Defining which cyclist profits the most from slipstream

[boneh3ad]

Let me first point out that I am not satisfied by any of the links posted in this thread. Neither of the two most relevant ones (the HPCWire link and the Bicycling one) cite their sources (a DOI link to the referenced papers would be nice) and pop-sci interpretations of fluid dynamic phenomena are notoriously terrible, even when reading straight off the abstract or conclusions of an actual research paper.

My very first inclination when reading the prompt at the beginning of the thread was that the middle rider would get the most benefit, and the answer that has been closest to how I would have explained that so far was given by @Ekooing. The front rider has to do the work of deflecting the oncoming air and the third rider has to deal with the turbulent wake, while the middle rider gets to exist in a bubble between the two that will largely consist of air moving an pretty close to the same average speed as the group.

If you read through the earlier responses in the thread you will see that neither the theory nor practice support the view that the middle of a long line is the optimum position.

So, according to what I have typed above, I would argue that yes, theory does support the view that the middle rider gets the most benefit in the short line depicted in the problem. In a long line, the system will likely be more complicated and I'd be surprised if it was exactly in the middle. In this regard, I especially doubt that earlier bicycling.com link that states that the final rider gets the most benefit in groups of up to 5. This does not pass the smell test for a fluid mechanician, and I suspect that statement stems from a misreading of the source material by the writer of that article. However, it did not cite its sources so I cannot confirm.

The "problem" with this problem is that there is no indication as to what speed the cyclists are travelling. All we know is that there is a crosswind of some sort. In the diagram of riders and wind, is the absolute velocity of the crosswind represented, or the airspeed that the riders experience?

I disagree that this is a problem. As is common when drawing out fluids problems, if you simply assume the problem was drawn in the frame of reference of the riders, then the figure simply shows that the combination of headwind and crosswind produces a resultant wind in the same direction as the riders' formation. That's a really simple assumption and one that is common enough in fluids that it is entirely justified, in my opinion. I'd also argue that the actual velocity doesn't really matter much, because any reasonable cycling situation is not going to be in the realm of Stokes flow ($Re\leq 1$) and isn't going to be occurring at extremely high $Re$ either. In the middle of those two, the qualitative principles remain unchanged.

 

[Physicsterian]

Thanks a lot for your views and the nice explanations @256bits , @Ekooing and @boneh3ad

Tomorrow, I will read through the info provided with the link and try to gain some more knowledge on terms like "eddies" and "stokes flow and try to link it to answering my question, and come back it it here.

 

[Ekooing]

Let me first point out that I am not satisfied by any of the links posted in this thread. Neither of the two most relevant ones (the HPCWire link and the Bicycling one) cite their sources (a DOI link to the referenced papers would be nice) and pop-sci interpretations of fluid dynamic phenomena are notoriously terrible, even when reading straight off the abstract or conclusions of an actual research paper.

My very first inclination when reading the prompt at the beginning of the thread was that the middle rider would get the most benefit, and the answer that has been closest to how I would have explained that so far was given by @Ekooing. The front rider has to do the work of deflecting the oncoming air and the third rider has to deal with the turbulent wake, while the middle rider gets to exist in a bubble between the two that will largely consist of air moving an pretty close to the same average speed as the group.
So, according to what I have typed above, I would argue that yes, theory does support the view that the middle rider gets the most benefit in the short line depicted in the problem. In a long line, the system will likely be more complicated and I'd be surprised if it was exactly in the middle. In this regard, I especially doubt that earlier bicycling.com link that states that the final rider gets the most benefit in groups of up to 5. This does not pass the smell test for a fluid mechanician, and I suspect that statement stems from a misreading of the source material by the writer of that article. However, it did not cite its sources so I cannot confirm.
I disagree that this is a problem. As is common when drawing out fluids problems, if you simply assume the problem was drawn in the frame of reference of the riders, then the figure simply shows that the combination of headwind and crosswind produces a resultant wind in the same direction as the riders' formation. That's a really simple assumption and one that is common enough in fluids that it is entirely justified, in my opinion. I'd also argue that the actual velocity doesn't really matter much, because any reasonable cycling situation is not going to be in the realm of Stokes flow ($Re\leq 1$) and isn't going to be occurring at extremely high $Re$ either. In the middle of those two, the qualitative principles remain unchanged.

Thank you for commenting here @boneh3ad and confirming my ascertain. As the forum's scientific adviser, I figure everyone will respect your opinion. I tend not to delve too much into my background when I'm answering questions such as these online as I don't want to sound like I'm bragging. However, I have realized that in this forum, people want to know that the information you provide is coming from a reliable source, so I figured I'd let you know my background for future reference. As stated before, I received my degree in chemical engineering, and from there I worked in pump design (all fluid mechanics), then worked in the aerodynamics and materials science departments for NASA for several years. Lastly, I have quite a bit of experience in the oil and gas industry. I am also the fluid mechanics consultant for a start up company designing a chemical sniffer system detecting chemical components in the ppb range.

Again, I provide this information to you not to show off, but simply to provide you with my background so you know where the information I post comes from.

 

[haruspex]

a DOI link to the referenced papers would be nice

The bicycling.com reference quotes Bert Blocken. Following that leads to https://www.europhysicsnews.org/articles/epn/pdf/2013/01/epn2013-44-1p20.pdf.

 

[Physicsterian]

Thanks a lot for your views and the nice explanations @256bits , @Ekooing and @boneh3ad

Tomorrow, I will read through the info provided with the link and try to gain some more knowledge on terms like "eddies" and "stokes flow and try to link it to answering my question, and come back it it here.

I went through the info about the eddies, nice to have learned about that as well.
Its a difficult decision, considering all the info, but I think I will go for B as my final answer for the particular echelon setting with all the info I have been able to gather till now. Any of you, who is advising to still absolutely not choose for B?

 

[haruspex]

who is advising to still absolutely not choose for B?

Bert Blocken for one. See figure 5 right at the end of the paper I linked in post #34. It shows quite clearly that in a group of four the fourth rider suffers the least drag. Despite @boneh3ad 's experience-based intuition, I find Blocken's research the more persuasive.

 

[Physicsterian]

Bert Blocken for one. See figure 5 right at the end of the paper I linked in post #34. It shows quite clearly that in a group of four the fourth rider suffers the least drag. Despite @boneh3ad 's experience-based intuition, I find Blocken's research the more persuasive.

I get the point, however, I have some doubts about whether or not those findings also applies for the echelon arrangements depicted in my illustration. Since I remind from the other link (https://www.hpcwire.com/2018/07/05/...veals-best-position-in-a-peloton-of-cyclists/) about Blocken's research, a v-formation peleton was used in that research (at least, that is the only picture I have been able to get access to). So do they refer to the row number in which the cyclist is settled with "cyclist". For instance, does "5 cyclists" mean that there is a total amount of six cyclists straight behind each other, or that there are six rows, in which "cyclists position in group: 5" means that the cyclist is settled in row number 5. Reading the PDF article, I would certainly say that they refer to just a straight row, but ain't sure about it, because of the peleton picture on the other website. I'm making this point, as it seems to me that an extra amount of riders (in reference to an echelon) at the "right side" of a v-formation peleton could have a different effect on the drag.

 

[boneh3ad]

The bicycling.com reference quotes Bert Blocken. Following that leads to https://www.europhysicsnews.org/articles/epn/pdf/2013/01/epn2013-44-1p20.pdf.

I appreciate the link, but I have some reservations about Europhysics News. It is not peer-reviewed, and in the past, has been known to publish junk science like 9/11 trutherism.

At any rate, the article does seem to indicate that, for small groups of riders, the rearmost rider gets the greatest benefit, but its explanation for why is extremely vague and would not stand up to peer review in a real journal (or at least not if I was reviewing it). It may well be true, but I find their evidence lacking. I've tried following their citations to see where that research was originally published, and I can't seem to find those claims in any of the citations so far, so my suspicion is that that portion of the article was original at the time and had not previously been published. Notably, the material regarding two cyclists was eventually published by the same authors (DOI: 10.1016/j.compfluid.2012.11.012) but it seems the data about multiple cyclists were never published. I have no idea if that was because they found issues with it or some other reason.

The same author also seems to make an argument that his CFD is more accurate than wind tunnel testing, despite using RANS modeling, which is notoriously inaccurate in predicting the structure of a rather important part of this problem: the wake. This also plays into the vague explanation the authors gave that I mentioned before, where they made some argument about a wider wake (that seemingly would have been just as applicable to the long chains of riders).

At any rate, I don't really trust that portion of the research, as it was never peer-reviewed and does not have sufficient supporting discussion to satisfy me. It may still be correct, of course, but based on this article, I would not treat it as gospel. My intuition still tells me that the middle rider should have the biggest advantage in most situations, but I suspect there will always be room for some doubt there unless someone definitively proves it.

 

[Ekooing]

I appreciate the link, but I have some reservations about Europhysics News. It is not peer-reviewed, and in the past, has been known to publish junk science like 9/11 trutherism.

At any rate, the article does seem to indicate that, for small groups of riders, the rearmost rider gets the greatest benefit, but its explanation for why is extremely vague and would not stand up to peer review in a real journal (or at least not if I was reviewing it). It may well be true, but I find their evidence lacking. I've tried following their citations to see where that research was originally published, and I can't seem to find those claims in any of the citations so far, so my suspicion is that that portion of the article was original at the time and had not previously been published. Notably, the material regarding two cyclists was eventually published by the same authors (DOI: 10.1016/j.compfluid.2012.11.012) but it seems the data about multiple cyclists was never published. I have no idea if that was because they found issues with it or some other reason.

The same author also seems makes arguments about how his CFD is more accurate than wind tunnel testing, despite using RANS modeling, which is notoriously inaccurate in predicting the structure of a rather important part of this problem: the wake. This also plays into the vague explanation the authors gave that I mentioned before, where they made some argument about a wider wake (that seemingly would have been just as applicable to the long chains of riders).

At any rate, I don't really trust that portion of the research, as it was never peer-reviewed and does not have sufficient supporting discussion to satisfy me. It may still be correct, of course, but based on this article, I would not treat it as gospel. My intuition still tells me that the middle rider should have the biggest advantage in most situations, but I suspect there will always be room for some doubt there unless someone definitively proves it.

I completely agree @boneh3ad. I have performed many wind tunnel tests myself, and have had many cfd models made while I was working for NASA and redesigning the external tank foam protrusions after the Columbia accident. Granted, none of them were of cyclists, but still, rarely did the experimental data match the wind tunnel results especially in the realm of the wake. Modeling was pretty good at predicting the wind at the point of contact of what we were testing, but not very good at predicting downstream of a protrusion. This lack of accurate wake modeling might make someone think the last position would be most advantageous if they are basing their findings on faulty modeling.

 

[rcgldr]

Link to yet another article. At least it states some numbers for reduction in drag: for the lead rider it is relatively small at 2% to 3%, versus the trailing riders that experience a reduction of 27% to 44% or so.

https://cyclingtips.com/2017/10/much-benefit-really-get-drafting

 

[boneh3ad]

Link to yet another article. At least it states some numbers for reduction in drag: for the lead rider it is relatively small at 2% to 3%, versus the trailing riders that experience a reduction of 27% to 44% or so.

https://cyclingtips.com/2017/10/much-benefit-really-get-drafting

Interesting that this article cites the Blocken article that I posted but makes claims about the third and fourth riders when the article only addresses two. In fact, the cited article specifically mentions that larger groups will need to be done in future studies.

 

[rcgldr]

I think the main issue is that the 1st rider only gets a 2% to 3% gain from the 2nd rider. I would assume the 2nd rider would get significantly less gain from a 3rd rider, but I'm not sure how much gain a 3rd rider would get from drafting behind both a 1st and 2nd rider. My impression is that for a group of 3 riders, the 3rd rider gets the most benefit of the draft, as the wake trailing the 2nd rider would be moving a bit faster (wrt pavement) than the wake from the 1st rider.

 

[Ekooing]

I think the main issue is that the 1st rider only gets a 2% to 3% gain from the 2nd rider. I would assume the 2nd rider would get significantly less gain from a 3rd rider, but I'm not sure how much gain a 3rd rider would get from drafting behind both a 1st and 2nd rider. My impression is that for a group of 3 riders, the 3rd rider gets the most benefit of the draft, as the wake trailing the 2nd rider would be moving a bit faster (wrt pavement) than the wake from the 1st rider.

The first and second rider wouldn't have a "wake". The converging air streams from either side of the body wouldn't come back together creating the vortices in the wake that cause the drag. The wake would only form behind the third rider (theoretically). So the first first gets a couple of percent benefit from the second rider, the third rider gets the big benefit of not having to push the air out of the way like the first rider but loses a little because of the wake drag, and the middle rider gets both benefits. So if we say pushing the air out of the way accounts for 80% of the energy input, and the wake resistance accounts for 2% (the other 18% goes to gravity, tire resistance, etc.), then the first rider would expend 98%, the third rider 20%, and the middle rider 18% (just from gravity, tie resistance, etc). Keep in mind these are not accurate numbers, and only theoretical numbers, not actual. Like the middle rider would never have his wind resistance lowered to 0%, but this is just an example to explain the theory.

 

[Ekooing]

I think the main issue is that the 1st rider only gets a 2% to 3% gain from the 2nd rider. I would assume the 2nd rider would get significantly less gain from a 3rd rider, but I'm not sure how much gain a 3rd rider would get from drafting behind both a 1st and 2nd rider. My impression is that for a group of 3 riders, the 3rd rider gets the most benefit of the draft, as the wake trailing the 2nd rider would be moving a bit faster (wrt pavement) than the wake from the 1st rider.

The three riders (theoretically) form a bubble that encompasses all the riders. So the first rider gets the wind resistance, the last gets the wake resistance, arms the middle doesn't get either since all three are moving together as one unit.

 

[rcgldr]

The three riders (theoretically) form a bubble that encompasses all the riders. So the first rider gets the wind resistance, the last gets the wake resistance, arms the middle doesn't get either since all three are moving together as one unit.

Since the 1st rider only gets a 2% to 3% decrease in resistance by having a 2nd rider behind him, it would seem that the 1st rider is getting most of or nearly all of the wake resistance in addition to the wind resistance.

 

[Ekooing]

Since the 1st rider only gets a 2% to 3% decrease in resistance by having a 2nd rider behind him, it would seem that the 1st rider is getting most of or nearly all of the wake resistance in addition to the wind resistance.

No - the wake resistance only counts for 2%, remember? So by not having a wake, he is saving that 2%. The last rider doesn't get the frontal wind resistance, but does experience the wake, so he saves 80%. The middle rider doesn't feel either, so he gets 82% benefit.

 

[rcgldr]

No - the wake resistance only counts for 2%, remember? So by not having a wake, he is saving that 2%. The last rider doesn't get the frontal wind resistance, but does experience the wake, so he saves 80%. The middle rider doesn't feel either, so he gets 82% benefit.

For common objects, most of the aerodynamic drag is due to wake resistance. At the front of an object, the air separates and flows around an object, but at the back of an object, the object leaves what would otherwise be a moving void behind it, and the air responds by accelerating in the same direction as the object (wrt the air). This is why low drag vehicles use a long tapered tail (variations of tear drop shapes are common), to gradually introduce that "void" so that the air can accelerate inwards to fill in that "void" as opposed to accelerating forwards.

 

[Ekooing]

For common objects, most of the aerodynamic drag is due to wake resistance. At the front of an object, the air separates and flows around an object, but at the back of an object, the object leaves what would otherwise be a moving void behind it, and the air responds by accelerating in the same direction as the object (wrt the air). This is why low drag vehicles use a long tapered tail (variations of tear drop shapes are common), to gradually introduce that "void" so that the air can accelerate inwards to fill in that "void" as opposed to accelerating forwards.

To say that "for common objects, most of the aerodynamic drag is due to wake resistance" is only correct when considering "drag". If you are considering all "resistance", drag from wake resistance is negligible as compared to the frontal air resistance experienced by the front rider biking into the wind with nobody in front of them. This force is MUCH greater of a resistance than any resistance caused by wake drag.

 

[Ekooing]

For common objects, most of the aerodynamic drag is due to wake resistance. At the front of an object, the air separates and flows around an object, but at the back of an object, the object leaves what would otherwise be a moving void behind it, and the air responds by accelerating in the same direction as the object (wrt the air). This is why low drag vehicles use a long tapered tail (variations of tear drop shapes are common), to gradually introduce that "void" so that the air can accelerate inwards to fill in that "void" as opposed to accelerating forwards.

There are two forces we are discussing. Frontal wind resistance (experienced by the front rider), and wake turbulence drag (experienced by the rear rider). The middle rider riders in a bubble of undisturbed air with neither force (theoretically - in actuality, the do experience a little of both, but less). Therefore, the middle rider gets the most benefit. The air resistance experienced but the front rider is much greater than the drag force experienced by the rear rider. This is explained in the latest reference article that was talked about a few posts ago.

 

[haruspex]

The middle rider riders in a bubble of undisturbed air

That sounds like some idealised structure which cannot be true in practice. A single rider in front of me is not going to protect me from the entire frontal resistance. Each additional rider in front is going to help, but with diminishing returns.
The debate is whether the second rider of a pair will gain more from one added in front or one added behind.

 

[Ekooing]

That sounds like some idealised structure which cannot be true in practice. A single rider in front of me is not going to protect me from the entire frontal resistance. Each additional rider in front is going to help, but with diminishing returns.
The debate is whether the second rider of a pair will gain more from one added in front or one added behind.

I understand that @haruspex. That is why I keep making the disclaimer that what I am saying is true in a completely theoretical world, not in the unpredictable real world. However since this is a physics forum, and this was asked as a physics question, answering with theoretical physics is the way in which I answered it. If you want someone to provide you with a real world answer, there are about 8 billion additional questions that we would need to ask in order to account for every single detail, however small. But from a theoretical physics standpoint, the answer is clearly rider "B". That's all I'm saying.

 

[Ekooing]

That sounds like some idealised structure which cannot be true in practice. A single rider in front of me is not going to protect me from the entire frontal resistance. Each additional rider in front is going to help, but with diminishing returns.
The debate is whether the second rider of a pair will gain more from one added in front or one added behind.

If the question is "is having a rider in front of you or behind you more advantageous", the answer is having one in front of you is more advantageous. In a group of three riders, the person in the middle gets the most advantage.

 

[haruspex]

If the question is "is having a rider in front of you or behind you more advantageous",

That is not what I wrote. I wrote that is whether the second of a pair gains more from one more in front (making her the third of three) or one behind (making her the middle of three).

 

[haruspex]

what I am saying is true in a completely theoretical world,

Only if the theory being applied is somewhat rudimentary.

 

[Ekooing]

That is not what I wrote. I wrote that is whether the second of a pair gains more from one more in front (making her the third of three) or one behind (making her the middle of three).

Whether you have one or two in front makes no difference from a physics standpoint because you have to make the assumption that the flow behind the first rider would be sufficiently displaced to account for the second rider, the third rider, fourth rider, etc as the flow would split at the first rider, would continue down the entire length of the line of riders without ever converging behind any rider but the last one. Again, this is all theoretical physics. In real life, the second rider may block the wind for the third rider some because they don't all like up in a completely straight line, and the wind is never constant in direction or velocity. So to say how much benefit you'd get from multiple people in front of you as opposed to one person in real life may be a measurable difference. In the theoretical world though, you get the same benefit if you have one rider in front of you or 100.

 

[Ekooing]

Only if the theory being applied is somewhat rudimentary.

Rudimentary is a relative concept. I have a math and science mind and love physics and chemistry. That along with my degree and work experience make this a rudimentary concept for me, and I truly apologize if I assumed everyone here would know it and didn't explain it properly. I sometimes forget that not everyone has received that training. If you ask me about English or another subject like that, I'm the one with no training. Green Eggs and Ham isn't even rudimentary enough for ne when it comes to that subject... :)

 

[rcgldr]

To say that "for common objects, most of the aerodynamic drag is due to wake resistance" is only correct when considering "drag". If you are considering all "resistance", drag from wake resistance is negligible as compared to the frontal air resistance experienced by the front rider biking into the wind with nobody in front of them. This force is MUCH greater of a resistance than any resistance caused by wake drag.

Maybe there is an issue with terminology here, but take the case of a bus on a highway, the ratio of (pressure at front of bus) / (ambient pressure) is much less than the ratio of (ambient pressure) / (pressure at rear of bus), because at the front of the bus, the air splits up into flows around the bus, but can't accelerate inwards enough at the rear of the bus so that it fills what would otherwise be a void, so most of the drag is due to the forwards acceleration of air behind a bus. Note that there is some inwards acceleration of air at the rear of the bus, but not enough to compensate for the reduction in pressure at the rear of the bus. Again, this is why highly aerodynamic shapes look similar to lengthened tear drops, where most of the reduction in drag is due to the extended tail of the aerodynamic body.

Getting back to the bicycle riders, there is some inwards acceleration of air behind the 1st rider, reducing the size of the wake behind the first rider, and the 2nd rider is not close enough to be fully enclosed by the wake created by the first rider, but does benefit from the reduced 1st rider's wake that the 2nd rider goes through. The 2nd rider's wake should be moving forwards a bit faster than the 1st rider's wake, since the 1st rider's wake is already moving forwards, requiring less acceleration of air for the 2nd rider's wake, and the 2nd rider's wake increases this speed a bit more, but it's a case of diminishing returns. The articles linked to imply that this chained wake effect stops at around the 4th or 5th rider, but don't cite any studies, although I assume they are based on the reported experiences of actual bicycle racers.

For a real world comparison, on a motorcycle following a large truck, the motorcyclist has to be fairly close to the truck to be fully enclosed in the truck's wake, and the truck is much bigger than the motorcycle and rider. This isn't going to happen with bicycle riders since they are the same size, move at slower speeds, and aren't following close enough to fit within the wake of the leading riders.

 

[Ekooing]

Maybe there is an issue with terminology here, but take the case of a bus on a highway, the ratio of (pressure at front of bus) / (ambient pressure) is much less than the ratio of (ambient pressure) / (pressure at rear of bus), because at the front of the bus, the air splits up into flows around the bus, but can't accelerate inwards enough at the rear of the bus so that it fills what would otherwise be a void, so most of the drag is due to the forwards acceleration of air behind a bus. Note that there is some inwards acceleration of air at the rear of the bus, but not enough to compensate for the reduction in pressure at the rear of the bus. Again, this is why highly aerodynamic shapes look similar to lengthened tear drops, where most of the reduction in drag is due to the extended tail of the aerodynamic body.

Getting back to the bicycle riders, there is some inwards acceleration of air behind the 1st rider, reducing the size of the wake behind the first rider, and the 2nd rider is not close enough to be fully enclosed by the wake created by the first rider, but does benefit from the reduced 1st rider's wake that the 2nd rider goes through. The 2nd rider's wake should be moving forwards a bit faster than the 1st rider's wake, since the 1st rider's wake is already moving forwards, requiring less acceleration of air for the 2nd rider's wake, and the 2nd rider's wake increases this speed a bit more, but it's a case of diminishing returns. The articles linked to imply that this chained wake effect stops at around the 4th or 5th rider, but don't cite any studies, although I assume they are based on the reported experiences of actual bicycle racers.

For a real world comparison, on a motorcycle following a large truck, the motorcyclist has to be fairly close to the truck to be fully enclosed in the truck's wake, and the truck is much bigger than the motorcycle and rider. This isn't going to happen with bicycle riders since they are the same size, move at slower speeds, and aren't following close enough to fit within the wake of the leading riders.

If you're taking which requires more force to overcome, the wind resistance from the wind pushing against the front of the speeding bus versus that of the drag created by the turbulent wake, the answer is overwhelmingly the force created by wind resistance at the front of the bus. As for how that relates to cyclists, in the theoretical world, they are the same (large frontal air resistance force, small wake turbulence drag force). Also, in the theoretical world, you only need one cyclist in the front of the line to give the benefit to every rider behind them. In the real world, this is not the case. But like I said, since I was answering a physics question in a physics forum, I did so using fundamental physics theory in my answers.

 

[rcgldr]

If you're taking which requires more force to overcome, the wind resistance from the wind pushing against the front of the speeding bus versus that of the drag created by the turbulent wake, the answer is overwhelmingly the force created by wind resistance at the front of the bus.

Below is a link to one of several articles that explains that the wind flows around a vehicle rather than pushing against a vehicle, but is forced to fill in what would otherwise be a void at the rear, and that most of the drag force is due to what happens behind a vehicle, such as the amount of turbulence.

"The reason keeping flow attachment is so important is that the force created by the vacuum far exceeds that created by frontal pressure ..."

http://www.up22.com/Aerodynamics.htm

Here is a link to an article about bicycle aerodynamics.

"In the following pictures, we can see the flow over the middle of the bike and cyclist in a straight riding condition without side wind, and notice that the flow behind the cyclist is a low kinetic energy flow, because of the turbulent wake. ... This creates the most part of the cyclist’s drag, but in fact, this low kinetic energy bubble can be really beneficial for the riders riding behind"

https://www.simscale.com/blog/2017/07/bike-aerodynamics

I would assume that a bicyclist has a lower coefficient of drag than a bus, but the principle is similar, the frontal pressure is limited by the fact that higher pressure air at the front can "escape" by flowing around the rider to the lower ambient pressure surrounding the rider. The lower pressure at the rear would depend on speed and the effective streamlining of a rider's body, allowing the air to flow inwards versus forwards to fill in what would otherwise be a void behind the rider.

 

[haruspex]

Whether you have one or two in front makes no difference from a physics standpoint

No, you are confusing "physics" with "a crude approximation to the physics".
Let's go back to the original question. It asks which position benefits most, not which benefits most according to some specific and rather artificial model.