Defining which cyclist profits the most from slipstream

[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.

 

[Ekooing]

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.

Can you help me out here @boneh3ad? I'm running out of ways to explain this...

 

[Ekooing]

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.

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...

 

[Ekooing]

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.

Well, I'll try to explain it...

The article does a poor job of explaining. Although I can't say much because I apparently do too...

Here's an experiment for you though. The next time your driving your car down the interstate, stick your hand out the window. Does it feel like the wind is pushing on you, or pulling on you? Its pushing (because the wind hitting the front of your hand has the highest force on it, not the turbulent wake pulling your hand.

Also, when drafting, is it more advantageous to be the very front car, or bicycle, or swimmer, or the 2nd or 3rd or 4th, in line? The answer is it's always better to NOT be the very first in line. While you do get some benefit from the ones behind you because you have less wake turbulence, it's not NEARLY as big of a benefit as someone in front of you blocking the frontal air resistance.

 

[Ekooing]

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...

We as scientists use assumptions all the time in the hard sciences. i.e.:

Physics: gravity is constant (9.8m/s^2). In reality, gravity varies with relation to how far you are from the center of the Earth (your elevation).

Chemistry: the ideal gas law (PV=nRT). In the real world, almost no gas behaves 100% like an ideal gas.

Most problems in the hard sciences (all least basic ones like this) are nothing more than a close approximation. In order to get a 100% correct answer, you would have to account for every single eventuality and would be running equations ad nauseam. So I guess technically speaking, it is a crude approximation. However, this is how basic physics calculations work.

 

[haruspex]

Physics is ripe with assumptions.

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.

This is not a "crude approximation of physics",

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]

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.

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.

 

[Ekooing]

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.

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]

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.

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.

 

[Ekooing]

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.

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... :)

 

[Ekooing]

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... :)

Sorry, that should be Plays With Squirrels.

 

[haruspex]

questioning the physics of why that is the right answer is ridiculous.

But it is not the right answer to the question posed, that is the point!

Would you set this question: "if a feather and a lead weight were to be dropped from the same height at the same time, which would hit the ground first?" and mark wrong the answer "lead weight"? I sincerely hope not. It would be ok if you were to specify "ignoring air resistance"; likewise there might be some form of words that could have qualified the question in this thread to make it work, but it was not.

I apologise for picking you up on ripe/rife. I was getting irritated.

 

[Ekooing]

But it is not the right answer to the question posed, that is the point!

Would you set this question: "if a feather and a lead weight were to be dropped from the same height at the same time, which would hit the ground first?" and mark wrong the answer "lead weight"? I sincerely hope not. It would be ok if you were to specify "ignoring air resistance"; likewise there might be some form of words that could have qualified the question in this thread to make it work, but it was not.

I apologise for picking you up on ripe/rife. I was getting irritated.

:)

 

[boneh3ad]

You guys have gone so far off the deep end that I am not even sure that I should risk "poking" this thread. However, the is one practice that really irritates me in discussions like these, and that is the practice of splitting up the effects of two sides of objects in a fluid flow in a way that totally ignores that you cannot have one without the other. Sure, you could integrate the pressure on the front of a cyclist and on the back of a cyclist and perhaps make an argument that the back side somehow has a greater "contribution" than the front. However, that ignores a couple of facts.

The first, and most important principle here is that the back actually does not provide any force opposing the movement of the cyclist. Pressure force always points normal to and into a surface upon which it acts. The only way you can come up with a force pointing away from the back surface of the cyclist such that it contributes to drag is if you have a negative pressure (e.g. using gauge pressure instead of absolute). This is a method of convenience, but is physically misleading. Pressure drag is due to the combined backward force on the front of an object less the forward force on the back of the object.

Second, fluid flows are elliptic in nature*, i.e. the Navier-Stokes equations are elliptic equations. Because of this, an effect at one point in a flow, such as in the wake, affects the flow in other locations. Practically, this means that placing a rider in the wake of another rider not only modifies that wake, but also the flow in front of the first rider. You can't just assume the frontal flow stays the same. Unfortunately, that makes analyzing these sorts of situations deceptively tricky at times.

The bottom line is that a single rider has both a high pressure frontal flow and a low pressure wake. If you add a second rider close enough, they will disrupt that wake substantially, including by diverting that wake flow around the second rider and creating a new wake behind the tandem. For closely-spaced riders, the flow, in a lot of ways, looks like it is flowing around one object. A third rider does the same thing to the second, who would then no longer have a huge wake. There are, of course, questions of spacing and Reynolds number and rider shape and the rest, which were clearly not the intent of the question that was asked. In a general sense, the middle rider should typically have an advantage according to standard fluid-dynamics reasoning.

Also, this article is unbelievably awful:

"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

*Caveat: supersonic flows are effectively hyperbolic in nature and therefore are, in some ways, more convenient, as there is no upstream influence. This isn't relevant here, but I thought I would add this footnote for completion.

 

[NascentOxygen]

It would be interesting to see these variations on the theme borne out in practice through experiments with models in a wind tunnel, or even the draught of a big fan in a high school science classroom.

 

[boneh3ad]

It would be interesting to see these variations on the theme borne out in practice through experiments with models in a wind tunnel, or even the draught of a big fan.

I could ask my colleague if he wants to do this in his wind tunnel, though I already know the answer would be "no" unless someone sponsored it. Someone call Specialized...

 

[rcgldr]

the is one practice that really irritates me in discussions like these, and that is the practice of splitting up the effects of two sides of objects in a fluid flow in a way that totally ignores that you cannot have one without the other. Sure, you could integrate the pressure on the front of a cyclist and on the back of a cyclist and perhaps make an argument that the back side somehow has a greater "contribution" than the front.

The statement I made was that the ratio of (pressure at front) / (ambient pressure) is less than the ratio of (ambient pressure) / (pressure at back), not that there was "negative" pressure at the back.

It should be noted that streamlining a vehicle, including bicycles used for top speed competitions, involves something similar to a tear drop shape, except that structural integrity puts limits on how the tail section can be tapered. The front is basically round, but the rear is a fairly long tapered tail. The explanations are that the air flow will separate and flow around at the front, but have to fill in what would otherwise be a void behind the vehicle. The long tapered tail introduces the void gradually, allowing what would otherwise be a void to be filled gradually enough that the air can accelerate mostly inwards (no drag) and only somewhat forwards (drag).

The bottom line is that a single rider has both a high pressure frontal flow and a low pressure wake.

I can't find a source for how much the cross-sectional area of the wake decreases by the time it reaches the rider behind. I know that it's smaller, but not by how much. I'm also wondering if the wake behind the 2nd rider decreases in size as much as the wake behind the first rider, and/or if the pressure of the wake behind the 2nd rider is greater than the pressure of the wake behind the 1st rider (both would still be below ambient, but the 2nd riders wake may be less below ambient than the 1st rider).

The only numbers I've seen in the articles linked to so far in this thread mention that the 1st rider only gets a 2% to 3% benefit from having a 2nd rider drafting. So far, I haven't seen any numbers that quantify the benefit of being the 3rd, 4th, 5th, ... rider in a line of drafters.

Also, this article is unbelievably awful

I just grabbed a link to the first article I found. I didn't read it much.

 

[boneh3ad]

The statement I made was that the ratio of (pressure at front) / (ambient pressure) is less than the ratio of (ambient pressure) / (pressure at back), not that there was "negative" pressure at the back.

First, pressure ratios aren't the important parameter here: pressure differences are. This is why gauge pressures are so convenient when analyzing these sorts of problems. In compressible flows, pressure ratios are often more appropriate for other reasons. The important thing, though, is that what you are describing doesn't fix the part that I mentioned about how you can't separate the stagnation flow from the wake flow. In system governed by elliptic equations, a change in one part of the domain has ramifications everywhere else in the domain.

It should be noted that streamlining a vehicle, including bicycles used for top speed competitions, involves something similar to a tear drop shape, except that structural integrity puts limits on how the tail section can be tapered. The front is basically round, but the rear is a fairly long tapered tail. The explanations are that the air flow will separate and flow around at the front, but have to fill in what would otherwise be a void behind the vehicle. The long tapered tail introduces the void gradually, allowing what would otherwise be a void to be filled gradually enough that the air can accelerate mostly inwards (no drag) and only somewhat forwards (drag).

"Streamlining" a vehicle doesn't have anything to do with a void. A void never forms. A void can't form. I do understand what I think you are trying to say, but this is a really terrible way of talking about fluid dynamics because it can ultimately lead to some weird and incorrect conclusions.

The actual reason this shape is used is inseparable from viscosity and the concept of the boundary layer. Large, unsteady wakes form (and cause massive drag) because adverse pressure gradients along the surface of the object cause the boundary layer to separate from the surface, which results in a region of recirculating back-flow and/or unsteady vortex shedding (see: Kármán vortex street). A circular cross section has a severe adverse pressure gradient that begins at the top and bottom of the cylinder, rapidly leading to separation and the formation of a large wake. A teardrop causes this adverse pressure gradient to have a smaller magnitude (while spreading it out over a longer distance) that, ideally, avoids separation entirely. This comes at the cost of increased viscous drag but greatly reduced pressure drag.

I can't find a source for how much the cross-sectional area of the wake decreases by the time it reaches the rider behind. I know that it's smaller, but not by how much. I'm also wondering if the wake behind the 2nd rider decreases in size as much as the wake behind the first rider, and/or if the pressure of the wake behind the 2nd rider is greater than the pressure of the wake behind the 1st rider (both would still be below ambient, but the 2nd riders wake may be less below ambient than the 1st rider).

This is precisely why the distance between riders is such an important factor. That said, the only source in this thread that mentions it is that Europhysics News article, which sort of described the wake(s) in vague terms and tried to use that vague description to justify their conclusions. As I pointed out previously, it is notable that the authors, in their subsequent paper that had to undergo actual peer review, had to leave out that portion. They do not appear to have published it subsequently.

There absolutely should be a diminishing return with each additional rider, but what that is quantitatively eludes simple analysis as far as I can tell.

I just grabbed a link to the first article I found. I didn't read it much.

That's really not a good practice, particularly in a forum where you are trying to discuss science. This is especially true of a science like fluid mechanics, about which have been written many awful, misleading, or just plain incorrect articles on the internet.

 

[rcgldr]

I just grabbed a link to the first article I found. I didn't read it much.

That's really not a good practice, particularly in a forum where you are trying to discuss science. This is especially true of a science like fluid mechanics, about which have been written many awful, misleading, or just plain incorrect articles on the internet.

I struck out the old link in my prior post and added another. This one appears to me to be a better article, although much of it focuses on side wind effects. Still, the part I was focusing on is the same, that most of the drag is related to what happens behind the rider.

"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

 

[boneh3ad]

I struck out the old link in my prior post and added another. This one appears to me to be a better article, although much of it focuses on side wind effects. Still, the part I was focusing on is the same, that most of the drag is related to what happens behind the rider.

"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

But again, this is another article that did not require peer review and does not go into a whole lot of detail about what they did. Based on simply the pictures in the article, I can tell you that the simulation is only resolving the very large scale motions and is averaging out a lot of the smaller features. Digging into the documentation for this company, it definitely appears they are employing RANS models, which, as I mentioned before, are particularly poor for predicting drag anyway. You can tune those models to a situation to give you some numbers that might do an okay job in terms of helping you design, but you absolutely cannot draw physical insight from a RANS simulation.

Also, I feel I again must stress that, while the wake may well have a pressure coefficient with a larger absolute value than the stagnation flow, it still does not help us here to try to separate the two effects when discussing drafting cyclists. As soon as you alter one, you alter the other, so any situation with a trailing rider necessarily affects the pressure in front of the front rider as well. These are not linear systems and they do not obey superposition.

 

[rcgldr]

I talked to an experienced bike rider, that does up to 100 mile rides, and some club level competitions. He pointed out this article (there are others similar to this), and clarified that in a 3 rider group, the 3rd rider gets the most benefit. Being last is the best place for up to 5 riders, then being next to last is best.

https://www.bicycling.com/training/a20026446/how-to-draft/

 

[boneh3ad]

I talked to an experienced bike rider, that does up to 100 mile rides, and some club level competitions. He pointed out this article (there are others similar to this), and clarified that in a 3 rider group, the 3rd rider gets the most benefit. Being last is the best place for up to 5 riders, then being next to last is best.

https://www.bicycling.com/training/a20026446/how-to-draft/

Meanwhile, the basis of that claim in this article is a quote from the guy who wrote the previous article that I dissected. Let me remind you, his claims were suspect in the previous article and he never actually published the data in a peer-reviewed journal. I see no reason that a quote from him in this article is any more ironclad.

 

[rcgldr]

Meanwhile, the basis of that claim in this article is a quote from the guy who wrote the previous article that I dissected. Let me remind you, his claims were suspect in the previous article and he never actually published the data in a peer-reviewed journal. I see no reason that a quote from him in this article is any more ironclad.

Either that article and others have permeated that premise into the bicycle community, or vice versa, but the person I know as a club level rider and the riders he knows also agree with the premise of it's better to be last until about 5 or 6 riders (a bit different than the article which states 6 riders).

 

[boneh3ad]

Since most cyclists, no matter how good or serious they are, are not aerodynamics experts, it would be relatively easy for shaky science to permeate the community. This is especially true if popular publications in that community are publishing articles like this that are based on science that is not peer reviewed and not very rigorous.

So far, the two articles that have been posted in this thread that make mention of groups of riders like this were both based on the work of one single researcher who didn't even publish that part of his results. Now, what he found may actually be true, but clearly either that researcher or the journal referees did not deem that portion of his work publishable, and therefore I remain unconvinced. The other aspect of that study (and therefore this most recent article you posted) that raises some red flags to me is that it was based entirely on RANS simulations. Given how important the wake is to getting this problem correct, I hesitate to believe the results of a simulation that is so poor at resolving the wake without some kind of experimental validation, which was not performed except for groups of two riders (if I remember correctly).

 

[rcgldr]

Since most cyclists, no matter how good or serious they are, are not aerodynamics experts, it would be relatively easy for shaky science to permeate the community.

True, but it seems that the strategies used in team trial road course events (6 or more riders) would get optimized as the strategies evolved, due to competition. The wiki article mentions that in the case of a team trial based on the time of the 4th rider, that any faster rider should not pull away from the pack, because the 4th rider benefits from the draft. Since any rider would include the 1st rider, that would imply that the 4th rider benefits enough from having 3 riders in front of him instead of 2 to make a competitive difference . Wiki also notes a 2 line strategy.

https://en.wikipedia.org/wiki/Team_time_trial

In the case of velodrome team trials (4 riders), the distance is relatively short (4 km), speeds are faster, and regardless of which position for the lead rider to drop back to is optimal based on drag, the lead rider probably drops to the back of the pack due the circumstances: the pack cycles fairly often, the core of the pack is not disturbed, and the lead rider can convert speed into gravitational potential energy by going up the banked track and gain the speed back by going back down to join at the back of the pack.

 

[Ekooing]

True, but it seems that the strategies used in team trial road course events (6 or more riders) would get optimized as the strategies evolved, due to competition. The wiki article mentions that in the case of a team trial based on the time of the 4th rider, that any faster rider should not pull away from the pack, because the 4th rider benefits from the draft. Since any rider would include the 1st rider, that would imply that the 4th rider benefits enough from having 3 riders in front of him instead of 2 to make a competitive difference . Wiki also notes a 2 line strategy.

https://en.wikipedia.org/wiki/Team_time_trial

In the case of velodrome team trials (4 riders), the distance is relatively short (4 km), speeds are faster, and regardless of which position for the lead rider to drop back to is optimal based on drag, the lead rider probably drops to the back of the pack due the circumstances: the pack cycles fairly often, the core of the pack is not disturbed, and the lead rider can convert speed into gravitational potential energy by going up the banked track and gain the speed back by going back down to join at the back of the pack.

There may very well be major differences between the answer to the basic physics question posed, what the testing and analysis that has been done shows, and the riders in the real world experience.

The simplified physics answer to this question is rider "B" gets the most benefit for the reasons I and others have already touched on. Hopefully this has been explained adequately so we do not have to revisit it.

In the "real world" (i.e. where should a cyclist be if they are in the Tour de France and riding in a pack of 3, or 5, or 8), it's entirely possible that the last position is the best because you have 5 or 6 bodies blocking the frontal air resistance instead of 1 or 2. The frontal air resistance provides by far the greatest resistance to forward motion in this scenario (I know someone said something about an article saying the greatest resistance to forward motion here is the wake resistance, but I assume whomever said that just misread it, or the article isn't explaining itself properly). That being said, having more riders in front of you blocking a constantly shifting wind direction due to the wind itself shifting direction, and the cyclists turning with the curves of the road, might give you more benefit than having someone behind you getting rid or your wake turbulence resistance which is a comparatively very small force in this case.

Simulations are notoriously unreliable especially in the wake area as has already been explained by others. Generally they are taken with a grain of salt, and used more in a generic "this is a hopefully somewhat close approximation of what should happen in real life" manner. Not as definitive replicas of real world scenarios.

So one question, three ways to answer it, and none of them are necessarily wrong. Welcome to the wonderful world of physics!

 

[Ekooing]

There may very well be major differences between the answer to the basic physics question posed, what the testing and analysis that has been done shows, and the riders in the real world experience.

The simplified physics answer to this question is rider "B" gets the most benefit for the reasons I and others have already touched on. Hopefully this has been explained adequately so we do not have to revisit it.

In the "real world" (i.e. where should a cyclist be if they are in the Tour de France and riding in a pack of 3, or 5, or 8), it's entirely possible that the last position is the best because you have 5 or 6 bodies blocking the frontal air resistance instead of 1 or 2. The frontal air resistance provides by far the greatest resistance to forward motion in this scenario (I know someone said something about an article saying the greatest resistance to forward motion here is the wake resistance, but I assume whomever said that just misread it, or the article isn't explaining itself properly). That being said, having more riders in front of you blocking a constantly shifting wind direction due to the wind itself shifting direction, and the cyclists turning with the curves of the road, might give you more benefit than having someone behind you getting rid or your wake turbulence resistance which is a comparatively very small force in this case.

Simulations are notoriously unreliable especially in the wake area as has already been explained by others. Generally they are taken with a grain of salt, and used more in a generic "this is a hopefully somewhat close approximation of what should happen in real life" manner. Not as definitive replicas of real world scenarios.

So one question, three ways to answer it, and none of them are necessarily wrong. Welcome to the wonderful world of physics!

I take that back. I was incorrect in saying all the answers "weren't wrong". The simulations are technically wrong, but in that "we know it's wrong, but it's the best we've got, so we'll take said results with a grain of salt", way. It still is actually wrong in the way that it is not a true representation of the actual aerodynamics from either a theoretical, or a real life sense. The air flow forward of the object is usually pretty accurate. But on the downstream side, and in my experience, at the boundary layer towards the downstream end of the item, and anywhere you might develop vortices along length of the object being analyzed, the simulations are not going to give you a 100% accurate depiction. And since the wake drag effect is such a minimal force compared to the rest of the forces such as forward air resistance (like 20 or 30 times smaller), any deviation in an accurate depiction at that location just amplifies the magnitude of the erroneous findings.

 

[Ekooing]

I would also presume that the reason it's beneficial to be the last rider in the group of 2-5 but second to last when you hit 6 riders in the real world (at least I think those were the numbers in the article quoted) is because it may take up to 5 riders being in front of you to block most of the wind hitting you in the face before it makes sense to put a rider behind you to lessen the wake turbulence drag (as it causes considerably less resistance to forward travel compared to the frontal air resistance). Consequently, the best way to get the maximum benefit from your positioning in a group would be place riders in front of you to block the headwind until the diminishing returns you receive from it are lower than the benefit you receive from having a rider reduce your wake drag by riding behind you and eliminating or disturbing your wake turbulence. So that may be the appropriate answer if this question were posted on a cycling enthusiasts board.

If you were to put three bicyclists in a wind tunnel, positioned perfectly like shown in the diagram associated with the original question, with the wind direction hitting them at the exact angle as shown in said diagram, and measured the force opposite the shown direction of travel of each rider, the second, or middle rider (in a group of three), would show the least "drag" force. This would be the correct answer is this problem were on a high school physics test. And since we're in a physics forum, that is the answer I provided.

A lot of the debating and arguing (mostly debating which is good, only a little arguing) has been centered around articles that are based on simulation data. Those of us who are intimately familiar with the unreliability of simulation data have started our shared distrust of the accuracy of said data. This is why I gracefully bowed out of the conversation when it started getting heated - because you can run the same simulation in 3 different programs and get three different results. This is where the discussion will devolve into infighting within the thread, and there is not much point in arguing it because more than likely, all three are faulty in their own way. This happens a lot when trying to simulate scenarios that involve enormous numbers of calculations to solve. The same thing happens if you try to simulate super critical CO2 in process simulation programs such as HYSYS or Pro-E. There are so many calculations involved in both that scenario and the one involving aerodynamic characteristics for compressible fluid flow around a non standard shape that started this thread. To my knowledge, there is not a simulator on the market that is capable of doing so with a high degree of accuracy.

I hope this message helps clear up some ambiguity. I apologize ahead of time if it sounds patronizing to the people who have a good, firm grasp of physics principles as that is not my intention. I just wanted to state everything in layman's terms so everyone can understand it regardless of level of schooling or experience in physics.

 

[boneh3ad]

True, but it seems that the strategies used in team trial road course events (6 or more riders) would get optimized as the strategies evolved, due to competition. The wiki article mentions that in the case of a team trial based on the time of the 4th rider, that any faster rider should not pull away from the pack, because the 4th rider benefits from the draft. Since any rider would include the 1st rider, that would imply that the 4th rider benefits enough from having 3 riders in front of him instead of 2 to make a competitive difference . Wiki also notes a 2 line strategy.

https://en.wikipedia.org/wiki/Team_time_trial

In the case of velodrome team trials (4 riders), the distance is relatively short (4 km), speeds are faster, and regardless of which position for the lead rider to drop back to is optimal based on drag, the lead rider probably drops to the back of the pack due the circumstances: the pack cycles fairly often, the core of the pack is not disturbed, and the lead rider can convert speed into gravitational potential energy by going up the banked track and gain the speed back by going back down to join at the back of the pack.

I'll be honest. I am not even sure what point you are trying to make at this point.

 

[berkeman]

I'll be honest. I am not even sure what point you are trying to make at this point.

Yeah, I think this thread has run its course pretty well by now. Thank you to everybody who contributed -- it's been an interesting discussion.