What makes a unicycle change direction smoothly?
A practical question:
can anyone give me some tips to help me turn smoothly, particularly on hills please.
An academic question:
Where does the rotational force come from to make the wheel turn a corner please?
Thanks.
Re: How do you turn corners?
Mike,
since you were putting emphasis on smooth turning, you may want to read the nicely phrased introduction to the theory of turning (as it related to spins, but you can ignore those paragraphs) by Ken Fuchs:
http://www.unicycling.org/unicycling/hypermail/0427.html
If you do not mind a more jerky turning style, a pure action/reaction turn from a standstill is another option. I am convinced that tire friction (and the relationship between friction and speed) plays a role here, but I will leave the details to the more theoretically inclined members of this group.
Have fun,
Fred
Thanks for the link to Ken’s excellent article.
Am I to take it from the lack of additional replies that this subject is a bit of a mystery? I thought there would be some advanced maths to be explained, and lots of experiences shared.
When I am cornering on my Uni I always feel like I am forcing it to do something it doesn’t want to do & consequently my turns lack the control I would like. This is particularly in the context of Muni.
Please help. Thanks.
Countersteer.
Do a Google search on “countersteer bicycle”
Google
Lots of stuff on the reason for and physics of countersteering.
Unicycles need to countersteer too. That’s how you force the uni to initiate a sharper turn.
There are two basic ways to turn a unicyle: the gradual curve, as in following the curve of a road or path, and the sudden sharp turn through 90 or 180 degrees (or more) almost on the spot. (This excludes hopping and turning and all that clever stuff.)
For the gradual turn, the unicycle leans in the general direction you want to turn, just like a bicycle or motorcycle. You need to keep the speed up. Long constant radius turns require concentration - the tighter the curve, the more concentration needed.
For the sharp turn, it is easiest to turn to the right as the right pedal goes down, or to the left as the left pedal goes down.
To see how this works, get off the uni, stand it up, and push down on the pedal with your hand. If you allow it to do so, the uni will lean slightly and turn sharply.
Virtually all of the steering effect comes from the lean and the curvature of the wheel. It is nothing to do with hip snad thighs, gripping the seat or waving your arms, although these things can help in some circumstances. ;0)
Back to counter steering, all you do is you use the pedal steering effect as for a ‘sharp turn’ to turn the uni a little way to the right, but with out allowing it to lean to the right. As your momentum is carrying you forwards, and the wheel is moved to the right, the effect is to tip the uni onto its left side quite quickly and smoothly, then you pedal round the curve as for a gentle curve.
Of course, once you can do it, you should seldom think about it - just do it. So if you want one simple answer: you steer with the pedals, not the seat.
Re: How do you turn corners?
>Back to counter steering, all you do is you use the pedal steering
>effect as for a ‘sharp turn’ to turn the uni a little way to the right,
>but with out allowing it to lean to the right. As your momentum is
>carrying you forwards, and the wheel is moved to the right, the effect
>is to tip the uni onto its left side quite quickly and smoothly, then
>you pedal round the curve as for a gentle curve.
>Of course, once you can do it, you should seldom think about it - just
>do it. So if you want one simple answer: you steer with the pedals, not
>the seat.
Pedals may have some part in steering a unicycle, but to say that
unicycles are steered with the pedals is misleading.
Almost all turning is initiated by a counter-steer. To counter-steer a
unicycle, angular action / reaction is used. To turn left, a
counter-steer to the right must first be done to establish a left lean.
To counter-steer to the right, the upper body must twist to the left (the
action) and in reaction the lower body must twist to the right which is
the right counter-steer. With the left lean established it is now
natural for the unicycle to circle to the left by just pedaling through
it. To get out of the left turn at the desired turn angle, just do a
counter-steer to the left to neutralize the lean and continue straight
forward.
The part the pedals play in counter-steering is they transmit some of
the lower body twisting to the unicycle, but the seat also plays this
role as well. Of course, the pedals have no role in the upper body
twisting other than being a part of the reaction to that action.
Sincerely,
Ken Fuchs <kfuchs@winternet.com>
of course, as ultimate wheel riders will tell us, the seat is not essential to the steering. I agree that all turns must start off with some good old Newtonian reaction against a mass - which means (in crude terms) you turn your lower body against the mass of your upper body and/or arms. I don’t agree that counter steering is always used - in a turn ‘on the spot’ for example. However, counter steering is an essential component of steering when riding at any sort of speed.
But back tot he steering with the pedals. It may or may not be literally true, but it is a useful way of ‘feeling’ what you are doing. Especially with sharp turns, or at low speed, timing the turn to coincide with the pedal going down is a useful skill.
When riding, we don’t consciously do physics calculations - we ride by feel. if the ‘steering with the pedals’ idea feels right and helps a new rider to develop the skill, surely that’s all to the good.
Re: How do you turn corners?
On Mon, 30 Sep 2002 03:25:18 -0500, mike.hinson
<mike.hinson.bsb8m@timelimit.unicyclist.com> wrote:
>An academic question:
>Where does the rotational force come from to make the wheel turn a
>corner please?
I read this question as: from what does a rider derive a reaction
force (moment) to turn the unicycle (and wheel) around its vertical
axis. I’m not sure that Mike meant it this way, but anyway this
question was not addressed yet. Countersteering is not an answer.
Whether we do initial countersteering or not, there must be a first
vertical twist but against what does a rider push or pull to bring it
about? This question can be so puzzling that some people are tempted
to say that unicycling is theoretically impossible.
I think Mikefule may be closest to an answer by pointing at the
pedals. If a rider rides relaxed and not in a corner/curved
trajectory, the tyre contact point will actually describe a wiggly
line. Every wiggle corresponds to one pedal stroke. On average, the
contact point is below our centre of gravity. If then the rider would
push one pedal a little harder, the corresponding wiggle will be
larger (or maybe smaller but at least different), hence the tyre will
deviate from the position under the centre of gravity, and here we
have the initial lean that will drive the rider automatically into
riding a curve.
Klaas Bil
If you had this signature, I have forged it.
Re: How do you turn corners?
On Mon, 30 Sep 2002 03:25:18 -0500, mike.hinson
<mike.hinson.bsb8m@timelimit.unicyclist.com> wrote:
>An academic question:
>Where does the rotational force come from to make the wheel turn a
>corner please?
I read this question as: from what does a rider derive a reaction
force (moment) to turn the unicycle (and wheel) around its vertical
axis. I’m not sure that Mike meant it this way, but anyway this
question was not addressed yet. Countersteering is not an answer.
Whether we do initial countersteering or not, there must be a first
vertical twist but against what does a rider push or pull to bring it
about? This question can be so puzzling that some people are tempted
to say that unicycling is theoretically impossible.
I think Mikefule may be closest to an answer by pointing at the
pedals. If a rider rides relaxed and not in a corner/curved
trajectory, the tyre contact point will actually describe a wiggly
line. Every wiggle corresponds to one pedal stroke. On average, the
contact point is below our centre of gravity. If then the rider would
push one pedal a little harder, the corresponding wiggle will be
larger (or maybe smaller but at least different), hence the tyre will
deviate from the position under the centre of gravity, and here we
have the initial lean that will drive the rider automatically into
riding a curve.
Klaas Bil
If you had this signature, I have forged it.
Re: How do you turn corners?
On Mon, 30 Sep 2002 03:25:18 -0500, mike.hinson
<mike.hinson.bsb8m@timelimit.unicyclist.com> wrote:
>An academic question:
>Where does the rotational force come from to make the wheel turn a
>corner please?
I read this question as: from what does a rider derive a reaction
force (moment) to turn the unicycle (and wheel) around its vertical
axis. I’m not sure that Mike meant it this way, but anyway this
question was not addressed yet. Countersteering is not an answer.
Whether we do initial countersteering or not, there must be a first
vertical twist but against what does a rider push or pull to bring it
about? This question can be so puzzling that some people are tempted
to say that unicycling is theoretically impossible.
I think Mikefule may be closest to an answer by pointing at the
pedals. If a rider rides relaxed and not in a corner/curved
trajectory, the tyre contact point will actually describe a wiggly
line. Every wiggle corresponds to one pedal stroke. On average, the
contact point is below our centre of gravity. If then the rider would
push one pedal a little harder, the corresponding wiggle will be
larger (or maybe smaller but at least different), hence the tyre will
deviate from the position under the centre of gravity, and here we
have the initial lean that will drive the rider automatically into
riding a curve.
Klaas Bil
If you had this signature, I have forged it.
Re: How do you turn corners?
On Mon, 30 Sep 2002 03:25:18 -0500, mike.hinson
<mike.hinson.bsb8m@timelimit.unicyclist.com> wrote:
>An academic question:
>Where does the rotational force come from to make the wheel turn a
>corner please?
I read this question as: from what does a rider derive a reaction
force (moment) to turn the unicycle (and wheel) around its vertical
axis. I’m not sure that Mike meant it this way, but anyway this
question was not addressed yet. Countersteering is not an answer.
Whether we do initial countersteering or not, there must be a first
vertical twist but against what does a rider push or pull to bring it
about? This question can be so puzzling that some people are tempted
to say that unicycling is theoretically impossible.
I think Mikefule may be closest to an answer by pointing at the
pedals. If a rider rides relaxed and not in a corner/curved
trajectory, the tyre contact point will actually describe a wiggly
line. Every wiggle corresponds to one pedal stroke. On average, the
contact point is below our centre of gravity. If then the rider would
push one pedal a little harder, the corresponding wiggle will be
larger (or maybe smaller but at least different), hence the tyre will
deviate from the position under the centre of gravity, and here we
have the initial lean that will drive the rider automatically into
riding a curve.
Klaas Bil
If you had this signature, I have forged it.
Re: How do you turn corners?
On Mon, 30 Sep 2002 03:25:18 -0500, mike.hinson
<mike.hinson.bsb8m@timelimit.unicyclist.com> wrote:
>An academic question:
>Where does the rotational force come from to make the wheel turn a
>corner please?
I read this question as: from what does a rider derive a reaction
force (moment) to turn the unicycle (and wheel) around its vertical
axis. I’m not sure that Mike meant it this way, but anyway this
question was not addressed yet. Countersteering is not an answer.
Whether we do initial countersteering or not, there must be a first
vertical twist but against what does a rider push or pull to bring it
about? This question can be so puzzling that some people are tempted
to say that unicycling is theoretically impossible.
I think Mikefule may be closest to an answer by pointing at the
pedals. If a rider rides relaxed and not in a corner/curved
trajectory, the tyre contact point will actually describe a wiggly
line. Every wiggle corresponds to one pedal stroke. On average, the
contact point is below our centre of gravity. If then the rider would
push one pedal a little harder, the corresponding wiggle will be
larger (or maybe smaller but at least different), hence the tyre will
deviate from the position under the centre of gravity, and here we
have the initial lean that will drive the rider automatically into
riding a curve.
Klaas Bil
If you had this signature, I have forged it.
Re: How do you turn corners?
On Mon, 30 Sep 2002 03:25:18 -0500, mike.hinson
<mike.hinson.bsb8m@timelimit.unicyclist.com> wrote:
>An academic question:
>Where does the rotational force come from to make the wheel turn a
>corner please?
I read this question as: from what does a rider derive a reaction
force (moment) to turn the unicycle (and wheel) around its vertical
axis. I’m not sure that Mike meant it this way, but anyway this
question was not addressed yet. Countersteering is not an answer.
Whether we do initial countersteering or not, there must be a first
vertical twist but against what does a rider push or pull to bring it
about? This question can be so puzzling that some people are tempted
to say that unicycling is theoretically impossible.
I think Mikefule may be closest to an answer by pointing at the
pedals. If a rider rides relaxed and not in a corner/curved
trajectory, the tyre contact point will actually describe a wiggly
line. Every wiggle corresponds to one pedal stroke. On average, the
contact point is below our centre of gravity. If then the rider would
push one pedal a little harder, the corresponding wiggle will be
larger (or maybe smaller but at least different), hence the tyre will
deviate from the position under the centre of gravity, and here we
have the initial lean that will drive the rider automatically into
riding a curve.
Klaas Bil
If you had this signature, I have forged it.
six times klaas!
a new record?
whatever caused this is causing more of it at the moment
mike, i’m curious, why the need for ‘smoother’ turns?
> I read this question as: from what does a rider derive a reaction
> force (moment) to turn the unicycle (and wheel) around its
> vertical axis. I’m not sure that Mike meant it this way, but
> anyway this question was not addressed yet.
All answers are interesting & lead to further understanding, I am also trying to understand where the force comes from to continue turning the unicycle (and wheel & unicyclist) around its vertical axis as the unicycle continues to be ridden around a curve.
//\
GILD wrote:
> mike, i’m curious, why the need for ‘smoother’ turns?
Two reasons:
1). In my ignorance I assumed that if I followed tips to ride “smoother” I would also be riding in a more controlled way and find it easier to stay in my balance envelope.
2). I was trying to define the part of cornering that my academic question referred to, that is to say the ongoing cornering, rather than the initial (often jerky for me) start of the corner.
//\
This bit is easy to understand in an intuitive way if not mathematically. Spin a coin on its axis and as it slows down it will flatten out so that the contact point between the edge of the coin and the table ‘moves’ around the coin. Roll an old tyre along the ground and see what happens as it slows and starts to fall to one side. The tyre is turning around its own curvature. Push your uni slowly and turn it and see what happens.
On a curve you are in a similar position to a body in orbit. Your momentum from the straight will tend to push you away from the centre of the corner (keep you going straight; make the uni stand up), and your lean will fight against that. On a smooth turn, the forces are balanced for longer; on a sharp turn, there are sudden imbalances and corrections.
But how do you start the turn? That was a good question. Intuitively, you’d think Newton’s laws would say that you can’t move your centre of mass sideways without something to push against. That is right. However, you can move part of your mass, by moving it agains the rest of your mass. So, you can start the uni turning by twisting your lower body, or by pushing the pedal in a certain way, by using your main body mass as something to react against.
You only need to start a slight lean of the wheel which then rolls out from under you a bit, and the centre of support (tyre contact patch) is no longer under the centre of mass. Then gravity starts to contribute (sometimes more than we would choose 
) and you need to accelerate to counteract the fall. You accelerate out of the turn, or steer the wheel back under your mass, whichever way you look at it.
So, to start the turn, part of you pushes against another part of you. Legs go one way, body goes slightly the other. To continue the turn, the natural curve of the wheel does the job. To end the turn, either countersteer or accelerate.
In real life, of course, it either works or it doesn’t.
As for turning smoothly… an excellent objective. For muni or road riding, you often need to follow a very specific path. When playing or performing, sudden sharp turns are more fun.
do you guys smack your pedles if you lean in too much in a quick turn!
how can i avoid doing it 
I can smack my pedals on the ground when doing a sharp turn on my 20" freestyle uni with 125mm cranks. Shorter cranks on the 20" would help avoid that. With 24" and larger wheels it is difficult to hit your pedals on flat ground when doing a sharp turn. I assume you’re having pedal strike problems on a 20"?
I am still on the trail of the maths & physics behind unicycling. I have found this link which has mathematical explanations for counter steering on bicycles.
I don’t yet understand the maths, perhaps there is someone here who could review it and extract any of the aspects that apply to unicycling? (please).
Roger Davies pointed me at the author of this paper “1988 Johnson, R.C. Unicycles and bifurcations, American J. of Physics, volume 66, no.7, 589-92”
I have also found the author requesting information about unicycling here: http://www.unicycling.org/unicycling/hypermail/0305.html
But I have not been able to locate the paper or get a response from his e-mail address.
Perhaps I will have to content myself with the image of a coin rolling across the desk & turning in tighter circles as it runs out of speed. I may not understand why it does it, but it intuitively seems right & reasonable to expect it to happen.
//\