Aerodynamic Design of HPVs

 

                                  

 

When considering the design of a human powered vehicle the aerodynamics of the design must be considered.  The fairing is the aerodynamic shell that is normally designed not to carry any structural loads but instead to minimize the aerodynamic drag on the vehicle.  However, hand calculations of the drag that will be produced due to the shape of the fairing cannot be done, thus computer tools need to be utilized.

 

Before a model can be produced to run aerodynamic calculations, the designer needs to know what is a good model.  Some of these factors include weight of the fairing, the science behind drag, reduction of frontal area, and how to model the fairing.  These factors need to set before a model is run because of computational effort involved in Computational Fluid Dynamics (CFD), because a model can take several days to reach convergence.

 

 

Weight of Fairing

The first consideration in fairing design is the drag to weight ratio.  Some fairing designs are not used because of one simple factor; the weight addition was more than the savings in terms of drag force.  A compromise needs to be made between the weight of the faring and the drag savings that will be made because of the fairing.  To determine this you need to look at the equation for aerodynamic drag.


(1)

 

 

Looking at equation (1), what factors contribute to the fairing’s design, the CD and Area terms represented by the term dl in (1).  In order to determine the weight limitations on the fairing one needs to determine the material that will be used to make the fairing.  Most fairings are made of lightweight materials like lexan because of its weight, transparency, and flexibility.  

The connections of the fairing to the frame or body of the vehicle must also be included in the weight considerations of the fairing.  If the fairing is not securely held to the designed shape then flow separation can occur because of the movement of the fairing, which would increase the drag on the fairing.  This is why the brackets used to attach the fairing can weight more than the fairing itself.  It is because of this that the method of attachment needs to be considered as part of the weight of the fairing.

 

The reason why weight is important in the design of the faring is obvious now but can be overlooked when it is being designed because of the importance of reduction of drag of human powered vehicles.  However the ratio of weight to drag is still important over the range of speeds to be traveled.  If the vehicle’s top speed is not the average running speed then the additional weight of the fairing to reduce the drag at top speed can be more than the drag saved at the average speed.  Thus the rider has to carry more loads than are needed for reduction of drag and can cause an even slower average speed if endurance is to be considered. 

 

Science Behind Drag

 

The speed ranges for human powered vehicles is relatively slow when compared to those of a car.  However, unlike a gas powered vehicle, small reductions in forces results in a grater increase in speed for a human powered vehicle.  The reason why the vehicle speed needs to be determined before the fairing can be designed is because it is considered in the drag equation.

 

            At relatively low speeds, 1-10 mph (.5-5 meters per second) at room temperature of 20 C the density of air is roughly 1.23 kg/m3.  So at the maximum slow speed of 5 m/s the air component of the drag equation (1) is roughly 15.375-kg/m s2.  The coefficient of drag for a non-faired bike with the rider in an upright position is 1.1 and a frontal area of .5 m2.  Using these values in the drag equation the drag for a non-faired vehicle is:

 

So as it can be seen, at low speeds the aerodynamic drag is not a major factor in the performance of the vehicle.  How do the calculations change with increasing speeds, well look at what changes in the drag equation with an increase in the speed.  Only the wind speed changes in the drag equation, however the drag coefficient is not the same for all speeds, the value changes with changing Reynolds number.  Reynolds number is defined as the following:

 

 

(2)

 

 

 

Where

r = Air density

m = Viscosity of fluid

V = Velocity

D = A length measurement

 

So as the velocity changes the Reynolds number changes also, which changes the drag coefficient but not by much because of the lower speeds of human powered vehicles.  The exact change in the drag coefficient is shape specific so a table or chart cannot be made for a fairing shape like can be made for simple geometric shapes like rods or spheres. 

 

A way of calculating the drag coefficient is to perform a wind tunnel test on a clay model of the fairing.  There are many different methods to determine the drag on the model but one must keep in mind the Reynolds number correlation between a model and the actual fairing.  

 

If one chooses to make a clay model of the fairing shape then one must keep in mind that the Reynolds number correlation is the opposite of the scale model.  Thus if one was to have a 1:42 model of the fairing then the ratio of wind speed on the model to wind speed on the actual fairing is 42:1 which can lead to problems if the wind tunnel cannot achieve the wind speed necessary.

 

A way to solve this problem is to look at the definition of Reynolds number as shown in equation (2).  If the equation for the model and actual fairing must equal each other and if limitations on wind speed prevent a wind tunnel test then either the density or the viscosity of the fluid must change on the model.  This is mainly done for scale models of large structures like bridges or buildings so it is not recommended for fairing design. 

 

Reduction of Frontal Area

 

            When looking at aerodynamic design of the fairing the frontal area plays an important factor in the fairing design.  However the rider position plays a major role in the frontal area of the fairing.  An upright rider requires more frontal area than a recumbent riding position.  According to Fundamentals of Fluid Mechanics page 595, the frontal area of an upright rider is approximately 5.5 ft2 and for a streamlined riding position it is only reduced to 5 ft2.  This is because the vehicle basically has the same frontal area and only the rider’s change of position causes the reduction of frontal area.

 

            Since the reduction of area in the change of rider position is only about 10% of frontal area then the reduction in drag, assuming that the other constants are held constant is only 10%, when looking at the example done in equation (2) that only amounts to a reduction of drag from 2 lbs to 1.8 lbs.  However, a streamlined bike design can reduce the drag coefficient as well.  This is where the reduction in drag force occurs, in the reduction of the drag coefficient.  The drag coefficient for an upright riding position is approximately 1.1 and for the streamlined position it is around 0.12.  This is a reduction by more than 90% of the drag in addition to the reduction of frontal area that makes the total drag experienced on the example (2) to go from 2 lbs to 0.18 lbs of force. 

 

Since the drag force increases by the velocity squared, the reduction of drag coefficient and frontal area plays a major role in the reduction of the drag forces experienced on the bike and rider.  Take an example of a racing bike traveling at approximately 55 mph, which according to Bicycle Science’s chapter on the relationship between power and speed is entirely possible to achieve with aerodynamic and lightweight materials.  If one were to assume that a non-faired upright rider could achieve this speed, as well as a streamlined rider then the drag forces experienced on each one would be:

 

The ratio of the drag forces between the upright and the recumbent riding positions is a 10:1 ratio.  So then if you were to calculate the drag forces on an upright riding position and wanted to know how it relates to a streamlined position then this ratio is a good approximation of drag forces.  Keep in mind that the fairing shape will determine the drag coefficient that needs to be calculated by computational fluid dynamics.

 

However, the rider position should not be determined by an aerodynamic standpoint alone.  Other factors in the design of the vehicle might call for an upright position to be utilized in the design for which the fairing design is then set to that position.  The drag can still be reduced by the aerodynamic shape of the shell that according to Fundamentals of Fluid Mechanics can reduce the drag by about 20-25% instead of the 90% done by utilizing a streamlined design.

 

How to model the fairing in a CFD solver

 

            Once all the design considerations on the fairing have been analyzed to determine the fairings limitations a computer model can be made to determine the aerodynamics of the fairing.  The program utilized by UNCCharlotte for CFD purposes is Fluent 5.1.  Before the model can be run in Fluent, a grid has to be generated in Gambit so that Fluent can run the discretization of the domain.

 

            When considering running a model in Gambit and Fluent one must know what the computational requirements are on the model.  A 3-D model of a fairing can take up to a week or more to run for convergence is met and spatial requirements can be up to 100 MB for storage of the grid and another 100 MB for storage of the data file.  It is because of this that one needs to consider all the factors in the design of the fairing before computer models can be run. 

 

            However, one can run some 2-D models of the fairing to show trends in the fluid flow around the fairing.  These models can run in under an hour and with space requirements around 10 MB or less.  The drag coefficients given by these models cannot be directly extrapolated to a 3-D model but the flow separation and pressure distribution can show trends on the model.  This can help in the designing of the length to width ratio of the fairing to allow the flow to remain fully attached to the fairing for as long as possible.  The optimum length to width ratio can be found in fluid dynamics books and in books on fairing design and can vary with the changes in Reynolds number, speed, height, etc. 

 

            Once a 2-D model has been run and all other design considerations have been met then one can generate a 3-D model of the fairing.  The 3-D model can be imported from a program such as ProEngineer into Gambit and a grid can then be made around it.  When making the grid for the 3-D model one needs to make sure that the surface of the fairing and the surrounding area close to it has a really fine grid where as the area away from the fairing can have a more courser grid. 

 

Conclusion

 

            Now that a computer model has been created for the fairing one should go back to the original design considerations and reevaluate the weight of the fairing now that the shape has been chosen to make sure that the weight is not more than the reduction in the drag force.  Shape modifications that were made with the 2-D models can make the weight calculations before the model was run inaccurate.  This makes it a good idea to reevaluate all calculations with the finished model.

 

            The aerodynamic design of a fairing can be the difference between winning a race and finishing last.  Even though other factors in the design can reduce the operating speed of the vehicle, the drag force increased by the velocity squared which can really slow a vehicle down at relatively lower speeds than those desired.  It is hoped that this guide to fairing design will help UNC Charlotte be more competitive in the future with its motor sports program and not just human powered engineering but in all racing applications where aerodynamic calculations need to be made.