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Home Performance Demand Flow Stagnation, Ideal Fluids, and You

Flow Stagnation, Ideal Fluids, and You

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Almost two years ago during the summer of 2004, I began fiddling with SRM power meter based field tests in an effort to see how this methodology might be used to evaluate the aerodynamic characteristics of different cycling positions.  I was never really satisfied with the results I obtained along the way – the downfall, for me, of this testing approach was too much variability (e.g. – even the slightest breeze effects results) and therefore, too much time involved to generate meaningful results.  In an effort to reduce and/or compensate for ambient wind conditions, I attempted to measure wind speed while conducting my field test trials.  The wind speed measurement didn’t seem to help things much; however, along the way I was successful in demonstrating that the flow in front of a cyclist stagnates.

 

The fact that air slows down in front of an object is nothing new, in fact the magnitude of this effect can be estimated by making some simplifying assumptions and doing some math.  The principles of ideal-fluid aerodynamics are pretty powerful when one stops and thinks about it for a second.

 

During my field test experiments I would simply hold my portable, data logging Kestrel anemometer in between my thumbs while simultaneously grasping the ends of my aero bar extensions.  Yeah, I took a bit of a hit on my overall aerodynamics because I was holding a bit of gadgetry, but I’m an experimenter at heart and was curious to see what the data would yield.  I estimate that the wind speed measurement was taken ~35-40cm in front of my shoulders as indicated below:

 

Figure 1:  my old TT setup in the summer of 2004 (I was already dreaming of my current TT bike, though, the ciocc!)

My crude field testing methodology involved riding back and forth on a section of road at different constant speeds (I would aim for at least 30 seconds of data that had the same initial and final ground speeds – more details about how to do this type of testing on the BTR forum).  On one particular day (June 6, 2004 to be exact), this is how the ground speed and air speed data looked:

Figure 2.  Noisy air speed data, and an offset!

 

Looking at the data a couple of things jumped out immediately – one, the air speed data is pretty noisy with lots of fluctuations and there was a noticeable offset of the measured air speed relative to the ground speed.  Below is a 30 second average extracted from each of the four runs above (net acceleration for the interval was <0.01 m/s^2):

 

Figure 3.  Avg wind and ground speeds for 30 second chunks of data.

 

I had this data that clearly showed a 20% reduction in air speed relative to ground speed, so I decided to see if the ideal fluid principles would predict a similar magnitude.  Armed with the bible of ideal fluids (Karamcheti’s Principles of Ideal-Fluid Aerodynamics, 1966) I busted out the math for the case of a doublet in a uniform flow ->  i.e, I assumed that my body was roughly approximated by a circular cylinder in 2-d flow…  there’s an engineer joke in there somewhere…  work with me!

 

Figure 4.  Ideal flow around a 2-d cylinder (Karamcheti, 1966)

 

Here’s the ideal fluid equation for velocity in the radial direction for a doublet in a uniform flow:

 

 

where:

a=cylinder radius

r=radial distance from center of cylinder

U=free stream velocity (ground speed in the cyclist case).

For the region directly in front of the cyclist, we are interested in the case where theta is 180 degrees and r is varied from the surface of the cylinder outward until we reach the undisturbed free stream speed.  We would expect the air speed to be zero/near zero on the surface of the cylinder (completely stagnated) and at a distance infinitely far away we would expect the air speed to be the same as our ground speed (assuming dead calm conditions and using a cyclist centered reference frame).  The air speed bits in between should transition smoothly.

To generate some data I estimated that my torso could be represented by a cylinder with a radius of 18cm and that the surface of that cylinder was located at about the same position as my shoulders.  Clearly, this is a rough approximation – a back of the envelope investigation!  With this crude model in hand I was able to plot the air speed as a function of distance for this case below:

 

figure 5.  Velocity ratio prediction and the actual value measured.

As you can see, the approximation was off by about 10% - the ideal fluid equation predicted a 10% reduction, while I measured a 20% reduction.  This difference could be due to a lot of things – I could be off on the distance between the wind meter and my shoulders, but also, I think that my body is probably behaving like a bigger cylinder.  How much bigger does the cylinder have to be in order to match the real-world measurements?  According to the math, I would need to be represented by a cylinder with a diameter of 66cm and whose surface is located near where my shoulders are.  That seems like kind of a wide cylinder, but just about right in terms of my torso length – maybe I’d be better represented by an oval rather than a cylinder.  That’s too much math for one day, though.  Pretty cool math, though, huh?

The stagnating flow in front of a cyclist may also reduce the aerodynamic forces of any gear you choose to hang off your aero bars (e.g., front drinking systems for those long-course triathletes).  Exploring these types of topics is generally reserved for higher resolution venues such as a wind tunnel, though.  Flow stagnation is something to consider when gearing up.

Due to the time-consuming nature of field tests I’ve since cut back on how frequently I conduct these, and I probably won’t be trying to make any more air speed measurements when I do choose to do a field test.  However, my experiences a couple years ago proved to be great fodder for this little BikeTechNote!

Last Updated on Monday, 15 March 2010 00:59  

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