Fixed gear/track frame geometry

[Benjamin Lewis]

[email protected] wrote:

> Benjamin Lewis wrote:
>> [email protected] wrote:
>>
>>> If you have zero trail you can't steer. You'll fall over.
>> Huh? I think you need to reexamine your model of how bicycle steering
>> works. Of course you can steer on a bicycle with zero trail. It's been
>> done. People have even successfully ridden bicycles with negative
>> trail.
>
> We aren't talking about negtive trail, we're talking about zero trail. If
> you have zero trail and you lean your bike over while riding it, how do
> you make the bike steer back under you?

By turning the handlebars.

I'm not sure what you're confused about here. If the wheel is turned the
front of the bike will move in the direction of the turn as the bike moves
forward.

--
Benjamin Lewis

Evelyn the dog, having undergone further modification, pondered the
significance of short-person behavior in pedal-depressed panchromatic
resonance and other highly ambient domains... "Arf", she said.

 

[ML]

Benjamin Lewis wrote:
> [email protected] wrote:
>
>
>>Benjamin Lewis wrote:
>>
>>>[email protected] wrote:
>>>
>>>
>>>>If you have zero trail you can't steer. You'll fall over.
>>>
>>>Huh? I think you need to reexamine your model of how bicycle steering
>>>works. Of course you can steer on a bicycle with zero trail. It's been
>>>done. People have even successfully ridden bicycles with negative
>>>trail.
>>
>>We aren't talking about negtive trail, we're talking about zero trail. If
>>you have zero trail and you lean your bike over while riding it, how do
>>you make the bike steer back under you?
>
>
> By turning the handlebars.
>
> I'm not sure what you're confused about here. If the wheel is turned the
> front of the bike will move in the direction of the turn as the bike moves
> forward.
>

I believe you are wrong on this but can't really prove it. Unless you
have a bike with true zero trail, you can't prove your point either so
these are just mind exercises.

If you consider your contact patch as a point on the pavement, turning
your handlebars on a bike with zero trail will not do anything for you.
It will continue to try to go forward (I believe) and ultimately you
will end up on the ground. Why do I say this? For a couple reasons.
Consider what happens to your bike when you lean it to the left while
walking it. The front wheel swings to the right and the bike turns into
the direction it was leaned. This is how a person is able to ride a
bike no handed. The bike naturally does the steering for you - you
affect your direction of travel by strictly leaning the bike through the
saddle. Now consider what would happen if you leaned a bike with zero
trail to the left - nothing. The bike would just lean, the front wheel
would continue straight down the road. Why? Because with zero trail
there is no torque component in either the CW or CCW direction. The
component of the force vector which is perpendicular to the fork (the
frame of reference at this point) is applied along the fork centerline.
In order to rotate the fork you must have a component of force offset
by some radius from the center or rotation. With zero trail, you don't
have this. So, if you were on this bike you would fall down. You can't
ride this bike no handed. Now consider what happens when you are on the
bike. You feel the bike start to fall over as you lean so you turn the
bars to steer into the turn. This is where the problem comes in. Since
you have zero trail all you are doing is rotating the contact point on
the pavement. A true point source does not have a directional
component. In this case though the reality is that the contact patch
looks more like a square or a rectangle than a point so it will have a
directional component. Will this directional component be enough to
actually direct the bike into the corner? Yes - the front end will act
like a unicycle. I'm not sure how rideable this bike would be. My
instincts tell me only at very slow speeds.

BTW, I briefly looked through my copy of Bicycle Science last night &
could find no reference to any experiments done with zero trail bikes.
All references were to various combinations of positive or negative
trail bikes. If you can direct me to references (or to the pages in
Bicycle Science) documenting zero trail bikes I'd love to read them. I
can't think of anything in normal usage that would be equivalent.
Shopping carts, cars, motorcycles, scooters - they all have trail
components.

Jobst, any thoughts on this subject?

MOO,
Matt

 

[[email protected]]

On Tue, 15 Jun 2004 07:54:28 -0400, ML
<[email protected]> wrote:

>Benjamin Lewis wrote:
>> [email protected] wrote:
>>
>>
>>>Benjamin Lewis wrote:
>>>
>>>>[email protected] wrote:
>>>>
>>>>
>>>>>If you have zero trail you can't steer. You'll fall over.
>>>>
>>>>Huh? I think you need to reexamine your model of how bicycle steering
>>>>works. Of course you can steer on a bicycle with zero trail. It's been
>>>>done. People have even successfully ridden bicycles with negative
>>>>trail.
>>>
>>>We aren't talking about negtive trail, we're talking about zero trail. If
>>>you have zero trail and you lean your bike over while riding it, how do
>>>you make the bike steer back under you?
>>
>>
>> By turning the handlebars.
>>
>> I'm not sure what you're confused about here. If the wheel is turned the
>> front of the bike will move in the direction of the turn as the bike moves
>> forward.
>>
>
>I believe you are wrong on this but can't really prove it. Unless you
>have a bike with true zero trail, you can't prove your point either so
>these are just mind exercises.
>
>If you consider your contact patch as a point on the pavement, turning
>your handlebars on a bike with zero trail will not do anything for you.
> It will continue to try to go forward (I believe) and ultimately you
>will end up on the ground. Why do I say this? For a couple reasons.
>Consider what happens to your bike when you lean it to the left while
>walking it. The front wheel swings to the right and the bike turns into
>the direction it was leaned. This is how a person is able to ride a
>bike no handed. The bike naturally does the steering for you - you
>affect your direction of travel by strictly leaning the bike through the
>saddle. Now consider what would happen if you leaned a bike with zero
>trail to the left - nothing. The bike would just lean, the front wheel
>would continue straight down the road. Why? Because with zero trail
>there is no torque component in either the CW or CCW direction. The
>component of the force vector which is perpendicular to the fork (the
>frame of reference at this point) is applied along the fork centerline.
> In order to rotate the fork you must have a component of force offset
>by some radius from the center or rotation. With zero trail, you don't
>have this. So, if you were on this bike you would fall down. You can't
>ride this bike no handed. Now consider what happens when you are on the
>bike. You feel the bike start to fall over as you lean so you turn the
>bars to steer into the turn. This is where the problem comes in. Since
>you have zero trail all you are doing is rotating the contact point on
>the pavement. A true point source does not have a directional
>component. In this case though the reality is that the contact patch
>looks more like a square or a rectangle than a point so it will have a
>directional component. Will this directional component be enough to
>actually direct the bike into the corner? Yes - the front end will act
>like a unicycle. I'm not sure how rideable this bike would be. My
>instincts tell me only at very slow speeds.
>
>BTW, I briefly looked through my copy of Bicycle Science last night &
>could find no reference to any experiments done with zero trail bikes.
>All references were to various combinations of positive or negative
>trail bikes. If you can direct me to references (or to the pages in
>Bicycle Science) documenting zero trail bikes I'd love to read them. I
>can't think of anything in normal usage that would be equivalent.
>Shopping carts, cars, motorcycles, scooters - they all have trail
>components.
>
>Jobst, any thoughts on this subject?
>
>MOO,
>Matt

Dear Matt,

I think that David Jones concluded that we can ride damned
near anything in terms of front-end geometry, although most
bizarre versions are good for little except for parking lot
demonstrations.

Below are some articles mentioned in a post elsewhere
by Jonathan Thornburg:

< [email protected]>

http://www.thp.univie.ac.at/~jthorn/home.html

Carl Fogel

David E. H. Jones
"The Stability of the Bicycle"
Physics Today , April 1970, 34-40

Framk Rowland Whitt and David Gordon Wilson
"Bicycling Science", 2nd edition
MIT Press, 1982, ISBN 0-262-73060-X (paperback), -23111-5
(hardcover)
... this book has a chapter devoted to stability,

J. Lowell and H. D. McKell
"The Stability of Bicycles"
American Journal of Physics 50(12), Dec 1987, 1106-1112

G Franke, W Suhr, and F Reisz,
"An advanced model of bicycle dynamics",
European Journal of Physics 11 (1990) 116-121

John Maddox's report of the Franke/Suhr/Reisz paper
in Nature 346, 2 Aug 1990, p 407.

 

[Benjamin Lewis]

[email protected] wrote:

> Benjamin Lewis wrote:
>> [email protected] wrote:
>>> Benjamin Lewis wrote:
>>>> [email protected] wrote:
>>>>
>>>>> If you have zero trail you can't steer. You'll fall over.
>>>>
>>>> Huh? I think you need to reexamine your model of how bicycle steering
>>>> works. Of course you can steer on a bicycle with zero trail. It's
>>>> been done. People have even successfully ridden bicycles with
>>>> negative trail.
>>>
>>> We aren't talking about negtive trail, we're talking about zero
>>> trail. If you have zero trail and you lean your bike over while riding
>>> it, how do you make the bike steer back under you?
>> By turning the handlebars. I'm not sure what you're confused about
>> here. If the wheel is turned the front of the bike will move in the
>> direction of the turn as the bike moves forward.
>
> I believe you are wrong on this but can't really prove it. Unless you
> have a bike with true zero trail, you can't prove your point either so
> these are just mind exercises.

Like I said before, it's been done, e.g.:
http://www.bikernet.com/garage/sugarbear.asp

From Scott Hand's PhD thesis, available at
http://tam.cornell.edu/~ruina/hplab/bicycles.html

d(t_r)/dt = (c_f/c_w)d(phi)/dt + phi*d(y_r)/dt*cos(l)/c_w

where
t_r = direction rear frame of bicycle is heading
c_f = mechanical trail (which = 0 when trail = 0)
c_w = wheelbase
phi = steering angle
d(y_r)/dt = speed (approximately)
l = 90 - headtube angle

With zero trail, the first term on the right becomes zero, but the second
term, which is generally larger, does not. This expression essentially
determines how fast the bike is turning.

> If you consider your contact patch as a point on the pavement, turning
> your handlebars on a bike with zero trail will not do anything for
> you. It will continue to try to go forward (I believe)

This would mean the front tire would be sliding rather than rolling. Why
would you think this would start to happen, and why only on a zero trail
bike?

> and ultimately you
> will end up on the ground. Why do I say this? For a couple
> reasons. Consider what happens to your bike when you lean it to the left
> while walking it. The front wheel swings to the right and the bike turns
> into the direction it was leaned. This is how a person is able to ride a
> bike no handed. The bike naturally does the steering for you - you
> affect your direction of travel by strictly leaning the bike through the
> saddle. Now consider what would happen if you leaned a bike with zero
> trail to the left - nothing. The bike would just lean, the front wheel
> would continue straight down the road. Why? Because with zero trail
> there is no torque component in either the CW or CCW direction.

You are forgetting:
- torque applied by the rider to the handlebars
- torque due to gyroscopic effects of the front wheel
- there is also torque in the proper direction if the centre of mass of
the front assembly (front wheel + fork, handlbars, etc) is in front of
the steering axis

> The component of the force vector which is perpendicular to the fork (the
> frame of reference at this point) is applied along the fork
> centerline. In order to rotate the fork you must have a component of
> force offset by some radius from the center or rotation. With zero
> trail, you don't have this. So, if you were on this bike you would fall
> down. You can't ride this bike no handed. Now consider what happens
> when you are on the bike. You feel the bike start to fall over as you
> lean so you turn the bars to steer into the turn. This is where the
> problem comes in. Since you have zero trail all you are doing is
> rotating the contact point on the pavement. A true point source does not
> have a directional component. In this case though the reality is that
> the contact patch looks more like a square or a rectangle than a point so
> it will have a directional component. Will this directional component be
> enough to actually direct the bike into the corner? Yes - the front end
> will act like a unicycle. I'm not sure how rideable this bike would be.
> My instincts tell me only at very slow speeds.

A typical model would constrain even a point contact patch not to slide on
the ground, even with idealized knife-blade wheels. A model that lets the
contact point slide would only be useful for modeling bicycles on, say, ice
rinks. I think you'll find *any* bicycle is difficult to steer in such a
situation.

--
Benjamin Lewis

I regret to say that we of the FBI are powerless to act in cases of
oral-genital intimacy, unless it has in some way obstructed interstate
commerce. -- J. Edgar Hoover

 

[ML]

[email protected] wrote:
> On Tue, 15 Jun 2004 07:54:28 -0400, ML
> <[email protected]> wrote:
>
>
>>Benjamin Lewis wrote:
>>
>>>[email protected] wrote:
>>>
>>>
>>>
>>>>Benjamin Lewis wrote:
>>>>
>>>>
>>>>>[email protected] wrote:
>>>>>
>>>>>
>>>>>
>>>>>>If you have zero trail you can't steer. You'll fall over.
>>>>>
>>>>>Huh? I think you need to reexamine your model of how bicycle steering
>>>>>works. Of course you can steer on a bicycle with zero trail. It's been
>>>>>done. People have even successfully ridden bicycles with negative
>>>>>trail.
>>>>
>>>>We aren't talking about negtive trail, we're talking about zero trail. If
>>>>you have zero trail and you lean your bike over while riding it, how do
>>>>you make the bike steer back under you?
>>>
>>>
>>>By turning the handlebars.
>>>
>>>I'm not sure what you're confused about here. If the wheel is turned the
>>>front of the bike will move in the direction of the turn as the bike moves
>>>forward.
>>>
>>
>>I believe you are wrong on this but can't really prove it. Unless you
>>have a bike with true zero trail, you can't prove your point either so
>>these are just mind exercises.
>>
>>If you consider your contact patch as a point on the pavement, turning
>>your handlebars on a bike with zero trail will not do anything for you.
>> It will continue to try to go forward (I believe) and ultimately you
>>will end up on the ground. Why do I say this? For a couple reasons.
>>Consider what happens to your bike when you lean it to the left while
>>walking it. The front wheel swings to the right and the bike turns into
>>the direction it was leaned. This is how a person is able to ride a
>>bike no handed. The bike naturally does the steering for you - you
>>affect your direction of travel by strictly leaning the bike through the
>>saddle. Now consider what would happen if you leaned a bike with zero
>>trail to the left - nothing. The bike would just lean, the front wheel
>>would continue straight down the road. Why? Because with zero trail
>>there is no torque component in either the CW or CCW direction. The
>>component of the force vector which is perpendicular to the fork (the
>>frame of reference at this point) is applied along the fork centerline.
>> In order to rotate the fork you must have a component of force offset
>>by some radius from the center or rotation. With zero trail, you don't
>>have this. So, if you were on this bike you would fall down. You can't
>>ride this bike no handed. Now consider what happens when you are on the
>>bike. You feel the bike start to fall over as you lean so you turn the
>>bars to steer into the turn. This is where the problem comes in. Since
>>you have zero trail all you are doing is rotating the contact point on
>>the pavement. A true point source does not have a directional
>>component. In this case though the reality is that the contact patch
>>looks more like a square or a rectangle than a point so it will have a
>>directional component. Will this directional component be enough to
>>actually direct the bike into the corner? Yes - the front end will act
>>like a unicycle. I'm not sure how rideable this bike would be. My
>>instincts tell me only at very slow speeds.
>>
>>BTW, I briefly looked through my copy of Bicycle Science last night &
>>could find no reference to any experiments done with zero trail bikes.
>>All references were to various combinations of positive or negative
>>trail bikes. If you can direct me to references (or to the pages in
>>Bicycle Science) documenting zero trail bikes I'd love to read them. I
>>can't think of anything in normal usage that would be equivalent.
>>Shopping carts, cars, motorcycles, scooters - they all have trail
>>components.
>>
>>Jobst, any thoughts on this subject?
>>
>>MOO,
>>Matt
>
>
> Dear Matt,
>
> I think that David Jones concluded that we can ride damned
> near anything in terms of front-end geometry, although most
> bizarre versions are good for little except for parking lot
> demonstrations.
>
> Below are some articles mentioned in a post elsewhere
> by Jonathan Thornburg:
>
> < [email protected]>
>
> http://www.thp.univie.ac.at/~jthorn/home.html
>
> Carl Fogel
>
> David E. H. Jones
> "The Stability of the Bicycle"
> Physics Today , April 1970, 34-40
>
> Framk Rowland Whitt and David Gordon Wilson
> "Bicycling Science", 2nd edition
> MIT Press, 1982, ISBN 0-262-73060-X (paperback), -23111-5
> (hardcover)
> ... this book has a chapter devoted to stability,
>
> J. Lowell and H. D. McKell
> "The Stability of Bicycles"
> American Journal of Physics 50(12), Dec 1987, 1106-1112
>
> G Franke, W Suhr, and F Reisz,
> "An advanced model of bicycle dynamics",
> European Journal of Physics 11 (1990) 116-121
>
> John Maddox's report of the Franke/Suhr/Reisz paper
> in Nature 346, 2 Aug 1990, p 407.

Carl:

The URL for jthorn is not valid. I did a websearch and found no other
information.

Thanks,
Matt

 

[[email protected]]

On Wed, 16 Jun 2004 08:11:40 -0400, ML
<[email protected]> wrote:

>[email protected] wrote:
>> On Tue, 15 Jun 2004 07:54:28 -0400, ML
>> <[email protected]> wrote:
>>
>>
>>>Benjamin Lewis wrote:
>>>
>>>>[email protected] wrote:
>>>>
>>>>
>>>>
>>>>>Benjamin Lewis wrote:
>>>>>
>>>>>
>>>>>>[email protected] wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>>>If you have zero trail you can't steer. You'll fall over.
>>>>>>
>>>>>>Huh? I think you need to reexamine your model of how bicycle steering
>>>>>>works. Of course you can steer on a bicycle with zero trail. It's been
>>>>>>done. People have even successfully ridden bicycles with negative
>>>>>>trail.
>>>>>
>>>>>We aren't talking about negtive trail, we're talking about zero trail. If
>>>>>you have zero trail and you lean your bike over while riding it, how do
>>>>>you make the bike steer back under you?
>>>>
>>>>
>>>>By turning the handlebars.
>>>>
>>>>I'm not sure what you're confused about here. If the wheel is turned the
>>>>front of the bike will move in the direction of the turn as the bike moves
>>>>forward.
>>>>
>>>
>>>I believe you are wrong on this but can't really prove it. Unless you
>>>have a bike with true zero trail, you can't prove your point either so
>>>these are just mind exercises.
>>>
>>>If you consider your contact patch as a point on the pavement, turning
>>>your handlebars on a bike with zero trail will not do anything for you.
>>> It will continue to try to go forward (I believe) and ultimately you
>>>will end up on the ground. Why do I say this? For a couple reasons.
>>>Consider what happens to your bike when you lean it to the left while
>>>walking it. The front wheel swings to the right and the bike turns into
>>>the direction it was leaned. This is how a person is able to ride a
>>>bike no handed. The bike naturally does the steering for you - you
>>>affect your direction of travel by strictly leaning the bike through the
>>>saddle. Now consider what would happen if you leaned a bike with zero
>>>trail to the left - nothing. The bike would just lean, the front wheel
>>>would continue straight down the road. Why? Because with zero trail
>>>there is no torque component in either the CW or CCW direction. The
>>>component of the force vector which is perpendicular to the fork (the
>>>frame of reference at this point) is applied along the fork centerline.
>>> In order to rotate the fork you must have a component of force offset
>>>by some radius from the center or rotation. With zero trail, you don't
>>>have this. So, if you were on this bike you would fall down. You can't
>>>ride this bike no handed. Now consider what happens when you are on the
>>>bike. You feel the bike start to fall over as you lean so you turn the
>>>bars to steer into the turn. This is where the problem comes in. Since
>>>you have zero trail all you are doing is rotating the contact point on
>>>the pavement. A true point source does not have a directional
>>>component. In this case though the reality is that the contact patch
>>>looks more like a square or a rectangle than a point so it will have a
>>>directional component. Will this directional component be enough to
>>>actually direct the bike into the corner? Yes - the front end will act
>>>like a unicycle. I'm not sure how rideable this bike would be. My
>>>instincts tell me only at very slow speeds.
>>>
>>>BTW, I briefly looked through my copy of Bicycle Science last night &
>>>could find no reference to any experiments done with zero trail bikes.
>>>All references were to various combinations of positive or negative
>>>trail bikes. If you can direct me to references (or to the pages in
>>>Bicycle Science) documenting zero trail bikes I'd love to read them. I
>>>can't think of anything in normal usage that would be equivalent.
>>>Shopping carts, cars, motorcycles, scooters - they all have trail
>>>components.
>>>
>>>Jobst, any thoughts on this subject?
>>>
>>>MOO,
>>>Matt
>>
>>
>> Dear Matt,
>>
>> I think that David Jones concluded that we can ride damned
>> near anything in terms of front-end geometry, although most
>> bizarre versions are good for little except for parking lot
>> demonstrations.
>>
>> Below are some articles mentioned in a post elsewhere
>> by Jonathan Thornburg:
>>
>> < [email protected]>
>>
>> http://www.thp.univie.ac.at/~jthorn/home.html
>>
>> Carl Fogel
>>
>> David E. H. Jones
>> "The Stability of the Bicycle"
>> Physics Today , April 1970, 34-40
>>
>> Framk Rowland Whitt and David Gordon Wilson
>> "Bicycling Science", 2nd edition
>> MIT Press, 1982, ISBN 0-262-73060-X (paperback), -23111-5
>> (hardcover)
>> ... this book has a chapter devoted to stability,
>>
>> J. Lowell and H. D. McKell
>> "The Stability of Bicycles"
>> American Journal of Physics 50(12), Dec 1987, 1106-1112
>>
>> G Franke, W Suhr, and F Reisz,
>> "An advanced model of bicycle dynamics",
>> European Journal of Physics 11 (1990) 116-121
>>
>> John Maddox's report of the Franke/Suhr/Reisz paper
>> in Nature 346, 2 Aug 1990, p 407.
>
>Carl:
>
>The URL for jthorn is not valid. I did a websearch and found no other
>information.
>
>Thanks,
>Matt

Dear Matt,

Try him at this page:

http://www.aei.mpg.de/~jthorn/home.html

Carl Fogel