It occurs to me that there’s another confounding factor here, in that even cars (which don’t lean and have trivial balance) sometimes do something resembling countersteering, to make a turn with a larger radius. And of course two-wheelers will sometimes do the same thing for the same reason.
Chronos, would you mind being more specific? “Something resembling countersteering?”
I suspect you mean that bicycle racers and motorsports competitors “go wide” when approaching a corner in order to describe the largest-radius arc possible within the boundaries of the road. Do I have this right?
If so, it does not resemble countersteering. Rather, it’s just an attempt to use the maximum radius arc possible. This is, generally speaking, the fastest way to get around a racetrack. Depending on which side of our current argument one falls, countersteering is either a way to initiate a leaning turn quickly or the only way to initiate a leaning turn.
If that’s not what you’re referring to, please explain what you were referring to.
I wouldn’t begin to guess what you mean by “cars have trivial balance,” but the way turns affect transient suspension loading is a rich field of inquiry in the world of mechanical engineering. Unfortunately, it’s often called “weight transfer” when “load transfer” would be more accurate.
(Then again, radiologists call the property of being transparent to X-rays “radiolucency,” which I find nonsensical. “Transradiance” might be better, but “radiolucency” makes it clear that radiologists don’t know Latin. Applied science is terrible when it comes to this sort of thing).
Again, vehicle dynamics is a field of study, even if you yourself haven’t bothered to derive it from first principles. I’m not saying you shouldn’t question the conventional wisdom of vehicle dynamics, but your questions imply that you think no one has ever given these things serious thought before.
I’ve lurked on these boards for years, so I’ve got a lot of respect for your opinions, especially on straight physics. So I’m surprised that you’re so resistant (or maybe naïve?) when it comes to applied physics. I’m not trying to be flippant; I’m just baffled.
Yes, I am referring to going wide, and it resembles countersteering in that one first turns left in order to turn right.
And when I say that cars have trivial balance, I mean that except in truly extraordinary situations, cars never fall over on their sides, and no special effort of design or operation is required to keep them upright. A mechanical engineer must of course still take into account things like differential loading on the suspension, but not to the same degree that one must take into account balance on a bicycle: A car with poorly-designed balance might be uncomfortable or wear out quicker, but a bike with poorly-designed balance probably can’t be ridden at all.
This is a great discussion. I think one of the first things I ever aspired to as a young lad was to ride “no hands” on a bicycle. Never much liked motorcycles tho, too much free power!!! Trouble!!:eek:
So, 55+ years later, reading this, I “understand”…countersteering, I just never have thought about it. Its just something one does to keep the bike going where you need it too.
Usually, I have beach stuff, wetsuits and board etc carried under one arm, so the whole thing is kind of off kilter to one side, no hands or not!
If I come to a dead stop…Im going over though, without first spotting a good place to stop.
I agree; that was a great writeup; thank you. While Machine Elf’s idea would certainly help with drift, I worry that the increased noise from gear lash (free play between the gear teeth) would continue to swamp the results. It may well still be worth a try.
Is it possible that the drift is due to slip not between your headset’s top cup (you refer to it as “the grommet on the bike”) and the encoder wheel, but between the wheel and the encoder shaft? Either way, you could get a little more precision out of it by replacing the encoder’s wheel with a smaller-diameter wheel. But I’m sure this has occurred to you.
Another way to address the drift is to significantly increase the normal force between the encoder and the headset top cup. In other words, I’m suggesting that you get a much bigger rubber band. 
Thank you for your writeup and the time and effort involved in collecting a round of data! Let me know if I can possibly help with amplifying the precision of your test gear.
Thank you, Chronos, for explaining.
I would argue that “going wide” is only notionally related to countersteering: it’s not a way to initiate a turn, as we both agree countersteering is, but rather a set of turns. From a steady-state linear-travel condition, countersteering causes a “high-side” and initiates a fall in the other direction. That fall is then “caught” with handlebar input and lateral acceleration, but this is a second turn after countersteering. Countersteering is the first input in a countersteered turn, regardless of whether one buys the idea that there are other, non-countersteering first inputs that initiate another kind of turn. I’m pretty sure we both agree on this.
I don’t think the concept of “going wide” confounds the issue at all, and I concede I’m not sure why you think it might. But that’s neither here nor there.
Single-tracked vehicles are typically modeled as inverted pendulums, which incorporates, I think, your concept of “balance.” It’s true that cars that are not turning don’t need to be modeled as pendulums.
But it would be perfectly valid to model a car and its suspension as an inverted pendulum with centering springs (and, optionally, dampers). In fact, the vehicle dynamics concepts of “roll stiffness” and “roll center” implicitly do just that. This matters more than you seem to anticipate, because when a car rolls on its suspension, it can cause unwanted steering inputs, as can bumps encountered mid-corner. So if this incorporates your idea of balance, it matters quite a bit for both cars and bicycles. A car with large steering inputs due to roll can experience what’s known colloquially as snap oversteer: “spinning out” with virtually no warning.
I admit I find your articulation of “poorly-designed balance” and “well-designed balance” a bit perplexing, but I strongly suspect we just differ on the terminology. I’d call most bicycles dynamically stable because they tend to go straight and not fall over if they have enough speed, regardless of whether anyone is riding them (this is due primarily but not exclusively to trail). Most cars would also be both statically stable and dynamically stable insofar as the trail in their steering geometry also tends to make the car go straight without any steering input.
It’s still unclear to me why you think that “going wide” would confound the issue.
Another thought: there are plenty of activities easily modeled as inverted pendulums in which acrobats manage to stay upright for long periods of time. However, all the ones I can think of involve either very short periods of uprightness punctuated by hopping or jumping or they diverge from bicycles in an important way.
Bicycle trials riders such as Danny Macaskill (arguably the most gifted acrobat-on-a-bike ever to walk the earth) can pause briefly, but then start to fall over and must hop into the air and move the contact patch beneath their CG in order to stop the fall. Seriously, they’re called “correction hops.”
Similarly, slackline athletes do astonishing things, and they can briefly walk slowly without falling over. But their “contact patch” is easily moved beneath them, which is not the case with a bicycle.
Tightrope walkers seem to be able to stand indefinitely on a wire, but they have a (literally) massive pole with a high polar moment of inertia, using it like a reaction wheel, which they can then “de-react” by moving their CG slightly beyond the “perfect” balance point so they can absorb the pole’s angular momentum.
Finally: bicycle trials riders, slackliners and tightrope walkers have all practiced for hundreds or thousands of hours to learn to stay upright as inverted pendulums. It’s a rare skill and requires a lot of practice. And yet somehow, any kid can learn to ride a bike. If initiating a non-countersteering turn–the sort you argue are most common–requires an imperfect version of these acrobats’ skills, shouldn’t most people be able to pickup slacklining as easily as they learn to ride a bike? Or shouldn’t they at least be less terrible at it than they are and learn faster than they do?
You’re asking some reasonable questions, but when the answer is “countersteering” your counterargument boils down to:
“I just think it happens another way, by leaning.”
How does that work?
“Like so. It’s hard to articulate.”
Hmmm.
Our only instrumented test was inconclusive, and the experiment you described performing isn’t exactly Michelson-Morley, if you take my meaning. I tried to reproduce it and failed, but it’s so loosely controlled that my failure doesn’t mean any more (to me, at least) than your success.
It’s all well and good to reject the prevailing theory, but if you don’t propose a convincing and testable alternative in its place, one is reduced to Pauli’s damning observation: “That’s not right. That’s not even wrong.”
For what it’s worth–maybe very little–I still think there’s merit in the wet-tire-track experiment. One could rig up a bottle and tubes to continuously apply water to both tires if puddles are in short supply.
Just a quick clarification: I wasn’t trying to be cute by applying a dismissive quote from a physicist to Chronos, who I understand is a physicist himself. It’s one of my favorite quotes, and I threw it in without thinking that it could be read as especially snarky. Sorry about that.
One alternative would be a synchronous belt and synchronous pulleys. Same opportunity for motion amplification and drift elimination, but without lash. Small belts can be had for a couple bucks, and pulleys for maybe $10-$15 each.
On “going wide” as a confounding factor: Suppose we have a bicyclist who is in the habit of going wide around turns. That bicyclist reads this thread, and decides to perform the mud-puddle experiment: He finds a nice open area with a mudpuddle, rides through the puddle, and then turns. But, as is his habit, he turns wide. If he then examines the tracks left by his tires, he might see the initial turn of his “going wide”, and identify it as evidence of countersteering, even though it is not.
On the stability of cars vs. bicycles: I was not aware that cars customarily had positive trail, but I’ll take your word on it. But a car could certainly be made with zero or negative trail, and still function. A bike with zero or negative trail, however, would be almost impossible to ride, except by an extraordinary acrobat.
I don’t know about the others, but so far as I can tell, slackline walking is easier to learn than riding a bike. I’ve never managed it myself, but then, I’m very poorly coordinated, and I haven’t spent nearly as long on it as I did on learning to ride a bike (which also took me longer than most kids). But I’ve seen plenty of neophytes to slack-lining manage it after only a half-hour of practice or so: There was a bit of a craze for it when I was in college, with folks setting up lines between any convenient pair of trees.
Actually, no. Gymnasts and divers and people who stand up (and cycle riders) do it all the time.
Bend, rotate, stand, rotate, bend.
On a roller bearing, you can rotate your c.o.g. out of plane, and restore balance.
On a point bearing, you can spin and lower and rotate your c.o.g.
(If is perhaps obvious that you can’t do it at all if there is no point of contact.)
Thanks for the comments, guys–I’ll try to tackle most of them, and hopefully won’t miss anything.
I did think about gears, but had the same thought as EdelweissPirate as far as lash is concerned. Gears are generally run with at least some small play so that the far side of the tooth does not rub; although I could apply possibly compression to prevent that, I’m not certain how well it would work.
The synchronous belt is a better idea–I actually have some handy (salvaged from inkjet printers and elsewhere), though I’d probably have to drill out the pulleys. I worry a little that the reduction might be a bit too much. Although the rotary encoder has pretty smooth bearings, the resistance might be just a tad too high for something like a 5:1 reduction, which is probably what I’d get with the typical size.
I think EdelweissPirate is correct that the next step is just a bigger rubber band. I had thought in advance that I was on the low side as far as tension is concerned; although it worked well “on the bench”, it’s obvious now that vibration is a problem, and more tension would likely solve that. I also have some stiff springs I could possibly employ.
The wheel and the encoder shaft will not slip–the shaft has a flat on it, and the wheel a set screw. So that at least is not going anywhere.
But between the top cup (thanks for the terminology correction!) and the headset I’m not that certain of. I haven’t yet tried moving it, and for all I know it’s held in place by not much friction. Something to check out.
I am sure that the drift isn’t caused on the software side. I did measure this: a quadrature sensor has four possible different state transitions, +1, -1, +/-2, and 0. +1/-1 correspond to the normal “good” case where things are ticking along in one direction. The +/-2 case is bad. If you jump by 2, you don’t know if you’ve gone forward or backwards. The 0 case is fine. In a perfect world, this wouldn’t happen, but real-world sensors are subject to bounce, which means that a nice 0-1 transition might actually look like 0-0-0-1-0-1-0-1-1-1. Sometimes bounce comes out looking like there should have been a transition when there wasn’t one.
At any rate, I measured these and never saw a +/-2 except when I spun the encoder really fast by hand and without the wheel. There were a fair number of 0s, but as I mentioned these are ok.
As said, I won’t be able to do much until this weekend. But the weather is good, so I should be able to collect something. There are some large parking lots nearby that I should be able to use. Another thing to play with is the data rate; I’m collecting at 20 Hz now, but I could certainly go higher. Or lower; maybe part of the solution to the noise problem is to just do a low-pass filter.
If the front and rear tire tracks are distinguishable, e.g. as by using different tread patterns, then the situation will be made more clear. A simple left-hand turn will leave tracks that look like this: the front wheel will first steer to the right before commencing the left-hand turn. If the cyclist is in the habit of running far to the outside just before starting the turn, then the mirror-imaged track pattern would appear before the main turn’s track pattern.
I didn’t get to collect as much data as I’d have liked this weekend–my little device suffered a minor structural failure and I didn’t have time to repair it. However, I did manage to collect some of me riding normally around a smooth parking lot. The data is much less noisy this time and there is a clear countersteer signal in many of the turns. See update 2.
The first turn was especially good–nice and sharp; almost a square wave. You can even see some ringing at the bottom.
None of this yet proves that countersteering is required to ride a bike, or that it is apparent in hands-free riding, but it certainly lends credibility to the hypothesis that it’s both necessary and natural for sharp turns in particular. Of course this isn’t a double-blind experiment so I can’t say it’s impossible that I did something unintentionally, but I certainly didn’t do anything special while riding.
I wonder if I can find a kid to test on. Hey kids, want some free candy? Just hop on this bike for a while…
Doc, don’t know where you’re at on this, but I downloaded a really cool app on my phone last night:
It turns your phone, with all of its sensors, into a pocket-sized data logger. You can record data from any of the built-in sensors, save it to a CSV file, and then email that file to yourself for review later. In addition to the 3-axis accelerometer (and compass, magnetometer, GPS, microphone, barometer, inclinometer, and lux sensor), phones also have a 3-axis rate gyro, which is relevant here. If you can secure your phone to the steering stem such that it’s perpendicular to the bearing axis, then one of the rate gyros will report movement of the handlebars separate from the lean of the bike (of course this information will eventually be confounded with the azimuth change of the whole bike once you have established a turn rate). If you have a second phone, you can secure it to the chassis so that it records lean angle; the data files on each phone should include atomically accurate timestamps, so syncing the data in a spreadsheet later on is a cinch.
I tried a quick data file last night, and the data rate appears to be variable and not user-selectable, with a range from maybe 0.008 seconds to 0.050 seconds; I guess it’s a matter of polling the sensors whenever the processor isn’t busy doing something else.
Anyway, this might be an option for gathering more/different data if your rotary encoder is difficult to repair.