seems drag should be displayed as a 3D surface map relative to yaw (x), wind speed (y) and wind direction (z). To display in 2D for comparative sake, create a slider tool from 15 to 30mph rider speed, a second slider tool for wind speed, and a third slider tool for wind direction. have the drag at yaw change accordingly per bike... or have rider time on a slider tool... and/or have a slider that combines wind speed and wind direction in a single slider tool with hashes on the slider with course names for each hash, using actual course data.

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wovebike.com | Wove on instagram

Funny that's exactly what I was thinking re wisdom of crowds. Just take everyone's and put them all together.

We tested 7 yaw points 9 times for each run -- well, one run was abbreviated to three angles because it was to validate a somewhat surprising result for one run.

On your proposal, hell yeah. It is pretty fun, actually. Fun with numbers. Maths you can apply.

I do generally agree with the outline of the approach, but Gaussian assumptions are often bad in the natural environment. I wouldn't treat them as Gaussian distributions without taking a good look at whether it was remotely justifiable; distributions of speeds are constrained to be positive, for starters. It's worth a quick look at distributions of measured wind speed at a couple of locations, but a log-normal might be more appropriate (truncated normals might be fine too). Similar checks should be done for rider speed.

If you aren't using normal distributions, then the standard deviations may not be telling you what you think. You're suggesting it as a measure of spread, but something like an appropriately scaled median absolute deviation, or another robust measure of spread (like the Sn estimator) may well be more appropriate than a standard deviation. The full rider speed distributions should be easy to pull out of a set of Garmin files from races. I'd be happy to provide some of mine (20k and 40k TTs; some 70.3s) if kileyay needs a giant stack of race files for building distributions of rider speeds.

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http://ironvision.blogspot.com ; @drSteve1663

Dan Connelly did some work on this a few years back on his blog: http://djconnel.blogspot.com/...-wind-speed-and.html

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http://bikeblather.blogspot.com/

Yes, very well said.

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Advanced Aero TopTube Storage for Road, Gravel, & Tri...ZeroSlip & Direct-mount, made in the USA.
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It seems to me that if you really wanted to understand the time that a particular rider spends at x yaw, what you would do in an ideal world is run 1000s of riders on 1000s of courses, rather than have it based on a few runs on a particular course.

Until you get a data set like that and then compare it against something like rider power (CDA would be too hard - power is an easier proxy and likely readily available) you're working on generalizations on a very specific rider or handful of riders - and your data set would be dominated by the conditions of that course on that particular day rather than a true reflection of what a rider would experience,

My guess is that the only way to get that type data would be to talk to Argon-18 in a few years.

Neither wind nor rider speed are well-modeled by gaussian distributions. Wind is better modeled with something like a Weibull distribution, and because the aero component of drag varies with the square of speed (so the power component of aero drag varies with the cube, while the rolling resistance varies linearly), speed distributions tend to be skew.

All-in-all, it's simpler to assume symmetry across negative and positive yaw, then report the drag at a handful of yaws; like, maybe, four or five. Then people can do their own weighting. Let them ponder on their own ponderation.

Data looks pointless to me. Just give me drag as a function of yaw angle and I'll do the rest. Wind direction, speed, gust conditions, and heading are too variable in real life to pigeon hole everything into some Kona model. But just the drag vs yaw is one of the golden inputs.

This reminds me of my second day in my first statistics course.
On day one the lecturer presented a set of numbers, then a formula and hey presto, one number came out the end. That number was deemed to represent the whole set of numbers.
On day 2 the lecturer presented the same set of numbers and a (different formula) and lo and behold, a different single number popped out the end. This number was also deemed by the lecturer to represent the entire set of numbers!
I piped up and said to the lecturer that it appeared he was using whatever formula he needed, to get the answer he wanted. His response was "You sir, will do very well in this course". He followed that up with the famous statistics line "There's lies, damned lies, and then there's statistics"

My point is that your goal of getting one number to represent the aero-ness (drag?) of each bike is laudible, but as this relies on statistics, it's flawed to believe you will ever get the right number.

While your experimentation seems to be fairly robust, repeatable etc, you are still hamstrung by needing to find a single number to represent the entire data set for each bike. Without being argumentative, you simply cannot succeed in your quest.

Your latest quandary, the subject of this thread, shows the cascading affect of using multiple factors in determining the final (un)representative number. I'd suggest that rather than trying to decide which method of determining yaw probability is 'right', that you simply choose one of them and move on to the next problem. When it comes down to it, the ST brains trust will find fault with whichever one you choose, so just accept defeat and move on.

And to start the non-sensical argument, it's agreed (I hope) that the aero impact on the front wheel is the most important. (this may be why Mavic chose their fork mount system, to evaluate the yaw on the front wheel, while Trek, primarily a bike manufacturer, had a head tube mounted rig, to more accurately test the bike/whole rig). For me, since you're testing bikes with riders, and are more interested in testing that, I'd suggest using the head tube mounted rig information.

And then there's the whole discussion of which course is most representative of wind direction (yaw) experienced by a rider on a bike. We all wanna race Kona, but even Kona varies from year to year so who the hell knows what course is best.

To try and actually be helpful, pick one, use it for all the bikes (of course) and begin formulating your counter-arguments before you publish your results :-)

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TriDork

"Happiness is a myth. All you can hope for is to get laid once in a while, drunk once in a while and to eat chocolate every day"

And this is exactly why I just buy the nicest looking bike.

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--Chris

With all due respect, your stats prof sounds terrible. The first day in my class, I explain that statistics is NOT a field of taking some numbers in and popping out some other numbers on the other side. Statistics is a way to tell a story of what data means in the real world. Heck, in my classes we don't even do manual calculations of any statistics because computers are good at that part.

As has been pointed out by others, there are better distributions to use than Gaussians. They are supported by what the raw data actually looks like. As I said, I have never worked on yaw, wind speed, bike speed, or anything related using statistics, so Normal was my default distribution suggestion. Using a more appropriate and data supported distribution that can be parameterized is obviously better and more accurate. It is definitely NOT arbitrary here, it is supported by the data of how these variables actually are distributed. As with any parametric statistic, the output is only as good as the fit to the assumptions. If you use Mean and SD and assume a Gaussian distribution but actually have a skewed or otherwise non-normal distribution, then your statistics will spit out flawed conclusions. The closer the data is to the shape of the actual distribution, the closer the output will be to the real world. The only reason you pretty much have to use a distribution in cases like this is that you need to parameterize the data to ease the calculations and because you generally lack sufficient data for all the situations you are trying to model. It obviously incurs errors, but statistics is all about limiting the amount of error and knowing where it will be and how big it will be. Kiley already knows that since he was already planning on using error bars (i.e. measures of errors in statistical estimates) on his graphs. Oh, and he never asked, but I vote for 95%CI error bars rather than something like SE error bars.

One other note. The debate over Yaw-at-front-wheel and Yaw-behind-steering-axis is probably irrelevant here for modeling the wind tunnel data. In the tunnel, I assume that the wheel is kept straight with the rest of the frame, so all data that is coming out of the tunnel (and is the input to these statistical equations) is stuck in a single wheel-frame relationship. I don't think you can model how the drag would change in other conditions unless you already had 2 other pieces of information:

1) How drag changes in a tunnel when the wheel and frame are not perfectly aligned
2) What the distribution of wheel-frame relationships are out on the road

But, again, if you had both of those pieces of information, you could these factors to your estimates and come up with an even better "real world" estimate of drag in the real world for a given set of wind-tunnel data.

"Me thinks the Lady doth protest too much" :-)
While I said that statistics is chosing the formula to get the number you want, I was being somewhat facetious of course. However, what I insinuated was choice by the statistician, you (to paraphrase) "fit to the assumptions". I guess I'm contending that statistics is an art, when it appears to be a science. Regardless of what your data set represents, there are a multitude of ways it can be interpreted and the validity of those ways can be argued by statisticians until the cows come home!
In the case of selecting bicycle for triathlon, we here at ST understand that the aeroness (drag) is a very important factor when considering what bike to purchase. We look to the testers for answers on which bike is most aero. the vast majority of us are looking for one number to tell us which bike is best. Most of us don't look at yaw angle performance and compare that to the wind direction (and apparent yaw we will experience on our bikes), we just want to know which bike is best. For that, we need one number. While statistics has the ability to pop out a single number at the end of the formula, it has the ability to pump out lots of single numbers that all represent the data set depending on your interpretation.
In this particular case I think the headtube mounted sampling apparatus gives the most accurate wind yaw information, I can also see the validity of the fork mounted apparatus since we wobble our way down the road, even in still air! I will leave it to others to argue the validity of each case, because it's almost beer O'clock here in New Zealand, but just like we anticipate that the bikes will all end up being dangerously close to each other in drag, which testing protocol results in the right answer will also be dangerously close. Potato, Potato :-)

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TriDork

"Happiness is a myth. All you can hope for is to get laid once in a while, drunk once in a while and to eat chocolate every day"

I would go with FLO's distribution. They've been open in their processes and had little criticism of either their methodology or results.

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'It never gets easier, you just get crazier.'

In general I like what Flo have done, and Trek's stuff is pretty good too.

A few observations I have on this:
Wind speed and direction is very noisy outside a wind tunnel. You are not in a stable environment when riding. And the bike is not fixed vertically.

When there is enough wind to generate larger wind angles (> 8° say) the data is very very noisy. You may be more interested in handling than drag at this point. I am quite happy for wheel designers to take high/varying wind angles into consideration.

8° isn't a very large angle. Measuring this is fun.

Using meteorological data is not straightforward due to gradient and the impact of objects at ground level.

Oh, and of course, bikes don't yaw unless things are going very wrong ;)

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Developing aero, fit and other fun stuff at Red is Faster

I would also like to underline this. Turbulence intensity in a wind tunnel is low. A highly turbulent flow will behave quite differently in a number of situations, especially in case of adverse pressure gradients. Then there is the dynamic effects, hysteresis of flow separation and so on... So for lager angles of attack, a wind tunnel measurement might not be a useful representation of what happens in the real world for that angle of attack.

I can empathise with your dilemma. You do not want to overwhelm people with a plethora of data, which they cannot usefully interpret; but at the same time, you must avoid 'molesting' the data too much for the sake of simplicity.

It's received wisdom that some set-ups will be good low-yaw performers & others will be better high(er)-yaw performers. I think what you ultimately want to do, is highlight which of these set-ups is best at either, or just a good all-round bike. No cherry-picking as it were. What's good for Starky, isn't necessarily good for an MOPer with $10k to drop. Maybe I've over simplified it.

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29 years and counting

+1

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29 years and counting

This is not directly answering your query about which data set to use but rather querying the validity of all 3 and consideration of wind impact altogether.

I have experience of wind tunnel testing but not in the field of cycling. Perhaps this has all been well discussed and there are generally accepted test practices I'm not aware of. However, since I don't know that to be the case, and I'm pretty skeptical of cycling aerodynamic testing robustness in general, I think it's worth questioning.

As I'm sure everyone's already aware, wind has an airspeed gradient such that airflow in contact with the ground is zero and it increases as you rise above it. However, the bike moves forward as one object so the speed and yaw of airflow impinging on the bike will NOT be uniform except in static air.

Let me give some examples to illustrate this....
(I'm ignoring the fact that rotating/reciprocating parts, i.e. wheels, cranks and legs don't have a constant airspeed)

Case 1: Still air
The bike and rider encounters an impinging airflow with a constant velocity from ground level all the way up to the top of the riders head. A wind tunnel test for this case would require a uniform airflow across the tunnel cross section or, if a significant gradient exists in the tunnel, compensation would be required.

Case 2: Headwind
The impinging airflow velocity at the base of the bike will be in the same direction but lower speed than the top of the bike/rider. In this case the rider position, helmet and aerobars will be of greater significance than in the still air case but the wheels and frame will be comparatively less relevant. An accurate wind tunnel test for this case would require a representative airspeed gradient across the tunnel section such that airspeed increases as you move higher in the tunnel.

Case 3: Tailwind
The impinging airflow velocity at the base of the bike will be higher than the top of the bike. Like the headwind case, the entire bike is not effected equally. The lower part of the bike will experience higher airspeeds than the upper parts of the bike and the rider. So, for example, the helmet and aerobars will be less relevant while the frame and wheels would be more relevant compared to the still air case. An accurate wind tunnel test for this case would require a representative airspeed gradient across the tunnel section such that airspeed is higher at the floor of the tunnel and decreases as you move higher in the tunnel. I've never seen this configuration.

Case 4: Crosswind (at right angles to direction of travel)
The lateral component of the airflow velocity will be lower at the base of the bike than the top of the bike/rider while the component in the direction of travel will be constant. Thus, the bottom of the bike will be at zero yaw and this angle will increase higher on the bike/rider as the lateral component becomes more significant. Bike yaw, as measured at handlebar level will not be representative of the yaw at the height of most parts of the frame or wheels for example. An accurate wind tunnel test for this case would be very difficult, probably impossible, to produce. A truly representative test would require a complex impinging flow, not only that but it would have to be adjustable to mimic different wind/speed permutations, which makes an accurate static test utterly unfeasible.

Case 5: Everything else (there is some wind, direction not exactly in line with or perpendicular to direction of travel)
There are infinite combinations of the above cases and the overall airspeed/yaw profile will vary widely depending on wind speed, wind direction and bike speed. As with Case 4, anything involving a crosswind is likely untestable in a static wind tunnel.


Question 1 - What is the airspeed velocity profile of the wind tunnel used for testing? This is a basic wind tunnel characteristic.
Question 2 - Does this allow useful/accurate analysis for a bike in still air?
Question 3 - How useful is this data once wind enters the equation (in axis of travel)?
Question 4 - How useful is this data once wind enters the equation (off axis of travel)?

great thread
this is above me but what i would suggest is less can be more
ie dont try to make it more complicated as it already is. I guess you are doing an FOP test focus on getting the numbers for that
otherwise you will have to come up which something that is even more time consuming than the task you have in hand right now.

and i think a cyclenutz has mentioned its likley that 5 degree of jaw could be the best indicator for most races ( the only consistent outlier would be kona. ( of course that is of course a goal race for many FOP s )

If you look at various photos of A2 you will see that the testing fixture for bikes sits on a splitter plate, so I guess you can safely assume a pretty constant profile.

Perhaps this will help allay your fears a bit:

https://www.academia.edu/...mech_1998_14_276-291

+1. The "whirly gig" wind speed/direction probe Jim Martin developed back in the 1990s would dance all over the place, especially when a car passed you.

That said, we know that wind tunnel-predicted and actual power agree to w/in ~1% of so, and we also know that wind tunnel drag data are not influenced by the act of pedaling per se. I'm therefore not convinced that such high-frequency components have any real impact on time-averaged data (i.e., hysteresis must be minimal).

Just an FYI: people in the "speedbike" (HPV) world have been measuring such things for at least 30 y (and Argon's probe appears to be too short to provide valid data).

Possibly not the only way.

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Developing aero, fit and other fun stuff at Red is Faster

As well, even without a splitter plate the only part of the bike that would be in the boundary layer of a decently-designed wind tunnel would be the bottom few centimeters of the wheel...and if the wheels are spinning at a speed close to the wind tunnel speed, the relative wind speed there would be minimal.