### Optimizing a Tail for Low Drag: Part 1

Now that the
semester is almost over and I have no plans for the summer, I decided to
revisit a modification I’ve cursorily stabbed at before, in a not-very-smart
manner: the drag-reducing tail.

**Streamlining**

*streamlined*shapes. Even the most perfectly shaped production car has a large area of separated flow at its back end:

…which you can see here. My Prius has attached flow over most of its upper and side surface, but that flow separates at the rear—seen clearly in the tufts. |

The Volkswagen XL1 is one of the lowest-drag cars ever sold to the public; it still has a large area at its rear that is in separated flow when the car is moving. |

*bluff*shapes rather than streamlined. Generally, bluff bodies have more drag than streamlined ones, as the large turbulent wake that forms after flow separation has fast-moving, chaotic airflow and consequently dissipates a lot of energy. The wake also develops lower pressure than attached flow over the sloping rear part of the car, as I found in my very first pressure measurements on my car (where a lip spoiler at the top of the rear glass, separating the flow there, dropped pressures on the rear window).

**Misconceptions**

**First, there is no perfect “template” that will tell you how to shape a tail on any/every car.**This is the big one, as many,

*many*amateur aerodynamicists believe they can simply follow a predetermined shape—often one that originates from one website in particular that keeps popping up in unexpected places—which obeys certain “rules” (such as “the tail should have a maximum taper angle of 22° from horizontal”). In reality, there is no single “perfect” shape (indeed, the early days of automobile streamlining were characterized by the multitude of shapes proposed as the "best" tail for a car).

One of the most popular was this, the Jaray Kombinationsform—made by "stacking" multiple airfoil shapes in different positions and orientations. While lower drag than contemporary cars, this Tatra T87 doesn't come close to the best production cars today, despite its flat underbody and "streamlined" shape (see Julian Edgar's A Century of Car Aerodynamics for more). |

The suitability of a shape depends on what you want it to

*do*aerodynamically, which will depend on the shape of the rest of the car that isn’t its tail and your goals. Many of these “rules” of the Template are based on boattail research on axisymmetric (circular cross section) bodies of very large length-to-depth ratio away from the ground i.e. missiles—not cars. Their wholesale application to cars is dubious at best—and unnecessarily limiting and ultimately detrimental to good, thoughtful, informed design at worst.**Second, a fully streamlined tail that tapers to a point with no flow separation does NOT result in zero pressure drag.**This is a fallacy that arises from an incomplete understanding of thin airfoil theory (TAT—yes, this area of study is so important we give it an acronym in the aerospace field!). In TAT, potential flow theory is used to predict the lift performance of airfoils to a high degree of accuracy.

This potential theory
only applies when the airfoil has no flow separation—which Template proponents
correctly transfer to their car analysis—but

*also*depends on several other assumptions (inviscid, incompressible, irrotational, steady flow) that provide the necessary theoretical simplifications to allow solving potential flow problems but do*not*apply to real flows. Potential flow theory correctly predicts lift over thin airfoils at low angles of attack but does*not*predict drag because it does not account for the effects of viscosity and rotationality in the fluid (this is named “d’Alembert’s Paradox” after French polymath Jean d’Alembert, who first deduced that potential flow theory will predict drag equal to zero for any body submerged in an inviscid flow—something he puzzled over at the time since experience clearly showed that ships were subjected to hydrodynamic drag despite the theory). And what’s more, simply adding in viscosity and its resultant shear stress on the body*still*does not result in pressure drag equal to zero as in potential flow! Viscosity and three-dimensional effects alter the pressure distribution over objects in real flows, which means even a fully streamlined shape has not just viscous drag, but pressure drag as well.**Third, no car (or any object with rotating wheels) can be fully streamlined.**In addition to the above, another huge caveat with applying TAT to cars is the fact that no car can be fully streamlined: unless you’re planning to turn it into an airplane or magically levitate it, your car must be in contact with the ground on rotating wheels, and these wheels will have areas of separated flow no matter how well they’re incorporated into or shielded by the body.

(Image credit: ecomodder.com). |

**Fourth, the method of images does not correctly predict the aerodynamic forces acting on cars.**You’ll see Template promoters online claim that their “perfect” shape derives from the “ideal” teardrop cut in half and brought into contact with the ground, doubling its drag and producing no lift (see the image above). This is another misunderstanding of potential flow theory. We can predict a flow field by superposing basic flows in a velocity potential function or stream function, from which flow velocity can be derived and then pressure from that velocity field.

In order to solve a
potential flow problem for an airfoil close to the ground (e.g. for an airplane
in takeoff roll), one must superpose its mirror image at the same distance
across the ground plane, which can then be represented by a horizontal streamline, to
correct the velocity field.

As in non-mirrored potential flow, this method
accurately predicts

*lift*for thin airfoils at small angles of attack but cannot account for*drag*due to the inviscid model. And even using mirrored models in a real, viscous flow does not give accurate results. This point is worth emphasizing: placing two car models in a wind tunnel (as has been done in the distant past)—one upside down, touching at the tires’ normal point of contact with the road—is only an approximation and does not accurately replicate the ground plane, does not account for viscous effects at the ground plane, and does*not*simply "double the drag" and "cancel out lift" of the car (testing in this manner, only the aerodynamic forces on the*upper*car are measured, not both! The mirror car's only purpose here is to correct the velocity field around the real car).Further, as Barnard points out, the “perfect”
teardrop cut in half and sliding along the actual ground (rather than a
dividing streamline) will have significant lift—besides being unrepresentative
of a real car rolling on wheels with some finite gap between the underside of
the body and ground. To reduce lift of a longtail streamlined car, the underside
of the body must be shaped carefully (for more on that, see the proceedings of
the 1976 GM conference on aerodynamics, which includes what must have been a
lively discussion after one paper presentation on the interaction between body
camber, drag, and lift).

**Fifth, cars are NOT infinite wings; three-dimensional effects must be taken into consideration when shaping a tail.**Template believers often make one of two mistakes: treating a tail design as if its profile extends to infinity (i.e. conceptualizing the tail as a 2D section of a wing), or treating it as a simple half-body of revolution and claiming there will be no ill effects such as vortices. Neither of these is true. Cars generate strongly three-dimensional flow fields, more so than finite wings; add in that they are characterized by flow separations (unlike wings), and you get a shape that generates complicated vortex systems which themselves alter the flow characteristics. Consequently, when designing a tail you will have to take this into consideration—and not in the arbitrary, “just overlay the Template on the side of the car!” way (see Point 1 above).

**Tail Theory**

*is*the best way to design a tail? If not by following a template, how should one go about figuring out what shape to build?

*1) Start with cheap/quick mockups (cardboard, coroplast, or plywood) to test angles for the top, sides, and bottom:*

*a. Tuft test: range of angles for each of top, side, bottom--identify max angle that has attached flow for each*

*b. Pressure measurement: at range of angles up to max angle with attached flow--see what the behavior of pressure is with angle (we're looking for the combination of greatest pressure + largest taper angle + shortest length + smallest wake for maximum drag reduction)*

*2) After completing the above, I would then mock up a full tail using the angles found in (b), and then tuft and measure pressures on top, bottom, sides to see how close they are to the individual components; adjust angles if something is different e.g. separated flow and retest*

*3) In combination with (2), I would probably also coastdown test at this point to estimate total drag change from acceleration change*

*4) Retest with any changed parameters e.g. curvature of panels, radiusing edges between top, sides, bottom--could incorporate this in (2)*

*5) If the mockup is strong enough, crosswind test and measure steering angle, also tuft test/pressure test in crosswind*

*6) Once that's all done and I have a good design, build the real thing and do a final tuft test to verify it behaves the same as the mockup, then log fuel economy for the next several months to a year*

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