What is the most efficient symmetrical airfoil shape to make for a covering for a round upright bar that measures 40mm outside diameter?

The speed of travel will be 25Kph and I also need a shape to travel at 30Kph. I assume these will be different to some extent?

  • $\begingroup$ Hello JJayes, welcome to aviation.stackexchange. How do you measure efficiency? Lowest weight? Lowest weight / lift ratio? Highest lift / drag ratio? Lowest drag at 0 lift? in other words, what are you trying to achieve? $\endgroup$
    – DeltaLima
    Jan 4, 2019 at 15:06
  • 1
    $\begingroup$ Do you actually want to generate lift with this airfoil or do you just want to minimize drag? $\endgroup$ Jan 4, 2019 at 15:09
  • $\begingroup$ Hi, I am looking for a tube to be shaped to pass through air in a upright position while travelling at both 25kph and another st 30kph. I do not require any lift. The tube needs to be 40mm in width. I need it to provide the least possible drag. The weight is not a issue. $\endgroup$
    – jjayes
    Jan 5, 2019 at 19:36

2 Answers 2


Truncation (chopping off the rear portion of the airfoil) does not reduce drag, although reducing up to 20% of the chord does not significantly increase it. As Peter says, "trade off between more separation and more wetted surface area. Hence "boat tail" bullets.

The 3:1 ratio of chord to width is apparently a bike racing specification. Nothing new here, the full airfoil produces the lowest drag. Hence the cone they put on the back of the Space Shuttle while it was piggybacked on its 747.

What they did to meet the 3:1 specification was to truncate 66% of a 9 to 1 airfoil. This produces the lowest drag within the specification.

The Kamm tail shape was designed for automobiles, providing a weight savings (as racers constantly accelerate and deccelerate) and to make the vehicle a little shorter, which can help changing lanes in a crowd. Two different applications. But a fully symmetrical airfoil, such as the struts of a Cessna 172 will do the job.

For an aircraft strut, if strength allows, make it as long and thin as possible until drag values begin to rise. 9 to 1 rings a bell from boat hull design, and would be a good place to start.

  • $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review $\endgroup$
    – Vikki
    Feb 4, 2019 at 5:41
  • $\begingroup$ 9 to 1 ratio thickness to chord added. Wind tunnel test for specific application may be best. $\endgroup$ Aug 23, 2022 at 10:44

This site discusses tube width and length ratios for least drag



Tyler just had a chance to speak directly with Scott regarding the final profile, and reported back that they found that a 9:1 ratio profile with a truncated tail was indeed the fastest, lightest, and most stiff. According to Scott, Scott Aero Science engineers began with various tubing shapes first in CFdesign programs to identify shapes before producing prototypes that would then be validated in the wind tunnel. Over 100 hours of wind tunnel validation time was invested solely in the F01 project using Drag2Zero facilities in Mercedes-Benz Grand Prix Wind Tunnel. Starting with raw tubes, shapes were identified and built into complete test mules, and then analyzed against current competitor designs. Over 60 tube shapes were tested in order to identify the optimum “cut ratio”. The engineers selected tube shapes that are wider than normal NACA aero tubes. They were designed with a “leading edge” and a ratio of height to width that complies with UCI regulations, while still maintaining the lowest air disturbance vis-àvis both individual tubes and the overall frame structure. The ratios of the aggregate tubes are between 6:1 and 12:1 resulting in a 9:1 average ratio, well within the UCI limits and actually going the opposite direction in relation to other manufacturers in this regard. The result is a virtual tube shape, a tube that is not NACA shaped but a truncated cross section, which acts in the same way. Each and every tube in the frameset is analyzed for cut position along the “chord”, or length of the tube profile. Most tubes are cut retaining between 25-35% of the overall chord length. This science of tube shape is a contrast to the Kamm tail designs that emerged 80 years ago in the auto industry in that we use the leading edge of the tube rather than simply cutting the trailing edge like some competitors practice.

Here's another site discussing the same shape. https://www.trekbikes.com/us/en_US/inside_trek/kammtail_virtual_foil/

  • $\begingroup$ While the idea of using bike profiles is very good, the Kamm tail has to meet the 3:1 length to width ratio of the UCI. Less truncation will lead to even lower drag. $\endgroup$ Jan 4, 2019 at 18:13
  • $\begingroup$ 30 kph = 18mph, so it seems fitting. "round upright bar" sounds like a bike vertical bar, as does 40mm diameter, about 1.6". Kamm tail may allow enough drag reduction while being truncated could help on overall weight. $\endgroup$
    – CrossRoads
    Jan 4, 2019 at 18:21
  • $\begingroup$ Yes, truncation is a tradeoff between more separation and more wetted surface area. I would expect that some truncation is beneficial and will lead to the overall optimum. But not a 3:1, more a 5:1 ratio - however, that is just a guess. $\endgroup$ Jan 4, 2019 at 19:27
  • $\begingroup$ Hambini roasts the kamm tail virtual foil and explains why, from a cfd and engineering perspective, that it is simply not as aero as a full airfoil. youtu.be/QqX3juRttP4 I always am skeptical of the self-reported research from bike manufacturers, especially when they don’t share their raw data and testing methods with the public. $\endgroup$
    – Chris
    Aug 23, 2022 at 5:06

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