Optimizing a Tail for Low Drag: Part 2

Formulating Requirements
Before I begin testing (and especially before I begin construction!), I want to identify the requirements my tail should meet. “Requirements” specify the objectives a design must fulfill and how it should achieve them. Requirements can be split into two categories: technical (or engineering) and stakeholder. Stakeholder requirements lay out the needs or desires of all stakeholders in a project (in this case, that’s just me). Technical requirements specify the performance objectives a design must fulfill in exact language with specific, measurable goals.
I wrote in my first post that tails are a good option for reducing drag if you don’t care about the length of your car—since a tail requires length to function, adding length to your car is unavoidable if you decide to build one.
But how much length you’re comfortable adding is something you’ll have to decide. My car still has to fit in my garage (first constraint), and since I street park on school days I want to be able to parallel park it easily (second constraint). The first of those is easily measured:

That’s a 48 in. straight edge. This is the absolute maximum length I could choose for my tail and still fit the car in my garage—but, given my second constraint, my final design length will need to be shorter than this.

The second constraint is less exact—but I can take a cue from production cars.
What I did was look up the 10 best-selling cars in the US last year and then visit each manufacturer’s website to get accurate dimensions. Then, I entered the vehicles’ lengths in a spreadsheet, calculated the average minimum and maximum lengths, took the midpoint of those, and subtracted my car’s length to get my maximum tail length:

A tail of this length will put my car right at the midpoint between the average shortest and longest length of the 10 most popular cars in the US—shorter than a full-size truck but longer than a sedan like the Camry. This gives me a metric that at least correlates to typical “parkability.” Now, I can write my first technical requirement for the tail design.
Technical Requirement #1: The tail shall have a length not exceeding 672 mm (26.5 in) extending from the furthest rearward point of the rear bumper cover.
You might decide on a different method to determine the allowable length of your tail—that’s perfectly fine! I could instead have decided to limit my tail to the average length of the shortest configuration of full-size pickups, for instance. Since that would make street parking a lot harder, though, I decided to go with my averaging method. That will constrain tail length and make its design more challenging, but by no means impossible.
Aerodynamic Drag
Now that I have a maximum length established, I’ll visit perhaps the most important requirement: by how much do I want this tail to reduce drag? “As much as possible” isn’t an answer to that; if you don’t have a number to shoot for, then your requirements are not fully established.

I decided to use a similar approach to my length requirement calculation. I have a pretty good idea which cars on the US market have the lowest drag, and which manufacturers tend to publish data such as drag coefficients. So, I made a list of some of the lowest-drag cars to get an idea of what OEMs have done so far and compare that to a 2013 Prius. Aside from the outlier of the XL1 (which was only sold in Europe in limited numbers), the standout is easily the Lucid Air, a stylish electric sedan with 15%-17% less drag than my car. That seems like a good target—so I decided on aiming at 15% drag reduction, bringing it in line with a Lucid Air.
This one’s kind of shooting in the dark but based on reported fuel economy from cars with (unoptimized) tails on Ecomodder and Youtube, I think it’s achievable. Now I can write my second technical requirement for the tail design.
Technical Requirement #2: The tail shall reduce aerodynamic drag of the vehicle by at least 15%.
Of course, if I can go lower than this, all the better. I'll elaborate on how I plan to measure this when I get to that point in the development process later this summer.
Since weight can affect fuel economy as much as aerodynamic drag, I want to be cognizant of adding as little of it as possible. A maximum weight target is a little harder to formulate since I don’t know what design I’ll use for the tail or exactly what materials I’ll use. But I’m pretty sure I’ll build it out of some sort of polystyrene board and fiberglass or carbon fiber reinforced plastic composite—similar to surfboard, solar car, experimental airplane or other lightweight vehicle construction. A quick estimate of 3.8 m2 tail surface with two transverse reinforcing ribs would require ~5 kg foam and ~15 kg fiberglass reinforced plastic. Taking a little more than these estimates gives me my third engineering requirement.
Technical Requirement #3: The tail shall have a mass less than or equal to 25 kg (55 lb).
Lastly for my engineering requirements, I need to identify a maximum cost so I can budget for this. As a home builder, my funds are not unlimited (especially since I’m paying tuition out of pocket)—so this requirement is especially important to me. This is another area where it’s tempting to say “as little as possible,” but that isn’t specific or helpful. Instead, I’ll take my estimates of the required 1” foam board and CFRP (the more expensive cloth) and sum their costs, plus a little extra for hardware and incidentals.
Technical Requirement #4: The tail, associated materials, and construction shall have a total cost less than or equal to $750.
As with my other technical requirements, if I can do better than this I will. Since I don’t have a design yet and consequently don’t know how I will construct this, this requirement has the potential to be undercut if I’m smart about reusing materials I already have on hand, for example.
These requirements are a bit easier to identify—since I am the only stakeholder here! It’s my car, my tail project, and ultimately, I can do whatever I want with it. With no investors, supervisors, marketers, accountants, or other engineers to satisfy, these requirements are literally just a list of what I want the tail to do:
Stakeholder Requirement #1: The tail shall be affixed to the rear of a 2013 Toyota Prius and shaped to reduce aerodynamic drag of the car.
Stakeholder Requirement #2: The tail shall be constructed of materials of sufficient stiffness and robustness that it is impervious to normal weather and atmospheric conditions, resistant to UV degradation in sunlight, and does not deflect, bend, oscillate, or otherwise behave undesirably under aerodynamic and dynamic loading.
Stakeholder Requirement #3: The tail shall conform to all Illinois state laws governing motor vehicles operated on public highways.
Stakeholder Requirement #4: The tail shall be removable from the vehicle with no permanent alteration to the vehicle aside from rivet nut inserts.
That’s really it for now—I can always add more requirements if I think of anything pressing. I did not add a requirement for hatch functionality since, after thinking about it, I’m okay with losing access to the back of the car through the hatch. There’s plenty of access through the rear doors, and while I will lose the use of my hatchback tent, the car is still perfectly suitable for camping.

It's surprisingly roomy back there.
Now that I’ve taken the time to identify and write out my requirements, the process of designing and building the tail will have some direction to it. In reality, any project like this has requirements, whether explicit or implicit—but making them explicit required that I think about them and identify what, exactly, I want this tail to do and how I want it to do it. That will make the process of design and construction easier in the long run.


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