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Article

Research on Instability and “Jack-Knifing” of Civil Aircraft Towing Taxi-Out System

1
College of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, China
2
Aviation Special Ground Equipment Research Base, College of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, China
3
Key Laboratory of Smart Airport Theory and System, College of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(6), 3636; https://doi.org/10.3390/app13063636
Submission received: 28 February 2023 / Revised: 9 March 2023 / Accepted: 10 March 2023 / Published: 13 March 2023

Abstract

:
A new towing taxi-out departure mode has become the preferred choice to replace the traditional departure mode of civil aircraft due to its obvious advantages of low energy consumption, low emissions, and high efficiency. However, the inertia may lead to potential lateral instability and even “Jack-knifing”, as the mass of the system is concentrated in the rear. In this paper, the lateral instability mechanism and influencing factors of the civil aircraft towing taxi-out system were studied using computer virtual simulation technology and taking Boeing 737–400 and AM210 tractors as research objects. The results show that the “Jack-knifing” phenomenon was caused by the lateral instability of the system when the sliding speed of the system was more than 15 km/h, and the system was accompanied by the lateral slip condition. Furthermore, the safety zone, side-show zone and jack-knifing zone of the system were defined in terms of towing speed and steering angle. Additionally, a towing safety zone was created under different airport track conditions by analyzing the lateral stability of the system. The conclusion of this study may provide a theoretical basis and reference for the safe application of the new taxi-out departure mode.

1. Introduction

During the embarkation of a flight from the airport, subsequent to a civil aircraft being towed out of the berth by the tractor (indicated by the red dashed line in Figure 1), it ignites its engines and proceeds to the takeoff runway under its own power, awaiting takeoff (represented by the red solid line in Figure 1). The civil aircraft engine remains idle and operates ineffectively in this departure mode, leading to a significant amount of fuel consumption [1], waste discharge [2], and engine maintenance cost [3]. Additionally, the low efficiency of flight departures due to the large number of participants [4] no longer satisfies the demands for high-quality and sustainable development in the global civil aviation industry.
In this respect, the novel towing departure mode (indicated by the blue dotted line in Figure 1), whereby the tractor clamps and holds the nose landing gear of the civil aircraft through the holding wheel mechanism as an integrated civil aircraft towing system (represented by the narrow figure at the bottom right of Figure 1), has become a focal point of research both domestically and internationally. However, the towing system of civil aircraft under the new departure mode possesses typical characteristics of high speed and heavy load. High speed implies that the system speed increases from a low speed (about 2–5 km/h) of the traditional mode to a high speed (about 30–44 km/h) [7]. Heavy load denotes that the mass ratio between the civil aircraft and the tractor is significant, with the weight concentrated in the rear of the system. The aforementioned characteristics give rise to the lateral instability phenomenon, including shimmy, sideshow, and even “jack-knifing” (where the longitudinal angle α of the front longitudinal of the tractor and the front longitudinal angle of the civil aircraft surpass 90°) when the system traverses turns, emergency obstacle avoidance conditions, or extreme airport roads (slippery and icy) caused by inclement weather.
The jack-knifing phenomenon is a result of the relative rotation between the hinge point and semi-trailer when a multi-body system with a similar structure to a semi-trailer undergoes corner braking, emergency obstacle avoidance, or high-speed steering due to the synergistic effect of single or multiple factors. This rotation forms an angle similar to a folding knife, causing serious lateral instability of the tractor and making it difficult to control [8], as shown in Figure 2a. The occurrence of this phenomenon is often accompanied by adverse effects, as shown in Figure 2b, which depicts a jack-knifing accident that resulted in severe fire damage to the system’s oil and electrical circuits [9], causing significant human and economic losses.
Thus, the examination of lateral stability within the civil aircraft towing system, avoidance of jack-knifing during extreme lateral instability events, and enhancement of driving safety are vital prerequisites to ensure successful application of the new departure mode. Nonetheless, given that this model remains in its exploratory phase, there exist scarce reports regarding relevant studies. Refs. [10,11,12,13] comprise over 15 years of tracking research on aircraft tractors, encompassing the kinematic and dynamic characteristics of both rod-tractors and rod-less tractors, optimization of body structure and ride comfort, design and development of multifunctional roller mechanisms, and more. Ref. [14] analyzed the ride comfort of rod-less tractors on B-class road surfaces, concluding that low-speed towing work can aid in enhancing ride comfort. Taking the Boeing 777 as an example, [15] scrutinized the braking performance of rod-less tractors and concluded that the use of tractor braking can effectively reduce braking risks. Ref. [16] established a six-degrees-of-freedom aircraft dynamics model for the fuselage, obtaining the ultimate sideslip speed during turns through Adams/Simulink co-simulation. Ref. [17] simplified the aircraft towing system into a three-degrees-of-freedom dynamics model, concentrating on the impact of the hinged angle between the wheel embrace mechanism and the nose landing gear on system handling stability, and proposed improving the system stability through active steering control of the front wheel. Ref. [18] constructed a model of the aircraft towing system and deduced that the braking effect is optimal when the rear wheel braking force of the tractor accounts for 0.6 of the total braking force. Refs. [19,20] established a nonlinear dynamic model of the towing system of ships on the plane, with the model taking into full account the irregular movement of the system, the effect of the deck on the movement of the towing system of ship motion, and the coupling relationship accurately described, based on which the straight-line driving stability and turning driving stability of the system were examined. Refs. [7,21] utilized the nonlinear calculation model of A320 developed by Airbus to study the steering nonlinear dynamics of the aircraft under various airport pavement conditions and used the generalized continuation method to solve and depict the instability process of the system, providing the system bifurcation diagram and the stability/instability zone.
Furthermore, it is noteworthy that the key connection component, known as the “fifth wheel,” in the trailer–semitrailer system, bears resemblance to the pickaback longitudinal three-point clamping connection mechanism present in the civil aircraft towing system. Both systems also exhibit structural features that concentrate mass towards the rear. Hence, research into the trailer–semitrailer system is of relevance to this project. Ref. [22] explored the stability parameters of the heavy-duty towing system and determined that vehicles with shorter wheelbases were more susceptible to lateral instability than those with longer wheelbases. Ref. [23] constructed a three-axle semitrailer model and verified that independent control of each wheel could enhance the driving stability of the semitrailer. Ref. [24] established a model of the trailer–semitrailer system and achieved real-time monitoring of jack-knifing stability by observing the angle between the trailer and semitrailer, as well as its rate of change. Ref. [25] developed a mathematical model of the trailer–semitrailer system through Lagrange and Newton methods and compared it with the simulation modelto verify its accuracy. Addressing the driving safety issues, such as roll, yaw, and jack-knifing, that are prone to occur when the trailer–semitrailer system is operating at high speeds, [26] conducted a meticulous study on the rollover–yaw model of the system, determined the dynamic instability threshold value, and tested the early warning controller on the self-designed trailer–semitrailer rollover–yaw warning vehicle test platform. The experimental outcomes indicate that the controller can efficiently detect the onset of instability accidents. Ref. [27] researched the driving conditions of the trailer–semitrailer system, such as lane changes, snake-shaped trajectories, and steady-state rotations, that are inevitable during the driving process. The primary factors influencing the lateral stability of the system were assessed and evaluated from a multi-body dynamics perspective. Based on the outcomes of the single lane change test, recommendations and cautionary notes for lateral stability evaluations were proposed. Table 1 shows the faults in the previous research. The analysis of the aforementioned literature illustrates that, despite the fact that research has been conducted on aircraft towing systems and semi-trailers, it is not applicable to novel towing and taxiing circumstances characterized by high speed and heavy loads. As such, targeted research is imperative to effectively promote its implementation.
In summary, in the towing taxi-out departure system, which consists of the tractor and the aircraft, the mass is concentrated at the rear of the system because the takeoff weight of the aircraft is much larger than that of the rodless tractor, and the inertia may lead to potential lateral instability and even “Jack-knifing” which is a potential major accident. Thus, there is great value for the safe application of towing taxi-out mode with an in-depth analysis of the mechanization of lateral instability and the definition of the safe working area. This paper investigates the civil aircraft towing system, comprising a Boeing 737–400 aircraft (The Boeing Company, Arlington, USA)and AM210 tractor (Weihai Guangtai Airport Equipment Co., Ltd, Weihai, China), as the research object. The multi-body dynamics model and mathematical model of the towing taxiing system are established through Adams dynamics simulation software, which is verified for its effectiveness and reliability. Based on these models, the preliminary investigation into the impact of towing speed, system steering angle, and airport ground adhesion coefficient on the lateral stability of the system is conducted, providing a theoretical foundation and reference for subsequent active stabilization control and intelligent taxiing of the system.

2. Model Construction and Experimentation

2.1. Adams Dynamics Model of Towing Taxiing System

For this research, we have chosen to focus on the Boeing 737–400 and AM210 rod-less tractor [28] as the primary subject matter. The essential parameters for these models are presented in Table 2 and Table 3.
During the modeling process, the rod-less tractor body was simplified and replaced by a frame with steering to ensure authenticity in simulation. The location of the center of mass was adjusted accordingly. The connection between the civil aircraft and tire is a rigid connection, disregarding the landing gear strut, while the connection between the civil aircraft and the tractor is a rigid connection of two rotating pairs to ensure accurate lateral stability during simulation, replacing the holding wheel mechanism. The model road surface was smoothed using 2D software and different influencing factors were transformed by adjusting the parameters of the tire and road surface. The Adams model created is depicted in Figure 3.
Furthermore, Table 4 and Table 5 present the essential parameters of the tractor and aircraft tire model, respectively [28].
With the incorporation of the aforementioned tire parameters into Adams, the multi-body dynamic model of the civil aircraft and rod-less tractor towing and taxiing system can be obtained.

2.2. Mathematical Model Construction and Verification

To ensure the reliability and validity of the dynamic model of the aircraft towing and taxiing system established in this study, a four-degrees-of-freedom dynamic model was constructed. This included both the lateral and yaw motions of the tractor, as well as the lateral and yaw motions of the aircraft. A schematic diagram of the two-centroid mathematical model is shown in Figure 4, and the parameters of the model is shown in table of nomenclature.
One of the dynamic models that can be constructed from the system is that of the lateral and yaw motion of the tractor, which can be expressed as follows:
{ m ( U ˙ sin β 2 + r U cos β 2 ) = c f [ α 1 - ( U sin β 2 + L 1 r ) U cos β 2 ] + c r [ α 2 - ( U sin β 2 - L 2 r ) U cos β 2 ] - F Y I Z r ˙ = L 1 c f [ α 1 - ( U sin β 2 + L 1 r ) U cos β 2 ] - L 2 c r [ α 2 - ( U sin β 2 - L 2 r ) U cos β 2 ] + L 3 F Y
The model describing the aircraft’s two degrees of freedom can be expressed as follows:
{ m ( U ˙ sin β 2 + U cos β 2 r ) = c r [ α 2 ( U sin β 2 L 2 r ) U cos β 2 ] + F Y I Z r ˙ = L 1 F Y L 2 c r [ α 2 ( U sin β 2 L 2 r ) U cos β 2 ]
During the process of constructing the model, the following plane coordinate transformation is utilized to convert the model into a unified coordinate system [29,30]:
[ X Y ] = [ cos θ sin θ sin θ cos θ ] [ X Y ]
[ U sin β 2 U cos β 2 + L 1 r ] = [ cos θ sin θ sin θ cos θ ] [ U sin β 2 U cos β 2 L 3 r ]
Based on the above model, the Matlab-Simulink mathematical model was constructed. Taking the towing speed of 30 km/h and the ground adhesion coefficient of 0.8 as the experimental conditions, the change trends of the angle between the system tractor and the aircraft in the Adams dynamic model and the mathematical model when the system steering angle was 4° and 15° were compared, respectively. The comparison test results are shown in Figure 5a,b.
Figure 5 demonstrate that the dynamic model and mathematical model accurately depict the changes in the angle between the aircraft and the tractor under two steering conditions. Specifically, as time progresses, the relative motion between the two bodies remains relatively stable, resulting in a stable angle. Hence, the verification process of the dynamic model and mathematical model supports the conclusion that the multi-body dynamic system of civil aircraft towing and taxiing is accurately described, indicating that the model is both reliable and valid.

3. Results and Discussion

Building upon the aforementioned model, this paper investigates the influence of various factors on the lateral stability of the system under idle running conditions, such as system speed, tractor steering angle, and friction factor, as well as the instability of jack-knifing. Furthermore, the study examines the impact of such differences on the safety domain of the towing system and defines the system’s warning data boundary. These findings provide a theoretical basis and support threshold for the lateral stability control of civil aircraft towing systems operating under different working conditions.

3.1. System Jack-Knifing Mechanism

To investigate the impact of the system’s velocity on the lateral stability of the civil aircraft towing and sliding system in an idle running state, the road adhesion coefficient and rolling resistance coefficient were established as 0.8 and 0.018, respectively. Then, the initial velocity of the system was gradually reduced from 45 km/h to 15 km/h. At every velocity, the steering angle of the tractor’s front wheel was elevated in increments of 0.1° up to the point of the jack-knifing phenomenon. The findings of the experiment are presented in Figure 6.
The present study employs the safety calibration curve to determine the curve wherein the angle between the civil aircraft and the tractor is less than 90°. Figure 6 depicts the jack-knifing zone diagram of the towing speed and tractor steering angle, with the initial velocity of the towing system ranging from 15–45 km/h. The diagram is divided into two segments; namely, the non-jack-knifing zone on the lower side of the curve and the jack-knifing zone on the upper side. Based on the image data obtained from Figure 6, it can be inferred that the jack-knifing phenomenon is more likely to occur with an increase in the initial speed of the system, thereby necessitating a smaller steering angle for the tractor.
In low-speed scenarios, excessive steering angle may result in the jack-knifing phenomenon. Despite the fact that the longitudinal angle between the civil aircraft and the tractor exceeds 90°, the system does not manifest instability. Thus, this cannot be the criterion to assess the loss of lateral stability of the system. Consequently, this paper proposes a methodology to evaluate whether the system has lateral instability by combining two factors: whether the tractor produces lateral slip and the angle of the system.
Figure 7 depicts the temporal variation of the system angle as the tractor’s steering angle increases from 9.0° to 9.1° during the taxiing of the towing system at an initial speed of 40 km/h. The sudden rise in the angle signifies the occurrence of the jack-knifing phenomenon due to the lateral instability of the system. Consequently, it can be inferred that the lateral instability of the system arises during the jack-knifing phenomenon at 40 km/h, and this continues until 25 km/h. As demonstrated in Figure 8, while the entire system is sliding at an initial speed of 25 km/h, there is no significant change in the system’s included angle as the tractor’s steering angle increases from 21.2° to 21.3°, making it impossible to determine the lateral instability of the system from this representation. Therefore, the most straightforward approach to detect the lateral instability of the system is to detect whether the lateral force of the tire surpasses the maximum static friction force of the lateral slip.
The crucial threshold for lateral slippage is determined by multiplying the maximum adhesion coefficient of the tractor tire by the pressure on the road surface. If the resulting value is less than zero, it is deemed that the tire is slipping laterally and the towing system is unstable.
As depicted in Figure 9, the lateral force diagram of the front and rear wheels of the tractor is illustrated when the towing system slides in at an initial speed of 25 km/h with a tractor steering angle of 21.2°. Due to the significant influence of the quality of the civil aircraft on the rear wheel load of the tractor, the front wheel is more susceptible to lateral slip. The portion of the front wheel force curve that is less than zero in Figure 6 indicates the presence of lateral instability in the towing system. Thus, in the 25 km/h state, the occurrence of the jack-knifing phenomenon is accompanied by lateral instability in the system.

3.2. Lateral Slip Instability

In practical towing operations, jack-knifing of the towing system is a rare occurrence. However, the system often struggles to maintain stable tire operation due to tire side deviation, leading to more frequent tire lateral slipping. Additionally, it should be noted that the boundary of the jack-knifing zone discussed earlier is based on the lateral instability resulting from tire lateral slip. Consequently, there is a need to investigate the non-jack-knifing zone further.
The lateral force diagram presented in Figure 10 depicts the behavior of the front and rear wheels of the tractor at a speed of 40 km/h when the tractor steering angle is 9.0°. It is apparent that as long as the tractor steering angle does not exceed 9°, the tire does not experience lateral slip, thus ensuring the lateral stability of the towing system.
As depicted in Figure 11, the lateral force diagram of the front and rear wheels of the tractor is illustrated when the steering angle of the tractor reaches 9.1° under the velocity of 40 km/h. It was discerned that the emergence of lateral slip on the tire and consequent lateral instability of the towing system occurs only when the steering angle of the tractor equals or exceeds 9.1°.
After conducting numerous experimental simulations and analyzing the outcomes, this research paper delineates the towing system’s range of stability and instability between 15 and 45 km/h, based on the presence or absence of lateral slip in the tractor tire, as depicted in Figure 12. The findings suggest that as the towing speed increases, the steering angle of the tractor causing the instability of the towing system decreases, thereby rendering the towing system more susceptible to lateral instability.
After combining Figure 12 with Figure 6, we can obtain the safety zone diagram for the towing system within the speed range of 15–45 km/h, as illustrated in Figure 13.

3.3. Definition and Analysis of Allowable Steering Range in Different Pavement Environments

To further investigate the impact of different factors on the lateral stability of the towing system within the instability jack-knifing zone, the system’s initial speed was fixed at 40 km/h, as this is when lateral instability is most severe. We examined the effect of changing the steering angle of the tractor and the road conditions of the towing system separately to evaluate the influence of various factors on the lateral stability of the towing system.
The pavements listed in Table 6 have been categorized into two classifications: ordinary pavement and extreme pavement. Using the same methodology as before, we depicted the safety zone diagram of the towing system moving at 40 km/h, with friction coefficients ranging from 0.45 to 0.8 and a tire rolling resistance coefficient of 0.018. The diagram, presented in Figure 14, showcases the effect of pavement wetness on the lateral stability of the towing system under regular pavement conditions that are predominantly comprised of concrete or asphalt.
On asphalt or concrete pavement, the lateral stability of the towing system is divided into three zones; namely, the jack-knifing zone, instability zone, and stability zone. It can be inferred that a higher adhesion coefficient of the ground leads to better lateral stability of the towing system and reduces the likelihood of instability.
Due to the snow and ice road surface being an extreme road surface, the ground adhesion coefficient is small, making it less likely for the jack-knifing phenomenon to occur and more prone to tire lateral slip. Therefore, the analysis of the jack-knifing phenomenon was not conducted, and the definition of the tire lateral slip instability zone was introduced, as depicted in Figure 15.
The lateral stability of the towing system under snow and ice road conditions can be categorized into two zones: the stability zone and the instability zone. It can be inferred that when operating on snow- and ice-covered roads at high speeds, the tractor should steer clear of causing any lateral instability of the towing system. Furthermore, it can be deduced that the stability of the towing system will increase as the adhesion coefficient of the snow- and ice-covered road increases.

4. Conclusions

This paper utilizes the Adams simulation platform to establish a multi-body dynamics model that examines the interaction between a Boeing 737–400 civil aircraft and the Weihai Guangtai AM210 rod-less tractor. The study conducts a simulation analysis of the system’s idle running condition. The experimental results reveal that as the system speed increases, the steering angle of the tractor required to produce the jack-knifing phenomenon is smaller. Moreover, the jack-knifing phenomenon in the towing speed range of 15–45 km/h is the lateral slip instability of the tire. The paper provides a safety zone diagram of the towing system within this speed range. The study further explores the lateral stability of the towing system under different road conditions, dividing road conditions under 40 km/h towing speed into ordinary and extreme roads, and determining the influence of the steering angle of the tractor and the adhesion coefficient of different roads on the lateral stability of the towing system. This paper presents the safety zone diagram of the lateral stability of the towing system on asphalt or concrete pavement and the stability zone diagram of the towing system on snow- and ice-covered pavement. An active control to recover the instability of system from a potential accident will be carried out as the aim of the research is ensuring the safety of towing taxi-out, and the results in this research will provide the control threshold in future research. The research findings can offer theoretical and practical support for the lateral stability control of civil aircraft towing and taxiing systems, and promote the secure landing application of the new towing and taxiing mode.

Author Contributions

Conceptualization, J.Q. and W.Z.; methodology, J.Q.; software, Jinwang Liu; validation, J.Q., Q.L. and W.Z.; formal analysis, Jinwang Liu; investigation, Q.L.; resources, W.Z.; data curation, Jinwang Liu; writing—original draft preparation, J.Q. and Jinwang Liu; writing—review and editing, J.Q. and W.Z.; visualization, Jinwang Liu and Q.L.; supervision, W.Z.; project administration, J.Q.; funding acquisition, J.Q. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by National Natural Science Foundation of China, grant number 52102446 and Fundamental Research Funds for The Central Universities, grant number 3122021050.

Data Availability Statement

All research data are supported for sharing. Please do not hesitate to email [email protected] if necessary.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

mMass of tractor (kg)
L 1 Distance from front axle to barycenter of tractor (mm)
L 2 Distance from rear axle to barycenter of tractor (mm)
L 3 Distance from towing point to barycenter of tractor (mm)
L 4 Rear wheel pitch of tractor (mm)
L 5 Front wheel pitch of tractor (mm)
r Rotational angular velocity of tractor around barycenter (rad/s)
UCenter of barycenter velocity of tractor (m/s)
F 1 Side-deviation force of tractor front wheel (N)
α 1 Side-deviation angle of tractor front wheel (deg)
α 2 Side-deviation angle of tractor rear wheel (deg)
F 2 Side-deviation force of the rear wheel of the tractor (deg)
β 2 Lateral-deviation angle of tractor barycenter (deg)
C f Lateral-deviation stiffness of the front wheel of the tractor (N/rad)
C r Lateral-deviation stiffness of the rear wheel of the tractor (N/rad)
F X Force in X-direction of tractor towing point (N)
F Y Force in Y-direction of tractor towing point (N)
m Mass of aircraft (kg)
L 1 Distance from front axle to barycenter of aircraft (mm)
L 2 Distance from rear axle to barycenter of aircraft (mm)
L 4 rear wheel Pitch of aircraft (mm)
r Angular velocity of aircraft rotating around the center of mass (rad/s)
U Velocity of aircraft barycenter (m/s)
F 2 Side-deviation force of aircraft rear wheel (N)
β 2 Lateral-deviation angle of aircraft barycenter (deg)
C r Lateral-deviation stiffness of aircraft rear wheel (N/rad)
α 2 Lateral-deviation angle of aircraft rear wheel (deg)
F X Force in X-direction of aircraft towing point (N)
F Y Force in Y-direction of aircraft towing point (N)
θ Angle between aircraft and tractor (deg)
φ Angle between tractor and ground coordinate system (deg)
φ Angle between aircraft and ground coordinate system (deg)
I Z Moment of inertia of tractor around barycenter (kg·m2)
I Z Moment of inertia of the aircraft around barycenter (kg·m2)

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Figure 1. Schematic diagram of civil aircraft departure and taxiing process [5,6].
Figure 1. Schematic diagram of civil aircraft departure and taxiing process [5,6].
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Figure 2. Accident diagram of lateral instability of civil aircraft towing system. (Note: (a) An accident scene of the “Jack-knifing”; (b) A scene of a fire accident in airport).
Figure 2. Accident diagram of lateral instability of civil aircraft towing system. (Note: (a) An accident scene of the “Jack-knifing”; (b) A scene of a fire accident in airport).
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Figure 3. Model drawing of aircraft and aircraft tractor.
Figure 3. Model drawing of aircraft and aircraft tractor.
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Figure 4. Double centroid model of aircraft and tractor.
Figure 4. Double centroid model of aircraft and tractor.
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Figure 5. Comparison test between Adams model and Simulink model of 30 km/h towing system. (Note: (a) the comparison of system stability; (b) the comparison of “Jack-knifing”).
Figure 5. Comparison test between Adams model and Simulink model of 30 km/h towing system. (Note: (a) the comparison of system stability; (b) the comparison of “Jack-knifing”).
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Figure 6. Jack-knifing zone diagram of 15–45 km/h towing speed and tractor steering angle.
Figure 6. Jack-knifing zone diagram of 15–45 km/h towing speed and tractor steering angle.
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Figure 7. Variation diagram of system angle under 40 km/h.
Figure 7. Variation diagram of system angle under 40 km/h.
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Figure 8. Variation diagram of system angle under 25 km/h.
Figure 8. Variation diagram of system angle under 25 km/h.
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Figure 9. Stress diagram of front and rear wheels of tractor at steering angle of 21.2° at a speed of 25 km/h.
Figure 9. Stress diagram of front and rear wheels of tractor at steering angle of 21.2° at a speed of 25 km/h.
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Figure 10. Stress diagram of front and rear wheels of tractor at a steering angle of 9.0° and speed of 40 km/h.
Figure 10. Stress diagram of front and rear wheels of tractor at a steering angle of 9.0° and speed of 40 km/h.
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Figure 11. Stress diagram of front and rear wheels of tractor at a steering angle of 9.1° and speed of 40 km/h.
Figure 11. Stress diagram of front and rear wheels of tractor at a steering angle of 9.1° and speed of 40 km/h.
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Figure 12. Stability zone diagram of 15–45 km/h towing speed and tractor steering angle.
Figure 12. Stability zone diagram of 15–45 km/h towing speed and tractor steering angle.
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Figure 13. Safety zone diagram of 15–45 km/h towing speed and tractor steering angle.
Figure 13. Safety zone diagram of 15–45 km/h towing speed and tractor steering angle.
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Figure 14. Safety zone map of 40 km/h asphalt or concrete pavement.
Figure 14. Safety zone map of 40 km/h asphalt or concrete pavement.
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Figure 15. Stability zone map of 40 km/h ice or snow pavement.
Figure 15. Stability zone map of 40 km/h ice or snow pavement.
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Table 1. The faults in the previous research.
Table 1. The faults in the previous research.
Reference No.AuthorsWork and ContributionDeficiencies of Work
[8,9,10,11]Wang, L.W; Xie, B.M.Load simulation of landing gear, analysis of clamping lifting mechanism of aircraft tractor.Have not studied the overall dynamics of the traction system.
[12]Zhang, J.H.Low-speed traction operation helps improve ride comfort.Analyzed only from the perspective of comfort.
[13]Gordon, F.Using tractor braking to reduce accident risk.Does not take the high-speed traction condition into account.
[14]Huang, MThe ultimate sideslip speed of the aircraft during turning is obtained.Does not take the side slip of the tractor at high speed into account.
[15]Wang, NThe wheel holding mechanism and the front landing gear have an impact on the stability of the traction system is concluded.Does not consider the role of multi-body dynamics composed of tractor and aircraft.
[16]Shi, H.T.The braking effect is best when the rear wheel braking force of the tractor accounts for 0.6 of the total braking force.Does not take the impact of the braking of the tractor on the traction system at high speed into account.
[17,18]Zhou, L.J; Xiao, HDefine the influence of deck on the motion of aircraft towing system.The research is not applicable to the traction conditions of large aircraft.
[19]Coetzee, EThe stable and unstable regions of the aircraft under various airport pavement conditions are obtained.The research object is the aircraft individual, and the multi-body dynamics effect of the traction system is not considered.
Table 2. Model parameters of Boeing 737–400 aircraft.
Table 2. Model parameters of Boeing 737–400 aircraft.
ParameterValue
Aircraft length/mm36,400
Wingspan/mm28,880
Aircraft height/mm10,567
Horizontal distance between nose and main landing gear/mm11,070
Horizontal distance between main landing gears/mm5230
Spacing between two wheels of nose landing gear/mm674
Spacing between two wheels of main landing gear/mm338.16
Weight of equipment/kg60,555
Moment of inertia of mass center around X-axis/(kg·m2) 8.12 × 1011
Moment of inertia of mass center around Y-axis/(kg·m2) 2.854 × 1012
Moment of inertia of mass center around Z-axis/(kg·m2) 2.704 × 1012
Table 3. Model parameters of rod-less aircraft tractor.
Table 3. Model parameters of rod-less aircraft tractor.
ParameterValue
Length/mm8000
Width/mm3750
Height/mm1975
Wheelbase/mm4500
Front wheel base/mm2100
Rear wheel base/mm2700
Weight of equipment/kg12,900
Moment of inertia of mass center around X-axis/(kg·m2) 6114
Moment of inertia of mass center around Y-axis/(kg·m2) 52,545
Moment of inertia of mass center around Z-axis/(kg·m2) 53,675
Table 4. Tire parameters of rod-less aircraft tractor.
Table 4. Tire parameters of rod-less aircraft tractor.
ParameterValue
Front tire specification285/70 R19.5
Rear tire specification385/65 R22.5
Tire weight/kg190
Coefficient of normal stiffness2000
Normal damping coefficient28
Rolling resistance coefficient0.0165
Longitudinal stiffness (N/mm) 5000
Lateral stiffness of tire80,000
Static friction factor of tire0.8
Dynamic friction factor of tire1
Table 5. Tire parameters of Boeing 737–400.
Table 5. Tire parameters of Boeing 737–400.
ParameterValue
Front tire weight/kg50
Rear tire weight/kg150
Front tire radius of freedom/mm340
Rear tire radius of freedom/mm551
Front tread width mm196.8
Rear tread width/mm411.44
Front wheel normal stiffness coefficient2400
Rear wheel normal stiffness coefficient2400
Normal damping coefficient28
Rolling resistance coefficient0.0165
Longitudinal stiffness of front wheels (N/mm) 2000
Longitudinal stiffness of rear wheels (N/mm) 6000
Lateral stiffness of tire80,000
Static friction factor of tire0.8
Dynamic friction factor of tire1
Table 6. Adhesion coefficient and rolling resistance of tires on different roads.
Table 6. Adhesion coefficient and rolling resistance of tires on different roads.
Road ConditionsAdhesion CoefficientRolling Resistance
Concrete or asphalt (dry) 0.55–0.800.010–0.018
Concrete or asphalt (wet) 0.45–0.700.018–0.020
Flat ice road0.10–0.250.015–0.030
Snow-compacted pavement0.30–0.400.030–0.050
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Qin, J.; Liu, J.; Lin, Q.; Zhang, W. Research on Instability and “Jack-Knifing” of Civil Aircraft Towing Taxi-Out System. Appl. Sci. 2023, 13, 3636. https://doi.org/10.3390/app13063636

AMA Style

Qin J, Liu J, Lin Q, Zhang W. Research on Instability and “Jack-Knifing” of Civil Aircraft Towing Taxi-Out System. Applied Sciences. 2023; 13(6):3636. https://doi.org/10.3390/app13063636

Chicago/Turabian Style

Qin, Jiahao, Jinwang Liu, Qiwei Lin, and Wei Zhang. 2023. "Research on Instability and “Jack-Knifing” of Civil Aircraft Towing Taxi-Out System" Applied Sciences 13, no. 6: 3636. https://doi.org/10.3390/app13063636

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