"Rules of Thumb" are Not Reliable
The claim: Modifying the aerodynamics of your
car is as easy as following some simple rules for boat tail angles, diffuser
angles, air dam height, and more. Lowest drag is guaranteed if you adhere to
these rules.
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| One particularly disingenuous feature of these "rules of thumb" is their common attribution to authoritative sources. Hucho did indeed include figures of various streamlined shapes in his book, but nowhere does he give a rule about maximum taper angle. |
The reality: Rules of thumb abound in online
aerodynamics discussions and message boards. One well-known web forum has
accepted, for example, that boat tail extensions should not deviate more than
22 degrees from horizontal and that air dams should not extend lower than the
lowest component underneath a car body (these rules are repeated ad
infinitum in forum threads and included in stickies, along with many
others).
The problem with these rules of thumb is that they are only
sometimes right. There may indeed be a car which, when a tapered tail is added
to it, suffers from increased drag if the angle exceeds 22 degrees. But not every
car; it depends on its geometry and the properties of the flow over it. Yet
this is how rules of thumb are transmitted and presented: as absolute and
exact.
Aerodynamics textbooks don’t generally give rules of thumb
because such simplifications are not appropriate and often misleading when
applied to the complex flow over a car. And when they do, they are neither absolute
nor exact.
A rare example can be found in Scibor-Rylski’s Road
Vehicle Aerodynamics (1984). In the chapter on aerodynamics and styling, the
author writes, “In general we can assume that the local declination of the
surface to the airstream should not exceed 3 to 5 degrees at the rear part of
the car.” Notice the difference between this advice and typical rules of thumb:
this is general rather than exact; it gives a range rather than a specific,
absolute number; and it qualifies the advice as an assumption, something
that may be proven wrong in the future and is therefore subject to emendation.
Hucho touched on the subject of rules of thumb, writing in Aerodynamics
of Road Vehicles (1998), “It is true that the mass of published experimental data
is now so great that, with the aid of this information, it is possible to estimate
drag from the geometrical particularities of any specific configuration….
However, as in the past, experiment remains the only means of obtaining
reliable quantitative data for drag” (emphasis original).
We should also distinguish between rules of thumb that are
drawn from actual research and those that appear to have sprung up ex nihilo,
such as the air dam height proscription I mentioned at the outset of this post.
A rule such as “removing external mirrors reduces drag by 4%” has its basis, at
least, in reality: almost all cars see a drag reduction from getting rid of
protuberances such as mirrors, even if the exact percentage reduction varies. There
is a grain of truth in this “rule,” and a home modifier can be reasonably
certain that removing the mirrors on their car will reduce its drag.
Similarly, the oft-repeated 22-degree boat tail angle “rule”
has its basis in research conducted by W.A. Mair in the 1960s and 1970s. Mair used
axi-symmetric bodies (shapes that are symmetric across their centerline
side-to-side and top-to-bottom) with various lengths of tapered tail
on them; basically, these looked like missiles with tail cones. He found that,
for a shape like this, a drag minimum was achieved when the taper angle
approached 22° in zero-yaw flow; as yaw angle increased, the 22°
tail made more drag than steeper angles. Internet sages have decided that this
means a 22-degree taper is the optimal angle for an extension on any car (this
is the origin of the idea that you can use an aerodynamic “template” overlaid
on any car to determine its optimal shape). This
isn’t true, but it at least has its roots in established research.
On the other hand, “air dams should only extend as low as
the lowest component hanging under the car” does not appear to have its origin
in any published research; I have several aerodynamics textbooks and
fluid mechanics textbooks in my library, and this appears in none of them. In
fact, Aerodynamics of Road Vehicles (which is widely seen as the
definitive reference for car aerodynamics) mathematically relates air dam
height and underbody roughness to arrive at an equation for predicting optimum
height that has nothing to do with the minimum height of underbody components—and
is, again, an estimate only and must be quantified by testing as the author
wrote previously (he goes on to give examples of air dam optimization with
measured results on several production cars).
“Rules” in aerodynamics textbooks most often take the form
of equations like this, relating two or more variables such as, in the
preceding example, air dam height and surface roughness. These are almost
always empirical rather than theoretical equations, drawn from experimental
results, subject to uncertainty and possibly nowhere close to true—very
different than the “rules of thumb” online commenters are more than happy to
repeat. Instead of adhering to some rule that may or may not apply to your car
specifically, you will need to test in order to
optimize modifications to your car.
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