A New Method to Optimize the Wake Flow of a Vehicle : The Leading Edge Rotating Cylinder

Thewake flowof a vehicle significantly influences its aerodynamic performance and the stability during high-speed drive.Therefore, optimization of the vehicle wake flow is an effective way to improve its aerodynamic performance and further improve the handling stability and fuel economy. In this paper, a new method, the leading edge rotating cylinder, is used to optimize the wake flow of a vehicle. According to the results of simulations, this method can reduce the pressure drag, increase the negative lift force, and strengthen the stability of the vehicle under crosswind. Furthermore, this method optimizes not only the wake flow of the vehicle with rotating cylinders but also the interactive vehicles in the driving route in overtaking maneuvers or platoon driving. In conclusion, this method effectively optimizes the flow fields around the vehicles, and it significantly helps to improve the handling stability and fuel economy of the vehicle.


Introduction
When a vehicle is driven at high speed, the wake flow influences many elements of its performance.In other words, wake flow optimization is an effective method to improve the performances of a vehicle.
The methods of the wake flow optimization can be divided into two categories: passive control methods and active control methods.One of the passive control methods is to change the appearance of the tail.Ouyang et al. 's [1] research verified that the change of the tail edge angle is an effective way to optimize the lift and drag force.One of the passive control methods is to fix flaps to the tail edges [2].Fixing flaps to different edges arouses different changes of wake flow, which generates different influences to the lift and drag force.Another common passive control method is to fix air deflectors to the surface of the tail [3].By changing the direction and the angle of the air deflectors, the velocity and structure of the wake flow can be changed.The advantages of passive control methods lie in its low cost and easy implementation.However, the optimizing effect of the wake flow can be further improved.As a result, the active control method was put forward.For example, a blower can be installed to the tail to optimize the wake flow [4].There have been some other active control methods used to optimize the wake flow.
In this paper, a new active control method called the leading edge rotating cylinder method is used to optimize the wake flow of a vehicle.The theoretical research of the rotating cylinder was conducted by Konstantinidis and Bouris [5], which has been proved to be able to cause the change of the flow fields.The applications of the leading edge rotating cylinder mostly focus on optimizing the outer flow fields of planes.Zhang et al. [6,7] optimized the flow fields around an airfoil with leading edge rotating cylinder through CFD simulation and obtained favorable results.Then, Lopes et al. [8] visualized the optimization results of the leading edge rotating cylinder by smoke flow method in laboratory, which confirms the validity of this method.Badry et al. [9] installed a pair of rotating cylinders to the edge of a lifting body to optimize the outer flow fields, which enhances the lift force coefficient and reduces the drag force coefficient.
In this paper, a pair of leading edge rotating cylinders are installed to the tail of a bus to optimize the wake flow.This method can reduce the pressure drag, increase the  45.600 Wheel base between front and back axles (m) 6.400 Radius of the cylinder at the upper leading edge of tail (m) 0.300 Radius of the cylinder at the lower leading edge of tail (m) 0.100  in Figure 1 (degree) 90  in Figure 1 (degree) 80.9 Length of the upper cylinder (m) 1.900 Length of the lower cylinder (m) 2.300 negative lift force, and strengthen the vehicle stability under crosswind.Furthermore, this method optimizes not only the wake flow of the vehicle with rotating cylinders but also the interactive vehicles without cylinders in the driving route in overtaking maneuvers or platoon driving.This method effectively optimizes the flow fields around the vehicles, and it significantly helps to improve the handling stability and fuel economy of the vehicle.

Description of the Bus Model
The bus model adopted in this simulation is shown in Figure 1.This model is chosen because of its simple appearance with typical characters of a common bus, and it has been widely investigated in the aerodynamic fields [10][11][12].The model dimensions shown in Table 1 come from Hoffman et al. [10].
The wake flow structure of this bus is shown in Figure 2; the flows from the upper surface and side surfaces meet in this region and form a pair of counterrotating trailing vortices.Similarly, the flows from the lower surface and side surfaces meet in this region and form another pair of counterrotating trailing vortices.Because of the gravity, the lower pair of vortices firstly disappears during the interaction with ground.As a result, the upper pair of vortices is the major factor that influences the aerodynamic forces.
Because the trailing vortices are the major factors that generate the pressure drag, trailing vortices should be avoided in reducing the drag force.There are three methods to avoid the formation of the trailing vortices: (1) The flow from the upper and side surface should be avoided to meet in the tail region.
(2) The flow from the lower surface should not roll up.
(3) The trailing vortices should be away from the tail as far as possible [12].
According to the methods above, a pair of rotating cylinders are installed to the upper and lower edge.The rotating directions of the cylinders are shown in Figure 1, which can decelerate the flow from the upper and lower surface.As a result, the position where the flows from the upper and lower surfaces meet will move backward, which makes the trailing vortices further away from the tail.The mathematical model of the aerodynamic coefficients is shown in the following formula: where C d , C y , C l , C m , and  pm are the drag force coefficient, side force coefficient, lift force coefficient, yaw moment coefficient, and pitching moment coefficient, respectively. is the air density, S is the body frontal area, l is the wheel base which is the distance between front and back axles, and  is the steady velocity.Correspondingly, D, Y, L, N, and P are the drag force, side force, lift force, yaw moment, and the pitching moment obtained by integrating the pressure and skin friction coefficients over the vehicle surface, respectively, which is shown in the following formula: where  and  are the pressure and shear stress on the vehicle surface,  ∞ is the freestream pressure which is set to 0, and  ∞ is the freestream dynamic pressure which is shown in the following formula:

Design of the Simulation
3.1.Mesh Generation.According to the characteristics of the shape of the bus, a rectangular computational domain is adopted.In order to determine the dimensions of the   2. By comparing the aerodynamical coefficients, the blockage ratio of 0.9% is chosen, because, under this ratio, the blockage effect to the aerodynamical coefficients reduced to the minimum while ensuring a relatively smaller dimensions of the computation domain at the same time.The dimensions of computation domain are shown in Figure 3, among which, , ,  is the length, width, and height of the bus, respectively.All meshes in the computational domain are tetrahedron elements.In order to improve the simulation quality, 6 layers of boundary meshes are established over the surface to catch more details of the viscous flow, shown as the red circle marks in Figure 4.The total height of the boundary layer meshes is set to 50 mm.The magnitudes of Y + shown in Figure 5 are all in the range of 10 to 300, which indicates  the rationality of the boundary layer meshes.Another way to improve the simulation quality is to establish mesh density around the bus.The mesh density is the grey cuboid shown with its dimensions in Figure 3.After calculation by the software named ICEM, the total number of the meshes is about 2,200,000.

Boundary Conditions.
The Reynolds number is calculated by (4), where  is the viscosity coefficient which equals 1.81 × 10 −5 Pa⋅s: The Reynolds number of the bus is 1.6 × 10 6 , which means that the flow in the computational domain is unsteady turbulence, and it is consistent to that in the experiment [1].A pressure-based transient solver is selected in order to improve the accuracy of the calculation.
According to the calculated Reynolds number and Y + , one of the RANS models, the realizable -epsilon model, is chosen as the turbulence model with nonequilibrium wall functions.A second-order upwind scheme is used to discretize the momentum, the turbulent kinetic energy, and the turbulent dissipation rate.The boundary conditions are shown in Table 3.

Verification of Simulation Validity.
The tested bus in the experiment is shown in Figure 6 [1], of which C d and C l are 0.47 and −0.24, respectively.In this paper, an approximate simplified model is selected with some subordinate details neglected including the windows, handles, and rearview mirrors.Also, the bottom of the vehicle is simplified to a    4, and they are set as the reference values of the following optimizations.

Procedure and Results of the Wake Flow Optimization
(2) Rotate the upper leading edge cylinder while the lower one keeps stationary.Then, calculate the variation of aerodynamic coefficients with the speed of the rotating cylinder as it increases from 0. Then, compare the calculation results to that in Table 4, and find the speed at which the optimal aerodynamic performance is reached.By comparing Figures 7(a) and 7(b), 250 rad/s is selected as the optimal speed of the upper leading edge cylinder.
Then, rotate the lower leading edge cylinder while the upper one keeps stationary, and calculate the variation of aerodynamic coefficients with the velocity of the lower cylinder.The results are shown in Figure 8.By comparing Figures 8(a) and 8(b), 1300 rad/s is selected as the optimal speed of the lower leading edge cylinder.
It can be concluded from above that the global optimizing speed of the cylinders when they rotate simultaneously is in the neighborhood of 250 rad/s of upper cylinder and 1300 rad/s of lower cylinder.
(3) Calculate C d of the bus with both cylinders rotating simultaneously at various speed.
The speeds of the upper and lower cylinder range from 100 rad/s to 500 rad/s and 1000 rad/s to 1600 rad/s, respectively, with a velocity step of 50 rad/s.Then we get 143 calculation results.Accordingly, a fitting 3D plot of the speed of the cylinders versus C d is shown as Figure 9.
(4) Find the minimum C d along the fitting surface in Figure 9; the method comes from Nocedal and Wright (1999) [13].In this situation, the minimum C d is 0.286;  the corresponding speeds of upper and lower cylinder are 293 rad/s 1241 rad/s, respectively.
(5) Calculate C d of the bus when the speeds of the upper and lower cylinders are 293 rad/s and 1241 rad/s, respectively, through simulation on the platform of ANSYS/Fluent.The simulation result of C d is 0.288 and the error is 0.70% compared to the mathematical result in step (4).The validity of the fitting method in step (3) is verified.
(6)   of the bus at the speeds of the upper and lower cylinders of 293 rad/s and 1241 rad/s is −0.33, and it is decreased by 13.8% compared to C l in Table 4, which helps to increase the ground adhesive force of the bus.
In conclusion, the most effective optimization occurs when the upper cylinder rotates at 293 rad/s and the lower cylinder rotates at 1241 rad/s.The aerodynamic coefficients after optimization are compared to the data in Table 4, which is shown in Table 5. C d is reduced by 24.7% and C l by 13.8%, which verifies the validity of this optimization.The pressure contours on the planes every 2 meters behind the tail are shown in Figure 11.There are four lowpressure regions on the first plane behind the original bus, which means there are four vortices in this region.Because of the gravity, the lower pair of vortices disappears earlier while the upper pair of vortices trails further.However, after the optimization, the pressure distribution on the first plane behind the tail is better distributed, and the length of the tailing vortices is shortened obviously, which can improve the crosswind stability of the bus.

Sensitivity of the Optimal Speeds of Cylinders to the Bus Velocity.
According to the procedure in Section 4.1, the optimal speeds of the cylinders are calculated at the bus velocity of 25 m/s to 35 m/s.The results are shown in Figure 12.Because C d is small at low velocities, the air drag accounts for a relatively minor portion of the vehicle driving resistance.Consequently, the optimizing effect of this method is not obvious at low velocities, so the situation of the bus velocity less than 25 m/s is not discussed in this research.Moreover, the upper limit of the vehicle velocity in highway in China is 35 m/s, and the limit of the bus is 30 m/s.As a result, the maximum velocity in this sensitivity research is set to 35 m/s and the situation in higher velocity is not discussed in this research.
The comparisons of C d between the original data and optimized data are shown in Figure 13.It can be concluded from Figure 13 that the higher the velocity of the bus is, the better the optimization effect will be.The most obvious drag reduction is in the velocity of 35 m/s, and the ratio of drag reduction is 24.7%.

System-Level Energy Study.
In order to explore the practicality of this method, this chapter tries to evaluate the method from the aspect of the vehicle driving energy consumption and verify the improvement of the vehicle fuel economy at high velocity.
In this chapter, the fuel economy of a bus with and without the optimization method under a driving condition of constant velocity of 35 m/s is calculated.

Power Required to Accelerate Cylinders to Target Speed.
The calculation method of the power required to rotate cylinders to target speed is explained as follows.
(1) Calculate the inertia moment of cylinders by the following formula: (see [14]) where  is the mass of cylinder and  is the radius of cylinder.
In order to reduce the mass and maintain the rigidity of cylinder, the material of cylinder is designed to aluminum, and the structure of cylinder is designed to an aluminum skin in 2 mm and a honeycomb core inside it.The density of the cylinder is 22 kg/m 3 [15].
Mass of upper cylinder is Mass of lower cylinder is where

Moment of inertia of lower cylinder is
(2) Calculate the angular acceleration of cylinders when the time of driving cylinders from 0 to the target speed is 60 s.
Angular acceleration of upper cylinders is Angular acceleration of lower cylinders is (3) Calculate torque of cylinders.Torque of upper cylinders is Torque of lower cylinders (see [16]) is (4) Calculate the power of cylinders.
Power of upper cylinder is Power of lower cylinder is where  up and  down are the numbers of revolutions in a minute of upper and lower cylinder: After the calculation,  up = 1.377 kW,  down = 0.372 kW. (17) Power of the rotating cylinders is Because the power required to rotate cylinders to speed is only 1.749 kW and the working time is only 60 s, the influences of this power to the fuel consumption can be ignored.

Power Required to Rotate the Cylinders at a Constant Speed.
Rotating the cylinders requires extra power from the vehicle, which will increase the fuel consumption.On the other hand, the rotating cylinders significantly decrease the air drag of the vehicle, which in contrast decreases the fuel consumption.After all, to evaluate the fuel economy optimization of this method, we should first calculate the power required to rotate the cylinders.The calculation method is as follows.
(1) Calculate the skin friction coefficients of cylinders using the facet-average method on the platform of ANSYS/Fluent.

Mathematical Problems in Engineering
Skin friction coefficient of upper cylinder is Skin friction coefficient of lower cylinder is (2) Surface shear stress of cylinders is calculated.Surface shear stress of upper cylinder is Surface shear stress of lower cylinder is where  ∞ is freestream dynamic pressure: where  ∞ is the density of air,  ∞ = 1.225 kg/m 3 ;  ∞ is the velocity of freestream,  ∞ = 30 m/s.After the calculation,  up = 7.166,  down = 24.806.
(3) Calculate the skin friction.The skin friction of upper cylinder is The skin friction of lower cylinder is where  up and  down are the contact areas between the cylinders and air: where Power of lower cylinder is where  up and  down are the numbers of revolutions in a minute of upper and lower cylinder: After the calculation, Power of the rotating cylinders is  =  up +  down = 1.564 kW. (36)

Verification of the Optimization to the Vehicle Fuel
Economy.To verify the optimization effect of this method from the aspect of the vehicle fuel economy, a vehicle model is established on the platform of AVL/Cruise which is a system-level vehicle performance simulation software that can calculate the fuel economy and power performance and so forth.The model is shown in Figure 14.
In this model, the appearance-related vehicle parameters come from Table 6, and the parameters of the powertrain come from the reference bus model in Cruise.The main specifications of the model are shown in Table 6.
A simulation is run at a constant bus velocity of 35 m/s based on the model above.Before optimization, the fuel consumption is 31.34L/100 km, while it is 30.38 L/100 km after optimization.The fuel economy is improved by 3.1%.The results verify that this optimization method can effectively improve the bus fuel economy.

The Application and Effect of This Optimization Method under Different Conditions
The effects of this optimization under such conditions as driving in crosswind, overtaking maneuvers, and driving in platoon are discussed below.In the discussions, the velocity of the bus is 35 m/s and the speed of upper and lower cylinder are 293 rad/s and 1241 rad/s.

The Optimization Results under
Crosswind.The computational domain and the bus model in crosswind driving are shown in Figure 15.The velocity of crosswind  ∞ is set to 5 m/s, the velocity of bus   is set to 35 m/s, and the attack angle  is between 0 and 60 ∘ .
In order to decrease the blockage effect of the computational domain and increase the airflow uniformity, the inlets and outlets are set as shown in Figure 15.The velocity of inlets is 5 m/s; the direction is changed with the attack angle .The pressure of outlets is 0. The bus body is set to a moving wall whose velocity is 35 m/s and the direction is shown in Figure 15.The floor is set to a stationary wall.The surfaces of upper and lower cylinders are set to a rotating wall at −293 rad/s and 1241 rad/s.The dimensions and the mesh design of the computational domain are the same as that in Section 3.
The aerodynamic coefficients under different attack angles are shown in Figure 16.This optimization works well in crosswind driving when the attack angle of crosswind ranges from 0 to 60 ∘ .  ,   ,  pm decrease with a narrow range after the optimization.Moreover,   and   , which are given more attention in crosswind, are optimized effectively.For   , the most effective optimization takes place when the attack angle is 20 ∘ .The original   is 0.645, and the optimized   is 0.369.The ratio of the reduction is 42.8%.Similarly, for   , the most effective optimization takes place when the attack angle is 40 ∘ .The original   is 3.323, and the optimized C s is 3.163.The ratio of the decreasing is 4.8%.
The maximum, minimum, and mean values of the aerodynamical coefficients in crosswind conditions are shown in Table 7.The optimizing rates of these values are computed and shown in the right line in Table 7.The optimizing rates of C d , C s , C l , and C m are all negative, and that of  pm is positive, which means that this method can effectively optimize all the aerodynamical coefficients in crosswind condition.
The flow fields in crosswind driving with an attack angle of 60 ∘ are shown in Figure 17.Before the optimization, there are three clear vortices on the leeward side shown in the red circle, which affects the bus stability under crosswind and increases C s .After the optimization, there is no clear vortex, and the stability increases.

The Optimization Results during Overtaking Maneuvers.
The physical model of overtaking maneuvers in which a car overtakes a bus at the relative velocity of 5 m/s is shown in Figure 18.Comparisons are made between aerodynamic coefficients of both vehicles before and after the optimization of the wake flow of the bus.The overtaking maneuvers begin at the position where the car is 2 car behind the bus, which is shown in Figure 18.During the overtaking maneuvers, the car totally moves 8 car .
A MIRA model without wheel is chosen as the car model, which is shown in Figure 19, and the bus model is shown in Figure 1.The dimensions of the car model [10] are shown in Table 8.
The computational domain of the overtaking simulation is shown in Figure 20.The overall domain is composed of two subdomains: SD-bus which contains the bus and remains fixed during the simulation and SD-car which contains car and moves with it at the same velocity.The movement of car is realized by adopting the sliding mesh method.The size of the computational domain is 7 outer side of the models and 4 upstream and 7 downstream of the models.The total height of the computational domain is 8.5 (, ,  are the length, width, and height of models, resp.).
The meshes in the computational domain are all tetrahedral structures generated on the platform of ICEM, and the meshes over the shell and the longitudinal symmetry plane of car are shown in Figure 21.In order to improve the simulation quality, 6 layers of boundary meshes are established along the surface to catch more details of the viscous flow, as the figure in the red circle shows.The total height of the boundary layer meshes is set to 50 mm.The magnitudes of  + at the end of the simulation are all in range of 10 to 300, which indicates the rationality of the design of the boundary layer meshes.Another way to improve the simulation quality is to establish mesh densities around the vehicles.The mesh densities are    9.
The variations of aerodynamic coefficients of both vehicles with the position of car are shown in Figure 22.All aerodynamic coefficients of the bus are optimized during the whole maneuvers.However, the optimizing effects of aerodynamic coefficients of car are divided by Position 3.6 at which the tail of car is parallel to the nose of the bus.Before Position 3.6, this optimization works well.The wake flow of the bus influences the outer flow fields of car a lot during this stage, so optimizing the wake flow of the bus is good for the outer flow fields of car.After Position 3.6, the wake flow of the    bus does not influence the outer fields of car anymore, so the outer flow field of car cannot be optimized by optimizing the wake flow of the bus during this stage.The reason why   is so different for the bus at Position 0 is explained as follows.
Before the optimization, along with the movements of the car, the low-velocity flow before the car decreases the velocity of the flow on the inner rear side of the bus.As a result, the pressure of the inner rear side of the bus increases and C m of the bus increases.
After the optimization, the leading cylinders rotate in high speed.Because the height of the car is lower than that of the bus, the rotation of the lower cylinder is the main cause of the influences on the flow fields between the two vehicles.On the one hand, the lower rotating cylinder increases the velocity of the flow before the car, which decreases the area of the high pressure before the car and decreases the pressure on the inner rear side of the bus.On the other hand, the lower rotating cylinder accelerates the flow on the inner front of the car, which increases the area of the low pressure on the inner front of car.Because of the two reasons, C m of the bus obvious decreases.
As a result, C m of the bus is so different at Position 0 before and after the optimization.
The pressure fields at Position 0 are shown in Figure 23.
In order to testify that the reason that causes the difference of C m at Position 0 is the rotation of the lower cylinder, a series of simulations in different lower cylinder speeds are conducted.The results are shown in Figure 24.It can be seen from Figure 24 that the lower the speed, the less the differences, which testifies the correctness of the reason.
The maximum, minimum, and mean values of the vehicle aerodynamical coefficients during the overtaking maneuvers are shown in Tables 10 and 11.
According to the optimizing rate, this method can effectively optimize all the bus aerodynamical coefficients during the overtaking maneuvers.
For the car aerodynamical coefficients, this method can effectively optimize C d , C s , C l of car, while the optimizing effects of  pm and C m are not satisfactory.The optimizing rates of the minimum and mean value are negative when the positive rates are needed.Similarly, the optimizing rate of the maximum and mean value is positive when the negative rates are needed.In general, the optimizing effects on the car aerodynamical coefficients can be acceptable.

The Optimization Results under Platoon
Driving.The physical model of platoon driving is shown in Figure 26.The two identical buses move in platoon at 30 m/s in the same path.The length of the bus is labeled as L, and the distance between the two buses is set to 0.5L (shown in Figure 26).The leading edge rotating cylinders are installed to the tail of the front bus, the boundary conditions are shown in Table 12, and the influences the wake flow of the front bus exerts on the back bus are discussed.The aerodynamic coefficients of both buses are shown in Table 13.C d , C l , and  pm of the front bus are optimized significantly, while those of the back bus are slightly optimized.As a result, optimizing the wake flow of the front bus is good for the outer flow fields of the back bus.
The streamline on the longitudinal symmetry plane in platoon driving is shown in Figure 27.The wake vortices of the front bus are smoothed obviously after the optimization.Meanwhile, the pressure in front of the back bus decreases and the wake vortices decelerates.The flow fields of both buses are optimized at the same time.

Conclusion
In this paper, the leading edge rotating cylinder is used to optimize the wake flow of a bus.It is installed at the upper and lower edge of the bus tail.The rotating directions of both   testify the applicability of this optimization in crosswind driving, overtaking maneuvers, and platoon driving.The aerodynamic performances after optimization are all better than those without optimization under different conditions discussed above.Furthermore, this method optimizes not only the flow fields of the bus with the rotating cylinders but also the interactive vehicles without the rotating cylinders in the driving route, such as the overtaking vehicle, and the back vehicle in platoon.In conclusion, this method to optimize the wake flow of the vehicles can effectively improve the aerodynamic performance, the handling stability, and the fuel economy.

Figure 2 :
Figure 2: Wake flow structure of bus.

Figure 3 :
Figure 3: The computational domain and the mesh density.

Figure 4 :
Figure 4: The meshes over the shell and the longitudinal symmetry plane of vehicles.

Figure 5 :
Figure 5:  + over the surface of the vehicles.

4. 1 .
The Procedure of the Wake Flow Optimization.(1) Calculate the original aerodynamic coefficients at the velocity of 35 m/s.The results of the calculations are shown in Table

Figure 7 :Figure 8 :Figure 9 :
Figure 7: Aerodynamic coefficients with different speed of the upper rotating cylinder.
Characteristics.The vorticity contours at the longitudinal symmetric plane of the bus are shown in Figure 10.By comparing Figures 10(a)-10(b), the velocity of the flow from the upper and lower surface decelerates obviously, and the area of high vorticity region

Figure 11 :
Figure 10: The vorticity contours at the longitudinal symmetry plane.

Figure 15 :
Figure 15: The computational domain and the model in crosswind.

Figure 16 :
Figure 16: The aerodynamic coefficients in different attack angle.

Figure 20 :
Figure 20: The computational domain of the overtaking simulation.

Figure 21 :
Figure 21: The meshes over the shell and the longitudinal symmetry plane of car.
Figure 22: The aerodynamic coefficients history during the overtaking maneuvers.
Figure 24:   of bus in different lower cylinder speeds.

Figure 26 :
Figure 26: The physical model of platoon.

Figure 27 :
Figure 27: The streamline on the longitudinal symmetry plane in platoon.

Table 1 :
The major dimensions of bus.

Table 4 :
The original aerodynamic coefficients without the optimization.
flat surface without considering the details of the chassis structure.As a result, C d and C l of this model are 0.38 and −0.29, respectively, which are smaller than the experimental data.

Table 5 :
The comparisons of aerodynamic coefficients.
up and  down are the radius of the upper and lower cylinder;  up and  down are the length of the upper and lower cylinder.up,down ,  up ,  down are shown in Table1.Moment of inertia of upper cylinder is The optimal speeds of cylinders at different bus velocities.Figure 13: The comparisons of C d at different bus velocities.
up and  down are the radius of the upper and lower cylinder;  up and  down are the length of the upper and lower cylinder.up,  down ,  up ,  down , ,  are shown in Table1.

Table 6 :
The main specifications of the bus model.

Table 7 :
The maximum and minimum of aerodynamical coefficients.

Table 8 :
Dimensions of car.

Table 13 :
The aerodynamic coefficients of both buses in platoon driving.C d of front bus C d of back bus C l of front bus C l of back bus  pm of front bus  pm of back bus