Welcome back to Sports & Building Aerodynamics, in the week on cycling aerodynamics. In this module, we're going to focus on two drafting cyclists. Let's start again with the module question. Two cyclists are riding closely behind each other, as shown on the image here. And, of course, it's well-known that the second rider benefits from the slipstream of the first one. But what about the aerodynamic effect of the second one on the first one? Which statement is correct? The second rider provides an aerodynamic benefit for the first rider. The aerodynamic effect on the first rider is zero. Or, the second rider provides an aerodynamic disadvantage for the first rider. Hang on to your answer and we'll come back to this question later on. At the end of this module you will understand the aerodynamic effects in drafting of two cyclists. You will understand the effect of the first rider on the second one, and the effect of the second one on the first one. More information about this study on two drafting cyclists can be found in this article. And at the moment that we launched those results, we also got quite some media attention. Also an additional publication in europhysicsnews was established and it also featured on different websites. This study led to quite some new insights and I would like to share those with you now. First of all, a little bit of literature review. By far, most of the aerodynamic studies in cycling have focused on a single cyclist, an isolated cyclist. But there have also been studies on drafting. But most of these studies focused on the effect of the first one on the second one, so the benefit of the slipstream. This has sometimes been done with field tests, or wind-tunnel measurements, sometimes on real cyclists, sometimes also dummy cyclists. And also CFD simulations have been made for simplified geometries like cylinders to investigate the effect and potentially extrapolate that to cycling aerodynamics. Let's view a few of those results of those studies. This is one of the first ones to say that there is clearly an aerodynamic improvement and it can go up to 38% on the air resistance in coast-down tests. Later on up to 40% reduction was found with both wind-tunnel runs and coast-down tests. Still later, VO2 reduction rates were quantified, also the benefit caused by slipstreaming, and Zdravkovich also found even a maximum drag reduction of 49% in wind-tunnel tests. So clearly, a very big advantage of a second rider to be in the slipstream of the first one. But what about the other way around? What about the effect, or potential effect, of the second one on the first one? Kyle in his early study did not find any effect in coast-down tests. But Olds actually made a very interesting statement in his article, and I would like to focus on this here. He says: 'It has been suggested that riding close behind a leading cyclist will also assist the leading rider in that the low pressure area behind the cyclist will be 'filled up' by the trailing rider. However, he says, both Kyle and McCole failed to find any measurable effect in rolldown experiments or in field VO2 measurements.' So this is a very interesting statement that certainly deserves a closer look. Later on, Iniguez-de-la-Torre and Iniguez did a study of the interference effect, the aerodynamic interference effect of cylinders behind each other, on each other, and they found a 5% drag reduction for the first cylinder. Potentially extrapolating that to cyclist aerodynamics, however, they stated: 'A realistic analysis of the complex geometry of a cyclist would require not 2D, but 3D numerical fluid dynamics simulations.' And this has incited us to embark on such computational tests. So, we looked at three computational geometries: the upright position, two cyclists riding behind each other. Same for the dropped position, same for the time-trial position. And then we focused at different separation distances between the cyclists from one centimeter up to one meter. And here you might wonder, is one centimeter between the tires, is that realistic? Is that not very dangerous for cyclists to ride this way? Well, it is realistic, but often what you see is that cyclists will not ride exactly behind each other, but sometimes also in a staggered position. But then even this one centimeter could be less, because the rear wheel of the first one and first wheel of the second one might be very close to each other. So we put those cyclists, one of them, but then also two of them, and three of them and so on, in a computational domain. A high-quality grid was made, for the two cyclists this led to a grid of 12 million computational cells. We also did grid-convergence analysis. You see other parameters here. We resolved the laminar sublayer, so the viscous part of the boundary layer, in order to be able to predict flow separation to a certain degree of accuracy. Here, you see part of the computational grid on the two cyclists in time-trial position. And of course we modeled the full body of the cyclist, but you only see half here, because I wanted to visualize the mesh in the center plane. So the mesh is actually, as you can imagine, all around the cyclists, but here only shown on the bodies, and in the center plane. Then boundary conditions were imposed, 15 meters per second, and very low turbulence intensity of the approach flow, because we want to simulate cyclists riding in still air. So we did not consider wind, or side wind, or head wind, or tail wind. The computational settings and parameters; the 3D steady RANS equations were used because we got quite some support in using those simulations from the previous validation studies. We used the standard k-epsilon model which performed very well in those validation studies and also low-Reynolds number modeling with the Wolfshtein model. Also Large Eddy Simulations were performed and you see the computational details specified here on this slide. Then let's have a look at some results. First some animations of the flow field around the cyclists. This is, of course, the result of the transient Large Eddy Simulation. You see here the wind speed in kilometers per hour being visualized for the two cyclists in dropped position. And it's here of course very clearly indicated that the second cyclist is in the slipstream of the first one and that the slipstream is also actually a very transient part of the flow field. And also that the slipstream actually increases, even beyond or behind the second one. So if you would put a third rider there, he would have an additional benefit. Then we can look here at the drag reduction that the second cyclist experiences from being in the slipstream of the first one. And you see that those are percentages ranging between, let's say, 12% and 27%. So the benefit is higher when the two cyclists are in the upright positions because then they are actually a larger obstruction to the flow, and it's less when they are both in the aerodynamic position. But now let's see what happens, what is the effect of the second one on the first one. And there, indeed, we find a significant effect. And the effect is actually the largest for the two cyclists in time-trial position. And you can see that for cyclists riding very close to each other, one centimeter here, you see that it amounts to 2.7%. Which is, of course, far less than the benefit of the second one from riding behind the first one, but it is certainly a significant number. You also see one diamond in this figure, and that's the wind-tunnel test. So we also did a wind-tunnel test for the case of the cyclists in the dropped position. And you see that this wind-tunnel test actually shows a very good agreement with the computational simulation. I just want to show you some of these pictures that we took during the wind-tunnel testing. So in this case, we put the first cyclist on the platform and the force balance. We put the second one behind him and we measured the effect, in drag reduction, that the first one would have. And here you see the two cyclists in the test section, again with the first one on the force balance. The second one nicely behind him, in this case with a separation distance of 15 centimeters. And then this was the result of the validation. We can then move on to the flow field analysis. Where again we are going to look at the pressure coefficients from, in this case, the steady RANS simulations. This was the result that we saw in the previous module for the single cyclist. In this case, time-trial position, and then when you put a second cyclist behind him, or behind her, you clearly see that the overpressure in front of the second cyclist starts interacting with the underpressure behind the first cyclist. So these pressure fields start interacting, and because of that, and that you can also see if you look closer to this image, the extent of this low-pressure area behind the first one will decrease. So, not only the area of this low-pressure region, or the volume of this low-pressure region will decrease, but also the numbers, the quantities of pressures in this region. And that is what you can see here. This is the cyclist riding alone in time-trail position. And these are the two cyclists riding nicely behind each other. And you can see here, from the value indicated as minimum pressure on the back, that if you have two cyclists, they both benefit. So the pressure that they have on their back, actually, in both cases, decreases. And the pressure in front, of course, of the second cyclist, decreases even more. So there is a clear benefit. So what is the physical reason for that? Because people might think that it's not possible for a second rider to have an effect on the first one because they are not touching each other. There's nothing between them. Well, actually there is. The air is between them and the air passes on the pressure waves and the pressure field. So what we see here is actually similar to what we saw in week four, on building aerodynamics. There is a very important subsonic upstream disturbance of the flow field. So the flow field in front of the second cyclist is disturbed by this cyclist. And therefore he has an effect on the first one. So air is indeed the medium here that allows this upstream disturbance. And these computational results, but also the validation with the wind-tunnel measurement is actually an interesting confirmation of the very nice and actually very accurate statement by Tim Olds, who said that the low-pressure area behind the cyclist will be filled up by the trailing rider. Because that is indeed what happens. There are, of course, some limitations in this research. We've looked at static cyclist positions, no pedaling, the two cyclists always have the same body shape and size and the same position on the bicycle, and there was no wind. So the conclusion from this study is actually the conclusion that researchers always give to any study, that is that further research is needed. Let's go back to the module question now. And of course the answer now is straightforward. Definitely the second rider provides an aerodynamic benefit for the first rider and it is quite substantial. It goes up to 2.7% in reduction in drag area. So in this module we've learned about the aerodynamic effects in drafting of two cyclists, the effect of the first rider on the second one, and the effect of the second one on the first one. But team time trials are performed with more cyclists, so in the next module we're going to focus on CFD simulations for cyclist groups. Thank you for watching, and we hope to see you again in the next module.