Based on the train-track coupling dynamics and high-speed train aerodynamics, this paper deals with an improved algorithm for fluid-structure interaction of high-speed trains. In the algorithm, the data communication ...Based on the train-track coupling dynamics and high-speed train aerodynamics, this paper deals with an improved algorithm for fluid-structure interaction of high-speed trains. In the algorithm, the data communication between fluid solver and structure solver is avoided by inserting the program of train-track coupling dynamics into fluid dynamics program, and the relaxation factor concerning the load boundary of the fluid-structure interface is introduced to improve the fluctuation and convergence of aerodynamic forces. With this method, the fluid-structure dynamics of a highspeed train are simulated under the condition that the velocity of crosswind is 13.8 m/s and the train speed is 350 km/h. When the relaxation factor equals 0.5, the fluctuation of aerodynamic forces is lower and its convergence is faster than in other cases. The side force and lateral displacement of the head train are compared between off-line simulation and co-simulation. Simulation results show that the fluid-structure interaction has a significant influence on the aerodynam- ics and attitude of the head train under crosswind conditions. In addition, the security indexes of the head train worsen after the fluid-structure interaction calculation. Therefore, the fluid-structure interaction calculation is necessary for high-speed trains.展开更多
Taking a high-speed train in China as an example,using computer simulation technology and comparing with the test data,the three current methods including linear stability analysis method,nonlinear stability analysis ...Taking a high-speed train in China as an example,using computer simulation technology and comparing with the test data,the three current methods including linear stability analysis method,nonlinear stability analysis method and the field testing criterion are studied to evaluate stability of high-speed trains.A new stability evaluation method is proposed which can be used to evaluate lateral stability of high-speed vehicle based on the codes of UIC 515and UIC 518.From the viewpoint of taking the most unfavorable track conditions into account and improving the safety margin,the new method uses the root mean square of bogie lateral acceleration as a criterion to evaluate the lateral stability of high-speed trains.Numerical example shows that the proposed method not only considers the forced vibration caused by track irregularities in the actual practice,but also takes the instability self-excited vibration into account,so it can realize early warning of bogie slight unstable oscillation,meanwhile the method itself does not involve complex algorithms which has the possibility of engineering applications.展开更多
To study the influence of the pantograph fixing position on aerodynamic characteristics of high-speed trains, the aerodynamic models of high-speed trains with eight cars were established based on the theory of com- pu...To study the influence of the pantograph fixing position on aerodynamic characteristics of high-speed trains, the aerodynamic models of high-speed trains with eight cars were established based on the theory of com- putational fluid dynamics, and eight cases with pantographs fixed on different positions and in different operational orientations were considered. The pantographs were fixed on the front or the rear end of the first middle car or fixed on the front or the rear end of the last middle car. The external flow fields of the high-speed trains were numeri- cally simulated using the software STAR-CCM＋. The results show that the pantograph fixing position has little effect on the aerodynamic drag force of the head car and has a large effect on the aerodynamic drag force of the tail car. The influences of the pantograph fixing position on the aerodynamic lift forces of the head car, tail car and pan- tographs are obvious. Among the eight cases, considering the total aerodynamic drag force of the train and the aerodynamic lift force of the lifted pantograph, when the pantographs are fixed on the rear end of the last middle car and the lifted pantograph is in the knuckle-upstream ori- entation, the aerodynamic performance of the high-speed train is the best.展开更多
Based on the experiments on a platform with real vehicle structure and finite element simulation, the vibration and interior acoustic radiation under random excitations of high-speed trains’ bogie area were studied. ...Based on the experiments on a platform with real vehicle structure and finite element simulation, the vibration and interior acoustic radiation under random excitations of high-speed trains’ bogie area were studied. Firstly, combined with line tests, a vehicle body with a length of 7 m was used as the research object. By comparing the results of experiment and simulation, the accuracy of the finite element model was verified. Secondly, the power spectral density curves at typical measuring points in bogie area were obtained by processing and calculating the line test data, which was measured when the vehicle ran at high speeds, and the standard vibration spectrum of the bogie area was obtained by the extreme envelope method. Furthermore, the random vibration test and simulation prediction analysis of the real vehicle structure were carried out to further verify the accuracy of the noise and vibration prediction model. Finally, according to the vibration and acoustic radiation theory, the indirect boundary element method was adopted to predict the acoustic response of the real vehicle. The analysis shows that the simulated power spectral density curves of acceleration and sound pressure level are highly consistent with the experimental ones, and the error between the simulated prediction and the experimental result is within the allowable range of 3 dB.展开更多
In tests on dynamic performance of high-speed trains, it is found that there is an unfavorable speed interval for some vehicles, which would he harmful to the daily operation of the vehicle. By analyzing the relations...In tests on dynamic performance of high-speed trains, it is found that there is an unfavorable speed interval for some vehicles, which would he harmful to the daily operation of the vehicle. By analyzing the relationship of vibration frequencies of the vehicle and its running speed, this paper finds that the unfavorable speed interval is caused by the vibration superposition of the natural frequency of the vehicle system with the frequency of external excitation. Taking some electric multiple units （EMUs） as examples, we proposed an approach to obtaining the unfavorable speed interval of vehicles. By analyzing the relation between vibration frequencies and the running speed of the vehicle, the natural frequencies of the vehicle system and the external excitations are distinguished. In the end, we suggest some measures to minimize the negative influences of the unfavorable speed interval, such as shifting frequency, reducing or eliminating external excitation.展开更多
The focus of this study is to explore the statis-tical distribution models of high-speed railway (HSR) train delays. Based on actual HSR operational data, the delay causes and their classification, delay frequency, nu...The focus of this study is to explore the statis-tical distribution models of high-speed railway (HSR) train delays. Based on actual HSR operational data, the delay causes and their classification, delay frequency, number of affected trains, and space–time delay distributions are discussed. Eleven types of delay events are classified, and a detailed analysis of delay distribution for each classifica-tion is presented. Models of delay probability delay prob-ability distribution for each cause are proposed. Different distribution functions, including the lognormal, exponen-tial, gamma, uniform, logistic, and normal distribution, were selected to estimate and model delay patterns. The most appropriate distribution, which can approximate the delay duration corresponding to each cause, is derived. Subsequently, the Kolmogorov–Smirnov (K–S) test was used to test the goodness of fit of different train delay distribution models and the associated parameter values. The test results show that the distribution of the test data is consistent with that of the selected models. The fitting distribution models show the execution effect of the timetable and help in finding out the potential conflicts in real-time train operations.展开更多
It is a complicated dynamic phenomenon when a transient pressure pulse is triggered by two high-speed trains passing each other in a tunnel. The air pressure pulse is a transient excitation to side wall of the car bod...It is a complicated dynamic phenomenon when a transient pressure pulse is triggered by two high-speed trains passing each other in a tunnel. The air pressure pulse is a transient excitation to side wall of the car body. It can stimulate almost all vibration modes of the car body and the correlated assemblies, cause serious aerodynamic noise, and have important impacts on car body distortion, train noise, and operation safety. This article analyzes the time- frequency characteristics and main parameters of field-measured the air pressure wave, and its relationship with the train velocity as well as the vibration of the car body. Cepstrum analysis concludes that in the process of the meeting, the air pressure wave in tunnel crossing is a multiplying pressure wave instead of a superposed wave. The pressure pulse during the meeting is non-symmetrical one featured with a sharp front, large amplitude, fluctuating central sec- tion, and less sharp tail. The pulse width is inversely proportional to the train speed. As the speed increases, the impulse amplitude is amplified, and the speed of pulse front is advanced.展开更多
This is a review of high-speed train development in the sense of technology advances all over the world. Three generations of high-speed trains are classified according to their technical characteristics and maximum o...This is a review of high-speed train development in the sense of technology advances all over the world. Three generations of high-speed trains are classified according to their technical characteristics and maximum operating speed. Emphasis is given to the newly developed high-speed train in China, CRH380. The theoretical foundations and future development of CRH380 are briefly discussed.展开更多
In this paper, we propose a new formula of the real-time minimum safety headway based on the relative velocity of consecutive trains and present a dynamic model of high-speed passenger train movements in the rail line...In this paper, we propose a new formula of the real-time minimum safety headway based on the relative velocity of consecutive trains and present a dynamic model of high-speed passenger train movements in the rail line based on the proposed formula of the minimum safety headway. Moreover, we provide the control strategies of the high-speed passenger train operations based on the proposed formula of the real-time minimum safety headway and the dynamic model of highspeed passenger train movements. The simulation results demonstrate that the proposed control strategies of the passenger train operations can greatly reduce the delay propagation in the high-speed rail line when a random delay occurs.展开更多
Increasing velocity combined with decreasing mass of modern highspeed trains poses a question about the influence of strong crosswinds on its aerodynamics. Strong crosswinds may affect the running stability of high sp...Increasing velocity combined with decreasing mass of modern highspeed trains poses a question about the influence of strong crosswinds on its aerodynamics. Strong crosswinds may affect the running stability of high speed trains via the amplified aerodynamic forces and moments. In this study, a simulation of turbulent crosswind flows over the leading and end cars of ICE2 highspeed train was performed at different yaw angles in static and moving ground case scenarios. Since the train aerodynamic problems are closely associated with the flows occurring around train, the flow around the train was considered as incompressible and was obtained by solving the incom pressible form of the unsteady Reynoldsaveraged Navier Stokes （RANS） equations combined with the realizable kepsilon turbulence model. Important aerodynamic coef ficients such as the side force and rolling moment coeffi cients were calculated for yaw angles ranging from 30° to 60° and compared with the results obtained from wind tunnel test. The dependence of the flow structure on yaw angle was also presented. The nature of the flow field and its structure depicted by contours of velocity magnitude and streamline patterns along the train＇s crosssection were presented for different yaw angles. In addition, the pressure coefficient around the circumference of the train at dif ferent locations along its length was computed for yaw angles of 30° and 60°, The computed aerodynamic coef ficient outcomes using the realizable kepsilon turbulencemodel were in good agreement with the wind tunnel data. Both the side force coefficient and rolling moment coeffi cients increase steadily with yaw angle till about 50° before starting to exhibit an asymptotic behavior. Contours of velocity magnitude were also computed at different cross sections of the train along its length for different yaw angles. The result showed that magnitude of rotating vortex in the lee ward side increased with increasing yaw angle, which leads to the creation of a lowpressure region in the lee ward side of the train causing high side force and roll moment. Generally, this study shows that unsteady CFD RANS methods combined with an appropriate turbulence model can present an important means of assessing the crucial aerodynamic forces and moments of a highspeed train under strong crosswind conditions.展开更多
In this paper, the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated. The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible...In this paper, the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated. The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible couplers, which is subject to rolling mechanical resistance, aerodynamic drag and wind gust. Based on Lyapunov＇s stability theory, the sufficient condition for the existence of the robust output feedback cruise control law is given in terms of linear matrix inequalities（LMIs）, under which the high-speed train tracks the desired speed, the relative spring displacement between the two neighboring cars is stable at the equilibrium state, and meanwhile a small prescribed H∞ disturbance attenuation level is guaranteed. One numerical example is given to illustrate the effectiveness of the proposed methods.展开更多
Based on incompressible viscous fluid Navier-stokes equation and k-ε 2-equations turbulent model, an investigation on 3D turbulent flow field around four kinds of train models has been made by finite element method. ...Based on incompressible viscous fluid Navier-stokes equation and k-ε 2-equations turbulent model, an investigation on 3D turbulent flow field around four kinds of train models has been made by finite element method. From the calculation, the pressure distribution characters of now field around high-speed trains have been obtained. It is significant for strength design of the high-speed train body, for resisting wind design of the facilities beside the high-speed railways and for determining the aerodynamic force of induced air to the human body near the railways.展开更多
This paper numerically investigates the influence of separation variation of the outriggers on the hydrodynamic performance of a high speed trimaran （HST） aiming at improving its applicability in diverse realistic d...This paper numerically investigates the influence of separation variation of the outriggers on the hydrodynamic performance of a high speed trimaran （HST） aiming at improving its applicability in diverse realistic disciplines. The present investigation was performed within the framework of the 2-D slender body method （SBM） by calculating the resistance of three symmetric trimaran series moving in a calm free surface of deep water. Each trimaran series comprises of 4681 configurations generated by considering 151 staggers （-50%≤a≤＋ 100%）, and 31 separations （100%≤β≤400%） for 81 Froude numbers （0.20≤Fn≤ 1.0）. In developing the three trimaran series, Wigley-st. AMECRC-09, and NPL-4a models were used separately for both the main and side hulls of each individu;d series models. A computer macro named Tri-PL was created using the Visual Basic for Applications~. Tri-PL~ sequentially interfaced Maxsurfe then Hullspeed to generate the models of the three trimaran series together with their detailed hydrostatic particulars, followed by their resistance components. The numerical results were partially validated against the available published numerical calculations and experimental results, to benchmark the Tri-PL macro and hence to rely on the analysis outcomes. A graph template was creaLed within the framework of SigmaPlot to visualize the significant results of the Tri-PL properlv.展开更多
基金supported by the National Natural Science Foundations of China(Nos.50821063 and 50823004)973 Program(No.2007CB714701)the Fundamental Research Funds for the Central Universities(No.2010XS34)
文摘Based on the train-track coupling dynamics and high-speed train aerodynamics, this paper deals with an improved algorithm for fluid-structure interaction of high-speed trains. In the algorithm, the data communication between fluid solver and structure solver is avoided by inserting the program of train-track coupling dynamics into fluid dynamics program, and the relaxation factor concerning the load boundary of the fluid-structure interface is introduced to improve the fluctuation and convergence of aerodynamic forces. With this method, the fluid-structure dynamics of a highspeed train are simulated under the condition that the velocity of crosswind is 13.8 m/s and the train speed is 350 km/h. When the relaxation factor equals 0.5, the fluctuation of aerodynamic forces is lower and its convergence is faster than in other cases. The side force and lateral displacement of the head train are compared between off-line simulation and co-simulation. Simulation results show that the fluid-structure interaction has a significant influence on the aerodynam- ics and attitude of the head train under crosswind conditions. In addition, the security indexes of the head train worsen after the fluid-structure interaction calculation. Therefore, the fluid-structure interaction calculation is necessary for high-speed trains.
基金Science and technology research and development program of the Ministry of Railways(1219YF1305)
文摘Taking a high-speed train in China as an example,using computer simulation technology and comparing with the test data,the three current methods including linear stability analysis method,nonlinear stability analysis method and the field testing criterion are studied to evaluate stability of high-speed trains.A new stability evaluation method is proposed which can be used to evaluate lateral stability of high-speed vehicle based on the codes of UIC 515and UIC 518.From the viewpoint of taking the most unfavorable track conditions into account and improving the safety margin,the new method uses the root mean square of bogie lateral acceleration as a criterion to evaluate the lateral stability of high-speed trains.Numerical example shows that the proposed method not only considers the forced vibration caused by track irregularities in the actual practice,but also takes the instability self-excited vibration into account,so it can realize early warning of bogie slight unstable oscillation,meanwhile the method itself does not involve complex algorithms which has the possibility of engineering applications.
基金supported by the High-Speed Railway Basic Research Fund Key Project of China(Grant No.U1234208)the National Natural Science Foundation of China(Grant Nos.51475394 and 51605397)
文摘To study the influence of the pantograph fixing position on aerodynamic characteristics of high-speed trains, the aerodynamic models of high-speed trains with eight cars were established based on the theory of com- putational fluid dynamics, and eight cases with pantographs fixed on different positions and in different operational orientations were considered. The pantographs were fixed on the front or the rear end of the first middle car or fixed on the front or the rear end of the last middle car. The external flow fields of the high-speed trains were numeri- cally simulated using the software STAR-CCM＋. The results show that the pantograph fixing position has little effect on the aerodynamic drag force of the head car and has a large effect on the aerodynamic drag force of the tail car. The influences of the pantograph fixing position on the aerodynamic lift forces of the head car, tail car and pan- tographs are obvious. Among the eight cases, considering the total aerodynamic drag force of the train and the aerodynamic lift force of the lifted pantograph, when the pantographs are fixed on the rear end of the last middle car and the lifted pantograph is in the knuckle-upstream ori- entation, the aerodynamic performance of the high-speed train is the best.
基金support for this work from the Ministry of Science and Technology of China(2016YFB1200500)
文摘Based on the experiments on a platform with real vehicle structure and finite element simulation, the vibration and interior acoustic radiation under random excitations of high-speed trains’ bogie area were studied. Firstly, combined with line tests, a vehicle body with a length of 7 m was used as the research object. By comparing the results of experiment and simulation, the accuracy of the finite element model was verified. Secondly, the power spectral density curves at typical measuring points in bogie area were obtained by processing and calculating the line test data, which was measured when the vehicle ran at high speeds, and the standard vibration spectrum of the bogie area was obtained by the extreme envelope method. Furthermore, the random vibration test and simulation prediction analysis of the real vehicle structure were carried out to further verify the accuracy of the noise and vibration prediction model. Finally, according to the vibration and acoustic radiation theory, the indirect boundary element method was adopted to predict the acoustic response of the real vehicle. The analysis shows that the simulated power spectral density curves of acceleration and sound pressure level are highly consistent with the experimental ones, and the error between the simulated prediction and the experimental result is within the allowable range of 3 dB.
文摘In tests on dynamic performance of high-speed trains, it is found that there is an unfavorable speed interval for some vehicles, which would he harmful to the daily operation of the vehicle. By analyzing the relationship of vibration frequencies of the vehicle and its running speed, this paper finds that the unfavorable speed interval is caused by the vibration superposition of the natural frequency of the vehicle system with the frequency of external excitation. Taking some electric multiple units （EMUs） as examples, we proposed an approach to obtaining the unfavorable speed interval of vehicles. By analyzing the relation between vibration frequencies and the running speed of the vehicle, the natural frequencies of the vehicle system and the external excitations are distinguished. In the end, we suggest some measures to minimize the negative influences of the unfavorable speed interval, such as shifting frequency, reducing or eliminating external excitation.
基金supported by the National Key R&D Plan (No.2017YFB1200701)National Nature Science Foundation of China (No.U1834209 and 71871188)the support of the Railways Technology Development Plan of China Railway Corporation (No.2016X008-J)supported by State Key Lab of Railway Control and Safety Open Topics Fund (No.RCS2019K007)
文摘The focus of this study is to explore the statis-tical distribution models of high-speed railway (HSR) train delays. Based on actual HSR operational data, the delay causes and their classification, delay frequency, number of affected trains, and space–time delay distributions are discussed. Eleven types of delay events are classified, and a detailed analysis of delay distribution for each classifica-tion is presented. Models of delay probability delay prob-ability distribution for each cause are proposed. Different distribution functions, including the lognormal, exponen-tial, gamma, uniform, logistic, and normal distribution, were selected to estimate and model delay patterns. The most appropriate distribution, which can approximate the delay duration corresponding to each cause, is derived. Subsequently, the Kolmogorov–Smirnov (K–S) test was used to test the goodness of fit of different train delay distribution models and the associated parameter values. The test results show that the distribution of the test data is consistent with that of the selected models. The fitting distribution models show the execution effect of the timetable and help in finding out the potential conflicts in real-time train operations.
基金supported by the National Science and Technology Pillar Programs of China (No.2009BAG12A01-E02,No. 2009BAG12A01-E03 and No. 2009BAG12A01-E04)
文摘It is a complicated dynamic phenomenon when a transient pressure pulse is triggered by two high-speed trains passing each other in a tunnel. The air pressure pulse is a transient excitation to side wall of the car body. It can stimulate almost all vibration modes of the car body and the correlated assemblies, cause serious aerodynamic noise, and have important impacts on car body distortion, train noise, and operation safety. This article analyzes the time- frequency characteristics and main parameters of field-measured the air pressure wave, and its relationship with the train velocity as well as the vibration of the car body. Cepstrum analysis concludes that in the process of the meeting, the air pressure wave in tunnel crossing is a multiplying pressure wave instead of a superposed wave. The pressure pulse during the meeting is non-symmetrical one featured with a sharp front, large amplitude, fluctuating central sec- tion, and less sharp tail. The pulse width is inversely proportional to the train speed. As the speed increases, the impulse amplitude is amplified, and the speed of pulse front is advanced.
文摘This is a review of high-speed train development in the sense of technology advances all over the world. Three generations of high-speed trains are classified according to their technical characteristics and maximum operating speed. Emphasis is given to the newly developed high-speed train in China, CRH380. The theoretical foundations and future development of CRH380 are briefly discussed.
基金supported by the National Basic Research Program of China (Grant No. 2012CB725400)the National Natural Science Foundation of China (Grant No. 71131001-1)the Research Foundation of State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University,China (Grant Nos. RCS2012ZZ001 and RCS2012ZT001)
文摘In this paper, we propose a new formula of the real-time minimum safety headway based on the relative velocity of consecutive trains and present a dynamic model of high-speed passenger train movements in the rail line based on the proposed formula of the minimum safety headway. Moreover, we provide the control strategies of the high-speed passenger train operations based on the proposed formula of the real-time minimum safety headway and the dynamic model of highspeed passenger train movements. The simulation results demonstrate that the proposed control strategies of the passenger train operations can greatly reduce the delay propagation in the high-speed rail line when a random delay occurs.
文摘Increasing velocity combined with decreasing mass of modern highspeed trains poses a question about the influence of strong crosswinds on its aerodynamics. Strong crosswinds may affect the running stability of high speed trains via the amplified aerodynamic forces and moments. In this study, a simulation of turbulent crosswind flows over the leading and end cars of ICE2 highspeed train was performed at different yaw angles in static and moving ground case scenarios. Since the train aerodynamic problems are closely associated with the flows occurring around train, the flow around the train was considered as incompressible and was obtained by solving the incom pressible form of the unsteady Reynoldsaveraged Navier Stokes （RANS） equations combined with the realizable kepsilon turbulence model. Important aerodynamic coef ficients such as the side force and rolling moment coeffi cients were calculated for yaw angles ranging from 30° to 60° and compared with the results obtained from wind tunnel test. The dependence of the flow structure on yaw angle was also presented. The nature of the flow field and its structure depicted by contours of velocity magnitude and streamline patterns along the train＇s crosssection were presented for different yaw angles. In addition, the pressure coefficient around the circumference of the train at dif ferent locations along its length was computed for yaw angles of 30° and 60°, The computed aerodynamic coef ficient outcomes using the realizable kepsilon turbulencemodel were in good agreement with the wind tunnel data. Both the side force coefficient and rolling moment coeffi cients increase steadily with yaw angle till about 50° before starting to exhibit an asymptotic behavior. Contours of velocity magnitude were also computed at different cross sections of the train along its length for different yaw angles. The result showed that magnitude of rotating vortex in the lee ward side increased with increasing yaw angle, which leads to the creation of a lowpressure region in the lee ward side of the train causing high side force and roll moment. Generally, this study shows that unsteady CFD RANS methods combined with an appropriate turbulence model can present an important means of assessing the crucial aerodynamic forces and moments of a highspeed train under strong crosswind conditions.
基金Project supported by the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant No.2014JBM150)
文摘In this paper, the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated. The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible couplers, which is subject to rolling mechanical resistance, aerodynamic drag and wind gust. Based on Lyapunov＇s stability theory, the sufficient condition for the existence of the robust output feedback cruise control law is given in terms of linear matrix inequalities（LMIs）, under which the high-speed train tracks the desired speed, the relative spring displacement between the two neighboring cars is stable at the equilibrium state, and meanwhile a small prescribed H∞ disturbance attenuation level is guaranteed. One numerical example is given to illustrate the effectiveness of the proposed methods.
文摘Based on incompressible viscous fluid Navier-stokes equation and k-ε 2-equations turbulent model, an investigation on 3D turbulent flow field around four kinds of train models has been made by finite element method. From the calculation, the pressure distribution characters of now field around high-speed trains have been obtained. It is significant for strength design of the high-speed train body, for resisting wind design of the facilities beside the high-speed railways and for determining the aerodynamic force of induced air to the human body near the railways.
文摘This paper numerically investigates the influence of separation variation of the outriggers on the hydrodynamic performance of a high speed trimaran （HST） aiming at improving its applicability in diverse realistic disciplines. The present investigation was performed within the framework of the 2-D slender body method （SBM） by calculating the resistance of three symmetric trimaran series moving in a calm free surface of deep water. Each trimaran series comprises of 4681 configurations generated by considering 151 staggers （-50%≤a≤＋ 100%）, and 31 separations （100%≤β≤400%） for 81 Froude numbers （0.20≤Fn≤ 1.0）. In developing the three trimaran series, Wigley-st. AMECRC-09, and NPL-4a models were used separately for both the main and side hulls of each individu;d series models. A computer macro named Tri-PL was created using the Visual Basic for Applications~. Tri-PL~ sequentially interfaced Maxsurfe then Hullspeed to generate the models of the three trimaran series together with their detailed hydrostatic particulars, followed by their resistance components. The numerical results were partially validated against the available published numerical calculations and experimental results, to benchmark the Tri-PL macro and hence to rely on the analysis outcomes. A graph template was creaLed within the framework of SigmaPlot to visualize the significant results of the Tri-PL properlv.
