To reduce the drag, flap in front!
|Leif Ristroph and Jun Zhang [Phys. Rev. Lett., 101, 194502 (2008)]|
|Taking a leading position in a group of fast-pedaling bicyclists is not easy, you have to overcome greater
resistance than your followers. Same for racing cars and queuing lobsters moving underwater. This is the so-called
hydrodynamical drafting or aerodynamical drafting effect. Such effect has been tested over and over with different shapes
and over many flow conditions in laboratory experiments. The most representative tests are the ones that dealt with rigid
cylinders in a moving fluid. The cylinder that first encounters the fluid always experience more drag compared to its follower.
This effect is so robust (never a surprise) that its conclusion was applied by many people when then dealt with
To an extreme, it is the common wisdom that birds in a flock and fish in a school also share the same drag allotments: it is more difficult
to lead in a group than to follow. However, so far there is no direct experiment that has been down with such systems. To be more specific, there
has been not a single experiment that measures the drag or the relative energy cost on a leading fish (or bird) in a group. It is
exceedingly hard, of course, to carry out such experiment with live animals especially when they tend to form a group on their own ``will".
It does not mean that we have no way to tackle this problem. Instead of working with actively locomoting animals, we
turn our attention to their passive counterparts: flapping flags that mimic the flapping motion of the swimming fish. Here, flags
are regarded as paralyzed fish that flap due to the interaction between its inertia and the surrounding fluid. In particular,
our experiment examines the fluid drag acting on a pair of tandem flags that are flapping in a fast moving fluid. In our experiment,
We used a flowing soap film (speed at 2 meter/sec) as an idealized 2D water tunnel and two short segments of rubber threads (2 cm long).
We used a simple custom-designed force gauge that is similar to the one used by Cavendish as he measured the gravitational attraction
between heavy masses. The reason, the drag force acting on a small object due to the flow of a thin soap film is very low, typically
on the order of a few dynes, which is a quarter of the weight of a grain of rice.
Our surprise finding is that, the leading flag always has less drag compared with the follower. Sometimes the drag is reduced by 50% for the leader
when two flags are closely placed (not touching, though). We now refer this anomaly as to the Inverted Hydrodynamical Drafting (IHD). The physical reason
for this effect lies in the intimate interaction between the deformable bodies and the surround fluid. The leader is affected by the presence
of the follower, which narrows the wake of the leading flag. As a result, the free end of the leader (which is also embedded within the wake) presents
a smaller flapping amplitude in the oncoming flow and thus the lowered drag. On the other hand, the follower flag is frequency locked with the leader
and lives in its wake, the resonance effect brings the amplitude of the trailing body to a greater value and thus the greater drag.
In short, the anomaly is directly attributed to the fact that flapping flags can change their shapes (amplitudes) in response to the fluid
environment and rigid bodies can't. We envision direct applications of this effect in some forms of locomotions and in other drag reduction schemes.
It should be noted, though, that this effect was discovered with passive bodies (no activation of muscles or alike). Animals may choose their phase
and amplitudes in an active manner and their drag distribution may be different compared to passives flags or rigid bodies. This says, we have now an
"anomalous hydrodynamic drafting of interacting flapping flags,"
by Leif Ristroph and Jun Zhang, Physical Review Letters, 101,
|The periodic flapping motion of the tandem flags is revealed by a strobe-light. The flapping frequency of two flags is the same, but they take
on different phases and amplitudes. (click on the picture for bigger size)
||Drag force measurement on each flags. The separation (gap G) measures the distance between the end of the leader to the head of the follower. Drag force "1" indicates the force magnitude for an isolated, lone flag.
(click on the picture for bigger size)
||The wake of the two flapping flags is visualized using a monochromatic light with the help of the flowing soap film. (click on the picture for bigger size)
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