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If cycling directly behind a bus that was travelling at 30mph on a flat road on a windless day, how far would the rider have to move away from it to receive zero drafting benefit?

Is the distance-to-benefit relationship linear, or does the benefit decrease more quickly the further away from the bus the rider is?

Is it possible that at certain distances the rider would be worse off, i.e. they would suffer from being in the wake of the bus more than they would if there was no bus at all?

If it makes any difference, assume the bus is 10m long, and the front and rear faces are 2.5m x 2.5m, and the cyclist is average height riding a road bike on the drops.

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    not an answer about the aerodynamics of the question but practically speaking I would be VERY careful about following a bus (or other large vehicles) too closely as a matter of safety – GageMartin Aug 24 '20 at 14:20
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    Sounds like a math story problem. The actual question should be: how long does it take for the rider to pass out due to diesel fume inhalation? – Argenti Apparatus Aug 24 '20 at 15:17
  • @ArgentiApparatus a few countries have started using electric buses (at small scale), so there is a small possibility to follow a bus and not choke to death. – Grigory Rechistov Aug 24 '20 at 16:59
  • Yeah, the faster the bus goes the further back I am, at 30mph I would be probably a bus length away (8-10m), hence wondering how much aero benefit I'm still getting (not that I would likely be able to stay with the bus by that point, but hey). – Wilskt Aug 24 '20 at 18:39
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    And when the bus needs to brake abruptly, you kiss its tail... Ok, not very likely, bus drivers drive very defensively (if they do their job well). But I don't think it's a smart idea to draft any non-cooperating vehicle. – cmaster - reinstate monica Aug 24 '20 at 21:25
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The zero benefit will theoretically only appear in infinity. In practice, it will of-course be non-measurable in a finite distance. The wake of a bluff body (like a bus) will consist of a recirculation zone, where the Reynolds-averaged streamlines are closed and the flow is actually reversed (in the coordinate system fixed with the bus) in some volume, and the rest where the flow is only slower. The benefit will be decreasing the most at the boundary of the recirculation zone. It will be relatively constant within the zone and it will be slowly decreasing in the wake farther behind. The length of the recirculation zone will be comparable to the lateral dimensions of the bus.

I do not have time nor resources for a proper literature review at the moment but I recommend looking at Figures 3 and 4 in Longa et al. JFM 866, pp. 791, https://doi.org/10.1017/jfm.2019.92 that show typical wakes for two lorry-like bodies.

simplified lorry

Ahmed body

(© 2019 Cambridge University Press, CC-BY 4.0)

The figures show that the region of decreased wind velocity can reach far behind the depicted region but is the strongest in a small blue region with dimensions comparable to the lateral dimensions of the vehicle, where the U velocity component is actually reversed. That means that the bus traveling in the still air effectively sucks the particles in that region towards its rear wall. The flow in that region can be complicated, the paper itself is about that (bistability etc.). Be aware that the details strongly depend on the shape of the rear of the body.

For a cyclist we have to consider the dimensions of the cyclist too because the low-momentum region is becoming lower and lower, see Fig. 4a. That means that it is difficult to predict the drag of the cyclist in that complicated region. It would be a difficult simulation. But we can still look where the flow is fast and where it is slow.

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  • A bus traveling at 13 m/s will have a different sized zone than one traveling at 1 m/s but otherwise this is a good short summary. – R. Chung Aug 24 '20 at 18:14
  • @R.Chung No, it wil not, 1 m/s is already well within the Reynolds-number independent regime. It is better to look at it in the wind-tunnel frame of reference. The wake properties of bluff bodies do not significantly change with the wind tunnel flow velocity. One just multiplies the dimensionless flow field with the reference speed. – Vladimir F Aug 24 '20 at 18:33
  • @VladimirF So in this case I would have to be within 2.5m of the bus to get a noticeable decrease in air resistance, no matter the speed? Safety issues certainly come into play then. – Wilskt Aug 24 '20 at 18:44
  • @Wilskt It will be much more for "noticeable effect" but the effect will be decreasing relatively fast in that distance range. And then more slowly. I would have to do some modelling to say more and I am at my holiday, away from the right computers. I might have some paper in my downloaded folder. – Vladimir F Aug 24 '20 at 21:12
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    @R.Chung More or less. Reynolds number independence is the basic assumption of all wind tunnel modelling with scaled models. Without that you would have to measure only full-scale cars, full-scale airplanes, full-scale buildings... Fortunately it is not necessary. Notice that the scale in the figures is dimensionless. – Vladimir F Aug 25 '20 at 19:10
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The distance-to-benefit ratio would not be linear. There is a pocket of still air close to the back of the bus, followed by a very turbulent area farther back where the airflow from each side of the bus rejoins, followed by a less turbulent wake. The buffeting in the turbulent area can be dangerous. You can read about a more extreme case of this in this article about Denise Mueller Koronek's motorpace record attempt.

If you picture a boat with a squared-off stern traveling through the water, you can picture how the water will not immediately fill the void behind the boat. The cyclist is in the equivalent of that void.

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    If you look at the wake of a boat crossing a calm pond, you can see that the water remains disturbed for quite a long time. Likewise, to get "zero benefit" from a passing bus you have to wait a long time. That's even true for a single passing rider: that was alluded to in this bike.SE answer. – R. Chung Aug 24 '20 at 15:46
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The airflow behind a bus is turbulent, so there isn't a simple answer.

You might find this link to be interesting - especially page 13.

https://www.grandmarq.net/blaze/Blaze_Pics/AE%20507%20lect%207%20Aero%20Drag%20of%20Autos.pdf

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    This site discourages answers that are just links, because links rot. Would you please edit your answer to summarize what the presentation says, and how it relates to the question? – rclocher3 Aug 24 '20 at 16:49
  • Turbulence is not a significant obstacle for an answer here. All flow in the atmospheric boundary layer is turbulent. Still, obstacle recirculation zones can be defined, measured and simulated in the Reynolds-averaged sense. – Vladimir F Aug 24 '20 at 17:37

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