# Aerodynamics of two objects closely following each other

On bicycles.se a question came up about whether one cyclist drafting another causes the lead cyclist to be slowed down. A contributor suggested that the opposite might be the case, that the leading cyclist would be 'helped' too. Clearly, in the real world of cycling there are winds, potholes, traffic and other variables, plus the lead cyclist would not necessarily notice a small bit of extra help. Therefore 'probably not' is not the answer I am looking for, a bit of theory would help.

Another 'drafting situation' happened at Monza today in the qualifying for the F1. The Ferrari team had one of their cars give the other an aerodynamic tow along one of the straights, this helped their number 1 driver get to 4th on the grid, a position he would not necessarily have achieved otherwise, in a race where fractions of a second do matter. If you can better visualize F1 cars than bicycles, then today at Monza is another situation where drafting went on. We know it helps the guy behind, but does it also help the guy up front?

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The effect that I think you are referring to when you say "help the guy up front", is one of a bow wave (or bow shock for very fast moving objects). You can see these types of waves at work on the bows of boats and ships, and they can indeed effect upstream objects. However, for something like a car or bicycle in air, this phenomenon will have an insignificant effect on other such objects. Moreover, in these examples the chasing object is moving into fully turbulent air which will have a dissipative effect on such waves and could even prevent their production altogether. – Killercam Sep 12 '11 at 17:16
I think the question isn't totally clearly written - the idea is: in an ideal case, what is the effect of the object behind on the object in front, and are there notable dependencies on variables like shape, speed, turbulence? – Jefromi Sep 13 '11 at 16:07
I think Camus hinted at what I was looking for, at modest speeds, in air, does an object behind another object help to increase the speed of the object in front? I think you do get 'bow waves' with big trucks on the road, if one of them follows another immediately behind, will the truck in front go quicker/use less fuel? – ʍǝɥʇɐɯ Sep 13 '11 at 16:16
The aerodynamics of F1 is a lot more complicated than bicycles: part of the limits on the straight-line speed is by available friction between the tyres and the road, which is effected by the downforce generated by the car body and the rear wing. Small changes in the air flow around the rear wing can lead to large effects (think the McLaren F-duct of yesteryear). So I am not so sure that the "observed" effect on an F1 circuit can be "intuitively explained" without referring to some wind-tunnel tests. – Willie Wong Sep 15 '11 at 13:12

I know this is an old thread. It was suggested that I post my answer to this same question from bicycles stackexchange. Link: http://bicycles.stackexchange.com/questions/10069/does-drafting-cause-resistance-to-the-lead-rider/32943#32943

I recall this thread, and thought I'd add a link to a post describing an impromptu experiment I conducted this week, which tested the impact on the power demand of a test rider (172cm 60kg female on a track pursuit bike riding at a quasi-steady state velocity on an indoor wooden velodrome) of another rider (185cm 80kg male on mass start track bike riding in close proximity), and to compare this with the test rider's solo ride power demand.

The tests examined the following locations of the other rider relative to the test rider:

• immediately in front of the test rider
• riding next to the test rider (on their outside)
• immediately behind the test rider
• completely away from the test rider and not riding on the track (to provide data on the solo power demand for the test rider).

I use specialist technology to assess rider aerodynamics in real time and had the chance to perform this experiment at an indoor velodrome (Dunc Gray Velodrome, Sydney), so that we could at least conduct such an experiment in well controlled, no wind, low yaw angle conditions.

Test runs were repeated for validation and confirmation of results. The testing protocols and analysis of data provide values for the apparent CdA (coefficient of drag x frontal area, units: m^2) value for each of the test conditions. I then use the apparent CdA data to show the power demand for the test rider to maintain a 40km/h average speed.

This is the link to my write up, which includes links to other experiments and published science on the topic.

Here are the summary of the data in chart and table form, which show the power required for the test rider to maintain 40km/h while riding solo, and with the other rider in various relative positions:

In summary, compared with the power required (195W) for her to maintain 40km/h (lap average speed) on the velodrome:

Drafting immediately behind the other rider gives massive benefit (-76W, -39%). No surprises there.

Having a rider immediately behind (~1/2 wheel gap) provided ~ -7W (-3%) benefit for the lead rider.

Having a rider ride right next to her (~0.8m - 1.0m lateral gap between wheels) created an additional power demand of ~ +10W (+5%).

The result of a 7W (3%) benefit to the lead rider of having a rider immediately behind is in line with previous experimental results and published studies. So while the effect is small, and would be difficult to feel while riding, it is a real effect, at least in low wind conditions.

The side by side ride result showing an additional power demand of 10W (5%) in low yaw conditions is more novel, and has interesting implications for team formation events (e.g. team pursuit and team time trial) and rider changeovers.

Of course different rider morphologies, individual aerodynamic properties, riding alignment configurations and wind conditions will yield different results to this impromptu experiment, but I thought it interesting none the less.

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According to this Wikipedia article and other on-line sources (search for "nascar drafting"), the effect is noticeable in other auto sport disciplines. The front car does notice reduced draft, and it's enough to make two cars close together go faster than one car alone:

On the faster speedways and superspeedways used by NASCAR, ARCA, and at one time the IROC series, two or more vehicles can race faster when lined up front-to-rear than a single car can race alone. The low-pressure wake behind a group's leading car reduces the aerodynamic resistance on the front of the trailing car allowing the second car to pull closer. As the second car nears the first it pushes high-pressure air forward so less fast-moving air hits the lead car's spoiler. The result is less drag for both cars, allowing faster speeds.

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This is all about drag. The current answer by xpda is the correct idea, but I thought it might be worth going into a little more detail, to explain exactly why there is "no suction to speak of pulling back on it" (in fact, I wouldn't say there is "no suction"...rather, "less suction" would be more apt).

Drag results from a difference in pressure between the regions of air in front and behind the moving object in question. As air hits a single cyclist (let's say a female), it stagnates (slows down, resulting in high pressure) and moves around her. At real-world velocities and scales (where the Reynolds number is many orders of magnitudes greater than unity), the air is travelling too fast to remain attached over the cyclist's non-streamlined body. The air on each side is therefore not able to "meet-up" again at the trailing edge of the cyclist, as would be the case on a more streamlined object like an airfoil. Instead, the air on each side separates, forming shear layers (narrow streams of high-gradient velocity) downstream either side of the cyclist. Immediately after separation, these are separate from one another, but not far downstream they begin to interact (due to opposite-signed vorticity drawing them together). This results in a "wake" region behind the cyclist, where the flow is turbulent, eddies are plentiful, and the pressure is low.

When a second cyclist (let's say a male) is placed behind the first, the wake is affected. The presence of the new cyclist disrupts the interaction of the shear layers. A small amount of air will be drawn inward to form a mini-wake between the two cyclists, but the majority will continue to travel past the second cyclist (and may even re-attach to him before separating again), before interacting and forming a wake behind him. It is clear then, that the end result is mutually beneficial for both: the front cyclist has an unchanged high pressure region in front of her, but a "less negative" low pressure region behind her; the second cyclist has a far lower pressure region in front of him, but an (essentially) unchanged pressure region behind him. The difference in pressure between front and rear for each cyclist is therefore significantly lower for both. They both experience a lower drag than they would alone, and are more efficient together than the sum of their parts! Note the true picture has many more three-dimensional and transient wake effects in play (many are still yet to be fully understood and much research is going into this as we speak!), but the general idea holds.

However, the reduction in drag for the lead cyclist is likely to be less than that experienced by the rear cyclist. The lead cyclist still has unchanged stagnation pressure to deal with - which is a pressure coefficient of, say, around +0.5 (averaged over her front body). The pressure coefficient acting on the rear, however, rarely approaches negative pressures of that magnitude - it might be somewhere around -0.2 (these are all very rough estimates, but I feel the point is made better with numbers involved). With the cyclist behind her, that may rise to around -0.1. So the lead cyclist will be experiencing a pressure difference of around 0.6, as opposed to 0.7 normally. The second cyclist however, will have that stagnation pressure in front of him cut significantly from +0.5 to around, say, +0.1. Let's assume the pressure behind him is the same as if he were alone - around -0.2. The second cyclist is therefore now experiencing a pressure difference of only 0.3 - around half the pressure difference (aka half the drag!) of the lead cyclist! This rough calculation (I've simplified things significantly to get the point across) shows that it still pays to be the second cyclist!

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Following closely would speed up both vehicles in certain cases. Consider two cylinders following each other, end to end, at 100 mph, 1000 feet apart. Each cylinder would have a lot of air resistance.

Now consider the cylinders following one another at 1mm separation. The wind resistance will be less for the second cylinder because it's not getting hit in the face with all the wind. There will be less resistance for the lead cylinder because there is no suction to speak of pulling back on it. So the two cylinders are more efficient when they're 1mm apart.

The same thing would apply to cars, depending on shape, separation, and speed.

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