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Fresh work on the mathematics of bicycles in motion (nature.com)
165 points by maximz on July 20, 2016 | hide | past | web | favorite | 95 comments

Avid cyclist, but I have no idea what this is talking about:

"...the phenomenon of 'countersteering', whereby the rider can steer to the left only by first briefly torquing the handlebars to the right, allowing the bike to fall into a leftward lean."

Am I just doing this subconsciously?


This PDF explains it very well, with illustrations, on the last page:


"Practically nobody is conscious of the fact that they must steer briefly to the left ion order to make a right-hand turn. But this is not so strange, because the swerve is very small (approximately 3 degrees) and happens very quickly – 0.5 seconds. The wet tire tracks from cycling experiments reveal that we all do this. Apparently we learn this unconsciously when we learn to ride a bike."

Another technical reference for this is here:


with plots of torque-vs-time and analysis here:


The author spends most of his time at CERN, but got interested in bike physics for a couple of years.

There's also a sort of "common sense" explanation relying on really basic physics:

Let's say you want to turn left. We know from experience that you will be leaning left when you turn: meaning, your weight is going to be on the left hand side of your wheels. (The common-sense explanation works really well because I'm not going to explain why you need to lean left to steer left, I'm just going to take it as a given.)

The basic-physics question is: if you're starting totally vertical, how the heck do you get your body mass to be on the left hand side of the wheels in the first place?

You can get a little bit of effect, of course, by simply leaning over left: but that leans the bicycle to the right because you can only lean over one way by pushing your bicycle the other way... and when you do this the bicycle briefly opposes you in the way it's leaning before your gravity can win out. That's less good.

So what your brain has actually learned to reflexively do is, to send your wheels going off to the right while your body continues in a straight line, hence your mass is now over the left-hand side of your bicycle and there is no competition. You then steer into the turn and complete it normally.

It seems that they are saying you have to steer right in order to initiate a left lean. But how do they account for steering with no hands?

I can steer pretty well without hands. It seems as if I must be able to initiate the left lean without pushing the handlebars right.

So why couldn't I also do this when not riding without hands?

I can ride pretty well without hands as well. When I heard about counter-steering a long time back I paid closer attention to what I was doing while riding hands-free. Turns out that I was doing a weird little bodily flick motion in to get the wheel pointing to the opposite direction of the turn before I started leaning into the turn.

Pay attention to yourself next time you ride and you might be surprised.

Yep. If you try to just lean right immediately, the bike will just.... fall over, because the wheel stayed straight.

The momentum from the flick your body creates begins to turn the wheel a small amount, and the forward momentum of the bike in combination with the lean keeps the wheel turned right. By contrast, if you flicked the bike/wheel but did not lean, the wheel would simply straighten itself again.

Even for automobiles this stuff is very simple suspension + steering mechanics. Due to how their suspension & steering components are designed, and assuming they are aligned properly, a car will always follow the road. If the road leans + curves, so does their steering.

Yes, I discovered my weird hip tilt when I was using a bad seat. It was then that I realised I barely used my hands to steer at all (sharp turns excepted)

There's a really cool video demonstrating the idea [0]. They took a set of handlebars and welded them to the frame. You'll see that you can affect a motorcycle, but only poorly. On a bicycle, you're much more top heavy and can force the vehicle to capsize far faster. On my motorcycle though? If I lightly increase the throttle it'll go absolutely straight (which is nice if you need to reseat your gloves, but scary if the road starts to veer to the side!)

[0] https://www.youtube.com/watch?v=4PbmXxwKbmA

You can, I think both were described in the theory book for notorcycle license when I glanced through it.

Fun fact: when I read about it I had to test and I had to make sure I wasn't deceiving myself so I put one palm in front of the handle on one side and the other one behind the handle on the other side. That way I could ensure I pushed it the correct way.

It worked exactly as advertised (50cc bike so somewhere below 60km/h).

Much simpler than using slow motion camera etc.

I was under the impression there is a speed at which countersteering becomes apparent and at low speeds it either is minimal or doesn't happen?

It doesn't just happen – you do it. I've never really considered it in the context of a bicycle, but it's the way to turn a motorcycle at any speed above 5mph or so. You'll hear non-riders say that you steer a motorcycle by leaning... Quite the opposite. You steer a motorcycle by steering away from the turn, which causes the bike to fall into the turn. It's the turn that makes you lean, not vice versa. Motorcycles have way too much inertia to affect their path of travel with body weight.

Thinking about it though, I think I did countersteer in order to drop into bowls while riding vert BMX.

That's interesting. In mountain biking it is taught that must lean the bike to turn properly at speed. Some even go a step further and say lean the bike but not your body. I was pondering the physics of why it works the other day but didn't reach a definite conclusion. I guess it makes sense that you can't muscle a heavy motorcycle to lean over, but you could on a much lighter MTB.

Edit: I should mention in mountain biking you are frequently dealing with a low traction environment, which I think has a large impact on the techniques.

You can steer a light motorcycle by leaning, without touching the handlebars.


Sure, and you can steer a heavy slow moving motorcycle by leaning. That's also not what people mean when they say you steer a motorcycle by leaning. Just because you can do it (under some conditions) doesn't mean that's how how steer a motorcycle. Especially since most people are under the impression that you lean into the turn, not out of it.

But yeah, hypothetically lower inertia = more ability to steer with weight, obviously.

Can vouch for this. I was very surprised when, after many years of bicycling, I went to motorcycle school and they taught us this principle. It was insanely cool that it worked.

Hmm, perhaps it's because I learned to cycle later than most people (at 18), but this phenomenon was always very apparent to me. When I first started, whenever I tried to steer I'd always end up going the wrong way.

Ever thought about why you can't "steer away" from a curb, how it appears to "suck you in" when you try? It's because that first, subconscious turn in the wrong direction takes you into the curb edge.

I've heard this was more of a psychological "target fixation" effect, unless I misunderstand the scenario you describe.

You heard wrong. It's because you can't countersteer, which is the only way to turn a bicycle or motorcycle at speed.

Try it. Get on a bike. Go straight, and pick up speed. Intentionally press the right side of the handlebar. Note which direction the bike is now aiming.

Yes, it's subconscious (and/or you are initiating the turn by leaning into it, which causes the bicycle to countersteer FOR you).

The way I describe it is that the wheels MUST be underneath the force exerted by the center of mass. In straight-line riding, this means your wheels are under you. In a corner, your mass is to the "inside" of the corner, but the centripetal force added to gravity's downward force ends up pushing down to where the wheels are.

So you need to steer a bicycle so that the wheels are always under this center of mass force (I'm sure there's a word for it).

Hence, if you were to turn the wheels in the direction you wanted to turn, you'd fall over, off the bike, to the outside of your intended turn.

Therefore, to initiate a turn, you have to steer the wheels out from under the bike (the "wrong" way) to initiate your mass's 'fall' into the corner. Then you steer the wheels back under you to balance the fall.

I've never noticed this on bicycles, but I also haven't ridden anything but a stationary in 5+ years now! But this is very noticeable in motorcycles.

Most riders don't really think about the torque they're applying to the handlebars, but when you lean into a turn you're definitely applying that torque to the handlebars. You're kind of putting the side of the wheel to the ground in the process, and the only way to put the side you want to turn to towards the ground is to torque the handlebars in the opposite direction.

I don't know why it's so much more important in motorcycles- even riders who have ridden bikes for many years like myself benefit from pointed instruction in "press right to go right".

Perhaps because the rake is so much greater, it's not a natural, immediate carryover from bicycles. Or perhaps because the motorcycle is much heavier, handlebar input becomes all the more important, relative to a bicycle you can steer with your body.

> even riders who have ridden bikes for many years like myself benefit from pointed instruction in "press right to go right".

I was taught that 2 hours into my training when I prepared for the exam to get my license. I remember my instructor telling me to ride in straight lines and try to gently push the handlebar to the left or right and "see what happens." Then he would make me try the slalom part of the exam.

I sometimes let go of the handlebar (when decelerating and when there's no traffic around me) and it takes a lot more effort to make minor adjustments to the trajectory by shifting my weight only.

It's that the motorcycle is much heavier. You need to countersteer first to get the wheels out from under the center of mass of the motorcycle, in order to initiate the lean in the opposite direction. A bicycle is much lighter so you muscle it around more solely by moving your body, which significantly outmasses the bike.

Yes. What's more you actually change the direction above a certain speed like 5km/h or so.

Prior to that you turn the bar into the direction you want to go, above that you do the opposite. The cerebellum rules.

When riding a motorcycle it's very noticeable. Just tipping the handlebar with the finger at 100km/h and it will lean into the other direction.

Yes, you're doing it subconsciously. Countersteering is only possible on two-wheeled vehicles, which means that tricycles handle very differently to bikes, and that learning to ride with stabilisers (training wheels) can be counterproductive.

This totally explains my early, only, very bad experience with training wheels. I went right out into the street because I turned the wrong way and my friend (who had the training wheel bike) thought I knew nothing about riding bikes. I just learned without training wheels...

You don't have to countersteer to turn on a bike.

When you are riding straight you are using a combination of balance and handlebar position to adjust the angle of the bike so it is directly between you and the ground. If you fail to do this you fall over. So to turn without countersteer just stop doing anything and start to fall over. When you reach your desired angle of bank then turn the handlebars in the direction you are falling just enough so the acceleration from turning exactly counteracts the force that is causing you to fall. You are now in a continuous turn and you didn't countersteer at all.

If you don't want to have to wait to fall or want to turn in a particular direction you will end up turning the handlebars in the opposite direction for a time. But that is just you continuing to adjust the angle of the bike to a desired angle like you do continuously all the time you are riding the bike. You haven't done anything different or counter intuitive. I personally don't consider "countersteer" to be a thing.

> I personally don't consider "countersteer" to be a thing.

It sounds like you've never ridden a motorcycle? Most safety courses on motorcycles teach counter-steering, precisely because it is a thing and failure to understand it can compromise your ability to recover from a bad situation.

On a motorcycle going fast, you counter-steer continuously. If you make a slow right turn on a freeway, you can turn for 30 seconds by only pushing forward on the right handle.

I'm pretty sure you always counter-steer even on a bike, it's just very hard to notice, especially going slow. We don't think about it. It's not really a choice though, there's only one way to turn without leaning, you don't get to pick counter-steering or not.

You should definitely try it on a bicycle while going fast. Once you consciously turn your handlebars right and end up steering right no matter what you do, it becomes really clear.

I mountain bike regularly, and I actively counter-steer all the time. It's super obvious if you know what to look for. I personally most feel it when doing fast, flat, sweeping turns. I lean the same direction as the turn, and the bike will feel like it wants to fall further in, making the turn sharper and sharper.

Pushing on the side of the handlebar on the direction I'm turning counters this desire of the bike to fall into the turn. That's counter-steering. It's a pretty unconscious action, and to most feels like what comes natural when one leans a bike to turn.

>there's only one way to turn without leaning

I generated an argument that refutes that statement in the post you are responding to. I am not arguing that the effect does not exist, only that it isn't interesting and is not worthy of a special term to describe it.

FWIW I ride motorcycles on a regular basis... I oppose the discussion on countersteering in the regular motorcycle training curriculum because it suggests that there is more than one type of turn for no real reason. It would be better just to say that you turn on a motorcycle by changing the angle of the motorcycle from vertical. Then there is only one thing to learn.

You actually described counter-steering, even though you might disagree. ;) You said that I can lean right to start a right turn, then turn the handlebars into the turn as soon as you want to stop decreasing the turning radius. That is part of counter-steering. Turn the handlebars right to begin turning the bike left -- that can and does include slowing down an increasing right turn until it's at a constant turning radius.

That's why you're always counter-steering on a two-wheeled vehicle; because turning the handlebars right of where they currently are always causes you to turn more right of where you'd have gone if you didn't move the handlebars.

Since you ride motorcycles, then you already know anyone who's facing a quick turn definitely does not want to wait to fall. To turn quickly, you must counter-steer.

I am curious why you think it's not worth a special term, when it's unintuitively opposite from the way car steering works, and it's important to know in order to stay safe?

>and it's important to know in order to stay safe?

I disagree with that. Before someone learns to turn a cycle, motorized or not, they have to learn to not fall over. So we tell them that they have to turn towards the direction they are falling. Once they master not falling then in practice there is nothing more to teach. They can easily generalize to adjusting the bike to any lean angle because the required motion of the handlebars is exactly the same. If we don't tell them about countersteering they will have no idea they are doing something different for steep turns vs shallow turns. They just have to establish a greater angle sometimes.

Back in the day prospective pilots were taught by having someone show them how to move the controls for each possible manoeuvre. These days the prospective pilot is first taught what the effects of the controls are. After that they are entirely responsible for achieving the required aircraft attitude using that knowledge. They are told to roll the aircraft to turn. They are not told that they have move the stick to the right for a while and then centre it even though that is something that would not produce a continuous turn in a car.

It's not my opinion that learning counter-steering is a safety issue, there's a reason that practically all motorcycle safety courses teach it, and that reason is outlined in the Hurt Report on motorcycle safety.


"28. Motorcycle riders in these accidents showed significant collision avoidance problems. Most riders would overbrake and skid the rear wheel, and underbrake the front wheel greatly reducing collision avoidance deceleration. The ability to countersteer and swerve was essentially absent."

Wikipedia's article on counter-steering with respect to motorcycle safety begins with:

"Even more so than on a bicycle, deliberately countersteering is essential for safe motorcycle riding"


You're free to argue against it using logic and analogies to pilot training, but both safety data and public opinion don't seem to agree. I would counter that pilots are most definitely taught that pushing forward (up) on the yoke causes the plane to dive (go down), that is somewhat analogous to counter-steering. They are also taught that turning left causes a left roll.

But this didn't answer my question either - counter-steering is so-called because you steer counter to the direction of turn, which is true. Even if it weren't a safety issue, why would it be inappropriate to name it? It is a thing that's different in some ways from other types of steering; we should have a name for that. We have names for everything.

> that pilots are most definitely taught that pushing forward (up) on the yoke causes the plane to dive (go down),

No, they are taught that pushing forward on the yoke causes the nose of the plane to pitch towards their feet. The result of that depends on the starting attitude of the aircraft. Think inverted flight as an extreme example. In exactly the same way, pushing on the right handlebar has results entirely dependent on the starting attitude of the bike.

Your comment about the roll is correct. That is an effect of a control.

If people are not swerving enough then wouldn't we want to teach them to swerve?

I am pretty sure that I have answered your question. It's just a pointless distinction to make. Such pointlessness detracts from actual important lessons. Should we come up with a name for the "oversteering" used to recover from a turn (pro-steering?)? After all, if you don't do it you will be stuck in the turn forever. That would be dangerous.

> Should we come up with a name for the "oversteering" used to recover from a turn

Ignoring the reductio ad absurdum, then if you're referring to how you have to steer the handlebars further into a turn in order to straighten out, there is a name for that: counter-steering. :)

There's a sort of subtle difference that plays out in how effective the turning is. In countersteering, you don't move the center of mass of the motorcycle-human system; the wheels pull out from under the bike and it naturally turns into the capsizing. Body steering actually moves the center of mass of the system out of the bike's vertical axis. (That is, you're no longer in plane with it.)

Because motorcycles are so massive (at least mine is), body steering is much less effective, but it does help if you want to lean the bike a bit further. That's sort of where the advice to "push down with your legs comes from", since it shifts the bike down as you push yourself up - voila, bike wheels make a deeper u shape, capsizes a bit more, and turns harder. It's a trim knob for turning, kind of how the rear brakes add stability while the front do most of the work.

Like a lot of the points in the MSF course, it's a useful detail to internalize so that when something inevitably dumb/awful happens on the road a poorly trained snap decision doesn't lead to panic (ohgodohgodohgodthebikeisntswervingfastenoug-), but in everyday life you won't be thinking about it directly.

* It would be better just to say that you turn on a motorcycle by changing the angle of the motorcycle from vertical.*

Better than teaching students, "push right, go right. Push left, go left"? Yeah, I'm thinking your way isn't better. Your way, as I read it, just reinforces the idea of "you turn a single track vehicle by leaning". That might have some technical correctness, but it's practically worthless information as far telling a rider what they physically need to do.

Makes for great arguments on the Internet, though, and I'll bet if I cruised over to rec.moto it is still going on some twenty-five, thirty years later after it first started.

Sorry, but this is flat-out incorrect.

Countersteer is the only way to turn a bicycle at speed. If you lean, you are simply inducing the bike to countersteer for you. The fact that you are not conscious of this act does not change the fact that it is happening regardless of your awareness.

More to the point, you cannot turn a bicycle at speed to the right by turning the handlebars to the right. The bicycle will go left, independent of your intentions.

Perhaps you meant to say that the only way to turn a bike in a particular direction involves countersteering. My scenario required no leaning.

If you are on a moving bike and you turn the handlebars to the right you will soon be on the ground. :) On a two wheeled vehicle the handlebars are used to adjust the angle of the bike/rider system with respect to the ground. The handlebars are not used for turning but for adjusting things so that a turn can occur. "Countersteering" is something that occurs at all times and in all situations. It has nothing special to do with turning.

Try doing it consciously! It's very fun & informative. Try not to lean, and do some experimenting while you're riding fast. The faster you go, the more noticeable the effect is. You can push forward on the right side, and it will immediately put you and your bike into a right lean. Hold your hand pushing slightly on the right side to continue turning right. The handlebars will push back a little and try to straighten out.

Many people that ride bikes never know about counter-steering, unless they ride motorcycles too. So, you're not alone. I didn't know about it on a bike until I learned riding motorcycles.

It's wildly unintuitive, so don't feel bad. When I was first learning to ride a motorcycle with the MSF, I damn neared dumped the practice bike a few times trying to manhandle it. You'll really quickly internalize push-left-go-left. And it turns out to work great on regular bikes, too. (But it's terrifyingly more responsive - I actually can't relax pedaling a bicycle because of the fear of how easy it is to flip the things and capsize them from countersteering.)

EDIT: There's a neat heuristic that was brought up in the course: the center of mass of the bike is above the bottom of the wheels, and a turning bike must lean into the turn (weird road geometries excepted), therefore to turn the stuff under the center of mass must counter the top leaning in. Thus to go left, you push left, causing the front wheel to pull out from under the bike right-wards, which starts to capsize the bike leftwards! Like I said before, a bicycle reacts really really hard to this, but a hefty motorcyle has a far lower center of mass and leans into it more gracefully.

What really made it intuitive for me was watching video of moto gp bikes gently "folding" into a turn.

> And it turns out to work great on regular bikes, too

Well yes, seeing as that's how you steer a bicycle. As a keen cyclist it annoys me when people (especially coaches) start harping on about countersteering being an additional technique you should learn, when it's what everyone has been doing intuitively since they first learned to ride a bike.

We learn counter-steering subconsciously, right? It's intuitive in the sense that it's muscle memory, but not in the sense that it's conscious and obvious why. A lot of people who've ridden bicycles initially refuse to believe counter-steering exists, I think that demonstrates that it's not completely intuitive. If the counter-steering part is obvious to you, then you're probably ahead of the curve, and you can certainly ignore when coaches harp about it.

Counter-steering is said to be important to learn consciously because it's unintuitive, and people have crashed and died on motorcycles in panic situations by turning their handlebars toward their escape route only to have the bike go the opposite direction. Or at least I heard a rumor about that in my MSF course.

I do think it's valuable to know this fact consciously and not rely on body intuition, but I'm also sure it's much more important for motorcycling than for bicycling.

Don't take it personally - I was always just a terrible rider when I was young; I meant that in a mildly sarcastic way. I never really figured out how to properly steer until I got a motorcycle, and that just about ruined my feeling of force in the other way. Put me on a bike and in 15 feet I'll accidentally steer so hard you'd think I was dodging semis / saw a hundred dollar bill on the pavement. (I assume as a kid I just always manhandled the bike so hard I never noticed. Always standing on the pedals and pumping them like I was running, wobbling the bike's center of gravity the whole way.)

Probably. If you care enough, and have the facilities, you can take a slo-mo video of yourself taking an abrupt and sharp turn. You will find that counter-intuitively, your bars first turn the opposite direction. In any experienced cyclist, this just becomes an innate instinct.

There's a very interesting video from Keith's Code's superbike school where they built a motorcycle with an extra handle bar that's fixed to the bike to prove that leaning doesn't actually turn the bike much at all.


I know this works for sure on a motorcycle, and I've tried this experiment on a bicycle too, you can turn a bike right just by pushing the handlebar forward with your right hand. Totally counter intuitive but it works and I'm pretty sure we do it subconsciously when we lean by pushing on the handlebar and we end up counter-steering.

This entire countersteering discussion is interesting for a site that often debates "consciousness".

It's an example of a skill most of us acquired and use every day all without being accessible to our conscious brain.

In fact, not only is it unconscious, most people consider it very counterintuitive.

What other types of cognition do our bodies perform everyday that we aren't aware of? I'd argue that the amount of cognition accessible to our conscious mind is only a small fraction.

I can't help wondering if everyone who has replied to you has mixed up cause and effect. My explanation would be:

"To turn left you need to lean to the left. Leaning to the left momentarily forces the handlebars to turn the right."

This describes an equivalent outcome to the quotation from the article but implication about what is cause and what is effect is quite different.

It's very easy to verify for yourself that the cause & effect goes "push right handlebar (or equivalently, pull left handlebar) to initiate a right hand turn/lean".

The countersteering argument has been repeated literally 100's of times on the internet on motorcycle forums. It's not worth debating as it is absolutely a real phenomena. It's counterintuitive yes, but there is no doubt that it is real.

Its crazy seeing motorcycle racers countersteer to get a deep, knee-on-the-ground lean into a turn, with the wheel and handlebars turned the opposite direction.

For cycling, I can only explain this passage by saying I lean a little left first, possibly providing that right torque, which then enables the handlebars to turn fully left into the turn.

But I have no idea what I'm talking about.

This phenomenon was the answer to a Car Talk Puzzler - http://m.cartalk.com/content/paging-sherlock-holmes

Twist of the wrist 2, a movie on how to lean on a motorcycle, explains it really well https://m.youtube.com/watch?v=JWuTcJcqAng

This is really apparent with motorcycles. I haven't personally noticed/tested with a bicycle, though.

Yes! If you own a motorcycle, you -have- to countersteer!

> ...an ambitious effort that would investigate everything from the strength of wheels...

My master touched this. Used AI to find spoke patterns. http://master.matsemann.com

> There were untested geometries out there that could transform bike design.

Better hardware and simulations makes it easier to test thousands of these, possibly with the help of AI. I wonder if any drastically new designs will be found in the feature, or if time will show the current design is the best.

Thats an interesting pattern - but the issue is how would you true a wheel like that?

If nothing else I find it quite fascinating how some bikes are easier to ride without holding the handle bars than others. I can balance much better on my 1998 Specialized Stumpjumper mountain bike (comfortable for minutes without hands) than I can on my 1998 Cannondale R900 racing bike (max 5 seconds without hand).

But for my colleague - he finds it much easier to balance his racing bike.

As the article suggest - the hope is that this will provide better guidelines for building bikes that are more stable.

The balance on my mountain bike definitely saved me from two near crashes of a knock to my rear wheel by a u-turning car and being hit on the handle bars by a wing mirror.

Some bikes that are hard to ride no-handed have "notched"/"indexed" headsets that are to blame. Small indentations in the headset prevent minor corrections from actually turning the wheel, making it hard to let go of the bars.


(see section on "Indexed Steering")

Thank you so much. My bike has been exhibiting this behavior but I just assumed the headset was designed to 'clip' into place. Looks like I need to see the mechanic.

Peter Sagan showing how well some people can ride with no hands: https://streamable.com/2u94

(From today's stage of the Tour de France)

And Ilnur Zakarin (also from today's stage) showing how others aren't as good! Starting at about 2:00 in: http://www.dailymotion.com/video/x4l18sa_flamme-rouge-etape-...

To be fair to Zakarin, the finish is substantially steeper than the section Peter was on, and he had just spent the 30 minutes on the rivet to get the stage win.

He can also do a wheelie on his racing bike which I definitely can't do either.

I would guess the frame geometry on your Stumpjumper is likely much more relaxed (specifically the head tube angle) than the Cannondale's.

Yeah - to me this made sense. Until my colleague was referring how he had the opposited where he was more balanced on his racing bike.

what was the conclusion ? it's not gyroscopic effects because they still balance with counter-rotating wheels, it's not trail because they can still balance with negative trail. Is it some of each of these effects, if so how much ? What else is involved ?

According to TFA (and to this avid cyclist it makes sense) it is the combination of the two effects you mention and weight distribution. Novel bikes can be constructed that tweak one of these inputs into an unsuitable range and yet still balance, but I really doubt you could mess up all three and still have a bicycle.

I think negative trail works pretty much the same way as positive trail; I think the question is, does a bike with zero trail work. I'm guessing it can be done, but experience with various motorcycles (which have a wide range of rake) suggest trail is desirable for other reasons too.

Well I haven't read the article (sorry), but on a bike with a rider you balance by active feedback. If you steer the way you are falling to right yourself.

OK - this is probably my ignorance talking, but why is it surprising that bike are balanced? The pedals are basically shoulder width and staggered, which is a very natural position for people to balance in as bipedal creatures? in addition, while the bike is moving, won't the inertia tend to keep things moving in the same direction?

This is all coupled by the fact that the rider is actively piloting and adjusting the bike to keep it under control at all times. The bike seems like it would balance to me because the control mechanisms are designed to keep things balanced easily.

Bikes balance themselves; they don't need a rider to do it for them. Watch https://www.youtube.com/watch?v=oZAc5t2lkvo

I just want to note that this also happens on motorcycles. On a cold winter day my bike dumped me off as I lost traction at a stop light. It started to fall over, bumped its saddle bags, and before the tilt sensor could stall the engine it righted itself in second gear and idled its way through the intersection... with me literally running after it. It hit a curb and eventually stalled upright.

Second most embarassing thing the bike ever did to me.

Dare I ask what was the most embarrassing thing the bike did to you?...};-)

Oh that was at a stop light shortly after it started raining in a Texas winter. I'm fully layered and geared up with leathers and full rain suit - I can walk a bit like a robot and look 150 pounds heavier. So I pull up to the light and just before I fully stop, my Dyna just ... slides out from under me. It's rush hour, a busy intersection, and my bike just sorta falls over in place while I'm sitting on it. Nothing you can do can stop it once it slowly starts properly tipping over, so it plonks onto the roll bars and bags (which are wide and leather, thank god). I scramble to haul it back upright on this oil slicked crowned lane, hop back on, and act like nothing at all happened.

Bike are balanced and symmetric side-to-side. Top to bottom they are not, obviously. The center of mass is above the ground , so a bike that is not moving will fall over to lower its center of mass. But this doesn't happen if the bike is moving. Push a bike without a rider and it will travel for a few feet without falling over, and take longer to fall over if just left standing still.

The surprising thing is that it is way more than "a few feet". Apologies for repeating myself, but watch https://www.youtube.com/watch?v=oZAc5t2lkvo (And that is not on smooth terrain)

And nitpick: typical bicycles aren't symmetric left-right. The chain and gears make them heavier at the right. Most mass is close to the center line, though, so its moment is negligible, especially when ridden by a human.

It's surprising to the extent that: balancing on a non-moving bicycle is hard. Riding a unicycle is hard. Riding a bike is easy.

bikes are balanced without a person on them

It might help if they program humanoid robots to ride bikes. The problem seems to be hard to analyze because there's a person on the bike, and the way the person moves with the bike is hard to track.

That's cool, but the robot there needs a large gyro stabilizer disc to keep balance. Not exactly the way we do it.

Regarding countersteering & bicycles (and motorcycles), I better understood the phenomenon by picturing a bar shoved horizontally through a basketball.

You can steer by either turning the basketball (horizontal plane) or leaning the basketball (vertical plane). In the case of a motorcycle at speed, the bike's effective turning radius is affected more by the lean than by how much the handle-bars are turned. The handle-bars are more about controlling the amount lean.

We changed this title to something less baity than the original (et tu, Nature?). If someone suggests a better (more accurate and neutral) title, we can change it again.

Pretty soon all of human language will consist of phrases like, "You won't believe what happens when this one weird news aggregator changes a submission title!" Is there some way we can try to reverse this trend outside of HN?

How complex can it be? If you have a bare minimum background in basic physics and control theory, and a bicycle in your hands, the qualitative reasons for balance and stability will jump at you in under 10 minutes...

Please don't post unsubstantive dismissals of others' work to HN.

If you know more than the rest of us, it would be good to post an informative comment that teaches the reader something. If you don't want to do that, it's fine to post nothing.

If you feel that something is trivial and potentially wasting other people's time by means of wasting pixels, I think it's fine to speak up. (Explaining why something is trivial may not be that effective, in general).

I was clearly wrong in that many people disagreed and found this to be an interesting and nontrivial subject.

Alright then, what are the reasons for bicycles being balanced? If it's not anything related to gyroscopic effects, then what is it?

Ok, I guess I could have provided more info. Do this if you own a bicycle: hold it by the saddle perfectly straight, front of the bike forward. Make it lean on the left (no forward movement). Look at the handle, it steers left. When you're moving this means that when you lean left there will be a torque, due to your circular path you'll be following, that will try to make the bike lean right.

Bend left -> torque to the right, bend right -> torque to the left. Here you have the basic ingredient for stability: the one torqueless angle is the bike going straight perfectly vertical wrt the ground, while any perturbation leads to a torque in the opposite direction.

I felt it was basic stuff maybe it's not?

ok, go on.

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