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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Downhill Time Trials

So last week I went to InterBike with Boyd Cycling. It was a pretty cool experience, really a thing I always see on all the bike tech sites out there but finally going there is a totally different experience. First of all, the coverage that all the online venues covering the event combined don’t even begin to scratch the surface of the number of exhibits there. It’s pretty overwhelming. For instance there are foreign sections, China, Japan, Italian “villages” that essentially get no media coverage. There was a HUGE e-bike section of the show as well (which also seemed to be the best funded). However the best section, in my opinion, was the “Urban” village. This encapsulated everything from custom cruisers, fixies, to folding bikes. By far these were the most creative and off the wall exhibits and products.

Our booth was tucked into the “Triathlon” section…..yeah yeah. I spent most of my time hand modeling for BikeRadar in the booth:Boyd Eternity Hub
Tubeless Nut

Hand ModelAnd also showing off our one gimmick:

Boyd Cycling Wheelset

Climber’s Wheelset

Yes the most entertaining part of the show for me was to tell people to go pick up our “Climbing Wheelset”. Weighing in at 15 lbs, this thing could serve as a flywheel for an old school steam tractor. There’s a lot of hype around 3D printing right now and a lot of questions were fielded at the show about why we didn’t go that route. The reason is two fold: 3D printing is finite and not continuous. This means that the finish for a curved surface would be stepped surface which would require further finishing (another possibility for imperfections). Additionally 3D printing is typically done with plastics which do not carry high loads well (think spoke tensions and tire pressure).

Why does all that matter? The Aerodynamics of bicycle wheels is converging onto a single (correct, sorry reynolds) design. This means that the variation between the best aerodynamic wheel-sets are getting smaller and smaller. Aerodynamics is VERY sensitive to small variations. Something like 20 psi vs 100 psi in a road tire or low tension (bent) spokes could also greatly alter aerodynamic drag results. So by doing a solid Aluminum wheelset in the wind tunnel we could model a REAL wheel.

Why go through all this trouble anyway? If you see a wheel company showing their slick carbon wheel in the wind tunnel, it means they’re testing a finished product (cough #AeroIsEverything cough). It’s well known carbon molds are very expensive, and if you’ve made the mold, you’re pretty much married to the shape you created, so you’re either wasting money and translating that stupidity to high costs to your customer, or you’re just going with a bad design. This prototyping allows us to make small design changes or evaluate several design at a relatively low cost before making the costly investment in a mold.

Mistakes are how you learn, so it’s better to make i

Bike Wheel Wind Tunnel Testing

Aluminum Prototype in A2 Wind Tunnel

nexpensive small ones than expensive big ones.

Also see my other post (excessive rant) on why Wind Tunnels are absolutely necessary.

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What is this…a Time Trial for CARS?!

It’s July, that means hours streaming the Tour de France through some pirated grainy feeds…AND a lot of bogus Aerodynamic information, including an ESPECIALLY ugly looking Giro helmet:Rohan Dennis Tour de France Time Trial

After the opening TT it’s important to remember the importance surroundings play on the Aerodynamics of a cyclist.A Center for Ants

 

Obviously drafting a car gives you a huge advantage, but a car drafting you? It turns out you can get a SIGNIFICANT advantage from a follow vehicle. Current UCI regulation is 10 meter minimum distance.

Bert Blocken has a great course on coursera.com about mostly cycling and some city/urban aerodynamics. You can check it out here.

He also recently published a research paper about the effect of follow cars in a TT situation.

When a body is moving subsonically through a fluid, an area of high pressure is created in front of the object as the air rushes to get out of the way of the moving body. Behind a body is an area of low pressure, this is basically the mechanism that creates pressure drag.

So how does a car help a rider from behind? The high pressure area in front of a vehicle (or even other rider) for that matter, acts to fill the low pressure region behind a cyclist. This acts almost as a fairing, increasing the pressure on the back side of the cyclist, reducing drag. A picture from the above mentioned paper gives a better example.followcar

The high (red) pressure area acts to fill the area behind the cyclist (which is pretty clear to see when the car gets real close). The effect is even noticeable at smaller distances:followCarDraftAs you can see here, the benefits get pretty drastic below 8 meters (26 feet). I took a quick look at the Tour de France prologue using a simple F=1/2 Cd A rho v^2 calculation for force then converting to power. Based on this calculation, Dennis put out 492 watts (neglecting drive-train/elevation losses) for almost 15 minutes over 13.8 km’s.

A car at 10 meters (UCI legal limit) give’s you a 0.23% advantage. Let’s say his car was only 2 meters closer, giving him double the car draft advantage of 0.45% (Thus a 0.22% difference). I’ll factor this in as a reduction of the CdA term and keep the wattage for Dennis constant for the calculation…

Given this ONLY 0.22% reduction in drag, Dennis would’ve saved a whopping 10 SECONDS!!!!!!

In a short TT decided by only 5 seconds across the top 3 riders…any team manager in their right mind would get FINED TO DEATH in order to drive as close to their rider as possible.

This isn’t even taking into account video moto’s…which somehow are above UCI rule and can drive as close to riders as they please (in front or behind).

So pay attention at the next short TT in this year’s tour to see if each respective DS is doing their jobs correctly (rider safety be damned!!!).

Given:

-This analysis is quick and dirty, CdA values are VERY approximated

http://www.cyclingpowerlab.com/CyclingAerodynamics.aspx

-TOTALLY neglecting acceleration

-Drive train losses neglected

-However the actual wattage produced by Dennis may be different, the benefit should be roughly the same since we are not looking at that side of the speed equation

 

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The Issue with “Cross Winds” in Wind Tunnels

A lot of wheel and bike companies like to put a lot of emphasis on their wheel performance in the cross winds. They show you a pretty graph that looks something like this:

What you’re generally seeing is the dip due to decreased drag then a steep increase when the flow finally and fully separates from the wheel.

The wind tunnel is a perfect environment while the real world is a very imperfect environment (duh right?). What wind tunnels don’t capture from the real world is something called boundary layer, due to the way that they operate.

Think about this, when you’re riding at 20 mph, how fast is the ground moving? Obviously it’s stationary, but relative to the rider and wheels it’s traveling at 20 mph backward (the same speed as the wind). Why does this matter? If you get down to the smallest levels air speed at the ground is going to be the same speed as the ground (zero). This effect is called the boundary layer, where on the surface of everything that’s moving through a fluid there is a very short transition area where stream velocity goes from zero right at the surface of an object to free stream. To remedy this problem and make the wheel “see” wind speed right at the ground level special platforms are used in wind tunnels:

Boundary Layer Table

As you can see on the velocity profile on left, there is a gradient next to the floor, the platform sucks in this low speed air and reestablishes what is the ground (there is inevitably a small BL but it is negligible)

This works great for head on velocity, however it doesn’t capture effects of the BL of the cross wind flow (which IS moving at a velocity different than the ground thus has a boundary layer).

Not only is there a simple ground boundary layer present, there is a larger velocity gradient that is a part of the atmospheric boundary layer (ABL). When the weather stations measure wind velocity it’s typically 10 meters (32 ft).

This is a good illustration of ABL. While most of the gradient is quite high, the steepest gradients are right at the bottom next to the ground (where we’re hopefully riding bikes). This means your 10 meter weather station is reading a significantly higher wind speed than your bike is seeing. This also shows the difference in gradients between different types of terrain

And anyone can tell you this, if you’re riding in the city rarely is it very consistently windy, while in Indiana it’s always windy. However the wheels are the closest component to the ground (again, hopefully).

Alright so now circle back to the neat drag image we first looked at. Zipp in particular likes to emphasize their performance at 15 degrees AoA. This is probably the point where the wheel drag data varies the most, we have also observed this divergence in wind tunnel and CFD results. However let’s think about this for a minute, if you’re traveling at 25 mph (pretty quick, but a good race speed) a 15 degree AoA means that you have almost a 7 mph of direct cross wind. A 7 mph wind seems pretty reasonable and average right?

Remember the wind table essentially eliminates the BL in both components of wind velocity, forward speed (which we want to eliminate) and cross winds (which we’d like to not eliminate but is not physically possible).

So when Zipp says the wheel is saying a 7 mph wind, what does the REAL wind speed have to be to get a 15 degree AoA?

I used this calculator: http://es.ucsc.edu/~jnoble/wind/extrap/index.html

The second set of calculations are applicable to heights under 100 meters, given that the height of a wheel is at the lower limit of this equations usefulness so take this with a grain of salt. To get the magical 7 mph cross wind, the weather station is going to have to measure a 20 mph wind (assuming Agricultural fields as your surface roughness, obviously a town, forest or city will be much higher).

So 20 mph is a VERY windy day without doubt. All I’m suggesting here is that bike companies have determined that 15 degrees AoA is a  mythical regime that we’re all riding in all the time, but it’s not QUITE the case.

So a real world measurement of this is what Mavic actually did with respect to the Kona Ironman course:

http://www.engineerstalk.mavic.com/yaw-angle-measurement-in-real-conditions-on-kona-ironman-course/

Kona is a notoriously windy place to ride and more importantly it’s this desolate lava field with nothing to protect you from the wind. They go into this exhaustive breakdown of each portion of the course (OMG triathletes YAWN) A more realistic distribution of wind speeds is observed when they take their setup to France:

A much more real world riding area in France…almost no cross wind!!!!!

Given this is a low wind day and they don’t actually tell you what the real wind speed is so I guess it’s not a perfect example. I also am VERY aware that the times at which you’re pinned in the gutter are usually the hardest parts of races.

However, bottom line is manufacturers like to play up their drag at high angles of attack, I think, because pretty much everything below 5 degrees is very closely packed together and it’s hard to really differentiate your brand. Is <2 grams of drag worth an extra $1000 of proprietary technology?

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Rough Draft

So I’ve finished my rough draft of wheel selector, it’s live here:

http://chrisuberti.com/wheelselector/

Mainly the biggest hurdle I’m having is coding the damn thing into a website.

So right now what it is essentially a power estimator given there’s zero cross wind, no rolling resistance, and you’re riding by yourself (aka Ironman). It’s estimating pretty high on the power/work numbers based on my own rides.

What it needs to be a viable wheel selector:

  • Wind included (with inclusion of atmospheric boundary layer effects)
  • Wheel drag across range of wind angles (currently only running for 0 degrees, which means all wheels are pretty much the same)
  • Add rolling resistance
  • Time spent Drafting?
  • TT position
  • Refined bicycle rider CdA (this is pretty rough currently, the topic of it’s own blog post)
  • Add more explanation to what the hell is going on

Other things I plan on doing

  • Some sort of submit to database, involving entering your ride metrics (from power meter). This could help refine CdA measurments, which are particularly difficult to estimate
  • Better interface (ajax implementation, oh the confusing computer languages, why cant everything be like matlab…easy)
  • Step 2:  ?????????
  • Step 3: Profit!

Ultimately I’d like to incorporate something like this into what this guy did here.

But that’s a LONG way off for a side project.

I don’t want a silly plain power estimator, that doesn’t really give you much (plus that’s kinda the reverse solving process from what you need to benefit you as a racing cyclist). With this tool, you could essentially calculate your power needed for say a mountain cilmb, pick which wheelset is best, etc.

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