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General Category => General Discussion => Topic started by: Huzo on March 21, 2019, 05:37:06 PM
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I’ve long read the comment regarding how a bike will change angle of lean quickly due to the “low centre of gravity”.
I have a working man’s level of scepticism regarding this but welcome educating.
As I see it, when you introduce an input from the ‘bars, the wheels are displaced laterally and the centre of mass initially tries to remain in the same plane of motion, centred somewhere around your nether region.
Hi there Isaac....!
Akin to, if you get a broom and stand it vertically on your palm, brush upward, you can keep it upright by moving the point of support around the C of M. The heavier is the head of of the broom, the quicker you can move your palm due to the higher centre of mass.
When you push on the bar of your new V85, the wheels will be moved an amount, out from under the C of M and the bike will begin to fall over, until the COUNTERSTEER...! Takes effect and balance is restored.
So in the real world, I’m suggesting that a given bike would be more “flickable” with a bag of cement strapped to the tank than without....!
Different thing in the static state at the lights though..
Comments...?
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Hugo, you seem to like mind stretches, concept manipulation - have you read "The Upper Half of the Motorcycle, on the unity of rider & machine", by Bernt Spiegel. Recommended. I think you'd like it. For example - part 1 is entitled "It's a miracle that motorcycling works at all".
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It is more complicated than that Huzo . Mighty Honda experimented with fuel tanks placed really low , not unlike a modern Gold Wing on their GP bikes sometime around 1990 . The results were mixed , apparently the bikes became more stable at really large lean angles and high speeds , but resisted quick steering inputs . On a GP bike with stupid steep steering head angles this wasn't a big deal , but the riders claimed it *felt weird* , so Honda gave up on the idea . As a general rule , at slow speeds a higher CoG is beneficial , at higher speeds like a GP bike is capable of a lower CoG is better . Confused yet ?
So like so many other hard and fast rules , it kinda depends . Probably for street purposes a CoG a around the gap between the fuel tank and the top of the engine is about right, depending on steering geometry and wheelbase .
Oh , heavier bikes probably work better with a slightly lower CoG , really light bikes don't seem to care as much , then again we are now dealing with center of mass, which is different than CoG .
Dusty
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As usual Dusty is pretty much spot on. Honda figured it out in the '80s. You can do the vectors if you wish but..
I prefer bikes with lower center of gravity. They feel like fun. A modern trials bike would be too far for a street bike but I liked the horizontal singles I've ridden.
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:popcorn: between Huzo + dUSTY MY HEAD IS SPINNING===EITHER TOO MUCH makers Mark or===lack of education on my part :weiner:
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Picture a lollipop. One standing with the pop on top, the other with the pop on bottom.
Which would tip over easier?
(https://i.ibb.co/SNJT6QZ/imagesx.jpg) (https://ibb.co/SNJT6QZ)
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Phil Irving wrote a book, Motorcycle Engineering . It's my go to book for questions like these for it covers this as well as other good stuff. When I go out to the shop tomorrow I'll look at it. See if you can find a copy, it'll make you the smartest guy in the room.
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we are now dealing with center of mass, which is different than CoG .
Dusty
Hmmm...
Just a couple of quick ones Dusty.
A bike does not “know” it is leaned over in a balanced turn because the sum of forces are zero, other than the centripetal force accelerating it towards the centre of the circle..
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Why is the centre of mass different than the centre of gravity, when the sum of gravitational vectors acts through the centre of mass ?
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As usual Dusty is pretty much spot on. Honda figured it out in the '80s. You can do the vectors if you wish but..
I prefer bikes with lower center of gravity. They feel like fun. A modern trials bike would be too far for a street bike but I liked the horizontal singles I've ridden.
I’m a big supporter of blind loyalty Aaron, but I was addressing the voracity of the statement that a bike is more “flickable” due to it’s “lower centre of gravity”.
If I wanted muddy waters, I’d go for a dip in the Mississippi, or put on a CD of an old blues man..
Just a bit of focus on what I was asking about and a response based on physics, not “how you feel”, or what you (or I), “prefer..”
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Picture a lollipop. One standing with the pop on top, the other with the pop on bottom.
Which would tip over easier?
(https://i.ibb.co/SNJT6QZ/imagesx.jpg) (https://ibb.co/SNJT6QZ)
The one with the pop on top is inherently more statically unstable, but can be stabilised more readily by moving the point of support back under the mass when displaced from vertical than the upside down one.
Put the one in the picture on your hand and balance it by moving your palm, you’ll have some success.
Now try moving the pop halfway down the stick, you’ll have less success maintaining dynamic stability.
When a point of support is moved under a mass to maintain balance, we rely on inertia to hold the c of m still, in a spatial sense as that point of support is re positioned.
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Phil Irving wrote a book, Motorcycle Engineering . It's my go to book for questions like these for it covers this as well as other good stuff. When I go out to the shop tomorrow I'll look at it. See if you can find a copy, it'll make you the smartest guy in the room.
I already am, I’m the only guy in the room.. :rolleyes:
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Hugo, you seem to like mind stretches, concept manipulation - have you read "The Upper Half of the Motorcycle, on the unity of rider & machine", by Bernt Spiegel. Recommended. I think you'd like it. For example - part 1 is entitled "It's a miracle that motorcycling works at all".
When considering this concept, the rider and machine are a single mass with only one centre of gravity (mass).
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Hmmm...
Just a couple of quick ones Dusty.
A bike does not “know” it is leaned over in a balanced turn because the sum of forces are zero, other than the centripetal force accelerating it towards the centre of the circle..
and
Why is the centre of mass different than the centre of gravity, when the sum of gravitational vectors acts through the centre of mass ?
You're doin' my head in cobber. One needs a few beers before contemplating this type of esoterica. Mass carried high, i.e further away from the pivot will have greater inertia at speed (in relation to the arc of leaning motion, not the bike's linear motion). Therefore, the whole mass becomes less 'chuckable' or 'flickable'. Greater countersteering effort is required to counter not just the gyroscopic effect of wheels in rotation, but the 'arc of inertia' (my own ridiculously pompous name for it) of mass. Once flicked or chucked over, the gyro effect counterbalances the combined mass through the bikes 'linear' cornering arc unless further attitude changes (lean angles) are called for, such as straightening up again. Think of it as an arc of a pendulum. The further away the mass is placed from the fulcrum, the greater the 'strain' on the pivot for a given velocity of motion..... I think! Bugger me, I'm not so sure at all anymore....
Sideways mobile masses have a greater effect the further they are from the pivot point. Which is why leaning my own corpulent, portly arse to the inside of a bend off the bike's seat makes a substantial difference to lean angles: not the prettiest sight, but extremely useful in the wet.
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When considering this concept, the rider and machine are a single mass with only one centre of gravity (mass).
Well , not exactly , the rider isn't static . The rider can and does affect both center of gravity and center of mass . See , here is the problem , you attempting to answer the question W/O allowing for the variables . In the simplest terms , yes a higher CoG will allow the bike to be more flickable , until as you mentioned , other accelerative forces come into play .
Oh , while the center of mass and the CoG will almost always be the same , once a rider is introduced , that changes .
Ain't motorbike physics fun :laugh:
Dusty
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You're doin' my head in cobber. One needs a few beers before contemplating this type of esoterica. Mass carried high, i.e further away from the pivot will have greater inertia at speed (in relation to the arc of leaning motion, not the bike's linear motion). Therefore, the whole mass becomes less 'chuckable' or 'flickable'. Greater countersteering effort is required to counter not just the gyroscopic effect of wheels in rotation, but the 'arc of inertia' (my own ridiculously pompous name for it) of mass. Once flicked or chucked over, the gyro effect counterbalances the combined mass through the bikes 'linear' cornering arc unless further attitude changes (lean angles) are called for, such as straightening up again. Think of it as an arc of a pendulum. The further away the mass is placed from the pendulum, the greater the 'strain' on the pivot for a given velocity of motion..... I think! Bugger me, I'm not so sure at all anymore....
Sideways mobile masses have a greater effect the further they are from the pivot point. Which is why leaning my own corpulent, portly arse to the inside of a bend off the bike's seat makes a substantial difference to lean angles: not the prettiest sight, but extremely useful in the wet.
You are correct, and it is officially called "moment of inertia".
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Hmmm...
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Dusty has done a nice job here. I'll add, and I wish I could remember exact, but several years ago Kevin Cameron wrote about how MotoGP bikes has their COG and Moment of Inertia in such a way that the COG was higher up. Something about a pendulum effect and getting the bike from one side over to the other quickly and with less effort. Bottom line was the COG was not low. There was also mention that a designer can get the COG below street level.
I don't remember all the engineering details but the fact that a MOTOGP bike (I know, not for the street!) didn't have that low GOG and for better, or worse, I stopped reading all the OEM marketing nonsense about it.
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The one with the pop on top is inherently more statically unstable, but can be stabilised more readily by moving the point of support back under the mass when displaced from vertical than the upside down one.
Put the one in the picture on your hand and balance it by moving your palm, you’ll have some success.
Now try moving the pop halfway down the stick, you’ll have less success maintaining dynamic stability.
When a point of support is moved under a mass to maintain balance, we rely on inertia to hold the c of m still, in a spatial sense as that point of support is re positioned.
Which would cause more reaction, an input on the "pop on top" or the other one?
Hugo asked---how a bike will change angle of lean quickly due to the “low centre of gravity”.
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Which would cause more reaction, an input on the "pop on top" or the other one?
Hugo asked---how a bike will change angle of lean quickly due to the “low centre of gravity”.
That’s right Yogi.
All I wanted to discuss without diverging down side streets of unrelated analogies was...
Is a low c of g a benefit in enhancing “flick ability”, the answer I suggest is no. I’d like to get an answer from a Physicist, because our knowlege can be contaminated from years of conventional wisdom.
We must remember that when viewed from the front, a bike does not have the rider move about above the wheels to initiate a lean, the wheels move about below the rider.
Have you ever ridden too close to a gutter on your left on your pushbike and tried to turn right to get away?
Sometimes you can’t because the wheels have to move out from under you to the left initially, to get the bike leaning to the right.
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I’m a big supporter of blind loyalty Aaron, but I was addressing the voracity of the statement that a bike is more “flickable” due to it’s “lower centre of gravity”.
If I wanted muddy waters, I’d go for a dip in the Mississippi, or put on a CD of an old blues man..
Just a bit of focus on what I was asking about and a response based on physics, not “how you feel”, or what you (or I), “prefer..”
Sheesh. Agreement is not blind loyalty.
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As I see it, when you introduce an input from the ‘bars, the wheels are displaced laterally and the centre of mass initially tries to remain in the same plane of motion, centred somewhere around your nether region.
We must remember that when viewed from the front, a bike does not have the rider move about above the wheels to initiate a lean, the wheels move about below the rider.
It's a fallacy.
Sure, you can weave at slow speeds and displace the wheels laterally, but the rider has to force that.
In normal riding, steering inputs at the handlebars push the bike over. The tires stay on the same line.
The steering input is resisted by the gyroscopic force of the wheels and the steering geometry.
(https://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Bike_weaving.gif/220px-Bike_weaving.gif)
(https://thumbs.gfycat.com/ContentKlutzyButterfly-size_restricted.gif)
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I already am, I’m the only guy in the room.. :rolleyes:
It hasn't exactly worked for me
https://www.google.com/search?client=safari&hl=en-us&q=Phil+Irving&stick=H4sIAAAAAAAAAONgVuLSz9U3MKm0TC4yfMToyi3w8sc9YSmbSWtOXmM04-IKzsgvd80rySypFNLgYoOy5Lj4pJC0aTBI8XAh8XkWsXIHZGTmKHgWlWXmpQMAyrE_n2QAAAA&sa=X&ved=0ahUKEwj-vu2q75XhAhVj7IMKHd0zC-gQgYUCCF0oADAH&biw=1024&bih=728
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Talking about CoM and polar moment of inertia as they affect "flickability" doesn't make much sense to me -- other parameters must be just as important or more so. These would be mainly steering geometry (rake, trail, wheelbase) and gyroscopic effects (weight of wheel rims/tires, rotational speed) and overall inertia (mass x velocity). Comparing my Mille with my '70 Triumph, the Triumph is absolutely more flickable -- it's 20% lighter (including rider weight), the steering geometry is close (about 27 degrees rake for the TR vs about 29 degrees Tonti) and 55 inches vs 58 inches wheelbase. The Guzzi wheels probably have more rotational inertia. Full fuel vs empty weight is only a 4.5% difference in both bikes so I don't think the high tank much affects the height of the CoM. So quantifying "flickability" could be a complex equation.
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Thinking I could hobble out to the shop, take down Phil Irving's excellent Motorcycle Engineering, scan through it, refreshing my feeble brain and be able to speak intelligently on the topic. After reading some of the first chapter: An outline of the Problem, I understand I forgot most of the rest of the book and need a couple weeks to read it again. Don't have time for that as its spring here and I have to get all the motorbikes ready. back to the original post, according to Phil, there are two considerations to start off with: the crew sits ON the machine, Not IN it. the second is that, by its very nature, a single-tracker is in unstable equilibrium, i.e., it cannot, when stationary, stand up by itself. so when we put such a thing in motion, it is complex enough for me to have to read over it.
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Math is hard! Did you make it around that last corner without falling over? Its all good then! :evil:
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Math is hard! Did you make it around that last corner without falling over? Its all good then! :evil:
that's the rub now aint it. My problem was that things were fine rolling down the road, but due to disease, my right leg wouldn't go down so id fall over at a stop. so on went a sidecar. everybody is happy!
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So in the real world, I’m suggesting that a given bike would be more “flickable” with a bag of cement strapped to the tank than without....!
Different thing in the static state at the lights though..
the bike with the added upper weight would be more flickable in that that it would be easier to start the lean with the added weight that high. but once the lean is started the inertia of the extra weight would make it harder to stop that motion. it would tend to keep going over until another force stopped it.
relates to polar moment of inertia on a race car in which one attempts to keep the weight between the wheelbase. weight at the extreme ends makes the vehicle easier to rotate around the central axis (hanging the tail out) but harder to stop that rotation. think corvairs and porsches
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the bike with the added upper weight would be more flickable in that that it would be easier to start the lean with the added weight that high. but once the lean is started the inertia of the extra weight would make it harder to stop that motion. it would tend to keep going over until another force stopped it.
There's a big difference between top-heavy and flickable. My VX800 felt topheavy -- it wanted to fall into slow turns -- but wasn't flickable. Thanks to a long wheelbase and I suppose relaxed head angle it felt stable in a straight line and in high-speed turns.
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I think low CG may be good when the roll rate is slow enough that the bike is rolling about the tire contact patch, and therefore the CG is changing elevation relative to the ground as the bike rolls. Higher CG and lower roll moment of inertia (around the CG) works better when the roll rate is higher and the CG is not changing elevation, the suspension is instead extending or compressing during the period over which the bike is rolling. The latter case is what a race bike more often does, hence Honda’s conclusion that low CG isn’t the point.
If ‘slow’ steering geometry means that the rider is not strong enough to roll the bike quickly, low CG is probably a good thing. The best example of that might be a bevel SS Ducati.
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There's a big difference between top-heavy and flickable. My VX800 felt topheavy -- it wanted to fall into slow turns -- but wasn't flickable. Thanks to a long wheelbase and I suppose relaxed head angle it felt stable in a straight line and in high-speed turns.
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my point exactly
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I’m beginning to accept that there will be an interdependence of one factor over another.
There are a lot of “Dusty” corners in my knowlege that remind me how old I’m becoming. I just perceived that the stock statement of nimbleness and flickability being a function of low C of G and 3/5th’s of 5/8th’s of SFA else....
Needed some examination. I like Tusayan’s approach to this stuff, he’s ahead of me but I like his approach to working man’s Physics discussions.
I don’t exactly know what a curmudgeon is, but I think I’m becoming one, because I bristle a bit, when I hear illadvised or inaccurate statements trotted out blithely, accompanied by the sage nodding of heads.
I’ve been pulled up here on that very issue by blokes of deeper knowlege occasionally and am the better for it.
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Oh, and response #16.
Duty has done a nice job, but I prefer Dusty’s take on things, although I’ll admit he does have a devotion to Duty...
Also, how does one manage to get the C of G below street level ?
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I’m beginning to accept that there will be an interdependence of one factor over another.
There are a lot of “Dusty” corners in my knowlege that remind me how old I’m becoming. I just perceived that the stock statement of nimbleness and flickability being a function of low C of G and 3/5th’s of 5/8th’s of SFA else....
Needed some examination. I like Tusayan’s approach to this stuff, he’s ahead of me but I like his approach to working man’s Physics discussions.
I don’t exactly know what a curmudgeon is, but I think I’m becoming one, because I bristle a bit, when I hear illadvised or inaccurate statements trotted out blithely, accompanied by the sage nodding of heads.
I’ve been pulled up here on that very issue by blokes of deeper knowlege occasionally and am the better for it.
You and others don't need to stop asking questions, and not every answer is going to be correct.
But it makes us all stop and think. And that's always a good thing.
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Oh, and response #16.
Duty has done a nice job, but I prefer Dusty’s take on things, although I’ll admit he does have a devotion to Duty...
Also, how does one manage to get the C of G below street level ?
Dig a tunnel? :shocked:
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You and others don't need to stop asking questions, and not every answer is going to be correct.
But it makes us all stop and think. And that's always a good thing.
Now THAT Sir..is my point exactly..! :bow:
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Hell , even the *experts* have a hard time coming to a consensus on this . The fact is , what works is what works , bending the math to suit comes later .
Dusty
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Hell , even the *experts* have a hard time coming to a consensus on this . The fact is , what works is what works , bending the math to suit comes later .
Dusty
:thumb:
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Peter , there is a young man in the physics dept at a large state U who worked for me in college , we run these motorbike experiments every so often, he lays all of the math out , then we discuss the real world effects , then we normally laugh about all of it . Carpenter math only gets me so far :laugh:
The concept of raising the forks to decrease rake angle comes up once a year or so , another misunderstood concept , because when you run the math , raising the fork 26 MM reduces rake by like .2 degrees using 28 degrees as a baseline . What most riders are feeling is increased weight on the front tire from tilting the chassis , and the increased feeling of control from having their body tilted forward . Once again , motorbike physics are fun , aren't they ? :grin:
Dusty
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Peter , there is a young man in the physics dept at a large state U who worked for me in college , we run these motorbike experiments every so often, he lays all of the math out , then we discuss the real world effects , then we normally laugh about all of it . Carpenter math only gets me so far :laugh:
The concept of raising the forks to decrease rake angle comes up once a year or so , another misunderstood concept , because when you run the math , raising the fork 26 MM reduces rake by like .2 degrees using 28 degrees as a baseline . What most riders are feeling is increased weight on the front tire from tilting the chassis , and the increased feeling of control from having their body tilted forward . Once again , motorbike physics are fun , aren't they ? :grin:
Dusty
Yes old mate.
Same with people who think that increasing preload on shocks, makes them stiffer... :evil:
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Ha ha. I corrected my typo-apologizes to DUSTY!
As for GOG below street level-it was a simple graph that illustrated an intersection of various factors that determine where COG is. That intersection can be below the bike to the extent that the lines intersect below grade. It's not that hard a concept. Something tells me I saw it in Camaron's book.
I'll have to dig it out and check. Nonetheless, if you understand that moment of inertia, COG, center of mass, and others are determined by vectors (I think that's it IIRC) than the concept of one or more of those measures being located above or below is not unreasonable.
The entire subject sounds like a perfect topic for "Ask Kevin" at CycleWorld.
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Ha ha. I corrected my typo-apologizes to DUSTY!
As for GOG below street level-it was a simple graph that illustrated an intersection of various factors that determine where COG is. That intersection can be below the bike to the extent that the lines intersect below grade. It's not that hard a concept. Something tells me I saw it in Camaron's book.
I'll have to dig it out and check. Nonetheless, if you understand that moment of inertia, COG, center of mass, and others are determined by vectors (I think that's it IIRC) than the concept of one or more of those measures being located above or below is not unreasonable.
The entire subject sounds like a perfect topic for "Ask Kevin" at CycleWorld.
I think you may be referring to the concept of taking moments to determine C of G..
It can be in relation to determining weight and balance when calculating loading in light aircraft or similar and C of G position to determine if it is within limits.
When calculating moments any point can be used and if the system is in equilibrium, the resultant will be zero.
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As for GOG below street level-it was a simple graph that illustrated an intersection of various factors that determine where COG is. That intersection can be below the bike to the extent that the lines intersect below grade. It's not that hard a concept. Something tells me I saw it in Camaron's book.
More likely the point below pavement was the center of rotation when the bike rocks forward and aft with braking and acceleration. Confusion may arise from the fact that a body in flight may rotate around the CoM (or CoG) (aerodynamics permitting) but a machine on the ground certainly will not.
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More likely the point below pavement was the center of rotation when the bike rocks forward and aft with braking and acceleration. Confusion may arise from the fact that a body in flight may rotate around the CoM (or CoG) (aerodynamics permitting) but a machine on the ground certainly will not.
Agreed..
But if you consider a bike coming head on that initiates a turn.
Let us say the bike turns to (our) right, or a left hander for the rider.
The wheels will be displaced to (our) left and the rider’s head will be displaced to (our) right. Somewhere in between these two points is a spot where the lateral displacement vector is zero, and that is the C of M of the system.
In the case of a 130 kg rider on a 10 kg pushbike, the lateral displacement of the wheels will be considerably more than that of the rider’s head, this is because the C of M is quite high.
The same rider on a wide glide with a lightweight flag above his bike to represent the same height as example #1, will exhibit a relatively small lateral movement of the wheels versus the top of the flag.
This is because the C of M is very low.
Guess which one is more umm.... “flickable”.
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But if you consider a bike coming head on that initiates a turn.
Let us say the bike turns to (our) right, or a left hander for the rider.
The wheels will be displaced to (our) left and the rider’s head will be displaced to (our) right. Somewhere in between these two points is a spot where the lateral displacement vector is zero, and that is the C of M of the system.
In the case of a 130 kg rider on a 10 kg pushbike, the lateral displacement of the wheels will be considerably more than that of the rider’s head, this is because the C of M is quite high.
The same rider on a wide glide with a lightweight flag above his bike to represent the same height as example #1, will exhibit a relatively small lateral movement of the wheels versus the top of the flag.
This is because the C of M is very low.
Guess which one is more umm.... “flickable”.
Can't agree with this. The tires are prevented from moving significantly outward from the arc by engagement with the pavement, and in fact the banking rotation has to be centered on the contact patches of the tires. Any outward movement of the front wheel -- maybe an inch or two -- is induced by the steering geometry and is what in turn induces lean angle when countersteering. I suspect the rear wheel actually tracks INSIDE the arc of the turn unless throttle-induced wheelspin breaks the traction for a power slide.
Comparing steering quickness or flickability with a bicycle or push bike is unrealistic not only because of the weight differences but also because bicycles typically have a 17 degree rake and trail is at the low end of what would be acceptable with a motorcycle -- just a bit more than 2 inches.
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This is the first thread on this forum I’ve ever read all the way through without understanding a single word. Congrats, guys!
:coffee:
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Can't agree with this. The tires are prevented from moving significantly outward from the arc by engagement with the pavement, and in fact the banking rotation has to be centered on the contact patches of the tires. Any outward movement of the front wheel -- maybe an inch or two -- is induced by the steering geometry and is what in turn induces lean angle when countersteering. I suspect the rear wheel actually tracks INSIDE the arc of the turn unless throttle-induced wheelspin breaks the traction for a power slide.
Comparing steering quickness or flickability with a bicycle or push bike is unrealistic not only because of the weight differences but also because bicycles typically have a 17 degree rake and trail is at the low end of what would be acceptable with a motorcycle -- just a bit more than 2 inches.
I think some of that is a bit sketchy, but I don’t have enough raw understanding to be able to engage.
The only thing I’d add, is that the engagement with the pavement is not “preventing” the tracking outside the arc, because the wider arc is initiated by the first countersteer input and that is only possible “because” of that engagement.
Imagine if you were on ice and there was no engagement, the first input on the ‘bar would result if an immediate crash.
The tyres are describing a larger radius than the rider’s head, gravity (downwards) is preventing the rider being thrown outwards (as if in a car), and centrifugal force (sic), is preventing the rider falling inwards due to lean, both are in equal measure.
The reason I introduced the heavy rider on the light bike, was to give an example of high C of G.
However..
The waters are becoming muddied and my original question is becoming blurred at the edges. Also I think I need to be schooled by someone way better than me at Physics, because I may be carrying some false ideas that have manifested over the years.
That great Physicist and Philosopher Albert Einstein put it best when he said..(and this applies to me)
“If you cannot explain something simply..
You probably don’t understand it properly yourself...”
So I guess is off to Princeton with me. :whip2: (Love the chat though..)
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I think some of that is a bit sketchy, but I don’t have enough raw understanding to be able to engage.
The only thing I’d add, is that the engagement with the pavement is not “preventing” the tracking outside the arc, because the wider arc is initiated by the first countersteer input and that is only possible “because” of that engagement.
Imagine if you were on ice and there was no engagement, the first input on the ‘bar would result if an immediate crash.
The tyres are describing a larger radius than the rider’s head, gravity (downwards) is preventing the rider being thrown outwards (as if in a car), and centrifugal force (sic), is preventing the rider falling inwards due to lean, both are in equal measure.
The reason I introduced the heavy rider on the light bike, was to give an example of high C of G.
Plus that aforementioned gyroscopic force from the wheels (& to a much lesser extent the rotating masses of the engine) which conspire to keep the bike perpendicular to the surface. The countersteering effort required to initiate the turn is to allow these gyroscopes to tilt sideways in the appropriate direction.
One can feel this effect quite easily with a power planer. At speed the planer's cutterhead (the rotating mass that forms a gyroscope) will try to stay perpendicular. If the planer is turned (rotated) around a vertical axis it will naturally try to tilt in the opposite direction, just as a bicycle (motorised or pedalled) will. Conversely, if the planer is tilted sideways, it will naturally wish to rotate horizontally opposite.
This clearly illustrates the interrelationship between gyroscopes and countersteering.
Any vehicle's wheels will be displaced outwards in a curve. Irrespective of how many individual wheels or even axles are involved, the steering axle (front in most vehicles, but rear in some machinery like the pea viners I used to drive in my school holidays) will always be displaced outwards in a curve. The steering axle must always describe an arc of greater radius than a fixed axle. The only exception that I'm aware of is articulated chassis vehicles, where the arcs tend to equalise.
When I was designing forest roads for large 22 wheel log-lorries in the 70s they were built as narrow as practicable. Curves were designed to connect the straightaways (obviously), but were carefully 'transitioned' (i.e. halved) for the first & last chord of radii to compensate for the differential radii described by the jinker as it enters & leaves a curve. The widest arc offset was from the steering axle of the prime mover, the tightest from the third & last trailing axle on the trailer. There was quite a difference in these radii: the 'tighter' the curve, the greater the offset required.
There was fairly basic geometry applied to the curve formula, but it was so long ago that it's all but disappeared into the sphagnum bog of trivia that clogs my mind.... Yes, there's probably some slight additional horizontal displacement (rotation) of fulcrum points as the mass of a bicycle in motion leans as it transitions through an arc, but the subtle interplay of Physics & Geometry is now well beyond my ageing comprehension to calculate, or even adequately describe.
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Geez Peter , I explained it as simply as possible , what do you want ? :shocked:
Dusty
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Geez Peter , I explained it as simply as possible , what do you want ? :shocked:
Dusty
I think you’re joking so I’ll chuckle then go on to something else Dusty.
Examples of what Honda did, or how different bikes “feel” and various analogies, do help to form a picture and provide some understanding, but I tend to look for explanations based on sound principles of Physics that are dumbed down to my level.
My University Engineering background has more dust on it than a Cedar Vale picnic table, so I lose track quicker than I used to..
I think I not only don’t remember some stuff that I used to have at my fingertips, but I’m starting to spruke and apply beliefs that are not soundly based.
Most of the responses here are equally as valid as mine or more so in some cases, but I can see patches of light coming through what is supposed to be a solid wall of factually based knowlege.
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Can't agree with this. The tires are prevented from moving significantly outward from the arc by engagement with the pavement, and in fact the banking rotation has to be centered on the contact patches of the tires.
Hard countersteering can steer the tires outward from under the CG. The effect of that model is that the bike rotates around the CG, which simultaneously translates downward. The suspension extends a little until the bike settles.
In actuality the bike rotates in a more complex way, somewhere between rotation around the tire patch and the CG... but I think that the harder the countersteering the closer the bike comes to rotating around the CG.
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Hard countersteering can steer the tires outward from under the CG. The effect of that model is that the bike rotates around the CG, which simultaneously translates downward. The suspension extends a little until the bike settles.
In actuality the bike rotates in a more complex way, somewhere between rotation around the tire patch and the CG... but I think that the harder the countersteering the closer the bike comes to rotating around the CG.
Ok.