# Low Speed Handling

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### Damian Harty

Apr 17, 2015, 12:28:53 PM4/17/15
O Learned Denizens,

At last, I have a question that feels (to me, at least) worthwhile bothering you chaps with.

It's about low speed handling for motorcycles.

At zero speed, when the handlebars are turned, because of trail, the bike moves bodily towards the direction of turn - ie the CG lateral motion is a scaled-down version of the lateral motion of the front edge of the front wheel. Since the CG is now offset from the line joining the centers of the contact patches, the result is a roll moment. This roll moment is into the turn and doesn't go away when the machine starts to move; in fact it is speed-independent.

At non-zero speed, the required centripetal force to make machine travel on a curved path is below the CG, giving a roll moment out of the turn.

When considering these two roll moments for a machine that is exactly upright, it seems there is a speed at which they cancel each other out - I might call this the "zero roll control" (ZRC) speed. It seems to me that at this speed, my ability to control the bike with the handlebars is essentially zero. (I attach some algebra to describe what I'm thinking more exactly - do feel free to lampoon any errors you observe in it).

This causes me to form a hypothesis:

If the ZRC speed occurs at a speed before I want to put my foot down, I find the bike awkward at low speed. (This manifests itself in increased upper body movements, or confusion about which foot I need to put down, or in other unspecified ways I haven't identified yet).

I have access to a large number of motorcycles of variable configuration here, so I can perform an experiment to refute the hypothesis and am presuming if I fail, I can let it stand.

I am going to say "the speed at which I want to put my foot down" is such that my foot "doesn't move much relative to the bike" (so I don't have to lift it and replace it). This might mean I don't want the bike to travel more than, say 0.4m during the stop. If I presume a typical "chauffeur stop" of a constant 0.5 ms^-2, this means about 0.6 m/s or about 1.5 mph.  2mph for a 1ms^-2 deceleration.

I make the ZRC speed for one of our bikes about 3mph. I suspect I can work "ballistically" by levelling the bike before I go through this ZRC region, so I can probably get away with the ZRC speed being "a little bit" above the "foot down speed".  I expect by thinking about the time constant for the bike's divergence in roll, I could come up with a time I can suffer a lack of control and not drop the bike, and give myself a design recommendation like ZRCS < FDS+X, where X is some generic window for the population. For a given "aspect ratio" of bike, this ends up setting a maximum tolerable trail for good low speed handling.

Of course this is one of a thousand things to think about, but since the metric ends up being quite simple, it points me at (I think) a no-go zone for trail and helps me identify some kind of high speed / low speed trade-off (in that trail is a modifier of weave damping and more is better).

So the actual question is: having read that, on a scale of 1 to 10 where 1 is "quite bonkers, you should go home now" and 10 is "that makes complete sense", where do you think my aspirations are in terms of setting a design boundary? (Note, I'm not asking for feedback on the boundary, just the idea of setting one).

Damian
MxG.docx

### Andrew Dressel

Apr 17, 2015, 1:26:26 PM4/17/15
At zero speed, when the handlebars are turned, because of trail, the bike moves bodily towards the direction of turn - ie the CG lateral motion is a scaled-down version of the lateral motion of the front edge of the front wheel. Since the CG is now offset from the line joining the centers of the contact patches, the result is a roll moment. This roll moment is into the turn and doesn't go away when the machine starts to move; in fact it is speed-independent.

Hmm. I see this a working opposite from the way you do. Turning the handlebars to the right, generates a horizontal force to the left from the front tire to the ground because of positive trail: the contact patch trails behind the steering axis. This leftward force from the tire to the ground is accompanied by a rightward force from the ground to the tire, by Newton's third law. Finally, this rightward force from the ground to the tire generates a counter-clockwise roll moment, when viewed from the rear, about the center of mass of the bike and rider, causing them to lean to the left, opposite to the direction in which the handlebars were turned.

Obviously, this chain of effects may be altered by several factors, including relative motion between the bike and rider and finite contact patch length and width.

I find the bike awkward at low speed.

This is likely due to several factors:
1. larger scrub torques in the contact patch due to slower forward motion
2. Much slower  lateral movement of contact patches for a given steer angle due to slower forward motion.
3. Much smaller gyroscopic contribution to self-stability from the front wheel.
4. etc.

Date: Fri, 17 Apr 2015 09:28:53 -0700
Subject: [stvdy] Low Speed Handling
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### William Patterson

Apr 17, 2015, 1:42:41 PM4/17/15
Low speed problems come from head tube angle, not trail. See "Lords of the chainring" or test ride a bikeE tandem.
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### Jason Moore

Apr 17, 2015, 6:18:50 PM4/17/15
to Single Track Vehicle Dynamics
Andrew,

Are you describing the dynamic action of rotating your handlebars while the motorcycle is otherwise at rest? I think Damian is describing the static forces while the bicycle is at rest with rotated handlebars.

I'm imaging holding the motorcycle (I'm a giant!) rotating the handlebars 10 degrees or so and assuming there is positive trail, setting the vehicle on flat ground such that the roll angle is zero. Then asking which way does the vehicle roll, to the right or left?

Assuming we have the "average" motorcycle design, it seems to me that it will roll in the direction the handlebars are turned (not necessarily just due to trail, the position of the CoM of the front assembly plays a role here too) as Damian suggests.

He then postulates that these static forces are still in place when the bicycle has some wheel rotation speed and that the roll moment generated by moving forward with handlebars locked in position will try to roll the vehicle in the opposite direction of the turned handlebars.

That makes sense to me and that there is some steady turning wheel rotational speed that will cause the system to dynamically balance around an equilibrium. This is, in fact, the definition of steady turning, no?

You can calculate what the roll angle must be given one wheel rotational speed and steer angle such that the vehicle is in a steady turn. These plots have been created in several papers.

If you happen to be in a steady turn I don't think this statement holds any water: "my ability to control the bike with the handlebars is essentially zero". You can apply forces to the handlebars and still control the vehicle if in a steady turn. The question is rather, are there configurations of the vehicle, at speed, that have less control authority than other configurations. Control authority equals something like (ability to accelerate the roll dof) / (force applied to handle bars).

Now trying to come up with a trail design guideline for an average motorcycle that ensures the rider won't have to put their foot down till a very slow speed is likely not defined well enough to nail that. It may be possible, but I'm not sure if the steady turning equilibrium speed will correlate because it is a function of roll and steer angle which are always changing.

### William Patterson

Apr 17, 2015, 9:36:27 PM4/17/15
Oops didn't see the zero speed.

### Andrew Dressel

Apr 17, 2015, 10:41:53 PM4/17/15
> Are you describing the dynamic action of rotating your handlebars while the motorcycle is otherwise at rest? I think Damian is describing the static forces while the bicycle is at rest with rotated handlebars.

> I'm imaging holding the motorcycle (I'm a giant!) rotating the handlebars 10 degrees or so and assuming there is positive trail, setting the vehicle on flat ground such that the roll angle is zero. Then asking which way does the vehicle roll, to the right or left?

>> At zero speed, when the handlebars are turned, because of trail, the bike moves bodily towards the direction of turn

Jason, it sure sounds to me like he (Damian) is describing what happens when the rider turns the bars will the bike is otherwise stationary, and he seems to then conclude that there is a change in behavior below some threshold speed where the bike leans in the direction of the steering motion instead of leaning in the direction opposite of the steering motion.

I did the thought experiment for a bike with zero forward speed and came to the opposite conclusion. Turning the bars to the right on a normal bike with positive trial while stationary causes the bike to roll to the left because of the right-ward reaction force from the ground below the bike and rider's combined CoM. Yes, the CoM of the front assembly would also play a role, and I believe, because of that CoM's location in front of the steering axis and above the contact patches, that it would be to contribute to the roll moment to the left, in the direction opposite to the steering motion.

From: moore...@gmail.com
Date: Fri, 17 Apr 2015 15:18:29 -0700
Subject: Re: [stvdy] Low Speed Handling

### Saccon, A.

Apr 18, 2015, 3:26:01 AM4/18/15
Andrew and all,
not sure it this will help, but if you are interested in getting an algorithm for solving two-wheeled vechile kinematics (with toroidal tires) to understand what is happening when you steer the handlebar you might want to take a look at the following paper of mine:

"An efficient Newton method for general motorcycle kinematics", Vehicle System Dynamics, 2008

http://www.tandfonline.com/doi/abs/10.1080/00423110801966108#.VTIF22ajRLg

Cheers,
Alessandro

-------------------------------------------

dr. Alessandro Saccon, Assistant Professor
Eindhoven University of Technology (TU/e)
Department of Mechanical Engineering
Dynamics and Control group
a.sa...@tue.nl<mailto:a.sa...@tue.nl> Tel: +31 (0) 40 247 5423
Webpage: www.dct.tue.nl/asaccon<http://www.dct.tue.nl/asaccon>

-------------------------------------------

From: Andrew Dressel <andrew...@hotmail.com<mailto:andrew...@hotmail.com>>
Date: Fri, 17 Apr 2015 22:41:52 -0400
Subject: RE: [stvdy] Low Speed Handling

> Are you describing the dynamic action of rotating your handlebars while the motorcycle is otherwise at rest? I think Damian is describing the static forces while the bicycle is at rest with rotated handlebars.

> I'm imaging holding the motorcycle (I'm a giant!) rotating the handlebars 10 degrees or so and assuming there is positive trail, setting the vehicle on flat ground such that the roll angle is zero. Then asking which way does the vehicle roll, to the right or left?

>> At zero speed, when the handlebars are turned, because of trail, the bike moves bodily towards the direction of turn

Jason, it sure sounds to me like he (Damian) is describing what happens when the rider turns the bars will the bike is otherwise stationary, and he seems to then conclude that there is a change in behavior below some threshold speed where the bike leans in the direction of the steering motion instead of leaning in the direction opposite of the steering motion.

I did the thought experiment for a bike with zero forward speed and came to the opposite conclusion. Turning the bars to the right on a normal bike with positive trial while stationary causes the bike to roll to the left because of the right-ward reaction force from the ground below the bike and rider's combined CoM. Yes, the CoM of the front assembly would also play a role, and I believe, because of that CoM's location in front of the steering axis and above the contact patches, that it would be to contribute to the roll moment to the left, in the direction opposite to the steering motion.

________________________________
From: moore...@gmail.com<mailto:moore...@gmail.com>
Date: Fri, 17 Apr 2015 15:18:29 -0700
Subject: Re: [stvdy] Low Speed Handling

Andrew,

Are you describing the dynamic action of rotating your handlebars while the motorcycle is otherwise at rest? I think Damian is describing the static forces while the bicycle is at rest with rotated handlebars.

I'm imaging holding the motorcycle (I'm a giant!) rotating the handlebars 10 degrees or so and assuming there is positive trail, setting the vehicle on flat ground such that the roll angle is zero. Then asking which way does the vehicle roll, to the right or left?

Assuming we have the "average" motorcycle design, it seems to me that it will roll in the direction the handlebars are turned (not necessarily just due to trail, the position of the CoM of the front assembly plays a role here too) as Damian suggests.

He then postulates that these static forces are still in place when the bicycle has some wheel rotation speed and that the roll moment generated by moving forward with handlebars locked in position will try to roll the vehicle in the opposite direction of the turned handlebars.

That makes sense to me and that there is some steady turning wheel rotational speed that will cause the system to dynamically balance around an equilibrium. This is, in fact, the definition of steady turning, no?

You can calculate what the roll angle must be given one wheel rotational speed and steer angle such that the vehicle is in a steady turn. These plots have been created in several papers.

If you happen to be in a steady turn I don't think this statement holds any water: "my ability to control the bike with the handlebars is essentially zero". You can apply forces to the handlebars and still control the vehicle if in a steady turn. The question is rather, are there configurations of the vehicle, at speed, that have less control authority than other configurations. Control authority equals something like (ability to accelerate the roll dof) / (force applied to handle bars).

Now trying to come up with a trail design guideline for an average motorcycle that ensures the rider won't have to put their foot down till a very slow speed is likely not defined well enough to nail that. It may be possible, but I'm not sure if the steady turning equilibrium speed will correlate because it is a function of roll and steer angle which are always changing.

Jason
moorepants.info<http://moorepants.info>
+01 530-601-9791

On Fri, Apr 17, 2015 at 10:26 AM, Andrew Dressel <andrew...@hotmail.com<mailto:andrew...@hotmail.com>> wrote:
> At zero speed, when the handlebars are turned, because of trail, the bike moves bodily towards the direction of turn - ie the CG lateral motion is a scaled-down version of the lateral motion of the front edge of the front wheel. Since the CG is now offset from the line joining the centers of the contact patches, the result is a roll moment. This roll moment is into the turn and doesn't go away when the machine starts to move; in fact it is speed-independent.

Hmm. I see this a working opposite from the way you do. Turning the handlebars to the right, generates a horizontal force to the left from the front tire to the ground because of positive trail: the contact patch trails behind the steering axis. This leftward force from the tire to the ground is accompanied by a rightward force from the ground to the tire, by Newton's third law. Finally, this rightward force from the ground to the tire generates a counter-clockwise roll moment, when viewed from the rear, about the center of mass of the bike and rider, causing them to lean to the left, opposite to the direction in which the handlebars were turned.

Obviously, this chain of effects may be altered by several factors, including relative motion between the bike and rider and finite contact patch length and width.

> I find the bike awkward at low speed.

This is likely due to several factors:
1. larger scrub torques in the contact patch due to slower forward motion
2. Much slower lateral movement of contact patches for a given steer angle due to slower forward motion.
3. Much smaller gyroscopic contribution to self-stability from the front wheel.
4. etc.

________________________________
Date: Fri, 17 Apr 2015 09:28:53 -0700
Subject: [stvdy] Low Speed Handling

O Learned Denizens,

At last, I have a question that feels (to me, at least) worthwhile bothering you chaps with.

It's about low speed handling for motorcycles.

At zero speed, when the handlebars are turned, because of trail, the bike moves bodily towards the direction of turn - ie the CG lateral motion is a scaled-down version of the lateral motion of the front edge of the front wheel. Since the CG is now offset from the line joining the centers of the contact patches, the result is a roll moment. This roll moment is into the turn and doesn't go away when the machine starts to move; in fact it is speed-independent.

At non-zero speed, the required centripetal force to make machine travel on a curved path is below the CG, giving a roll moment out of the turn.

When considering these two roll moments for a machine that is exactly upright, it seems there is a speed at which they cancel each other out - I might call this the "zero roll control" (ZRC) speed. It seems to me that at this speed, my ability to control the bike with the handlebars is essentially zero. (I attach some algebra to describe what I'm thinking more exactly - do feel free to lampoon any errors you observe in it).

This causes me to form a hypothesis:

If the ZRC speed occurs at a speed before I want to put my foot down, I find the bike awkward at low speed. (This manifests itself in increased upper body movements, or confusion about which foot I need to put down, or in other unspecified ways I haven't identified yet).

I have access to a large number of motorcycles of variable configuration here, so I can perform an experiment to refute the hypothesis and am presuming if I fail, I can let it stand.

I am going to say "the speed at which I want to put my foot down" is such that my foot "doesn't move much relative to the bike" (so I don't have to lift it and replace it). This might mean I don't want the bike to travel more than, say 0.4m during the stop. If I presume a typical "chauffeur stop" of a constant 0.5 ms^-2, this means about 0.6 m/s or about 1.5 mph. 2mph for a 1ms^-2 deceleration.

I make the ZRC speed for one of our bikes about 3mph. I suspect I can work "ballistically" by levelling the bike before I go through this ZRC region, so I can probably get away with the ZRC speed being "a little bit" above the "foot down speed". I expect by thinking about the time constant for the bike's divergence in roll, I could come up with a time I can suffer a lack of control and not drop the bike, and give myself a design recommendation like ZRCS < FDS+X, where X is some generic window for the population. For a given "aspect ratio" of bike, this ends up setting a maximum tolerable trail for good low speed handling.

Of course this is one of a thousand things to think about, but since the metric ends up being quite simple, it points me at (I think) a no-go zone for trail and helps me identify some kind of high speed / low speed trade-off (in that trail is a modifier of weave damping and more is better).

So the actual question is: having read that, on a scale of 1 to 10 where 1 is "quite bonkers, you should go home now" and 10 is "that makes complete sense", where do you think my aspirations are in terms of setting a design boundary? (Note, I'm not asking for feedback on the boundary, just the idea of setting one).

Damian

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### Damian Harty

Apr 21, 2015, 10:26:24 AM4/21/15
> Jason, it sure sounds to me like he (Damian) is describing what happens when the rider turns the bars
> will (sic) the bike is otherwise stationary, and he seems to then conclude that there is a change in
> behavior below some threshold speed where the bike leans in the direction of the steering motion instead
> of leaning in the direction opposite of the steering motion.

So I'm trying not to presume anything, and just start with the geometry then sum the roll moments using my old friend, linear superposition. I'm not predicting a lean angle outcome but merely observing that, as I have my algebra, there is definitely a speed at which these two mechanisms cancel each other out. My experience with real motorcycles suggests that some of them have a speed at which I feel "uncontrolled" and don't know which foot will need to go down. I'm trying to understand whether the algebraic description is really a causal explanation, or I am just seeing a pattern where there isn't one.

Below the algebraic cancellation speed the roll moments don't cancel out and the "trackstand" method of roll control dominates, albeit with a limited control authority, and in any case all of it is fixed by putting my foot on the ground. The "tightrope walker" upper body control mechanism is always available, if a little undignified with a large motorcycle. At higher speeds, the normal "steer torque as roll acceleration demand" mechanism is well understood and not in question.

I don't dispute the description of action/reaction force generation when the steer velocity is non-zero, but that's not the case I was describing.

I can build complicated multi-body models, of course; it's my job. I was wanting to think a bit before I do that. Thanks for your replies.

Damian

### andy ruina

Apr 21, 2015, 10:53:14 AM4/21/15
I am not paying attention to every detail.  However, I have a few thoughts.

a) When looking at the effect of steering at zero forwards velocity it seems to me it is easy to think casual, and sometimes backwards, thoughts.  Assuming positive trail, an initial lean and steer of zero, does a sudden clockwise (looking down, ie right turn) steer, and no body English,  cause a fall to the right or to the left?  My guess is that if we took a poll of those reading this thread that, without discussion first, there would be no clear consensus on the answer.

My answer:  it would cause a fall to the left. (But my opinion doesn’t matter. I just put it so people can see that some will agree and some disagree.).

b) For there to be a critical speed for which steering-for-balance strategy reverses there has to be a reasonable strategy below and above that speed. I think there is no reasonable strategy at zero speed.  That is, I think a track stand at zero speed, with balance only from steering, is essentially impossible.

Expanding. As I recall, this is the reasoning in the nice 1948 Maunsel paper.  Assuming negligible mass in the steering assembly, the effect of steering right at zero speed is to move the support point of the bike to the right (yes, relative to the frame the point moves to the left, but out here in the newtonian world, the bottom of the bike as a whole is moved right.    How far?  Trail x angle.  So, with 1” trail and 30 degree steer that’s .25”.  But that’s only the front
wheel.  The rear wheel doesn’t move.  So the average motion of the base is about .25” with a 30 degree steer.  Assume
a Center of Mass height of 36”   that’s an angle of about 1/144 ~ .4 degrees.  I don’t think the human senses are that good.
Thus the control authority is less than the sensing ability and balance by steer alone is essentially impossible.  Certainly
I can’t do it and I’ve never seen anyone who can.

Assuming my answer to part (a) is wrong, there could be, in principle, a control reversal.  But I think it is not a real thing as balance by means of moving the bike because of trail is a negligible effect.

Clear?

-Andy Ruina,   ru...@cornell.edu,  http://ruina.tam.cornell.edu
cell:         607 327-0013,       Skype: andyruina

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### Damian Harty

Apr 21, 2015, 4:08:54 PM4/21/15
Thanks Andy, your clarity is very welcome. And candour about the likely level of confusion.

Can back up and ask: Presuming I am a competent observer and have observed the "don't know which foot" effect on at least two "kissing cousins" of motorcycles, is there another explanation?

The pairs kissing cousins to which I refer are the 2000ish Honda Goldwing GL1500 and its cousin, the same era Valkyrie, and the Victory Cross Country and the Victory Vision. I distinctly remember the Goldwing because I hired one and nearly dropped it on multiple occasions, then shortly after used a Valkyrie as a reference bike while engineering the Triumph Rocket III - the difference was pretty startling and jumped out at me. The Victories are more recent experiences and I remember the difficulty riding the Vision (but not the Cross Country) into a garage stall crowded with other equipment. I am a professional "subjective observer" of many things dynamic with vehicles of varying wheel count, so I don't think I'm making it up. Which, I realise is a useless statement for anyone other than me. But humor me for now, I'm not trying to pick a troll fight...

I assert (I choose the word carefully) that one of the cousins is difficult at low speed and the other is easy at low speed. I can see a pattern in that it's the Gold Wing and the Vision that are the difficult ones and the Valkyrie and the Cross Country that are the easy ones. I make no claims about other handling qualities in any other circumstance. The difficult cousins have "somewhat heavy" large fairings attached to the frame, and can be expected therefore to be more nose-heavy than the other cousins. But that feels too simplistic an explanation to me, since the Valkyrie and Cross Country are not by any stretch of the imagination "light" bikes per se, and I can't believe that an elephant is that much easier to handle than an elephant with a hat. I don't think it's about the hat.

When I dig into the trail numbers particularly, I note the Hondas have their trail the wrong way round to be consistent with the algebraic explanation, as do the Victories (longer trail goes with the bikes that are easy). So, that, at the very least, is a blow against the idea.

When I rode the Hondas I formed the impression it was about lateral or torsional stiffness in the steered mass, but on reflection it seemed preposterous that such small strains could change the way the operator interacts with the vehicle.

Damian

### andy ruina

Apr 21, 2015, 8:22:59 PM4/21/15
Damian:  April 21, 2015

I cannot doubt that one bike is easier to balance than another at low speed.
Can you a bit more slowly/clearly lay out the measured quantities that you think correlate with easy or difficult handling. Not that I or anyone else is likely
to figure this out in an email exchange.  But then we could think about it more.

-Andy Ruina,   ru...@cornell.edu,  http://ruina.tam.cornell.edu
cell:         607 327-0013,       Skype: andyruina