AlexS wrote:
Since Re is directly proportional to fluid
velocity x linear dimension then increasing the size of the object means the "critical" velocities drop.
The "critical" velocities you've shown are for a sphere of diameter 10cm. Putting aside that we are not exactly spherical, increasing a sphere's size to 1m (order of magnitude of the human body) and the corresponding "critical" velocity range drops to 10% or so of those values (i.e. 7mph smooth to 3mph rough).
We don't ride that slowly generally, and when we do, it's because overcoming gravity has become the primary energy demand factor rather than aerodynamic drag.
There are body parts however that fit into a size and velocity range of interest, e.g. upper arms and lower legs for instance, which are approximate cylinders with diameters that potentially place them in the "critical" velocity zone where strategic roughness elements may indeed have significant beneficial effects due to this Cd v Re relationship. But only in the sense of of reducing drag significantly for those elements, and of course it provides for a marginal (but useful) reduction in Cd for the whole body + bike system.
Measurable reductions in Cd are definitely possible with the strategic use of trips or seams on the upper arm and lower leg and so it's feasible there are various factors in play that result in a reduction in Cd including Re effects, but Re impacts may not for example apply to objects that are an order of magnitude larger (e.g. the torso) or smaller (e.g. the front forks) because the velocities at which they apply are either too fast or slow to be relevant.
Thanks for the comment - this thought stream is right on the mark. I didn't include notes on larger bodies to keep things simple. The whole body situation is a little more complicated to think about since it depends heavily on which position you're in and the general shape is significantly different from canonical experiments/examples. For situations where the shape doesn't match experiments, it is usually more helpful to think of things in terms of how fast the pressure is changing along your body (or more simply how much the flow is being deflected) since it is the pressure gradient that really determines how likely the flow will separate, and evaluating the boundary layer state at these points.
For example, say you're in the aero position, the flow is being deflected much more around your shoulder/collar bone than it will be along your back. That means the pressure gradient is much higher at the shoulders than the back and the flow has a higher tendency to separate. Next, to evaluate whether a trip will be helpful, we have to guess at what the boundary layer state is. Since it is kind of the "first point of contact" of the incoming air, the effective Re will be low and the boundary layer is likely laminar. Therefore in this situation a trip may help. While in the back situation, the flow has been going along the body for a while so it is likely turbulent and combined with a smaller pressure gradient, means only having a smooth surface here is likely most desirable.
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