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Aerodynamics of an unloaded timber truck - A CFD investigation.


Reducing energy consumption and emissions are ongoing challenges for the transport sector. The increased number of goods transports emphasize these challenges even more, as greenhouse gas emissions from these vehicles increased by 20 % between 1990 and 2013, in Sweden. One special case of goods transports is the transport of timber. Today in Sweden, around 2000 timber trucks transport around six billion ton kilometers every year. For every ton kilometer these vehicles use around 0.025 liter diesel, and there should exist large possibilities to reduce the fuel consumption and the emissions for these vehicles. Timber trucks spend most of their operation time travelling in speeds of around 80 km/h. At this speed aerodynamic drag contributes to around 30 % of the total vehicle resistance, which makes the aerodynamic drag a significant part of the energy consumption. One of the big challenges with timber trucks is that they travel unloaded half of the time. This put higher demands on possible drag reduction modifications, as they need to function and be practical for both when the timber truck is loaded and unloaded. In this study an unloaded timber truck has been investigated by use of computational fluid dynamics. The recently released Stress Blended Eddy Simulation model has been used for simulating the flow over a timber truck at a Reynolds number of 1.1 million, based on the square root of its frontal area. From the results it could be seen that 52.8 % of the drag is generated by the cab. By investigating a drag reduction device that covered the gap between the bulkhead and the first stake pair, a drag reduction up to 6.7 % was possible, which shows potential for simple modifications that not influence the daily usage.

CITATION: Ekman, R, Gardhagen, R., Virdung, T., and Karlsson, M., "Aerodynamics of an Unloaded Timber Truck - A CFD Investigation," SAE Int. J. Commer. Veh. 9(2):2016, doi: 10.4271/2016-01-8022.


The demand for reduced emissions and energy consumption are ongoing challenges for the transport sector. Between 1990 and 2013 a 20 % increase of greenhouse gas emissions from road goods transports, has been seen in Sweden, as a result of increased amount of goods transportation [1]. A significant cause of the energy consumption and hence the source for emissions, is the aerodynamic drag. Typically, goods transportation trucks travel in speeds of 80 km/h, where the aerodynamic drag is responsible for 25 to 50 % of the energy consumption, depending on the shape and weight of the vehicle [2], making aerodynamics an area of interest for potential reduction of energy usage.

One special case of transports is the transport of timber. In 2015, about 2000 timber trucks in Sweden, hauled about six billion ton-km (metric ton kilometers) of timber [3]. These timber trucks have an averaged fuel consumption of about 0.025 liter diesel per ton-km, which is between 30 to 50 % higher than ordinary tractor-trailer configurations. No encouraging improvements have been seen for the averaged fuel consumption over the last 20 years for these timber trucks. One of the main reasons for this is the poor aerodynamic development of these vehicles. Typically, between 20 to 30 % of the fuel consumption is caused by the aerodynamic drag for a fully loaded timber truck [4], and the number become even higher when the truck is unloaded. Even though a lot of aerodynamic development has been done on the cab, rarely the entire vehicle has got the proper attention. There exist several reasons for this, where one is that the truck manufacturers' development focus is on tractor for tractor-trailer configurations, as it constitutes most of their customers. Another reason is the number of manufacturers involved in the making of the complete timber truck. Typically, the cab and chassis of a timber truck are manufactured by a truck manufacturer, while several other manufacturers are responsible for the stakes, bunks, trailer, bulkhead, and for some configurations a truck mounted crane. Often these manufacturers (except the truck manufacturer) do not have the resources or knowledge of investigating their parts influence on the aerodynamic performance.

In Swedish forest industry there is currently a lot of effort put in different areas to reduce the fuel consumption and develop more environmentally friendly transport vehicles. One of the areas is to increase the maximum weight of the timber trucks from 60 tons to 74 tons, without increasing the length of the vehicles, Figure 1. If designed properly this can lead to less number of required vehicles and also increase the freight efficiency of these vehicles [3].

The tractive resistance of a ground vehicle can be divided into four separate parts [2], Equation 1.


where [F.sub.ROLL] is the rolling-, [F.sub.ACC] the acceleration-, [F.sub.CLMB] the hill climb- and [F.sub.DRAG] the aerodynamic drag resistance.

For a vehicle driving with constant speed on a relatively flat road the rolling resistance and aerodynamic drag are the dominating forces. While the rolling resistance varies linearly with the speed of the vehicle, the aerodynamic drag varies with the square of this speed, Equation 2, which increases the importance of it at higher speeds.


where [C.sub.D] is the drag coefficient, [[rho].sub.air] the density of air, [U.sub.[infinity]] the free stream velocity and A the reference area.

Extensive studies of drag reduction devices exist for the tractor-trailer configuration, e.g. [2, 5, 6, 7, 8, 9, 10, 11] to name a few. However, for timber trucks only a few studies exist for its aerodynamics [3,4, 12, 13,14]. These studies also mostly cover class 8 tractors and how the loading of the timber affect the drag.

One substantial difference to regular truck transportation vehicles is that the timber truck travels unloaded half of the time. This does not only have an impact on the weight of the vehicle but also affects the shape of the vehicle, and hence the aerodynamic performance. From previous wind tunnel tests a 3.3 % higher wind averaged drag value has been seen for the unloaded timber truck compared to when it is fully loaded [3, 15]. At smaller yaw angles this increase could reach 10 %. In order for drag reduction devices to be feasible they need to work for both when the timber truck is fully loaded and unloaded and also be structurally robust, as these vehicles operate in harsh terrain and weather conditions.

In this study the flow around an unloaded timber truck is investigated by use of computational fluid dynamics (CFD). The investigated timber truck is a geometrical updated version of the one studied in [3].


The aim of this study is to investigate the flow around an unloaded timber truck, by use of CFD. A geometrical modification between the bulkhead and the first stake pair is also to be investigated, in order to reduce the aerodynamic drag of the vehicle. This modification does, however, need to be feasible for both an unloaded and fully loaded timber truck and not limit the daily usage. A secondary aim of this study is also to increase the knowledge about these type of modifications for upcoming wind tunnel test sessions and full scale road tests.


The geometry consists of a 1:6 scale model of a 74-ton timber truck with 1-3-2-3 axle configuration, Figure 2. The used geometry is based on an updated version of the model used in [3] and has been slightly simplified, as nuts, screws and the balance have not been included in the model.

The dimension and used reference area of the model can be seen in Table 1.

Numerical set-up

As flows around bluff bodies are highly unsteady and time dependent a transient simulation method is often necessary to achieve sufficient accuracy for simulations. Therefore, in this investigation the recently released Stress Blended Eddy Simulation (SBES) model has been used. The SBES model is built upon the same approach as for the Detached Eddy Simulation (DES) approach, by using a Reynolds Averaged Navier-Stokes (RANS) model for the near wall flow and Large Eddy Simulation (LES) further away from the wall [16], However, the SBES model uses a different shielding function and definition of the grid scale [16], This shielding function is much stronger than in ordinary DES and Delayed Detached Eddy Simulation (DDES) models and also has an improved transition between RANS and LES regions. This makes it possible to specify different model formulations of the RANS and LES regions. From previous work [17] it has been seen that the k-[omega] Shear Stress Transport (SST) model [18] as RANS model and the dynamic Smagorinsky sub-grid model [19] is the preferred choice for bluff body simulations, and has therefore also been used in this study.

The used computational domain consisted of a rectangular cylinder with a length of 40.2 m, a width of 6.5 m and a height of 5.6 m, Figure 3. The model was placed 15 m (3.5 model lengths) from the inlet. The frontal area of the model covered less than 1 % of the cylinder cross section area to minimize possible blockage effects.

The inflow to the domain was modeled with a velocity inlet (with a prescribed uniform velocity profile with turbulent intensity and turbulent viscosity ratio of 1 % and 50, respectively) and the outflow with an outlet with zero static pressure. The walls for the domain were modeled with free-slip condition as they were deemed to be too far away to affect the flow around the model. The floor of the domain was modeled as a stationary ground but was divided into two separate zones, where the zone adjacent the model (dark gray colored in Figure 3) was modeled with no-slip condition and the zones farther away (light gray in Figure 3) was modeled with free-slip condition. This was done to imitate the same boundary layer thickness build up in front of the model, as in [3]. All the surfaces of the truck were modeled with no-slip conditions together with stationary wheels. A free-stream velocity of 30 m/s was used which resulted in a Reynolds number of 1.1 million, based on the square root of the models reference frontal area (Table 1).

All simulations were performed with the commercial Navier-Stokes solver ANSYS Fluent [20]. The Semi-Implicit Method for Pressure Linked Equations-Consistent (SIMPLEC) was used as p-v coupling scheme, least square cell based for the gradient discretization and the 2nd order discretization scheme for pressure [16]. The bounded central difference discretization scheme was used for the momentum equations, the 1st order upwind for the turbulent kinetic energy and turbulent dissipation rate, and the bounded second order implicit time integration was used for the temporal discretization [16].

A physical time step size of [10.sup.-5] s was used to keep the Courant-Friedrichs-Lewy (CFL) number below 1 for essentially (>99.9 %) all cells in the domain. Five inner-loop iterations were used for every time step to ensure convergence below [10.sup.-4] for the residuals. The simulations were initialized from a previous k-[omega] SST RANS simulation and run for a physical time of 1.0 s to remove possible effects from the initialization. Data was sampled during a physical time of 1.5 s and used for computing the time-averaged values. The sampled time corresponds to an air particle travelling 10.6 lengths of the model, based on the free-stream velocity.

The numerical set-up follows the SAE J2966 standard [21],

All simulations were performed on the Triolith cluster at National Supercomputer Centre atLinkoping University, Sweden [22].

Mesh Set-Up

The meshes were created in two steps. The surface meshes were created in ANSA [23], while the volume meshes were created in ANSYS Fluent [20]. The surface mesh consisted of triangle and quad elements with an edge length of 1.5 to 4.5 mm. Inflation layers were created on all the surfaces of the truck and on the ground, to properly capture the near wall flow and the boundary layer build up in front of the model. The inflation layers consisted of hexahedral and prisms elements. The first node height was set from 0.01 to 0.02 mm to ensure [ay.sup.+] [less than or equal to] 1 for the trucks surfaces. The first node height on the ground was set to give the first cell an aspect ratio of 12. This resulted in a varied [y.sup.+] value of less than 5 adjacent to truck and between 30 and 100 in the rest of the domain. 10 to 20 inflation layers were created on the surfaces of the truck, while 10 layers were created on the ground. The volume mesh consisted of a Cartesian grid with refinement zones where high pressure and high velocity gradients were expected, Figure 4. The inflation layers and the Cartesian grid were connected by use of tetrahedral and pyramid elements. The mesh consisted of 56 million cells for the baseline configuration. A cell skewness quality of less than 0.95 was achieved for both the meshes.


Seen in [15] the cab is responsible for most (57 %) of the drag for an unloaded timber truck, as it causes a large low pressure wake. By adding a device which increases the base pressure of the cab and the bulkhead, may therefore lead to a substantial drag reduction. Boat tails and cab extenders are typically add-on devices which are used for controlling the wake and increasing the base pressure of trucks [5, 8, 9,10]. In [1] a boat tail behind the bulkhead showed promising potential by reducing the wind averaged drag value by 12 % for a fully loaded timber truck.

A similar concept was investigated in this study where a shield was placed between the bulkhead and the first bunk and stake pair, Figure 5. The idea of the modification was to have a passive add-on device which not needed to be changed or moved during daily operation, it was strongly shaped and dimensioned by the shape and position of the bunk and the first stake pair. The shield only covered the side of the sides of the gap between the bulkhead, bunk and first stake pair, as timber trucks normally are loaded from the top and it may otherwise risk to be too unpractical for daily operation.

The shield was modeled to go from the trailing edge of the bulkhead to the outward face of the bunk and stakes. This resulted in a constant height of the shields top edge and a slightly sloped height of the bottom edge. The length and height of the shield corresponded to 60 % of the width and 62 to 64 % of the height of the model, respectively.


One of the dominating flow features of transportation vehicles is the low pressure rear wake of the vehicle. This feature also occurs for timber trucks but is, however, a bit different when the truck is unloaded. Instead of having a large low pressure wake at the rear of the vehicle, the wake is instead directly downstream of the cab and bulkhead and covers the rest of the vehicle downstream. This can clearly be seen in Figure 6, where the time-averaged total pressure coefficient is seen in planes along the vehicle. A Separation on the cab roof can also be seen as it causes a low pressure bubble. This effect was also seen in earlier simulation for a lower Reynolds number [15], but not in previous wind tunnel measurements at higher Reynolds numbers [3]. The separation is therefore an effect of the lower Reynolds number compared to the previous wind tunnel measurements [3]. However, the separation is not so significant that it removes the function of the cab deflector. An increase of the boundary layer thickness on the ground can be seen along the domain, due to the stationary ground.

In Figure 7, the total pressure equal to zero is illustrated with an iso-surface. The low pressure wake caused by the cab can clearly be seen, as it covers the first stake pair. This resulted in a low drag contribution from the first bunk and stake pair, previously also seen in [15]. Low pressure wakes also appear from the bunks and stakes as they block the flow. For the most rearward wheels and stake pairs a strong flow interaction occurs between the wheels and the bunks. This is due to the wheels push the flow up onto the bunks, resulting in a larger low pressure wakes from the bunks and stakes.

In Figure 8, the total pressure coefficient can be seen for planes along the configuration fitted with the drag reduction shield. A noticeable smaller wake from the cab and bulkhead can be seen when comparing it to the wake for the baseline configuration (Figure 6), as the shield works similar to a boat tail and increase the pressure behind the cab and bulkhead. Due to the drag reduction shield reduces the outward push of the flow from the cab extenders a narrower wake is obtained compared to the baseline configuration.

The total pressure equal to zero show the wake from the cab and how it is directed more downwards to the chassis, for the configuration fitted with the drag reduction shield, Figure 9. Flow into the first bunk is also removed as a smoother behavior of the total pressure occur downstream of the first stake pair.

In Figure 10, the rear base pressure of the bulkhead can be seen both for the baseline configuration and the one fitted with the drag reduction shield. A significantly higher pressure can be seen for the configuration fitted with the shield as the low pressure region at the lower part of the bulkhead is removed. However, a slightly lowered pressure occurs at the middle of the top part of the bulkhead for the configuration with the drag reduction shield.

In Figure 11, the time-averaged velocity streamlines projected on to a plane (at the middle width of the model) colored with the time-averaged pressure coefficient is seen. This illustrates the dominating vortical structures in the wake from the cab and bulkhead. For the baseline configuration two strong vortices with low pressure at the vortical center occur. The smaller one at the bottom of the bulkhead causes a lowered pressure on the bottom part of the bulkhead, seen in Figure 10. Weaker vortical structures can be seen for the configuration fitted with the drag reduction shield, as higher pressure is contained in the vortices center. The large vortex influences the flow field more, and directs more flow on to the top part of the bulkhead for the baseline configuration. This results in a higher pressure at the top part of the bulkhead, seen in Figure 10.

In Figure 12, the time-averaged drag coefficient history for the time-averaged interval can be seen for both the investigated configurations. A lowered drag can in general be seen for the configuration fitted with the drag reduction shield. Similar fluctuations occur for both configurations and have a maximum amplitude of [+ or -] 6 % of the total drag coefficient.

In Table 2 the drag coefficients for the two simulated geometries is presented. A drag reduction of 6.7 % is achieved by adding the shield between the bulkhead and the first bunk and stake pair. 52.8 % of the total drag is generated from the cab itself for the baseline configuration, possibly indicating were most of the drag can be reduced for an unloaded timber truck.

As this drag reduction shield does not require substantial modifications of bulkhead, bunks and stakes it should be possible to implement it on existing timber trucks. As the shield is placed on the outward face of the bulkhead, first bunk and stake pair it should have little or no contact with the timber when fully loaded. This is important as the timber otherwise may risk to damage the shield, and hence making it unpractical for daily operation. Less drag reduction effect is also expected from it when fully loaded, as the wake of the cab is reduced by the timber. However, the shield will limit the horizontal flow through the first timber stack and possibly reduce drag.

This drag reduction concept could also be possible for similar truck configurations, as for example flatbed trucks, and does not limit the space of the load.


In this paper the aerodynamics of an unloaded timber truck is investigated by use of CFD. As little research exists for drag reduction of timber trucks there should be a large room for improvement. Most of the drag for an unloaded timber truck is caused by the large low pressure wake from the cab and bulkhead.

This paper investigates a drag reduction shield placed between the bulkhead, first bunk and stake pair. This resulted in a 6.7 % reduced drag as higher pressure is obtained in the low pressure wake. The shield cause weaker vortical structures in the low pressure wake, resulting in higher base pressure of the bulkhead. This paper show that a small and simple modification can lower the drag significantly for an unloaded timber truck or other similar shaped vehicles.


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[2.] Hucho,W.-H., "Aerodynamics of Road Vehicles," (Warrendale, Society of Automotive Engineers, Inc., 1998), ISBN 978-0-7680-0029-0.

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Petter Ekman and Roland Gardhagen

Linkoping University

Torbjorn Virdung

ANSYS Sweden

Matts Karlsson

Linkoping University


Petter Ekman

Linkoping University

Applied Thermodynamics and Fluid Mechanics

581 83 Linkoping




This work is carried out within the ETTaero2 project. The financial support by the Swedish Energy Agency is gratefully acknowledged. National Supercomputer Centre at Linkoping University, Sweden ( is acknowledged for providing computational resources.


A - Characteristic Area

CFD - Computational Fluid Dynamics

CFL - Courant-Friedrichs-Lewy

[C.sub.D] - Drag Coefficient

DDES - Delayed Detached Eddy Simulation

DES - Detached Eddy Simulation

[F.sub.ACC] - Acceleration Resistance

[F.sub.CLIMB] - Climb Resistance

[F.sub.Dr] - Aerodynamic Drag Resistance

[F.sub.T] - Tractive Resistance

[F.sub.ROLL] - Rolling Resistance

LES - Large Eddy Simulation

p - Pressure

RANS - Reynolds-Average Navier-Stokes

SIMPLEC - Semi-Implicit Method for Pressure Linked Equations-Consistent

SST - Shear Stress Transport

SBES - Stress Blended Eddy Simulation

[U.sub.[infinity]] - Free Stream Velocity

v - Velocity

[y.sup.+] - Dimensionless Wall Distance

[[rho].sub.air] - Density of air

Table 1. Dimensions and reference frontal area of the investigated

Length                  4.25 m
Height                  0.70 m
Width                   0.42 m
Reference Frontal Area  0.2889 [m.sup.2]

Table 2. Drag coefficients for the simulated vehicle configurations.

Configuration          [c.sub.D]

Baseline               0.665
Drag reduction shield  0.620
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Author:Ekman, Petter; Gardhagen, Roland; Virdung, Torbjorn; Karlsson, Matts
Publication:SAE International Journal of Commercial Vehicles
Article Type:Report
Date:Oct 1, 2016
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