, the results are summarized as follows: when the CRJ-900 is 13km away from the A380, the maximum lift variation is 11334N, 8157N, and 7366N; the maximum rolling moment variation is 43836N•M, 35274 N•M, and 28487 N•M; the maximum value of the rolling moment coefficient (RMC) is 0.0171, 0.0160, and 0.0130; when the RMC critical value is 0.031, the maximum safe separation for different flight stages is 11960m, which is 1040m shorter than the existing separation; when the RMC critical value is 0.05, the maximum safe separation distance of each stage is 10083m, a reduction of 2917m compared with the existing separation; when the RMC threshold is 0.07, the maximum safe separation of different flight stages is 9021m, a reduction of 3979m compared to the existing separation; when the RMC value is between 0.031-0.07, the fuel consumption can be reduced by 7.9%–12.8%, and the pollutant emission can be reduced by 9.1%–12.8%.


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## Body

## 1. Background

Wake vortex is a by-product of aircraft lift, which affects the safety of aircraft operation. In particular, the wake generated by super-heavy aircraft has the characteristics of large initial circulation, long transmission distance, and long duration, which may bring safety hazards to the trailing aircraft. In practice, the design of regional airliners is different from that of conventional airliners. At the same time, the impact of the aircraft wake in front on the regional airliners is still unknown, yielding a large approach and take-off interval used by airports during the control process. That will result in low runway utilization and limit the capacity of controlled airspace, also increase fuel consumption and pollutant emissions. To achieve the purpose of energy saving and emission reduction, it is necessary to study and analyze the safety of the wake vortex that encountered on the regional airliner, allowing for the reduction of the wake interval and the improvement of the control operation efficiency.The outline of this paper is shown in Figure 1. First, the models of wake generation and evolution were analyzed, and different models of wake-induced velocity were compared to determine the mathematical model of wake dissipation. Second, we analyzed the possible scenarios of wake encounters in different flight stages, and the aerodynamic response model of the aircraft's overall wake encounters was constructed. Finally, to study the impact on energy saving and emission reduction under this separation, we selected the appropriate safety index and analyzed the safety of wake encounter, and also calculated the critical safety separation of wake in different flight stages according to the limit value of rolling moment coefficient.Figure 1
The framework of this research.


## 2. Literature Review

Based on the research ideas of this paper, the research status of wake generation, evolution, and wake encounter is summarized.The generation and development of aircraft wake is related to factors such as aircraft configuration and atmospheric environment. The atmospheric environment is unpredictable, and the evolution and dissipation of the wake also changes, which is difficult to predict. Experts and scholars have carried out a lot of research on this.For the study of wake generation and subsequent encounter, Crow conducted a large number of observations and experiments in the 1970s to study the generation and dissipation mechanism of approach wake [1]; NASA Langley Research Center analyzed the effects of turbulence and Reynolds number on the motion and attenuation of wake vortex in the atmospheric environment, and established the first wake dissipation model [2].Luton et al. [3] used numerical simulation technology to study the wake evolution in the near-earth stage, and found that the mutual induction between the wake vortex and its mirror vortex would cause Crow instability; Sarpkaya [4] used numerical simulation and by means of the detection experiment at Memphis Airport; the simulation and measurement data were compared, and a new wake dissipation model was established on the basis of the Green model to predict the wake dissipation in the real atmospheric environment [5]; at the same time, this model has been used in the Aircraft Vortex Spacing System developed by NASA [6]; Proctor and Han [7] used the three-dimensional large eddy simulation method to study the influence of ground effects on wake dissipation. It was shown that the ground effect will affect the wake vortex trajectory and descent rate at a height of about 3 times the initial vortex core spacing. When the vortex core drops to 0.6 times the initial vortex core spacing from the ground, the ground effect will rapidly reduce the wake intensity; Robins et al. [8] proposed an algorithm for predicting the trajectory and intensity decay of aircraft trailing vortices and used a database to compare the algorithm prediction and measurement data; Holzäpfel [9–11] comprehensively considered the effects of turbulence, atmospheric formation, and wind on wake dissipation, and proposed a two-stage wake dissipation model to represent the dissipation of the entire wake vortex field, and this model has been used in the Wake Vortex Advisory System; Proctor et al. [12] proposed a wake for real-time prediction of wake transmission and intensity attenuation tass driven algorithm for wake prediction, which takes into account the influence of meteorological factors on wake evolution; at the same time, through the research method of large eddy simulation, a three-stage wake dissipation model was proposed on the basis of the two-stage wake dissipation model [13]; [14]; Breitsamter [15] explained the wake from near-field to far-field by combing wake research projects, models, flight experiments, and numerical simulations. In the same year, Hennemann and Holzäpfel [16] conducted a large eddy simulation of the wake evolution under different atmospheric conditions, and analyzed the influence of turbulence level and temperature split on wake generation and evolution; De Visscher et al. [17] considered the influence of wind (crosswind and headwind components) on wake transport dissipation and developed a rapid prediction of wake behavior; the software could predict in real time the time evolution of the wake vortex generated by the evolution of a given aircraft under given environmental meteorological conditions; the influence of terrain changes on wake dissipation was studied, and plate-like lines were added on the ground to achieve accelerated wake dissipation [18, 19]; the dissipation of near ground wake can be studied by lidar detection [20, 21].The formulation of wake separation standard not only considers the dissipation of wake in the atmospheric environment but also needs to consider the resistance of aircraft when encountering wake. Therefore, it is of great research significance to evaluate the safety of wake encountering. NASA obtains wake dissipation and aircraft response data in the actual atmospheric environment through actual flight experiments, and establishes a wake encounter database [22]; Netherlands Aerospace Center has developed wake (wake vortex induced risk assessment) for S-wake, ATC wake, and I-wake projects to evaluate the safety of reduced separations [23, 24]; The safety assessment of wake encounter severity can be reflected by the required angular velocity [25], maximum roll angle velocity [26], roll moment coefficient [27], wake encounter roll control ratio [28], wake vortex kinetic energy and vortex resistance when the roll torque and damping torque are turned parallel [28] WSVS is used to study the aircraft type pairing, main weather conditions, and the resulting wake vortex behavior. It is found that the great potential of safely reducing aircraft spacing mainly exists in sufficiently strong crosswind conditions [29] by comprehensively considering the final approach track, the influence of crosswind, and the wake bearing capacity of rear aircraft, an optimization model of wake separation under paired approach is established [20, 30].With regard to the research on aircraft pollutant emission, the International Civil Aviation Organization [31] established the model emission database and used the standard takeoff and landing cycle to calculate the pollutant emission of aircraft below 1000 m in different flight stages within the airport; based on the ICAO emission model, the pollutant emission estimation during thrust reduction is studied by using discrete data [32]; The Federal Aviation Administration has developed sage (Global airspace aviation emission assessment system); Boeing proposed BM2 method to modify the ICAO model and estimate the pollutant emission in actual flight more accurately; based on ICAO database, BM2 model, and basic aircraft data (Bada), European Air Traffic Control Agency developed advanced emission model to estimate actual pollutant emissions through 4D track data (Euro control); Cook et al. studied the weight relationship between different pollutants, obtained the concept of dynamic cost index covering emission cost, and used it for flight delay analysis [33]; the four-dimensional emission database list is established by using ATC track data [34]; Schumann optimized route pollutant emission through wake cloud and fuel consumption [35]; Jiang et al. analyzed the new aircraft ground taxiing mode and study its impact on airport pollutant emission [36]. Combined with the single runway ground taxiing method, the aircraft pollutant emission assessment model of Regional Airport is established [37].In this paper, by analyzing the generation and dissipation process of tail vortex in different flight stages, the stress model of CRJ-900 encountering wake is established by using the aerodynamic method of strip model. According to the aircraft operation performance and relevant risk safety indicators, the safety of CRJ-900 encountering wake in different flight stages is studied and analyzed. Using the limit value of safety index, the critical safety separation in different flight stages is deduced, its impact on operation efficiency is analyzed, and the reduction of pollutant emission is estimated.


## 3. Materials and Methods

The wake encounter safety mainly depends on the wake vortex strength of the aircraft generating the wake and the response of the follower aircraft when encountering the wake. Therefore, it is necessary to study the wake vortex characteristics, dissipation, and the response model of the wake encounter.


### 3.1. Wake Dissipation Model

In the initial dissipation stage, the strength of the wake decreases mainly by itself, so the dissipation speed is slow; the time for the wake vortex to enter the fast dissipation stage is related to the dimensionless vortex dissipation rate; the calculation formula of wake vortex entering fast dissipation timetw is as follows:(1)tw=tz0.7475ε∗0.75,ε∗≥0.2535,twε∗=twtz0.25e−0.7twtz,0.0121≤ε∗≤0.2535,tw=tz9.18−180ε∗,0.001≤ε∗≤0.0121,tw=9tz,ε∗<0.001,where tw is the time to start the rapid dissipation phase, tz is the characteristic time, and its calculation formula is(2)tz=bxvx,where bx is the initial wake distance and vx is the initial characteristic velocity of the wake.ε∗ is the eddy dissipation rate, and its calculation formula is as follows:(3)ε∗=εbx1/3vx=2πbxεbx1/3Γx=π2ρVBbxεbx1/32mg,where ε is the turbulent dissipation rate, and the calculation formula is as follows:(4)ε=Cmu0.75k1.5l,where Cmu=0.09 is a constant, k is the turbulent kinetic energy, and l is the characteristic scale of turbulence.By calculating the wake duration in the near-field region and comparing it with the time of CRJ-900 encountering wake, we can determine whether CRJ-900 is encountering near-field wake or far-field wake.(5)Γx=4MgρπBV,bx=π4B,rx=5.2%bx,where M is the weight of the aircraft, g is the acceleration of gravity, B is the wingspan of the aircraft, and V is the flight speed of the aircraft.Based on the AVOSS system, NASA has developed an APA model of wake dissipation. The equation is(6)Γ∗=ΓΓ0=exp−C+0.25N∗2t−twtw,where C is a constant, usually 0.4525; tw is the time for the wake vortex to enter and dissipate rapidly; 0.25N∗2 represents the effect of atmospheric stratification on the dissipation of the wake vortex.In this paper, A380 aircraft is selected as the aircraft to produce wake vortex for calculation, and the specific model parameters are shown in Table1.Table 1
A380 type parameters.
TypeWingspan (m)Cruise speed (m/s)Final approach speed (m/s)Maximum takeoff/landing weight (kg)Wing area (m2)Wake classificationA380-80079.75290.96770.993560000/386000845HThrough the customs clearance calculation, we can get the dissipation of the wake vortex of A380 in different flight stages under different atmospheric stratification and turbulence degree, as shown in Figure2. From this, we can know the dissipation of A380 aircraft wake vortex at different time and distance, as shown in Table 2.Figure 2
Variation of wake vorticity in different flight stages. (a) Circulation changes with time. (b) Circulation varies with separation distance.
(a)(b)Table 2
A380 wake dissipation parameters.
Flight phaseΓ (m2/s)vx (m2/s)tz (s)ε (m2/s4.5)ε∗ (s−0.5)tw (s)Circulation value at different separationΓlm2/s7.49.311.113Takeoff11372.5324.750.1440.8223.26142.070.838.018.3Level flight5531.4143.976.30310.885.971.436.520.510.3Landing7731.9631.870.1050.9526.56101.850.927.513.4


### 3.2. Wake Encounter Analysis

There are three ways for aircraft to enter the wake vortex field of the front aircraft: (1) across the front wake; (2) longitudinal entry into double wake vortex of front aircraft; (3) longitudinal entry into the single vortex of the front aircraft. The details are shown in Figure3.Figure 3
Schematic diagram of different modes of wake vortex field before aircraft entering.


#### 3.2.1. Across the front Wake Vortex

When the aircraft crosses the wake vortex of the front aircraft, as shown in modea in Figure 3, it will experience a backward wash up wash down wash up force, which will cause a large turbulence of the aircraft, resulting in a sudden change in the altitude, speed, and attitude of the aircraft. In serious cases, it will cause the aircraft out of control, or even cause a safety accident.


#### 3.2.2. Longitudinal Entry into Double Wake Vortex of front Aircraft

As shown in modeB in Figure 3, when entering the double vortex of the front aircraft longitudinally, the aircraft will suddenly drop height due to the influence of downwash air flow. At high altitude, the pilot has enough time to respond to the adjustment;.In the takeoff and approach phase, sudden height drop is easy to cause safety accidents.


#### 3.2.3. Longitudinal Entry into Single Wake Vortex of front Aircraft

When the aircraft enters the center of the single vortex in the wake of the front aircraft, as shown in modeC in Figure 3, the two wings are subjected to the upwash force and downwash force, respectively, causing the aircraft to roll. When the roll angle is too large, it will cause the aircraft to lose lift, or even enter the weightlessness state, causing safety accidents.The velocity field generated by the wake pair when encountering an aircraft is not uniform. The velocity of the flow field varies greatly on the surface of the aircraft, as shown in Figure4. The classical aerodynamic model suitable for uniform flow field is not suitable for calculating the aerodynamic force and torque generated by flow field, so a distributed aerodynamic model is needed [38]. Standard methods include strip method and lifting surface method. They require the velocity vector of each time step discrete point (generally one point for each aerodynamic section) to be simulated, as shown in Figure 4(b).Figure 4
Strip model of wake vortex encountering. (a) Aircraft encountering wake vortex. (b) Discretization of strip method and local airspeed.
(a)(b)In the strip model, the aircraft is simplified as wing, fuselage, horizontal, and vertical tail surfaces. The black lines in Figure4(b) represent a simplified aircraft model. For each strip element, the angle of attack caused by eddy current is calculated. In order to prevent the local angle of attack from exceeding the maximum angle of attack, the strip model realizes the special limitation of the maximum angle of attack.


### 3.3. Response Analysis of CRJ-900 Aircraft

When following the front aircraft, the wake of the front aircraft will mainly cause the force change, roll change, and height change of the rear aircraft, while when crossing the wake of the front aircraft, it will mainly cause the force change, pitch change, and height change of the rear aircraft. In this paper, the calculation method of each physical quantity of CRJ-900 encountering wake is given, and the simplified force model of CRJ-900 is given. The parameters of CRJ-900 are shown in Table3.Table 3
Geometric main dimensions of CRJ-900-700 aircraft.
Wingspan (m)Wing area (m2/s)Maximum takeoff weight (kg)Maximum landing weight (kg)Cruise altitude (m)Cruise speed (m/s)24.8570.61365043334012496245.83


#### 3.3.1. Aircraft Lift

The calculation of wing lift variation is shown in formulas (7) and (8):(7)ΔL=12ρV2∫−B/2B/2Cl′yCLydy,where ΔL is the lift variation, Cl′y is the lift coefficient variation, CLy is the spanwise coordinate of the aircraft wing, and y is the chord length. The lift variation of aircraft is mainly caused by the wing, so only the lift variation of the wing is considered when calculating the lift variation in this paper.(8)Cl′y=fΔαy=f arctanVvyV≈fVvyV,where f is the lift line slope, Δαy is the angle of attack variation of the wing section, and Vvy is the induced velocity of the wake field on the wing section.According to the momentum theorem, the calculation method of the force on any part of the body when encountering the wake is given in equation (9) as follows:(9)F=ρSVvy2,where F is the force on any part of the aircraft body and S is the projected area of any part of the aircraft.


#### 3.3.2. Calculation of Rolling Moment

The calculation of wake induced torque revolves around the basic principle of torque, that is, a force multiplied by a certain distance (torque arm). Therefore, for the wing, the rolling moment generated only by the wake is expressed as follows:(10)Z=D×F,where Z is the rolling moment generated by the wake vortex, D is the position of a certain point on the wing from the center of the wing, and F is the induced rolling force of the wake vortex, which is equal to the lift of the aircraft changed by the wake vortex.Because the position of the following aircraft entering the front engine’s wake is uncertain, the maximum induced torque can be obtained by the strip model, and the safety analysis can be carried out according to the maximum induced torque.Based on the strip method (Figure5), this paper calculates the lift variation caused by the wake vortex on a strip and then obtains the induced torque on the strip.(11)dΓx=12ρVr2flxfxΔβxdx,ΔZv=dΓx⋅x=12ρVr2flxfxΔβxxdx,where dΓx is the local lift variation; ΔZv is the local induced moment; Vr is the incoming velocity of the air, which is approximately equal to the flight velocity of the aircraft; flx is the lift line coefficient at position x; fx is the chord length; Δβx is the change in angle of attack.Figure 5
Strip model of CRJ-900 stress calculation.Because the change of angle of attack is very small, it is approximately equal to(12)Δβx≈VθxVf,where Δβx is the change of angle of attack caused by wake vortex.After integration, the induced momentZv of wake vortex to aircraft can be obtained as follows:(13)Zv=ρfVf2∗∫−bA/2bA/2Vθxfxxdx,where Vθx is the induced velocity of the front aircraft’s wake; f is the slope of the lift line.As an index to measure the safety of wake encounter [26], the rolling moment coefficient (RMC) can be expressed as(14)RMC=Zv1/2ρVf2Sfbf,where Sf is the wing area of follow aircraft; bf is the wingspan of follow aircraft.At the same time, according to the limit value of aircraft rolling moment coefficient, the maximum rolling moment can be obtained as follows:(15)Zvmax=12RMCmaxρVf2Sfbf,where Zvmax is the maximum rolling moment; RMCmax is the maximum rolling moment coefficient.


#### 3.3.3. Force Model Calculation of Wake Vortex before Crossing

Taking the position of the rear aircraft shown in Figure6 as an example, the forces on the wing, airframe, engine, and horizontal tail of the rear aircraft are analyzed, respectively.Figure 6
Schematic diagram of stress calculation model of cross wake vortex.It can be concluded that the stress calculation formula of engine block and engine is as follows:(16)Ff=2ρ∫df∫0L/2−D/2/e−hr−1+j/2Vr2dsdr+∫fl∫0L/2Vr2dsdr+∫l0∫0L/2−M/2/0−kr−1+L/2Vr2dsdr+∫fh∫0BET/2Vr2dsdr−∫fh∫0H/2Vr2dsdr,where Ft is the force on the rear fuselage, d is the length of the aircraft fuselage, j is the length of the wing extension line from the fuselage, l is the length of the fuselage, L is the width of the fuselage, M is the width of the fuselage at the fuselage, D is the width of the fuselage d from the fuselage, and h to f are the length of the engine.The calculation formula of wing downwash force is as follows:(17)Fw=2ρ∫ik∫0B/2−K/2/i−kr−1+B/2Vr2dsdr+∫gi∫0B/2Vr2dsdr−∫gj∫0B/2−J/2/g−jr−1+B/2Vr2dsdr−∫jk∫0L/2Vr2dsdr,where Fw is the force on the wing, g to i is the wingtip length, j to k is the wingroot length, B is the wingspan, J is the distance between the trailing edge of the wing and the fuselage axis, and L is the fuselage width.The shape of the horizontal tail is similar to that of the wing, and the force calculation formula is as follows:(18)Fht=2ρ∫be∫0A/2−0/b−er−1+A/2Vr2dsdr+∫ab∫0A/2Vr2dsdr−∫ab∫0A/2−0/a−br−1+A/2Vr2dsdr,where Fht is the force on the flat tail, a to b is the tip length of the horizontal tail, c to e is the heel length of the horizontal tail, and A is the span of the horizontal tail.Therefore, the force exerted on the following aircraft by the wake vortex of the front engine can be obtained according to equation (16), equation (17), and equation (18):(19)FA=Fw+Ff+Fht,where FA is the overall force of the aircraft.


#### 3.3.4. Height Change Calculation

When the aircraft encounters the wake, the calculation formula of altitude change is shown in equation (12) as follows:(20)H=12FAMtm+tn2,where H is the descending or ascending height, FA is the force on the whole aircraft, which can be calculated by equation (20), tm is the pilot response time, and tn is the aircraft response time.


#### 3.3.5. Turbulence Intensity

In this paper, the overload increment is used as the criterion to measure the turbulence intensity, and its corresponding turbulence intensity level is shown in the table below. The overload increment is the acceleration of the aircraft flying in the turbulent atmosphere, expressed as a multiple of the gravity accelerationg; the calculation formula is as follows:(21)Δn=FAMfg,where Mf is the mass of the following aircraft.


#### 3.3.6. Fuel Consumption and Pollutant Emission

The ideal landing and takeoff cycle under international standard atmosphere (ISA) is divided into four stages, and the engine power setting of each stage is different. Table4 lists the LTO cycles of the CF34-8C5 engine.Table 4
Emission data for CF34-8C5 engine at international (ISA).
ModeTime (minute)Power setting (%)Fuel flow (kg/s)Emission indices (g/kg)HCCONOxIdle/Taxiing2670.0640.1318.254.6Approach4300.1790.064.2410.75Climb2.2850.530.020.5712.6Takeoff0.71000.6480.020.6414.69The calculation formula of aircraft fuel consumption is(22)Fc=∑i,jNi×Si,j×Ti,where Ni is the number of type I aircraft engines; Fi is the working time of type i aircraft in phase j; Ti is the fuel consumption of single engine of model i aircraft (kg/s).The fuel saving rate is(23)τC=FC−FC′FC.where FC′ is the fuel consumption of the aircraft when the calculated safety separation is used.Pollutant emissions can be calculated as(24)Ek=∑i,jkNi×Si,j×Ti×Ui,k,where Ui,k is the emission index of pollutant k in a single engine of type i aircraft.The pollutant emission reduction rate is(25)τe=Ek−Ek′Ek,where Ek′ is the pollutant emission when the calculated safety separation is used.


## 3.1. Wake Dissipation Model

In the initial dissipation stage, the strength of the wake decreases mainly by itself, so the dissipation speed is slow; the time for the wake vortex to enter the fast dissipation stage is related to the dimensionless vortex dissipation rate; the calculation formula of wake vortex entering fast dissipation timetw is as follows:(1)tw=tz0.7475ε∗0.75,ε∗≥0.2535,twε∗=twtz0.25e−0.7twtz,0.0121≤ε∗≤0.2535,tw=tz9.18−180ε∗,0.001≤ε∗≤0.0121,tw=9tz,ε∗<0.001,where tw is the time to start the rapid dissipation phase, tz is the characteristic time, and its calculation formula is(2)tz=bxvx,where bx is the initial wake distance and vx is the initial characteristic velocity of the wake.ε∗ is the eddy dissipation rate, and its calculation formula is as follows:(3)ε∗=εbx1/3vx=2πbxεbx1/3Γx=π2ρVBbxεbx1/32mg,where ε is the turbulent dissipation rate, and the calculation formula is as follows:(4)ε=Cmu0.75k1.5l,where Cmu=0.09 is a constant, k is the turbulent kinetic energy, and l is the characteristic scale of turbulence.By calculating the wake duration in the near-field region and comparing it with the time of CRJ-900 encountering wake, we can determine whether CRJ-900 is encountering near-field wake or far-field wake.(5)Γx=4MgρπBV,bx=π4B,rx=5.2%bx,where M is the weight of the aircraft, g is the acceleration of gravity, B is the wingspan of the aircraft, and V is the flight speed of the aircraft.Based on the AVOSS system, NASA has developed an APA model of wake dissipation. The equation is(6)Γ∗=ΓΓ0=exp−C+0.25N∗2t−twtw,where C is a constant, usually 0.4525; tw is the time for the wake vortex to enter and dissipate rapidly; 0.25N∗2 represents the effect of atmospheric stratification on the dissipation of the wake vortex.In this paper, A380 aircraft is selected as the aircraft to produce wake vortex for calculation, and the specific model parameters are shown in Table1.Table 1
A380 type parameters.
TypeWingspan (m)Cruise speed (m/s)Final approach speed (m/s)Maximum takeoff/landing weight (kg)Wing area (m2)Wake classificationA380-80079.75290.96770.993560000/386000845HThrough the customs clearance calculation, we can get the dissipation of the wake vortex of A380 in different flight stages under different atmospheric stratification and turbulence degree, as shown in Figure2. From this, we can know the dissipation of A380 aircraft wake vortex at different time and distance, as shown in Table 2.Figure 2
Variation of wake vorticity in different flight stages. (a) Circulation changes with time. (b) Circulation varies with separation distance.
(a)(b)Table 2
A380 wake dissipation parameters.
Flight phaseΓ (m2/s)vx (m2/s)tz (s)ε (m2/s4.5)ε∗ (s−0.5)tw (s)Circulation value at different separationΓlm2/s7.49.311.113Takeoff11372.5324.750.1440.8223.26142.070.838.018.3Level flight5531.4143.976.30310.885.971.436.520.510.3Landing7731.9631.870.1050.9526.56101.850.927.513.4


## 3.2. Wake Encounter Analysis

There are three ways for aircraft to enter the wake vortex field of the front aircraft: (1) across the front wake; (2) longitudinal entry into double wake vortex of front aircraft; (3) longitudinal entry into the single vortex of the front aircraft. The details are shown in Figure3.Figure 3
Schematic diagram of different modes of wake vortex field before aircraft entering.


### 3.2.1. Across the front Wake Vortex

When the aircraft crosses the wake vortex of the front aircraft, as shown in modea in Figure 3, it will experience a backward wash up wash down wash up force, which will cause a large turbulence of the aircraft, resulting in a sudden change in the altitude, speed, and attitude of the aircraft. In serious cases, it will cause the aircraft out of control, or even cause a safety accident.


### 3.2.2. Longitudinal Entry into Double Wake Vortex of front Aircraft

As shown in modeB in Figure 3, when entering the double vortex of the front aircraft longitudinally, the aircraft will suddenly drop height due to the influence of downwash air flow. At high altitude, the pilot has enough time to respond to the adjustment;.In the takeoff and approach phase, sudden height drop is easy to cause safety accidents.


### 3.2.3. Longitudinal Entry into Single Wake Vortex of front Aircraft

When the aircraft enters the center of the single vortex in the wake of the front aircraft, as shown in modeC in Figure 3, the two wings are subjected to the upwash force and downwash force, respectively, causing the aircraft to roll. When the roll angle is too large, it will cause the aircraft to lose lift, or even enter the weightlessness state, causing safety accidents.The velocity field generated by the wake pair when encountering an aircraft is not uniform. The velocity of the flow field varies greatly on the surface of the aircraft, as shown in Figure4. The classical aerodynamic model suitable for uniform flow field is not suitable for calculating the aerodynamic force and torque generated by flow field, so a distributed aerodynamic model is needed [38]. Standard methods include strip method and lifting surface method. They require the velocity vector of each time step discrete point (generally one point for each aerodynamic section) to be simulated, as shown in Figure 4(b).Figure 4
Strip model of wake vortex encountering. (a) Aircraft encountering wake vortex. (b) Discretization of strip method and local airspeed.
(a)(b)In the strip model, the aircraft is simplified as wing, fuselage, horizontal, and vertical tail surfaces. The black lines in Figure4(b) represent a simplified aircraft model. For each strip element, the angle of attack caused by eddy current is calculated. In order to prevent the local angle of attack from exceeding the maximum angle of attack, the strip model realizes the special limitation of the maximum angle of attack.


## 3.2.1. Across the front Wake Vortex

When the aircraft crosses the wake vortex of the front aircraft, as shown in modea in Figure 3, it will experience a backward wash up wash down wash up force, which will cause a large turbulence of the aircraft, resulting in a sudden change in the altitude, speed, and attitude of the aircraft. In serious cases, it will cause the aircraft out of control, or even cause a safety accident.


## 3.2.2. Longitudinal Entry into Double Wake Vortex of front Aircraft

As shown in modeB in Figure 3, when entering the double vortex of the front aircraft longitudinally, the aircraft will suddenly drop height due to the influence of downwash air flow. At high altitude, the pilot has enough time to respond to the adjustment;.In the takeoff and approach phase, sudden height drop is easy to cause safety accidents.


## 3.2.3. Longitudinal Entry into Single Wake Vortex of front Aircraft

When the aircraft enters the center of the single vortex in the wake of the front aircraft, as shown in modeC in Figure 3, the two wings are subjected to the upwash force and downwash force, respectively, causing the aircraft to roll. When the roll angle is too large, it will cause the aircraft to lose lift, or even enter the weightlessness state, causing safety accidents.The velocity field generated by the wake pair when encountering an aircraft is not uniform. The velocity of the flow field varies greatly on the surface of the aircraft, as shown in Figure4. The classical aerodynamic model suitable for uniform flow field is not suitable for calculating the aerodynamic force and torque generated by flow field, so a distributed aerodynamic model is needed [38]. Standard methods include strip method and lifting surface method. They require the velocity vector of each time step discrete point (generally one point for each aerodynamic section) to be simulated, as shown in Figure 4(b).Figure 4
Strip model of wake vortex encountering. (a) Aircraft encountering wake vortex. (b) Discretization of strip method and local airspeed.
(a)(b)In the strip model, the aircraft is simplified as wing, fuselage, horizontal, and vertical tail surfaces. The black lines in Figure4(b) represent a simplified aircraft model. For each strip element, the angle of attack caused by eddy current is calculated. In order to prevent the local angle of attack from exceeding the maximum angle of attack, the strip model realizes the special limitation of the maximum angle of attack.


## 3.3. Response Analysis of CRJ-900 Aircraft

When following the front aircraft, the wake of the front aircraft will mainly cause the force change, roll change, and height change of the rear aircraft, while when crossing the wake of the front aircraft, it will mainly cause the force change, pitch change, and height change of the rear aircraft. In this paper, the calculation method of each physical quantity of CRJ-900 encountering wake is given, and the simplified force model of CRJ-900 is given. The parameters of CRJ-900 are shown in Table3.Table 3
Geometric main dimensions of CRJ-900-700 aircraft.
Wingspan (m)Wing area (m2/s)Maximum takeoff weight (kg)Maximum landing weight (kg)Cruise altitude (m)Cruise speed (m/s)24.8570.61365043334012496245.83


### 3.3.1. Aircraft Lift

The calculation of wing lift variation is shown in formulas (7) and (8):(7)ΔL=12ρV2∫−B/2B/2Cl′yCLydy,where ΔL is the lift variation, Cl′y is the lift coefficient variation, CLy is the spanwise coordinate of the aircraft wing, and y is the chord length. The lift variation of aircraft is mainly caused by the wing, so only the lift variation of the wing is considered when calculating the lift variation in this paper.(8)Cl′y=fΔαy=f arctanVvyV≈fVvyV,where f is the lift line slope, Δαy is the angle of attack variation of the wing section, and Vvy is the induced velocity of the wake field on the wing section.According to the momentum theorem, the calculation method of the force on any part of the body when encountering the wake is given in equation (9) as follows:(9)F=ρSVvy2,where F is the force on any part of the aircraft body and S is the projected area of any part of the aircraft.


### 3.3.2. Calculation of Rolling Moment

The calculation of wake induced torque revolves around the basic principle of torque, that is, a force multiplied by a certain distance (torque arm). Therefore, for the wing, the rolling moment generated only by the wake is expressed as follows:(10)Z=D×F,where Z is the rolling moment generated by the wake vortex, D is the position of a certain point on the wing from the center of the wing, and F is the induced rolling force of the wake vortex, which is equal to the lift of the aircraft changed by the wake vortex.Because the position of the following aircraft entering the front engine’s wake is uncertain, the maximum induced torque can be obtained by the strip model, and the safety analysis can be carried out according to the maximum induced torque.Based on the strip method (Figure5), this paper calculates the lift variation caused by the wake vortex on a strip and then obtains the induced torque on the strip.(11)dΓx=12ρVr2flxfxΔβxdx,ΔZv=dΓx⋅x=12ρVr2flxfxΔβxxdx,where dΓx is the local lift variation; ΔZv is the local induced moment; Vr is the incoming velocity of the air, which is approximately equal to the flight velocity of the aircraft; flx is the lift line coefficient at position x; fx is the chord length; Δβx is the change in angle of attack.Figure 5
Strip model of CRJ-900 stress calculation.Because the change of angle of attack is very small, it is approximately equal to(12)Δβx≈VθxVf,where Δβx is the change of angle of attack caused by wake vortex.After integration, the induced momentZv of wake vortex to aircraft can be obtained as follows:(13)Zv=ρfVf2∗∫−bA/2bA/2Vθxfxxdx,where Vθx is the induced velocity of the front aircraft’s wake; f is the slope of the lift line.As an index to measure the safety of wake encounter [26], the rolling moment coefficient (RMC) can be expressed as(14)RMC=Zv1/2ρVf2Sfbf,where Sf is the wing area of follow aircraft; bf is the wingspan of follow aircraft.At the same time, according to the limit value of aircraft rolling moment coefficient, the maximum rolling moment can be obtained as follows:(15)Zvmax=12RMCmaxρVf2Sfbf,where Zvmax is the maximum rolling moment; RMCmax is the maximum rolling moment coefficient.


### 3.3.3. Force Model Calculation of Wake Vortex before Crossing

Taking the position of the rear aircraft shown in Figure6 as an example, the forces on the wing, airframe, engine, and horizontal tail of the rear aircraft are analyzed, respectively.Figure 6
Schematic diagram of stress calculation model of cross wake vortex.It can be concluded that the stress calculation formula of engine block and engine is as follows:(16)Ff=2ρ∫df∫0L/2−D/2/e−hr−1+j/2Vr2dsdr+∫fl∫0L/2Vr2dsdr+∫l0∫0L/2−M/2/0−kr−1+L/2Vr2dsdr+∫fh∫0BET/2Vr2dsdr−∫fh∫0H/2Vr2dsdr,where Ft is the force on the rear fuselage, d is the length of the aircraft fuselage, j is the length of the wing extension line from the fuselage, l is the length of the fuselage, L is the width of the fuselage, M is the width of the fuselage at the fuselage, D is the width of the fuselage d from the fuselage, and h to f are the length of the engine.The calculation formula of wing downwash force is as follows:(17)Fw=2ρ∫ik∫0B/2−K/2/i−kr−1+B/2Vr2dsdr+∫gi∫0B/2Vr2dsdr−∫gj∫0B/2−J/2/g−jr−1+B/2Vr2dsdr−∫jk∫0L/2Vr2dsdr,where Fw is the force on the wing, g to i is the wingtip length, j to k is the wingroot length, B is the wingspan, J is the distance between the trailing edge of the wing and the fuselage axis, and L is the fuselage width.The shape of the horizontal tail is similar to that of the wing, and the force calculation formula is as follows:(18)Fht=2ρ∫be∫0A/2−0/b−er−1+A/2Vr2dsdr+∫ab∫0A/2Vr2dsdr−∫ab∫0A/2−0/a−br−1+A/2Vr2dsdr,where Fht is the force on the flat tail, a to b is the tip length of the horizontal tail, c to e is the heel length of the horizontal tail, and A is the span of the horizontal tail.Therefore, the force exerted on the following aircraft by the wake vortex of the front engine can be obtained according to equation (16), equation (17), and equation (18):(19)FA=Fw+Ff+Fht,where FA is the overall force of the aircraft.


### 3.3.4. Height Change Calculation

When the aircraft encounters the wake, the calculation formula of altitude change is shown in equation (12) as follows:(20)H=12FAMtm+tn2,where H is the descending or ascending height, FA is the force on the whole aircraft, which can be calculated by equation (20), tm is the pilot response time, and tn is the aircraft response time.


### 3.3.5. Turbulence Intensity

In this paper, the overload increment is used as the criterion to measure the turbulence intensity, and its corresponding turbulence intensity level is shown in the table below. The overload increment is the acceleration of the aircraft flying in the turbulent atmosphere, expressed as a multiple of the gravity accelerationg; the calculation formula is as follows:(21)Δn=FAMfg,where Mf is the mass of the following aircraft.


### 3.3.6. Fuel Consumption and Pollutant Emission

The ideal landing and takeoff cycle under international standard atmosphere (ISA) is divided into four stages, and the engine power setting of each stage is different. Table4 lists the LTO cycles of the CF34-8C5 engine.Table 4
Emission data for CF34-8C5 engine at international (ISA).
ModeTime (minute)Power setting (%)Fuel flow (kg/s)Emission indices (g/kg)HCCONOxIdle/Taxiing2670.0640.1318.254.6Approach4300.1790.064.2410.75Climb2.2850.530.020.5712.6Takeoff0.71000.6480.020.6414.69The calculation formula of aircraft fuel consumption is(22)Fc=∑i,jNi×Si,j×Ti,where Ni is the number of type I aircraft engines; Fi is the working time of type i aircraft in phase j; Ti is the fuel consumption of single engine of model i aircraft (kg/s).The fuel saving rate is(23)τC=FC−FC′FC.where FC′ is the fuel consumption of the aircraft when the calculated safety separation is used.Pollutant emissions can be calculated as(24)Ek=∑i,jkNi×Si,j×Ti×Ui,k,where Ui,k is the emission index of pollutant k in a single engine of type i aircraft.The pollutant emission reduction rate is(25)τe=Ek−Ek′Ek,where Ek′ is the pollutant emission when the calculated safety separation is used.


## 3.3.1. Aircraft Lift

The calculation of wing lift variation is shown in formulas (7) and (8):(7)ΔL=12ρV2∫−B/2B/2Cl′yCLydy,where ΔL is the lift variation, Cl′y is the lift coefficient variation, CLy is the spanwise coordinate of the aircraft wing, and y is the chord length. The lift variation of aircraft is mainly caused by the wing, so only the lift variation of the wing is considered when calculating the lift variation in this paper.(8)Cl′y=fΔαy=f arctanVvyV≈fVvyV,where f is the lift line slope, Δαy is the angle of attack variation of the wing section, and Vvy is the induced velocity of the wake field on the wing section.According to the momentum theorem, the calculation method of the force on any part of the body when encountering the wake is given in equation (9) as follows:(9)F=ρSVvy2,where F is the force on any part of the aircraft body and S is the projected area of any part of the aircraft.


## 3.3.2. Calculation of Rolling Moment

The calculation of wake induced torque revolves around the basic principle of torque, that is, a force multiplied by a certain distance (torque arm). Therefore, for the wing, the rolling moment generated only by the wake is expressed as follows:(10)Z=D×F,where Z is the rolling moment generated by the wake vortex, D is the position of a certain point on the wing from the center of the wing, and F is the induced rolling force of the wake vortex, which is equal to the lift of the aircraft changed by the wake vortex.Because the position of the following aircraft entering the front engine’s wake is uncertain, the maximum induced torque can be obtained by the strip model, and the safety analysis can be carried out according to the maximum induced torque.Based on the strip method (Figure5), this paper calculates the lift variation caused by the wake vortex on a strip and then obtains the induced torque on the strip.(11)dΓx=12ρVr2flxfxΔβxdx,ΔZv=dΓx⋅x=12ρVr2flxfxΔβxxdx,where dΓx is the local lift variation; ΔZv is the local induced moment; Vr is the incoming velocity of the air, which is approximately equal to the flight velocity of the aircraft; flx is the lift line coefficient at position x; fx is the chord length; Δβx is the change in angle of attack.Figure 5
Strip model of CRJ-900 stress calculation.Because the change of angle of attack is very small, it is approximately equal to(12)Δβx≈VθxVf,where Δβx is the change of angle of attack caused by wake vortex.After integration, the induced momentZv of wake vortex to aircraft can be obtained as follows:(13)Zv=ρfVf2∗∫−bA/2bA/2Vθxfxxdx,where Vθx is the induced velocity of the front aircraft’s wake; f is the slope of the lift line.As an index to measure the safety of wake encounter [26], the rolling moment coefficient (RMC) can be expressed as(14)RMC=Zv1/2ρVf2Sfbf,where Sf is the wing area of follow aircraft; bf is the wingspan of follow aircraft.At the same time, according to the limit value of aircraft rolling moment coefficient, the maximum rolling moment can be obtained as follows:(15)Zvmax=12RMCmaxρVf2Sfbf,where Zvmax is the maximum rolling moment; RMCmax is the maximum rolling moment coefficient.


## 3.3.3. Force Model Calculation of Wake Vortex before Crossing

Taking the position of the rear aircraft shown in Figure6 as an example, the forces on the wing, airframe, engine, and horizontal tail of the rear aircraft are analyzed, respectively.Figure 6
Schematic diagram of stress calculation model of cross wake vortex.It can be concluded that the stress calculation formula of engine block and engine is as follows:(16)Ff=2ρ∫df∫0L/2−D/2/e−hr−1+j/2Vr2dsdr+∫fl∫0L/2Vr2dsdr+∫l0∫0L/2−M/2/0−kr−1+L/2Vr2dsdr+∫fh∫0BET/2Vr2dsdr−∫fh∫0H/2Vr2dsdr,where Ft is the force on the rear fuselage, d is the length of the aircraft fuselage, j is the length of the wing extension line from the fuselage, l is the length of the fuselage, L is the width of the fuselage, M is the width of the fuselage at the fuselage, D is the width of the fuselage d from the fuselage, and h to f are the length of the engine.The calculation formula of wing downwash force is as follows:(17)Fw=2ρ∫ik∫0B/2−K/2/i−kr−1+B/2Vr2dsdr+∫gi∫0B/2Vr2dsdr−∫gj∫0B/2−J/2/g−jr−1+B/2Vr2dsdr−∫jk∫0L/2Vr2dsdr,where Fw is the force on the wing, g to i is the wingtip length, j to k is the wingroot length, B is the wingspan, J is the distance between the trailing edge of the wing and the fuselage axis, and L is the fuselage width.The shape of the horizontal tail is similar to that of the wing, and the force calculation formula is as follows:(18)Fht=2ρ∫be∫0A/2−0/b−er−1+A/2Vr2dsdr+∫ab∫0A/2Vr2dsdr−∫ab∫0A/2−0/a−br−1+A/2Vr2dsdr,where Fht is the force on the flat tail, a to b is the tip length of the horizontal tail, c to e is the heel length of the horizontal tail, and A is the span of the horizontal tail.Therefore, the force exerted on the following aircraft by the wake vortex of the front engine can be obtained according to equation (16), equation (17), and equation (18):(19)FA=Fw+Ff+Fht,where FA is the overall force of the aircraft.


## 3.3.4. Height Change Calculation

When the aircraft encounters the wake, the calculation formula of altitude change is shown in equation (12) as follows:(20)H=12FAMtm+tn2,where H is the descending or ascending height, FA is the force on the whole aircraft, which can be calculated by equation (20), tm is the pilot response time, and tn is the aircraft response time.


## 3.3.5. Turbulence Intensity

In this paper, the overload increment is used as the criterion to measure the turbulence intensity, and its corresponding turbulence intensity level is shown in the table below. The overload increment is the acceleration of the aircraft flying in the turbulent atmosphere, expressed as a multiple of the gravity accelerationg; the calculation formula is as follows:(21)Δn=FAMfg,where Mf is the mass of the following aircraft.


## 3.3.6. Fuel Consumption and Pollutant Emission

The ideal landing and takeoff cycle under international standard atmosphere (ISA) is divided into four stages, and the engine power setting of each stage is different. Table4 lists the LTO cycles of the CF34-8C5 engine.Table 4
Emission data for CF34-8C5 engine at international (ISA).
ModeTime (minute)Power setting (%)Fuel flow (kg/s)Emission indices (g/kg)HCCONOxIdle/Taxiing2670.0640.1318.254.6Approach4300.1790.064.2410.75Climb2.2850.530.020.5712.6Takeoff0.71000.6480.020.6414.69The calculation formula of aircraft fuel consumption is(22)Fc=∑i,jNi×Si,j×Ti,where Ni is the number of type I aircraft engines; Fi is the working time of type i aircraft in phase j; Ti is the fuel consumption of single engine of model i aircraft (kg/s).The fuel saving rate is(23)τC=FC−FC′FC.where FC′ is the fuel consumption of the aircraft when the calculated safety separation is used.Pollutant emissions can be calculated as(24)Ek=∑i,jkNi×Si,j×Ti×Ui,k,where Ui,k is the emission index of pollutant k in a single engine of type i aircraft.The pollutant emission reduction rate is(25)τe=Ek−Ek′Ek,where Ek′ is the pollutant emission when the calculated safety separation is used.


## 4. Results and Discussion

The most important influence of the wake vortex field on its safety is that its velocity field will change the lift of the aircraft, which in turn will cause changes in the aircraft’s flight attitude, resulting in changes in roll, pitch, altitude loss, etc., which will affect the control stability of the aircraft. In order to quantify the response of the aircraft when a wake encounter occurs, the wake encounter model established in Section3 is used, and the effect of the wake vortex field is introduced to calculate the additional induced force and moment generated by the aircraft wake encounter. The numerical changes of each safety index are used to evaluate the wake encounter risk of the CRJ-900 following the A380 in different flight stages under the RECAT-CN wake separation standard, and give the limit value of the rolling moment coefficient to analyze the critical safety separation of the wake.


### 4.1. Longitudinal Encounter with Front Wake Vortex

According to the calculation of CRJ-900 longitudinal encounter wake vortex, we can get the changes of aerodynamic characteristics of CRJ-900 aircraft in takeoff, level flight, and landing stages, and analyze the safety of encounter wake vortex. In order to facilitate calculation, the force in this paper is negative in the direction of gravity, negative to the left from the vortex core, and negative in the counterclockwise direction of rolling moment.


#### 4.1.1. Lift Variation

The lift variation of single vortex before longitudinal encounter of CRJ-900 aircraft is shown in Figure7. The lift variation first increases sharply and then decreases with the distance. In the takeoff and landing stages, the lift is the largest when it is 6.3 m away from the vortex core center, and the lift reaches the maximum at 7.8 m in the level flight stage. The maximum lift in different stages is shown in Table 5. At the same time, with the increase of separation, the influence of wake vortex on the lift variation of CRJ-900 aircraft is also decreasing.Figure 7
Variation curve of lift of a single wake vortex with the position of the aircraft from the vortex core. (a) Take off phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 5
Variation of maximum lift of single vortex encountered in longitudinal direction.
Flight phaseMaximum lift position (m)Maximum lift variation at different separation (N)7.49.311.113Takeoff6.369286.2434552.2118545.818931.40Level flight7.843346.2622158.8512445.396253.04Landing6.344087.3022046.4211911.495804.20When the CRJ-900 aircraft longitudinally encounters the twin vortices of the front aircraft, the maximum lift variation is shown in Figure8. In the takeoff and landing stages, the maximum position where the lift is generated is −6.7 m from the vortex core. When the aircraft moves outward from the vortex core position, the whole aircraft is subjected to the downwash force, the lift increases rapidly, and then begins to weaken and tend to be stable; in the level flight stage, due to the low air density and high cruise speed, the maximum lift position is −10.5 m from the vortex core. The maximum lift variation at different flight stages is shown in Table 6.Figure 8
Variation curve of double vortex lift with aircraft distance from vortex core. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 6
Maximum lift variation of longitudinal encountering double vortices.
Flight phaseMaximum lift position (m)Maximum lift variation at different separation (N)7.49.311.113Takeoff−6.7−87938.51−43850.85−23536.46−11334.77Level flight−10.5−55549.54−28908.40−16236.23−8157.71Landing−6.7−55954.09−27979.31−15116.82−7366.06


#### 4.1.2. Rolling Moment Variation

The rolling moment of CRJ-900 aircraft longitudinally encountering the single vortex of the front aircraft is shown in Figure9 and Table 7. At the vortex core, the maximum rolling moment will be generated due to the upper and lower washing forces on the wings on both sides. As the aircraft center is far away from the vortex core, the rolling moment gradually decreases, and then the torque direction changes. Finally, with the increase of distance, the force on the wings on both sides is stable; the rolling moment approaches zero.Figure 9
Variation of rolling moment when encountering a single wake vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 7
Variation of maximum rolling moment of single vortex encountered in longitudinal direction.
Flight phaseMaximum rolling moment positionVariation of maximum rolling moment at different separation7.49.311.113Takeoff14.797718.7548721.6526150.0312593.300−340145.25−169594.98−91025.73−43836.10Level flight14.774058.8437859.2121263.3910678.620−245234.25−125364.87−70410.40−35274.49Landing14.762173.5031086.7216795.388183.920−216418.26−108209.72−58463.09−28487.48The rolling moment of CRJ-900 aircraft longitudinally encountering the front double vortex is shown in Figure10 and Table 8. At the same separation, the maximum rolling moment of CRJ-900 when encountering the double vortex wake is greater than that when encountering the single vortex. When the aircraft is 0 away from one side vortex core, the rolling moment is the largest. When it is on the center line of the two vortices, the forces on the wings on both sides are the same, so the rolling moment is reduced to 0.Figure 10
Variation of rolling moment in takeoff stage when encountering double vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 8
Maximum value of double vortex rolling moment encountered.
Flight phaseMaximum positionVariation of rolling torque at different separation7.49.311.113Takeoff−14.579753.6739764.8221342.7310278.220−348878.42−173949.19−93362.73−44961.55Level flight−14.281640.6041735.0423440.2311777.280−291611.09−149072.95−83725.91−42067.16Landing−14.168380.6234181.2818467.318998.620−259737.77−129871.20−70166.46−34190.25


#### 4.1.3. Rolling Moment Coefficient

The rolling torque coefficient values in different flight stages are shown in Figures11 and 12, and its variation law is roughly the same as that of rolling torque. At the center of the vortex core, due to the maximum rolling moment, the rolling moment coefficient of the wake vortex is also the maximum. As the aircraft center is far away from the center of the vortex core, its RMC value continues to decrease, and then the direction of the rolling moment changes, and the RMC value also changes from negative to positive.Figure 11
Variation of rolling moment coefficient with distance from vortex core when encountering single vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Figure 12
Variation of rolling moment coefficient with distance from vortex core when encountering double vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)According to relevant experiments under ICAO and RECAT-PWS-EU separation standards [31], the maximum value of rolling torque coefficient of heavy machine following medium-sized machine under reasonable worst case (RWC) is between 0.031 and 0.068. At the same time, the rolling moment coefficient control authority of the aircraft using ailerons is 0.05 to 0.07 [39]. As A380 is a super heavy aircraft, RMC of 0.031, 0.05, and 0.07 is selected as risk critical values to analyze its safety. It can be seen from Table 9 that the RMC value at the separation of 12 km is less than 0.05. Therefore, in the case of this example, it is safe to use the wake separation of the current super heavy aircraft following the medium-sized aircraft for CRJ-900 aircraft in different flight stages and has a large safety margin. Using the critical value of RMC, the safety critical separation of CRJ-900 aircraft is analyzed. The critical rolling moment and critical separation in different stages are shown in Table 10. When the critical value of RMC is 0.031, the maximum safety separation in different flight stages is 11960 m, which is reduced by 1040 m compared with the existing separation.Table 9
Maximum rolling moment coefficient.
Flight phaseMaximum positionMaximum rolling moment coefficient at different separation7.49.311.113Takeoff/single vortex0−0.1292−0.0644−0.0346−0.0166Level flight/single vortex0−0.0931−0.0476−0.0267−0.0133Landing/single vortex0−0.0821−0.0411−0.0222−0.0108Takeoff/twin vortex0−0.1325−0.0661−0.0355−0.0171Level flight/double vortex0−0.1107−0.0398−0.0318−0.0160Landing/double vortex0−0.0987−0.0566−0.0267−0.0130Table 10
Critical separation of different flight stages.
RMC thresholdTakeoffLevel flightLanding0.03111960 m/149.5 s11040 m/44.2 s10820 m/152.4 s0.0510083 m/126.0 s9075 m/36.3 s10425 m/146.8 s0.079021 m/112.8 s8643 m/34.6 s8868 m/124.9 s


### 4.2. Transverse Encountering Front Wake Vortex

#### 4.2.1. Force Variation of Aircraft

Taking the initial wake vortex circulation of A380 aircraft as an example, this paper calculates the position of the maximum up wash force and down wash force when CRJ-900 encounters the wake vortex laterally, and analyzes its stress under the wake vortex of different circulation. The distance through the vortex core and the stress of CRJ-900 are shown in Figure13. The positions where CRJ-900 crosses the front turbine wake vortex and receives the maximum up washing force and down washing force are 13.6 m and 20.9 m through the vortex core, respectively. Since the maximum up washing force of the aircraft is greater than the maximum down washing force, the analysis of the most dangerous situation is mainly focused on the upwashing force.Figure 13
Stress diagram of CRJ900 across the front wake vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)


#### 4.2.2. Height Variation

As shown in the figure below, the variation of vortex height can be calculated according to the variation of vortex dissipation in different wake force stages, as shown in Figure14.Figure 14
Schematic diagram of height variation of wake vortex before CRJ900 crossing. (a) Height change of maximum washing force. (b) Height change of maximum washing force.
(a)(b)


#### 4.2.3. Turbulence Intensity

According to the variation law of the maximum up wash force and down wash force with the wake vortex dissipation time, the variation law of the overload increment with the wake vortex dissipation in different flight stages is calculated.Table11 shows the classification of turbulence intensity by overload increment. When the aircraft suffers from moderate and above turbulence, it will produce difficult operation, abnormal instrument indication and other conditions; especially in the process of taking off and landing, it is easy to cause safety accidents when encountering more than moderate turbulence. As shown in Figure 15 above, under the condition of this example, the change of overload increment under the maximum washing force takes the overload increment as the critical value, the critical value in the takeoff stage is the wake vortex dissipation of 89.5 s, the level flight stage is 24.6 s, and the landing stage is 78.2 s.Table 11
Classification of turbulence intensity corresponding to overload increment.
Turbulence intensityOverload increment rangeNo turbulenceΔn≤0.15Mild turbulence0.15<Δn≤0.5Moderate turbulence0.5<Δn≤1.0Strong turbulenceΔn≥1.0Figure 15
Schematic diagram of variation of wake vortex overload increment with wake vortex dissipation time before CRJ900 crossing. (a) Maximum up wash overload increment. (b) Maximum down wash overload increment.
(a)(b)


### 4.3. Analysis of Pollutant Emission Reduction

The takeoff and landing phase is close to the safety separation calculated according to different RMC values. Through this separation value, the control separation time that can be reduced in each phase of the aircraft can be obtained. By bringing the reduced time into the LTO cycle, the reduction of fuel and pollutant emissions can be calculated, as shown in Table12. When the RMC values are 0.031, 0.05, and 0.07 respectively, the fuel consumption can be reduced by 7.9%–12.8%, and the pollutant emission can be reduced by 9.1%–12.8%.Table 12
Fuel consumption and pollutant emission reduction under different RMC values.
RMCFuel consumption reduction (kg)Fuel saving rate (%)Pollutant emission reduction (g)Pollutant emission reduction rate (%)HCCONOx0.03118.97.91.8202.6151.69.10.0525.010.42.1234.0209.711.40.0730.712.82.5261.927712.8


## 4.1. Longitudinal Encounter with Front Wake Vortex

According to the calculation of CRJ-900 longitudinal encounter wake vortex, we can get the changes of aerodynamic characteristics of CRJ-900 aircraft in takeoff, level flight, and landing stages, and analyze the safety of encounter wake vortex. In order to facilitate calculation, the force in this paper is negative in the direction of gravity, negative to the left from the vortex core, and negative in the counterclockwise direction of rolling moment.


### 4.1.1. Lift Variation

The lift variation of single vortex before longitudinal encounter of CRJ-900 aircraft is shown in Figure7. The lift variation first increases sharply and then decreases with the distance. In the takeoff and landing stages, the lift is the largest when it is 6.3 m away from the vortex core center, and the lift reaches the maximum at 7.8 m in the level flight stage. The maximum lift in different stages is shown in Table 5. At the same time, with the increase of separation, the influence of wake vortex on the lift variation of CRJ-900 aircraft is also decreasing.Figure 7
Variation curve of lift of a single wake vortex with the position of the aircraft from the vortex core. (a) Take off phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 5
Variation of maximum lift of single vortex encountered in longitudinal direction.
Flight phaseMaximum lift position (m)Maximum lift variation at different separation (N)7.49.311.113Takeoff6.369286.2434552.2118545.818931.40Level flight7.843346.2622158.8512445.396253.04Landing6.344087.3022046.4211911.495804.20When the CRJ-900 aircraft longitudinally encounters the twin vortices of the front aircraft, the maximum lift variation is shown in Figure8. In the takeoff and landing stages, the maximum position where the lift is generated is −6.7 m from the vortex core. When the aircraft moves outward from the vortex core position, the whole aircraft is subjected to the downwash force, the lift increases rapidly, and then begins to weaken and tend to be stable; in the level flight stage, due to the low air density and high cruise speed, the maximum lift position is −10.5 m from the vortex core. The maximum lift variation at different flight stages is shown in Table 6.Figure 8
Variation curve of double vortex lift with aircraft distance from vortex core. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 6
Maximum lift variation of longitudinal encountering double vortices.
Flight phaseMaximum lift position (m)Maximum lift variation at different separation (N)7.49.311.113Takeoff−6.7−87938.51−43850.85−23536.46−11334.77Level flight−10.5−55549.54−28908.40−16236.23−8157.71Landing−6.7−55954.09−27979.31−15116.82−7366.06


### 4.1.2. Rolling Moment Variation

The rolling moment of CRJ-900 aircraft longitudinally encountering the single vortex of the front aircraft is shown in Figure9 and Table 7. At the vortex core, the maximum rolling moment will be generated due to the upper and lower washing forces on the wings on both sides. As the aircraft center is far away from the vortex core, the rolling moment gradually decreases, and then the torque direction changes. Finally, with the increase of distance, the force on the wings on both sides is stable; the rolling moment approaches zero.Figure 9
Variation of rolling moment when encountering a single wake vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 7
Variation of maximum rolling moment of single vortex encountered in longitudinal direction.
Flight phaseMaximum rolling moment positionVariation of maximum rolling moment at different separation7.49.311.113Takeoff14.797718.7548721.6526150.0312593.300−340145.25−169594.98−91025.73−43836.10Level flight14.774058.8437859.2121263.3910678.620−245234.25−125364.87−70410.40−35274.49Landing14.762173.5031086.7216795.388183.920−216418.26−108209.72−58463.09−28487.48The rolling moment of CRJ-900 aircraft longitudinally encountering the front double vortex is shown in Figure10 and Table 8. At the same separation, the maximum rolling moment of CRJ-900 when encountering the double vortex wake is greater than that when encountering the single vortex. When the aircraft is 0 away from one side vortex core, the rolling moment is the largest. When it is on the center line of the two vortices, the forces on the wings on both sides are the same, so the rolling moment is reduced to 0.Figure 10
Variation of rolling moment in takeoff stage when encountering double vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 8
Maximum value of double vortex rolling moment encountered.
Flight phaseMaximum positionVariation of rolling torque at different separation7.49.311.113Takeoff−14.579753.6739764.8221342.7310278.220−348878.42−173949.19−93362.73−44961.55Level flight−14.281640.6041735.0423440.2311777.280−291611.09−149072.95−83725.91−42067.16Landing−14.168380.6234181.2818467.318998.620−259737.77−129871.20−70166.46−34190.25


### 4.1.3. Rolling Moment Coefficient

The rolling torque coefficient values in different flight stages are shown in Figures11 and 12, and its variation law is roughly the same as that of rolling torque. At the center of the vortex core, due to the maximum rolling moment, the rolling moment coefficient of the wake vortex is also the maximum. As the aircraft center is far away from the center of the vortex core, its RMC value continues to decrease, and then the direction of the rolling moment changes, and the RMC value also changes from negative to positive.Figure 11
Variation of rolling moment coefficient with distance from vortex core when encountering single vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Figure 12
Variation of rolling moment coefficient with distance from vortex core when encountering double vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)According to relevant experiments under ICAO and RECAT-PWS-EU separation standards [31], the maximum value of rolling torque coefficient of heavy machine following medium-sized machine under reasonable worst case (RWC) is between 0.031 and 0.068. At the same time, the rolling moment coefficient control authority of the aircraft using ailerons is 0.05 to 0.07 [39]. As A380 is a super heavy aircraft, RMC of 0.031, 0.05, and 0.07 is selected as risk critical values to analyze its safety. It can be seen from Table 9 that the RMC value at the separation of 12 km is less than 0.05. Therefore, in the case of this example, it is safe to use the wake separation of the current super heavy aircraft following the medium-sized aircraft for CRJ-900 aircraft in different flight stages and has a large safety margin. Using the critical value of RMC, the safety critical separation of CRJ-900 aircraft is analyzed. The critical rolling moment and critical separation in different stages are shown in Table 10. When the critical value of RMC is 0.031, the maximum safety separation in different flight stages is 11960 m, which is reduced by 1040 m compared with the existing separation.Table 9
Maximum rolling moment coefficient.
Flight phaseMaximum positionMaximum rolling moment coefficient at different separation7.49.311.113Takeoff/single vortex0−0.1292−0.0644−0.0346−0.0166Level flight/single vortex0−0.0931−0.0476−0.0267−0.0133Landing/single vortex0−0.0821−0.0411−0.0222−0.0108Takeoff/twin vortex0−0.1325−0.0661−0.0355−0.0171Level flight/double vortex0−0.1107−0.0398−0.0318−0.0160Landing/double vortex0−0.0987−0.0566−0.0267−0.0130Table 10
Critical separation of different flight stages.
RMC thresholdTakeoffLevel flightLanding0.03111960 m/149.5 s11040 m/44.2 s10820 m/152.4 s0.0510083 m/126.0 s9075 m/36.3 s10425 m/146.8 s0.079021 m/112.8 s8643 m/34.6 s8868 m/124.9 s


## 4.1.1. Lift Variation

The lift variation of single vortex before longitudinal encounter of CRJ-900 aircraft is shown in Figure7. The lift variation first increases sharply and then decreases with the distance. In the takeoff and landing stages, the lift is the largest when it is 6.3 m away from the vortex core center, and the lift reaches the maximum at 7.8 m in the level flight stage. The maximum lift in different stages is shown in Table 5. At the same time, with the increase of separation, the influence of wake vortex on the lift variation of CRJ-900 aircraft is also decreasing.Figure 7
Variation curve of lift of a single wake vortex with the position of the aircraft from the vortex core. (a) Take off phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 5
Variation of maximum lift of single vortex encountered in longitudinal direction.
Flight phaseMaximum lift position (m)Maximum lift variation at different separation (N)7.49.311.113Takeoff6.369286.2434552.2118545.818931.40Level flight7.843346.2622158.8512445.396253.04Landing6.344087.3022046.4211911.495804.20When the CRJ-900 aircraft longitudinally encounters the twin vortices of the front aircraft, the maximum lift variation is shown in Figure8. In the takeoff and landing stages, the maximum position where the lift is generated is −6.7 m from the vortex core. When the aircraft moves outward from the vortex core position, the whole aircraft is subjected to the downwash force, the lift increases rapidly, and then begins to weaken and tend to be stable; in the level flight stage, due to the low air density and high cruise speed, the maximum lift position is −10.5 m from the vortex core. The maximum lift variation at different flight stages is shown in Table 6.Figure 8
Variation curve of double vortex lift with aircraft distance from vortex core. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 6
Maximum lift variation of longitudinal encountering double vortices.
Flight phaseMaximum lift position (m)Maximum lift variation at different separation (N)7.49.311.113Takeoff−6.7−87938.51−43850.85−23536.46−11334.77Level flight−10.5−55549.54−28908.40−16236.23−8157.71Landing−6.7−55954.09−27979.31−15116.82−7366.06


## 4.1.2. Rolling Moment Variation

The rolling moment of CRJ-900 aircraft longitudinally encountering the single vortex of the front aircraft is shown in Figure9 and Table 7. At the vortex core, the maximum rolling moment will be generated due to the upper and lower washing forces on the wings on both sides. As the aircraft center is far away from the vortex core, the rolling moment gradually decreases, and then the torque direction changes. Finally, with the increase of distance, the force on the wings on both sides is stable; the rolling moment approaches zero.Figure 9
Variation of rolling moment when encountering a single wake vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 7
Variation of maximum rolling moment of single vortex encountered in longitudinal direction.
Flight phaseMaximum rolling moment positionVariation of maximum rolling moment at different separation7.49.311.113Takeoff14.797718.7548721.6526150.0312593.300−340145.25−169594.98−91025.73−43836.10Level flight14.774058.8437859.2121263.3910678.620−245234.25−125364.87−70410.40−35274.49Landing14.762173.5031086.7216795.388183.920−216418.26−108209.72−58463.09−28487.48The rolling moment of CRJ-900 aircraft longitudinally encountering the front double vortex is shown in Figure10 and Table 8. At the same separation, the maximum rolling moment of CRJ-900 when encountering the double vortex wake is greater than that when encountering the single vortex. When the aircraft is 0 away from one side vortex core, the rolling moment is the largest. When it is on the center line of the two vortices, the forces on the wings on both sides are the same, so the rolling moment is reduced to 0.Figure 10
Variation of rolling moment in takeoff stage when encountering double vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Table 8
Maximum value of double vortex rolling moment encountered.
Flight phaseMaximum positionVariation of rolling torque at different separation7.49.311.113Takeoff−14.579753.6739764.8221342.7310278.220−348878.42−173949.19−93362.73−44961.55Level flight−14.281640.6041735.0423440.2311777.280−291611.09−149072.95−83725.91−42067.16Landing−14.168380.6234181.2818467.318998.620−259737.77−129871.20−70166.46−34190.25


## 4.1.3. Rolling Moment Coefficient

The rolling torque coefficient values in different flight stages are shown in Figures11 and 12, and its variation law is roughly the same as that of rolling torque. At the center of the vortex core, due to the maximum rolling moment, the rolling moment coefficient of the wake vortex is also the maximum. As the aircraft center is far away from the center of the vortex core, its RMC value continues to decrease, and then the direction of the rolling moment changes, and the RMC value also changes from negative to positive.Figure 11
Variation of rolling moment coefficient with distance from vortex core when encountering single vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)Figure 12
Variation of rolling moment coefficient with distance from vortex core when encountering double vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)According to relevant experiments under ICAO and RECAT-PWS-EU separation standards [31], the maximum value of rolling torque coefficient of heavy machine following medium-sized machine under reasonable worst case (RWC) is between 0.031 and 0.068. At the same time, the rolling moment coefficient control authority of the aircraft using ailerons is 0.05 to 0.07 [39]. As A380 is a super heavy aircraft, RMC of 0.031, 0.05, and 0.07 is selected as risk critical values to analyze its safety. It can be seen from Table 9 that the RMC value at the separation of 12 km is less than 0.05. Therefore, in the case of this example, it is safe to use the wake separation of the current super heavy aircraft following the medium-sized aircraft for CRJ-900 aircraft in different flight stages and has a large safety margin. Using the critical value of RMC, the safety critical separation of CRJ-900 aircraft is analyzed. The critical rolling moment and critical separation in different stages are shown in Table 10. When the critical value of RMC is 0.031, the maximum safety separation in different flight stages is 11960 m, which is reduced by 1040 m compared with the existing separation.Table 9
Maximum rolling moment coefficient.
Flight phaseMaximum positionMaximum rolling moment coefficient at different separation7.49.311.113Takeoff/single vortex0−0.1292−0.0644−0.0346−0.0166Level flight/single vortex0−0.0931−0.0476−0.0267−0.0133Landing/single vortex0−0.0821−0.0411−0.0222−0.0108Takeoff/twin vortex0−0.1325−0.0661−0.0355−0.0171Level flight/double vortex0−0.1107−0.0398−0.0318−0.0160Landing/double vortex0−0.0987−0.0566−0.0267−0.0130Table 10
Critical separation of different flight stages.
RMC thresholdTakeoffLevel flightLanding0.03111960 m/149.5 s11040 m/44.2 s10820 m/152.4 s0.0510083 m/126.0 s9075 m/36.3 s10425 m/146.8 s0.079021 m/112.8 s8643 m/34.6 s8868 m/124.9 s


## 4.2. Transverse Encountering Front Wake Vortex

### 4.2.1. Force Variation of Aircraft

Taking the initial wake vortex circulation of A380 aircraft as an example, this paper calculates the position of the maximum up wash force and down wash force when CRJ-900 encounters the wake vortex laterally, and analyzes its stress under the wake vortex of different circulation. The distance through the vortex core and the stress of CRJ-900 are shown in Figure13. The positions where CRJ-900 crosses the front turbine wake vortex and receives the maximum up washing force and down washing force are 13.6 m and 20.9 m through the vortex core, respectively. Since the maximum up washing force of the aircraft is greater than the maximum down washing force, the analysis of the most dangerous situation is mainly focused on the upwashing force.Figure 13
Stress diagram of CRJ900 across the front wake vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)


### 4.2.2. Height Variation

As shown in the figure below, the variation of vortex height can be calculated according to the variation of vortex dissipation in different wake force stages, as shown in Figure14.Figure 14
Schematic diagram of height variation of wake vortex before CRJ900 crossing. (a) Height change of maximum washing force. (b) Height change of maximum washing force.
(a)(b)


### 4.2.3. Turbulence Intensity

According to the variation law of the maximum up wash force and down wash force with the wake vortex dissipation time, the variation law of the overload increment with the wake vortex dissipation in different flight stages is calculated.Table11 shows the classification of turbulence intensity by overload increment. When the aircraft suffers from moderate and above turbulence, it will produce difficult operation, abnormal instrument indication and other conditions; especially in the process of taking off and landing, it is easy to cause safety accidents when encountering more than moderate turbulence. As shown in Figure 15 above, under the condition of this example, the change of overload increment under the maximum washing force takes the overload increment as the critical value, the critical value in the takeoff stage is the wake vortex dissipation of 89.5 s, the level flight stage is 24.6 s, and the landing stage is 78.2 s.Table 11
Classification of turbulence intensity corresponding to overload increment.
Turbulence intensityOverload increment rangeNo turbulenceΔn≤0.15Mild turbulence0.15<Δn≤0.5Moderate turbulence0.5<Δn≤1.0Strong turbulenceΔn≥1.0Figure 15
Schematic diagram of variation of wake vortex overload increment with wake vortex dissipation time before CRJ900 crossing. (a) Maximum up wash overload increment. (b) Maximum down wash overload increment.
(a)(b)


## 4.2.1. Force Variation of Aircraft

Taking the initial wake vortex circulation of A380 aircraft as an example, this paper calculates the position of the maximum up wash force and down wash force when CRJ-900 encounters the wake vortex laterally, and analyzes its stress under the wake vortex of different circulation. The distance through the vortex core and the stress of CRJ-900 are shown in Figure13. The positions where CRJ-900 crosses the front turbine wake vortex and receives the maximum up washing force and down washing force are 13.6 m and 20.9 m through the vortex core, respectively. Since the maximum up washing force of the aircraft is greater than the maximum down washing force, the analysis of the most dangerous situation is mainly focused on the upwashing force.Figure 13
Stress diagram of CRJ900 across the front wake vortex. (a) Takeoff phase. (b) Level flight phase. (c) Landing phase.
(a)(b)(c)


## 4.2.2. Height Variation

As shown in the figure below, the variation of vortex height can be calculated according to the variation of vortex dissipation in different wake force stages, as shown in Figure14.Figure 14
Schematic diagram of height variation of wake vortex before CRJ900 crossing. (a) Height change of maximum washing force. (b) Height change of maximum washing force.
(a)(b)


## 4.2.3. Turbulence Intensity

According to the variation law of the maximum up wash force and down wash force with the wake vortex dissipation time, the variation law of the overload increment with the wake vortex dissipation in different flight stages is calculated.Table11 shows the classification of turbulence intensity by overload increment. When the aircraft suffers from moderate and above turbulence, it will produce difficult operation, abnormal instrument indication and other conditions; especially in the process of taking off and landing, it is easy to cause safety accidents when encountering more than moderate turbulence. As shown in Figure 15 above, under the condition of this example, the change of overload increment under the maximum washing force takes the overload increment as the critical value, the critical value in the takeoff stage is the wake vortex dissipation of 89.5 s, the level flight stage is 24.6 s, and the landing stage is 78.2 s.Table 11
Classification of turbulence intensity corresponding to overload increment.
Turbulence intensityOverload increment rangeNo turbulenceΔn≤0.15Mild turbulence0.15<Δn≤0.5Moderate turbulence0.5<Δn≤1.0Strong turbulenceΔn≥1.0Figure 15
Schematic diagram of variation of wake vortex overload increment with wake vortex dissipation time before CRJ900 crossing. (a) Maximum up wash overload increment. (b) Maximum down wash overload increment.
(a)(b)


## 4.3. Analysis of Pollutant Emission Reduction

The takeoff and landing phase is close to the safety separation calculated according to different RMC values. Through this separation value, the control separation time that can be reduced in each phase of the aircraft can be obtained. By bringing the reduced time into the LTO cycle, the reduction of fuel and pollutant emissions can be calculated, as shown in Table12. When the RMC values are 0.031, 0.05, and 0.07 respectively, the fuel consumption can be reduced by 7.9%–12.8%, and the pollutant emission can be reduced by 9.1%–12.8%.Table 12
Fuel consumption and pollutant emission reduction under different RMC values.
RMCFuel consumption reduction (kg)Fuel saving rate (%)Pollutant emission reduction (g)Pollutant emission reduction rate (%)HCCONOx0.03118.97.91.8202.6151.69.10.0525.010.42.1234.0209.711.40.0730.712.82.5261.927712.8


## 5. Conclusion

The front aircraft wake vortex dissipation and induced velocity model has been setup to analyze the dynamic response state of CRJ-900 aircraft encountering wake longitudinally and transversely at different flight stages and separation. The main research is as follows:(1)
An aerodynamic response model of wake encounter is optimized. For the front engine dissipation model, the influence of environmental parameters is added. According to the longitudinal and transverse encounter conditions, the strip method is introduced to establish different rear aircraft response models, calculate the wing, fuselage, and flat tail in sections, and then analyze the response states of CRJ-900 in different flight stages.(2)
Based on current safety indexes, it is verified that the wake separation standard is safe for the super heavy aircraft followed by medium-sized aircraft such as CRJ-900. Meanwhile, CRJ-900 aircraft has the potential to reduce the separation, for example, when the RMC critical value is 0.031, the critical distance of longitudinal encountering wake vortex is 11.94 km in takeoff stage, 11.04 km in level flight stage, and 10.82 km in landing stage. When encountering A380 wake vortex laterally, the safety critical time in takeoff stage is 89.5 s and that in landing stage is 78.2 s.(3)
An efficient air traffic operation could reduce aircraft fuel consumption and pollutant emission. Optimizing the control separation can shorten the waiting time of aircraft at the airport and in the air, allowing the reductions of fuel consumption and pollutant emission. For the critical safety separation calculated in this paper, fuel consumption can be reduced by 7.9%–12.8%, and pollutant emission can be reduced by 9.1%–12.8%.Further research work needs to optimize the response model, verify it with simulator and flight experimental data, and establish a dynamic wake separation system to achieve the goal of improving control operation efficiency, energy conservation, and emission reduction.



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*Source: 3584461-2022-08-04.xml*