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>>
Reply-To: <
st...@googlegroups.com<mailto:
st...@googlegroups.com>>
Date: Fri, 17 Apr 2015 22:41:52 -0400
To: "
st...@googlegroups.com<mailto:
st...@googlegroups.com>" <
st...@googlegroups.com<mailto:
st...@googlegroups.com>>
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
To:
st...@googlegroups.com<mailto:
st...@googlegroups.com>
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
From:
damian...@googlemail.com<mailto:
damian...@googlemail.com>
To:
st...@googlegroups.com<mailto:
st...@googlegroups.com>
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).
Thanks in advance,
Damian
--
You received this message because you are subscribed to the Google Groups "Single Track Vehicle Dynamics" group.
To unsubscribe from this group and stop receiving emails from it, send an email to
stvdy+un...@googlegroups.com<mailto:
stvdy+un...@googlegroups.com>.
To post to this group, send email to
st...@googlegroups.com<mailto:
st...@googlegroups.com>.
To unsubscribe from this group and stop receiving emails from it, send an email to
stvdy+un...@googlegroups.com<mailto:
stvdy+un...@googlegroups.com>.
To post to this group, send email to
st...@googlegroups.com<mailto:
st...@googlegroups.com>.
To unsubscribe from this group and stop receiving emails from it, send an email to
stvdy+un...@googlegroups.com<mailto:
stvdy+un...@googlegroups.com>.
To post to this group, send email to
st...@googlegroups.com<mailto:
st...@googlegroups.com>.
To unsubscribe from this group and stop receiving emails from it, send an email to
stvdy+un...@googlegroups.com<mailto:
stvdy+un...@googlegroups.com>.
To post to this group, send email to
st...@googlegroups.com<mailto:
st...@googlegroups.com>.