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 said:who is advising to still absolutely not choose for B?
haruspex said: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.
haruspex said: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 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.boneh3ad said: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 It is not peer-reviewed, and in the past, has been known to publish junk science like 9/11 trutherism.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.
rcgldr said: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
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.rcgldr said: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 said: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.
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 said: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.
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 said: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.
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 said: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.
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.rcgldr said: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.rcgldr said: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.
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.Ekooing said:The middle rider riders in a bubble of undisturbed air
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.haruspex said: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 said: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.
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).Ekooing said:If the question is "is having a rider in front of you or behind you more advantageous",
Only if the theory being applied is somewhat rudimentary.Ekooing said:what I am saying is true in a completely theoretical world,
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.haruspex said: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).
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... :)haruspex said:Only if the theory being applied is somewhat rudimentary.
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.Ekooing said: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.
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 said: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 said: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.
No, you are confusing "physics" with "a crude approximation to the physics".Ekooing said:Whether you have one or two in front makes no difference from a physics standpoint
Can you help me out here @boneh3ad? I'm running out of ways to explain this...rcgldr said: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
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.
Physics is ripe with assumptions. If not, you'd never be able to solve any politics equation because you otherwise have to account for literally millions of variables. This is not a "crude approximation of physics", but is actually how physics works. You can nitpick every detail about what I say, or you can realize that when solving physics questions, you must make certain assumptions if you ever want to get an answer...haruspex said: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.
Well, I'll try to explain it...rcgldr said: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
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.
We as scientists use assumptions all the time in the hard sciences. i.e.:Ekooing said:Physics is ripe with assumptions. If not, you'd never be able to solve any politics equation because you otherwise have to account for literally millions of variables. This is not a "crude approximation of physics", but is actually how physics works. You can nitpick every detail about what I say, or you can realize that when solving physics questions, you must make certain assumptions if you ever want to get an answer...
The distinction I am making is between physics, in the sense of physical processes, laws of physics, etc., and the art of applying a convenient subset so as to extract roughly correct results for real world problems. It is not the physics that is rife (not "ripe") with assumptions, but the application of our knowledge thereof.Ekooing said:Physics is ripe with assumptions.
Had the question specified a large group of riders and compared front, middle and back there would have been no issue. But with just three it would seem that the approximation you favour produces the wrong answer, so is by definition a too crude approximation to the actual physics.Ekooing said:This is not a "crude approximation of physics",
The question was asked in a physics forum. It had a diagram and question that looked like it could have been pulled right from a high school physics test. If it was, I provided the answer that would be given in the answer key to that question. If you don't like the answer, that's fine. But questioning the physics of why that is the right answer is ridiculous. And attacking me for overlooking a typo just makes you look desperate (yes, I know it's rife, but its close enough to ripe in my phone, it thought I meant ripe. If you keep an eye out for every time I use that phrase, you might catch my phone corrective correcting it to ride, rope, type, etc.)haruspex said:The distinction I am making is between physics, in the sense of physical processes, laws of physics, etc., and the art of applying a convenient subset so as to extract roughly correct results for real world problems. It is not the physics that is rife (not "ripe") with assumptions, but the application of our knowledge thereof.
Had the question specified a large group of riders and compared front, middle and back there would have been no issue. But with just three it would seem that the approximation you favour produces the wrong answer, so is by definition a too crude approximation to the actual physics.
Ut oh @haruspex, I added a superfluous word into that last message. Better read it fast and find it so you can be the first to point it out...Ekooing said:The question was asked in a physics forum. It had a diagram and question that looked like it could have been pulled right from a high school physics test. If it was, I provided the answer that would be given in the answer key to that question. If you don't like the answer, that's fine. But questioning the physics of why that is the right answer is ridiculous. And attacking me for overlooking a typo just makes you look desperate (yes, I know it's rife, but its close enough to ripe in my phone, it thought I meant ripe. If you keep an eye out for every time I use that phrase, you might catch my phone corrective correcting it to ride, rope, type, etc.)
Had he said, I'm a cyclist and about to compete in the Tour de France and I would like to know exactly where I should be positioned in a group of people riding the mountainous region after I ate a bowl of spaghetti the night before and a storm system had moved into the region dropping the barometric pressure by 27 millibars, my answer would have been different. I'm sorry if that offends you.
One more thing - here's another way to think about it. What if the cyclists were riding at 20mph with a 40mpg wind at their back. Would you expect everyone to "draft" backwards there the rear rider is peddling the hardest because they are not getting as much assistance from the wake turbulence in front of the front rider (since the net wind velocity is 20mph pushing at their back, which would result in a wake turbulence in front of the riders that would be creating a low pressure that would pull them forward)? No, everyone would spread out so that they all get the wind at their back because that force is much greater than the minor assistance they would get from the low pressure caused by the turbulence in front of them.rcgldr said: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
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.
Just one last thing. I want to tell you a story about a time my dad and I got into an argument (God rest his soul) during the summer between by freshman and sophomore year of college. That was the only summer I went back home, and he got sick shortly thereafter, so this was pretty much my last normal summer with him. And with me being in school to be a Chemical Engineer, and him a Civil Engineer, we had a mutual respect for one another's opinion.haruspex said:The distinction I am making is between physics, in the sense of physical processes, laws of physics, etc., and the art of applying a convenient subset so as to extract roughly correct results for real world problems. It is not the physics that is rife (not "ripe") with assumptions, but the application of our knowledge thereof.
Had the question specified a large group of riders and compared front, middle and back there would have been no issue. But with just three it would seem that the approximation you favour produces the wrong answer, so is by definition a too crude approximation to the actual physics.
Sorry, that should be Plays With Squirrels.Ekooing said:Just one last thing. I want to tell you a story about a time my dad and I got into an argument (God rest his soul) during the summer between by freshman and sophomore year of college. That was the only summer I went back home, and he got sick shortly thereafter, so this was pretty much my last normal summer with him. And with me being in school to be a Chemical Engineer, and him a Civil Engineer, we had a mutual respect for one another's opinion.
He had purchased a deer slayer (or dear hunter, or something like that) .44 cal hunting rifle. It was basically a hunting rifle that shot .44 magnum pistol rounds. He was very proud of it and showing it off to me when he got it before we went to the shooting range to try it out. He shot it once or twice, and looked at me with a puzzled look and said "There's something wrong with this gun. I think the spring that absorbs the shock is set to tight." That didn't sound right to me, so I got behind it, took one shot, stood up, handed it back to him, and said "you're shooting the wrong, or bad ammunition". He immediately went into a tirade about how ridiculous that was, and that he had just bought it, and it couldn't be bad! We argued for about 5 minutes about this until I finally looked him in the eye and said, "Dad, if you could adjust a spring in a gun so you would feel more or less kick, why wouldn't marine snipers to that with their .50 cal sniper rifles that kick like a mule?" He looked at me with a dumbfounded look and stormed off muttering under his breath.
Two days later, he walked into my room with two boxes of ammunition. He held up a box of .44 cal cartridges (I almost called them bullets, but I figured you might call me out on that) and said "I accidentally bought these when...", he then held up his other hand with a box of .44 MAGNUM cartridges and stated, "I should have been using these". I was lying on my bed, my body facing away from him, but I was looking over my shoulder at him while he spoke, and when he was done I simply lifted my thumb up. He then said "I still think there's something wrong with that damn spring..." as he walked away. I just smiled and shook my head.
We had a similar argument when I tried to explain to him that table salt (NaCl) dissociates to Na+ and Cl- when dissolved in water. He died still believing that they floated around as little NaCl molecules in the water, so small you couldn't see them, but still together as a molecule. And he died around 8 years ago, so even the internet couldn't convince him despite overwhelming evidence (go figure).
So that's basically what I'm doing here. I'm shaking my head, smiling, and walking away. Bash me or the basic physics all you'd like. If anyone else has any questions for me, feel free to ask, but I'm not going to get into a "dad conversation" with you. For me at least, those conversations died with him.
I wish you luck on your quest to find the precise location that receives the most benefit for every possible eventuality. When you go crazy trying to do so and change your name to "Plays Worth Squirrels", grow a long beard you keep an open lollipop in, and start writing your life's memoirs (bonus points for those who catch the "Boy Meets World" episode - what can I say, I had a crush on Topanga), don't come crying to me... :)