Wheel Design How-To Part 5 (and hopefully last)

The previous four posts generally outlined the design methodology for individual wheels. I may not have stated it but you can see in the photos posted in the previous posts that the modeling only included a single wheel by itself. This was an intentional choice. Generally speaking a wheel that will be more aerodynamic in the front will be more aerodynamic in the front. The reason why we didn’t specifically optimize front and rear independently is that each rim shape that we start manufacturing is a high fixed cost for the mold, so doubling rim shape (front/rear individual) essentially doubles cost. Also since the rear wheel is in a lot of dirty air (really only the trailing edge of the rear wheel has significant drag effects), the assumption was made that if a particular rim depth is good enough for the front, it’s good enough for the rear.

Additionally you’ll notice that the frame/bike we setup here is pretty old school/plane jane. This was done very much intentionally (had nothing to do with ease of CAD’ing). We didn’t’ want to do a complex Aerodynamic frame-set since there is so much variation in Aero frames out there (cut-outs, airfoil shapes, etc). This basic frameset would give us a good baseline to analyze the wheel-set without worrying about further complex interactions. Steel Frameset CAD

If for whatever reason you’re interested in the frameset I used, check it out HERE

However, when we started looking into a disc wheel, there is no way getting around NOT analyzing a full bike model. Obviously 99% of the time, a disc wheel that we’ll be producing gets used as a rear wheel. So the decision was made to not even bother analyzing the wheel by itself. And since we were not going after the ultra-elite track cyclist market (you got it covered Mavic), the wheel would never be used as a front wheel.

Disc Poly Mesh

General mesh for Disc Wheelset

Anyway since the disc wheel is essentially used only as a rear wheel we needed to analyze the whole wheel bike system. Again another assumption we made was to exclude the rider in the CFD model. There were a couple of reasons for this. First a persons body is too variable and constantly moving to accurately model in our CFD model. Second, we wanted to purely examine the rear wheel, and attempting to model legs would only dirty the air going to the rear wheel, further confusing results. So it was decided to model just the full bike and rear wheel without rider to get the best stratification of results for the different rim shapes while still maintaining the effects of the bike (which will always be present regardless of how erratically you might be pedaling)

Side View Disc CFD Results

90mm/disc blended wheel CFD case at 0deg AoA (don’t mind the seat angle)

There were fewer differences in the disc wheelset results as the Disc design is already naturally pretty aerodynamic. We also took a look at a few more parameters when analyzing the results. Due to limitations in computational power and time constraints we only executed a 0 degree AoA case and a 10 degree case. However the 10 degree case we did from both sides (wind coming from drive side, and non-drive side). We wanted to look at that to determine if there were significant differences or benefits of a particular design on drive side or non-drive side due to flow differences.

Shear stress on disc wheelset

Wall Shear Stress on disc wheel (aka skin friction drag)

After running probably 5 different rim shapes (after the baseline straight disc, 90mm case, and sub-9 type cases), I came up with what I thought was a pretty good design that appeared to be lower drag over most cases than either the straight disc or Sub-9 disc. This is yet to be confirmed by wind tunnel results (we’re still a work in progress). But I’m pretty happy with the design because it’s backed up by making intuitive sense and is fairly simple. And if you’ve read any of my other blog posts on engineering you know that I always thing elegant and simple designs are the best.

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Wheel Design How-To Part 4

Wind Tunnel Methodology

Wind tunnel testing was done at the A2 wind tunnel outside of Charlotte NC. The wind tunnel  is an open circuit wind tunnel with a lot of experience with cycling equipment. The tunnel itself is equipped with a boundary layer table that helps the incoming flow around the test section remain as uniform as possible (reducing boundary layer thickness), helping to correctly mimic real world moving ground conditions.

Great care was taken with tires when testing wheels. For all tests Continental GP4000 tires were used. The GP4000 gives the best drag results and is the unofficial industry standard for wind tunnel testing. New tires were also used for all tests in order to keep tests focuses on rim shape and not tire/rim interaction (an area for much further research). It was found through experience that wear as little as 100 miles of wear would significantly influence drag results. Pro-tip: GP4000’s are always the most Aero tire.

Bike Wheel Wind Tunnel Testing

Aluminum Prototype in A2 Wind Tunnel

In addition to existing rims from the industry and current production rims, future designs were modeled with machined metal prototyping. In many Wind tunnel tests you’ll see finished carbon rims being tested. This means that the rim design is already set and carbon molds have been created. Since the carbon mold is usually the most expensive fixed cost when setting up manufacturing it is very difficult to change a design that the wind tunnel shows to be ineffective. We found an alternative solution in machining a solid metal mock-up of the rim. This would allow us to cheaply create the prototype and also have enough structural integrity to actually build up with spokes and hold an aired up tire (3D printing was was also evaluated and not chosen for those reasons). Since machining typically leaves a rough surface that does not replicate production the prototype rims were smoothed then finished with the same finish coating that is applied to the production rims. 

Boyd Cycling Wheelset

Climber’s Wheelset

After our first set of tests at the wind tunnel we were able to refine the CFD model, which is when we decided to use a 3D model to increase fidelity. This two pronged approached allowed me to tweak the CFD model and mesh to further match up with real world results. Additionally the the production rims (Zipp, Enve, etc) provided further data points to check the CFD model.

The top two lines from wind tunnel are an alloy wheel and some bad test data. So here you see were getting the same effect on the 60mm of the dip around 15 deg AoA. You may ask why were getting negative drag in CFD results but not on Wind Tunnel Results. The reason for this is neglecting spokes in the computer model, which would essentially add a constant amount of drag regardless of the rim.

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Wheel Design How-To Part 3

Detailed CFD procedures

Going to go over some details in setting up our computer model for running simulations.

As requested in a previous comment here is the Bontrager white paper that provided some resource in our initial research phase of development.

Mesh Definition

The initial 3D mesh was fraught with convergence and generation issues:InitialQuadMesh

Instead we decided to use a Polyhedral mesh type for simulation. The main concerns were limited computational resources and ease/automation with which we could mesh the components. Polyhedral meshes have a few advantages over more traditional Hex and Tet mesh procedures. Mainly in a comparison of element count and time to convergence is much improved with a poly mesh. This is a result of poly meshes having a higher number of interfaces with other elements per element, thus making the mesh more efficient and robust in resolving to a solution. 

This allowed us to create a script to run several flow cases in sequence for different angles, each of which required a new mesh to be created.

Turbulence Modeling

Given limited time frame and computational resources the run was done as a steady state simulation. It was found by Defraeye that a RANS k-w model provided the most accurate results for a cyclist in a wind tunnel without using a more computationally expensive turbulence model.

Wheel Boundary Layer Mesh

Wheel Boundary Layer Mesh

Overall Wheel Mesh

Overall Wheel Mesh

Boundary Layer Thickness

A boundary layer height of 5 mm was used for wheel

Boundary Layer Thickness estimation

Boundary Layer Thickness estimation

 

Where x is set as depth of rim to obtain a rough general estimation of propagation length (without having to spend excessive time creating BL mesh areas). This 5mm thickness was applied as a 10 element thick BL mesh (expansion ratio set to 1.2).

Speed Selection

CFD domain run speeds were set at 30 mph (13.4 m/s). This was chosen to provide some spread between wheelsets. Reynolds numbers for bicycle wheels range from 11,000-650,000 (20mm rim @ 20mph and Full Disc at 30mph). This is sufficiently high to place wheel aerodynamics in the fully developed turbulent region of air flow (i.e. Re>4000). This means that flow structures remain relatively constant throughout interested flow speeds and Drag will scale directly with a square relation to velocity. It was found at low speeds drag differences between manufacturers only vary slightly, meaning experimental or computational error would make it difficult to determine which wheel design is in fact better. A higher wind speed amplifies This further lent itself to our design theory of creating a wheel based on multiple factors instead of just Aero Performance.

Wheel rotation

Many existing CFD studies neglect rotational effects of the wheel. It is computationally easier to solve for a stationary solution. While we don’t have a lot of computational power on hand, we still achieve rotational modeling by eliminating our spokes. This allows us to set the wheel boundary surfaces with a rotation condition. Eliminating spokes is a safe assumption since their requirement is largely dependent on structural and governing body concerns. Additionally eliminating them will not greatly affect the drag results of a particular rim design. 

Disc Wheel Streamlines

Disc Wheel Streamlines

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Wheel Design How-To Part 2

General Aerodynamic Design Methodology:

From the start it was desired to implement Computational Fluid Dynamics in the design process of the rim shapes. CFD breaks a fluid (in our case air) into small computational blocks that we can setup around various shapes and configurations. We decided to stage the design process of the various rim depths. This would make it possible to iterate between CFD and wind tunnel results. While CFD has advanced tremendously over the past years, the amount of non-linear flow systems involved in a bicycle wheels will not be fully modeled by CFD for some time. This means that the wind tunnel is a crucial stopping point in not only design of the wheel, but in verification and refinement of the CFD modeling, this means that as we went through different wheelsets, we arrived at each desired wheelset configuration with less computational time required .

Early on several research papers were taken as a point of reference for completing CFD analysis of Wheels. The knowledge leveraged from these papers helped set up some basic parameters for the model.

Initially for the 44mm depth rim a 2D model was used for rapid runs and design iterations to setup a design space of possible shapes. The 2D model has smaller mesh and computational requirements meaning we can run through a large number of rim designs relatively quickly.

Many companies follow this 2D methodology. Bontrager, for instance, has a great white paper on their design methodology. However in order to extrapolate the 2D results to 3D they use an empirically determined factor. I decided not to try to artificially fit the 2D results into 3D numbers for reasons I’ll explain shortly.

With this CFD setup we aimed for a relatively wide rim, 28 mm, that was wide, while just as if not more Aerodynamic as leading industry competitors (Zipp, Enve, Bontrager, etc).

Comparison of Wind Tunnel (left) to 2D CFD (right)

After the first trip to the wind tunnel with 44mm prototypes (which will be detailed later), it was decided that the results obtained with the 2D models were not getting enough separation in results between the top performing rim shapes in order to determine which rim shapes were actually more aerodynamic. However in the wind tunnel we were seeing significant variation between rims especially at higher angles of attack. This means that the 2D model was significantly missing something that could likely be attributed to the overly simplified 2D model. There are several factors this can be attributed to: spokes, hub, rotational effects, ground interactions, and other 3D effects.

In order to increase the fidelity of our runs and capture the differences between the rims, the domain was expanded to encompass the entire wheel/tire system. The mesh used increased in size to ~3.5M elements. The total number of elements was kept from increasing too much (and impeding run time) by using some very basic local mesh refinement around the rim where the flow is most complex.

Rotational effects were also captured in the 3D modeling. Commonly rotating components are modeled with over-set mesh domains. This essentially overlays a rotating set of mesh elements that encompasses the rotating component and iterates between the stationary mesh and rotating/translating mesh. This technique is the most accurate and would allow for the modeling of spoke elements. However due to the complex nature of the mesh, this technique would be too computationally exhaustive for our limited computing resources. Instead we decided to ignore spokes since their effect would be largely secondary to any changes made to the actual wheel shape. Since spokes were ignored the wheel surface could remain stationary, but with a rotational surface velocity assigned to each individual mesh surface. This technique is a variation of the no-slip condition. Instead of the wheel surface having a zero velocity assigned to it (no-slip), each element was assigned a rotational velocity based on its location relative to a central point of rotation.

Vertical velocity on wheel surface

This accomplishes modeling a rotating wheel, without the high computational costs associated with an over-set mesh.

The final aspect that was added into the model for 3D analysis was a floor or road interface with the wheel. Since the entire domain was a wind-tunnel setup, the floor boundary condition was set to a slip boundary condition. This meant that the velocity along the floor of the domain was the same as the free-stream velocity. The reasoning for this is to mimic real world situations. When a wheel is riding outdoors, the wheel itself sees non-zero airspeed, but the airspeed relative to the ground is zero (except in windy conditions). If this slip condition was NOT applied to the floor the flow in the domain would be zero and near-zero near the floor of the model. This would result in the rotating wheel essentially pushing against the stationary air at the floor, artificially reducing total drag on the wheel.

These small changes to the model setup not only gave a larger spread of wheel drag results, but it also gave drag profiles that actually matched real world conditions:90mm Rim CFD resultsThat’s enough for a single post, next post I’ll dive into some further nitty-gritty of how the CFD model was setup

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Wheel Design How-To Part 1

I think it’d be interesting to write a little bit about what all went into a wheel design for Boyd cycling this past year. The rims which are currently in production I’m super proud of because as a Pro-level racer they’re a set of wheels that I’d choose over almost any other wheels, most of this design work took place in 2014. This will probably be broken up into several manageable parts, enjoy.

Design Goals

Arguably the most important part of any design is setting out the initial design requirements. This sets the ‘ship of design’ on course and becomes very difficult to change once you have sunk costs in a given design philosophy. Working with Boyd (who has extensive feedback of what cyclist want out of their wheels) we set out a number of goals to strive for: 

  • Aerodynamics
  • Wide Rim/Tire Compatibility
  • Clincher rim brake track heat dissipation
  • Tubeless compatibility

We weighted these components in a design matrix to help evaluate different rim shapes.

The primary improvement we hoped to achieve was to design an Aerodynamic wheelset. A secondary but closely related goal was to design a wheelset to accommodate a wider tire. Traditionally road cyclists use narrow road tires measuring 21mm or 23mm, however the current trend is towards wider tires 25mm and larger. The larger tire has numerous advantages over a narrow tire: better grip, improved rolling resistance and is less prone to puncture. The two main disadvantages are weight and aerodynamics. The goal of an Aerodynamic wheelset and a wide tire are closely coupled, especially for the increasingly prevalent clincher wheelset. This means that some of the negative aerodynamic effects of a wide tire can be negated with proper design of the rim.

Composite clinchers have, in the past, had a dubious reputation. The thermal conductivity of Carbon Fiber is two orders of magnitude less than Aluminum. Low thermal conductivity coupled with the low melting point of the resin used in the some Carbon Fibers meant that under heavy braking the large heat built up through friction was not dissipated as it is with Aluminum (where heat build-up is not a concern). A two fold effect then takes place: the heat in the rim is transferred to the air in the tire, increasing the tire’s pressure and load on the rim hooks, and the material around the brake track softens allowing the rim to open up. Since braking is always heavier in the front, this leads to a catastrophic blow-out. This is a relatively rare failure, but due to its catastrophic nature (front wheel, downhill, usually at high speed), has been a fairly singular deterrent for people purchasing a carbon clincher wheelset.

The final goal is achieving improved tubeless compatibility with the rims. A tubeless rim replaces a traditional tire/tube setup with a heavier duty tire with stronger bead and latex based sealant. Nearly every Mountain Bike rim sold today is setup without tubes due to their puncture resistance, lower tire pressure that can be used, and better grip. There has been much slower adoption among road users. This can be attributed to a number of factors including but not limited to: limited tire availability, limited tubeless ready rim availability, the unproven technology factor, and difficulty of setup. There are essentially no disadvantages to producing a rim that is compatible with a tubeless and normal tube setup versus a tube setup alone.

 

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