question about frame geometry

[jroden]

I ride a real steady bike on the road, an Eddy Merckx MX Leader with a low BB, long (for a road bike) chain stays and heavy construction.

I threw some road wheels on my guru cross bike yesterday and was reminded again of the handling differences. Not a big deal, but less fun to ride around of the road, kind of topheavy and twitchy without feeling nimble.

So i slapped a tape on it and was surprised to find the cross bike:

-had the same bottom bracket height
-had a 2 inch longer wheelbase
-had the same bb drop
-was the same bar and saddle ht from the floor
-had longer chainstays
-had same saddle to bb relationship
-was a little shorter in cockpit
- same bar drop

So, why I wonder do the two bikes handle differently--it must be angles, which I did not measure.

and, would a geometry like my road bike work OK as a cross bike? I had always assumed the road bike had a much longer wheelbase and would be like turning a bus.

where I'm going with this dull post is wondering if "old school" Euro road race bike geometry would make for a decent riding cross bike that would be fun on the road?

[Peter P.]

What you've learned is a frame is the sum of its parts and design and not just an isolated feature.

In many cases it doesn't matter/bother the rider but if you're fussy, particular, or just plain tuned in to how bikes handle, then you'll notice a difference and will prefer one design over another.

But think about it this way: some sponsored professional would likely not be given a choice of frame design and would be handed an off the rack frame, yet they'd still go fast. You'd never hear them complain-heaven forbid they bad mouth their sponsor's bikes-they'd just deal with it.

Your 'cross bike handled differently partly because it's designed around larger diameter wheels i.e., perhaps a 35mm tire. By installing road wheels with a smaller say, 23mm tire, you reduced the trail figure and thus brought about the twitchy feeling you experienced. Sure; you could still ride it with road tires but as you discovered, wheel diameter plays a large part in how a bike handles and the difference between say, 23-35mm tires is significant. Too bad you couldn't fit fat tires on your Merckx to see how it's ride changes.

The top heaviness you felt could be due to heavier tubing used on the 'cross bike (I'm guessing here), or the slacker head tube angles common to 'cross bikes.

Road bike geometry wouldn't be optimum for a 'cross bike; you need more tire clearance for larger tires and mud. The slower handling and sometimes higher trail figure is to keep the bike in a straight line when hitting obstacles like roots, rocks, and bumpy terrain.

I'm not too sure what you mean by "old school" Euro road race geometry ('70's?, ''80's?, 'X0's?) but it's conceivable you could build a bike that would be a good compromise and a pleasure to ride both road and 'cross. This is where a colloboration with a custom builder comes in. It's quite possible this has already been achieved with Rivendell's Roadeo frame.

[Kontact]

While people talk about head tube angles a lot, the primary things that affect handling are trail and wheelbase. Trail determines how much effort it takes to establish and hold a turn, and wheelbase determines how tight a turn radius you'll have for a given lean angle.

[oldpotatoe]

I ride a real steady bike on the road, an Eddy Merckx MX Leader with a low BB, long (for a road bike) chain stays and heavy construction.

I threw some road wheels on my guru cross bike yesterday and was reminded again of the handling differences. Not a big deal, but less fun to ride around of the road, kind of topheavy and twitchy without feeling nimble.

So i slapped a tape on it and was surprised to find the cross bike:

-had the same bottom bracket height
-had a 2 inch longer wheelbase
-had the same bb drop
-was the same bar and saddle ht from the floor
-had longer chainstays
-had same saddle to bb relationship
-was a little shorter in cockpit
- same bar drop

So, why I wonder do the two bikes handle differently--it must be angles, which I did not measure.

and, would a geometry like my road bike work OK as a cross bike? I had always assumed the road bike had a much longer wheelbase and would be like turning a bus.

where I'm going with this dull post is wondering if "old school" Euro road race bike geometry would make for a decent riding cross bike that would be fun on the road?

You mentioned why in your first sentence..Merckx MXLeader, not many(none?) better riding frames in existence now or then. The very best riding frame I have ever owned, period.

[Mark McM]

... and wheelbase determines how tight a turn radius you'll have for a given lean angle.

I think you mean that the wheelbase determines how tight a turn radius you'll have for a given steering angle (or how much steering angle you'll need for a given turn radius). The lean angle is determined solely by radius and speed (assuming gravity is constant).

[John M]

Bikes properly designed for a specific purpose will function best when used for that purpose and when put to other uses will present compromises. Although a cyclocross racing bike can be ridden on the road acceptably, it will not be as good of a road bike as a properly designed race bike. Same applies to TT bikes, loaded touring, etc.... All should have special design considerations that optimize them for their intended use.

[Kontact]

I think you mean that the wheelbase determines how tight a turn radius you'll have for a given steering angle (or how much steering angle you'll need for a given turn radius). The lean angle is determined solely by radius and speed (assuming gravity is constant).
No, I meant lean angle. The further apart the wheels, the larger the circle they can describe at a given angle of bank. Steering angle figures into this, but only because the steering angle changes with different lean angles.

Long story short, a long wheel base bike will have to be leaned further over than a short wheel base bike to follow the same line in a turn.

It would probably be better to have a term for the combined steering and lean angle, since they exist together, but I think lean angle or bank angle more accurately represents what's happening since the steering angle is dependant on other factors, like trail.

[Mark McM]

No, I meant lean angle. The further apart the wheels, the larger the circle they can describe at a given angle of bank.

While this is true, the affect is insignificant. For example, at 20 mph turning with a 1 g lateral force (roughly the limit of traction of bicycle tires) the turn radius of the rider's CG. is 26.7 feet, which puts the radius that the wheels track at roughly 30 feet. The difference in the actual wheel track radius between a bike with 36" wheelbase and a bike with bike with 48" wheelbase is about 1/3rd of an inch, resulting in a bicycle lean angle difference of about 1/4 degree (or roughly 0.5% of lean angle). Higher speeds, lower lateral g forces or smaller differences in wheelbases will mean smaller differences in lean angles. Wheelbase is not a significant factor in bicycle lean angles.

[jroden]

While this is true, the affect is insignificant. For example, at 20 mph turning with a 1 g lateral force (roughly the limit of traction of bicycle tires) the turn radius of the rider's CG. is 26.7 feet, which puts the radius that the wheels track at roughly 30 feet. The difference in the actual wheel track radius between a bike with 36" wheelbase and a bike with bike with 48" wheelbase is about 1/3rd of an inch, resulting in a bicycle lean angle difference of about 1/4 degree (or roughly 0.5% of lean angle). Higher speeds, lower lateral g forces or smaller differences in wheelbases will mean smaller differences in lean angles. Wheelbase is not a significant factor in bicycle lean angles.

In cyclocross, it's not uncommon to have the bike slowed nearly to the point where it will fall over, crank over the steering wheel and turn it in tight around the inside post. From a rider perspective it feels like a real "tippy" sort of move.

What suprised me when I measured my bikes was the cross bike had quite a bit longer wheelbase, about half of the length seems to come from chainstays and the other half happens somewhere forward of the bottom bracket.

I assumed a bike with a longer wheelbase would tend to want to go straight, similar to a car with a longer wheelbase

[Germany_chris]

Wow,like math much? :banana: too much for me.

I ride mu cross bike in the road and it just feels slower also and I really don't like it..I ride my cross bike on single track and it feels like a really agile light weight XC mountain bike..If you take something out of context or out of it's element it'll fell wrong.

While this is true, the affect is insignificant. For example, at 20 mph turning with a 1 g lateral force (roughly the limit of traction of bicycle tires) the turn radius of the rider's CG. is 26.7 feet, which puts the radius that the wheels track at roughly 30 feet. The difference in the actual wheel track radius between a bike with 36" wheelbase and a bike with bike with 48" wheelbase is about 1/3rd of an inch, resulting in a bicycle lean angle difference of about 1/4 degree (or roughly 0.5% of lean angle). Higher speeds, lower lateral g forces or smaller differences in wheelbases will mean smaller differences in lean angles. Wheelbase is not a significant factor in bicycle lean angles.

[Kontact]

While this is true, the affect is insignificant. For example, at 20 mph turning with a 1 g lateral force (roughly the limit of traction of bicycle tires) the turn radius of the rider's CG. is 26.7 feet, which puts the radius that the wheels track at roughly 30 feet. The difference in the actual wheel track radius between a bike with 36" wheelbase and a bike with bike with 48" wheelbase is about 1/3rd of an inch, resulting in a bicycle lean angle difference of about 1/4 degree (or roughly 0.5% of lean angle). Higher speeds, lower lateral g forces or smaller differences in wheelbases will mean smaller differences in lean angles. Wheelbase is not a significant factor in bicycle lean angles.
Mark,

Unless I misunderstood your example, I think you are over-simplifying the problem. Bicycle wheels don't actually follow each other in a turn - the front wheel is in a larger arc than the rear. Because of that, a longer wheelbase bike has to have a greater degree of both lean angle and steering angle in the turn to keep the front wheel arc the same as that of a short wheelbase bike to affect a given line. It comes down to a question of matching the both the front and rear wheel arcs to match the turn, and that requires more overall angle by the longer bike.

Real world - short wheel base bikes handle quicker and are less stable at high speeds because they will make smaller arcs for less lean and steering angle.

You can modify this with trail effects, but all you're doing is making the bike more or less likely to get into and hold a turn. Once the turn is set, wheelbase determines how tight that turn can be for angles used.

[Mark McM]

Mark,

Unless I misunderstood your example, I think you are over-simplifying the problem. Bicycle wheels don't actually follow each other in a turn - the front wheel is in a larger arc than the rear.

Yes, I think you are misunderstanding the example. The lean angle is not just a matter of the front describing a (slightly) larger arc than the rear wheel - more importantly, both wheels describe significantly larger arcs than the CG of the rider. This difference in the radii of the CG and wheel track(s), as well as the height of the CG, is what creates the lean angle. However, as I mentioned, the relative difference in wheel track radius with wheelbase is very small and inconsequential.

Real world - short wheel base bikes handle quicker and are less stable at high speeds because they will make smaller arcs for less lean and steering angle. .

You are confusing cause and affect - the reason short wheelbase bikes handle quicker is because less steering angle is required to change lean angle at any given speed, not because they require less lean angle to turn.

Once the turn is set, wheelbase determines how tight that turn can be for angles used.

Ok, If you believe wheelbase is important, then tells us: For a 30% lean angle, what radius turn can be maintiained for a 36" wheelbase bike compared to a 48" wheelbase bike? When you work it out you'll find the difference to be too small to be meaningful.


P.S.: This wikipedia article describes the affects of speed, turn radius and lean angle pretty well:

http://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics (This wikipedia article describes the affects of speed, turn radius and lean angle pretty well: )

[Kontact]

the reason short wheelbase bikes handle quicker is because less steering angle is required to change lean angle at any given speed


Which equation makes this statement true?

In non-leaning vehicles, wheelbase affects turn radius, and in leaning vehicles it also still affects turn radius (equation in "Turning" and second equation in "Leaning"). But I don't see anything that suggest that changing the lean angle is a function of either equation using wheelbase.

Could you explain?

[Mark McM]

Which equation makes this statement true?

In non-leaning vehicles, wheelbase affects turn radius, and in leaning vehicles it also still affects turn radius (equation in "Turning" and second equation in "Leaning"). But I don't see anything that suggest that changing the lean angle is a function of either equation using wheelbase.


In non-leaning vehicles, wheelbase is only one variable that affects turn radius - steering angle obviously also affects turn radius. The equations in "Turning" and the second equation in "Leaning" show how both the wheelbase and the steering angle relate to the radius of the turn:

http://upload.wikimedia.org/math/9/0/4/9047d49cd6058d833b135af82492b1f2.png

http://upload.wikimedia.org/math/4/d/e/4defe7aa9b93c1fc48dbbadd3f13ffcc.png

The first equation is the special case for when the lean angle is very close to zero ( cosine(0) = 1 ), such as for non-leaning vehicles or for leaning vehicles traveling very slowly. The second equation factors in the lean angle for leaning vehicles. However, neither equation says anything about what determines what the lean angle needs to be - it just shows what the turn radius would be at a a given lean angle. (Notice that neither of these formulas includes speed, which we know affects lean angle).


It is this equation, which appears on the web page between the other two equations, which determines the actual lean angle:

http://upload.wikimedia.org/math/0/7/f/07fd3b65e47914906f79ff4dea573708.png

The lean angle (for a steady state turn) is the angle required to balance the centripital (lateral) acceleration, which is determined by the velocity and turn radius, with the vertical acceleration of gravity. Hence, the three variables are only velocity, radius and gravitational acceleration. If gravity is constant, the only variables in lean angle are velocity and radius. Plugging the the radius and lean angle from this formula into the second formula above will yield the steering angle required for a given wheelbase for that particular turn.

[Germany_chris]

I'm sure you guys a really fun to hang out with geeezz equations and everything, you probably write and solve these for fun :hello: but this is called thread drift or creep..CX ≠ road bike but that ≠ no fun..

[Kontact]

In non-leaning vehicles, wheelbase is only one variable that affects turn radius - steering angle obviously also affects turn radius. The equations in "Turning" and the second equation in "Leaning" show how both the wheelbase and the steering angle relate to the radius of the turn:

http://upload.wikimedia.org/math/9/0/4/9047d49cd6058d833b135af82492b1f2.png

http://upload.wikimedia.org/math/4/d/e/4defe7aa9b93c1fc48dbbadd3f13ffcc.png

The first equation is the special case for when the lean angle is very close to zero ( cosine(0) = 1 ), such as for non-leaning vehicles or for leaning vehicles traveling very slowly. The second equation factors in the lean angle for leaning vehicles. However, neither equation says anything about what determines what the lean angle needs to be - it just shows what the turn radius would be at a a given lean angle. (Notice that neither of these formulas includes speed, which we know affects lean angle).


It is this equation, which appears on the web page between the other two equations, which determines the actual lean angle:

http://upload.wikimedia.org/math/0/7/f/07fd3b65e47914906f79ff4dea573708.png

The lean angle (for a steady state turn) is the angle required to balance the centripital (lateral) acceleration, which is determined by the velocity and turn radius, with the vertical acceleration of gravity. Hence, the three variables are only velocity, radius and gravitational acceleration. If gravity is constant, the only variables in lean angle are velocity and radius. Plugging the the radius and lean angle from this formula into the second formula above will yield the steering angle required for a given wheelbase for that particular turn.
Right. Where does it follow that a change in lean angle is faster with shorter wheelbases?

In aviation, this would be known as roll rate. How does a shorter wheelbase increase roll rate?

[RPS]

Right. Where does it follow that a change in lean angle is faster with shorter wheelbases?

In aviation, this would be known as roll rate. How does a shorter wheelbase increase roll rate?
I find this a very interesting subject. I’d like to reply to your question, but would like clarification that you are indeed asking about a transient response (i.e. – like roll angle changing as a function of time), and not steady state. I want to avoid getting into a discussion like the one above which at times seemed like it was in two languages.

Also, are you in agreement with Mark’s assessment regarding the differences between lean angle and steering angle? Without a clear distinction and acceptance that they are not “directly” related it’s hard to discuss this subject further.

[Mark McM]

Right. Where does it follow that a change in lean angle is faster with shorter wheelbases?

Ah, sorry, I missed meaning of your question.

As mentioned in the wikipedia article, bicycles are maneuvered and turned by countersteering - momentarily steering opposite to the direction of intended travel, in order to establish a lean angle. The rate of change of the lean angle is related to speed at which the front wheel moves laterally (in response to a steering input), and the distance between the front wheel and the CG of the bicycle. To achieve the same lean angle by countersteering, the front wheel of a long wheelbase bike will have to move laterally further than it does for a shorter wheelbase bicycle. This means that at the same steering angle (and laterally movement rate), the long wheelbase bike will change lean angle more slowly, or that to acheive the same rate of lean change the front wheel of a long wheelbase bike will have to be steered at a larger angle.

The upshot is that changes of lean angle (and therefore changes of direction) required less steering input with short wheelbase bikes than for long wheelbase bikes, generally making the short wheelbase bike more agile and manueverable.

[RPS]

Ah, sorry, I missed meaning of your question.

As mentioned in the wikipedia article, bicycles are maneuvered and turned by countersteering - momentarily steering opposite to the direction of intended travel, in order to establish a lean angle. The rate of change of the lean angle is related to speed at which the front wheel moves laterally (in response to a steering input), and the distance between the front wheel and the CG of the bicycle. To achieve the same lean angle by countersteering, the front wheel of a long wheelbase bike will have to move laterally further than it does for a shorter wheelbase bicycle. This means that at the same steering angle (and laterally movement rate), the long wheelbase bike will change lean angle more slowly, or that to acheive the same rate of lean change the front wheel of a long wheelbase bike will have to be steered at a larger angle.

The upshot is that changes of lean angle (and therefore changes of direction) required less steering input with short wheelbase bikes than for long wheelbase bikes, generally making the short wheelbase bike more agile and manueverable.
Nicely stated. The only concern I sometimes have with analyzes like those in Wikipedia pages is when they oversimplify to make it easier to understand. For instance, I’m not sure that treating total mass as if it existed in a single point defined by the center of gravity is always a good idea. Most of the time it works out OK and is good enough, but when analyzing transient responses it doesn’t depict the entire picture.

I haven’t read the Wikipedia article you refer to in a while (couldn’t pull it up from your link) so I don’t know if it implies that (as stated in the highlighted area above) the rate of change in lean angle is a function of front wheel-to-CG distance assuming everything else is equal or not (i.e. – same bike with same wheelbase?). If not and it ignores the distance from CG to rear wheel then I’d have to take exception. I guess it depends on what "the bicycle" means. ;)

This last point is related to one of the reasons why changing weight distribution changes the way a bike feels. Many riders think it’s primarily because it affects the tires and therefore traction, slip angle, etc…, but I think it has more to do with where the CG is relative to both the front and rear tires and its affect on how quickly the bike leans over following a steering input.

[benb]

For another real world example a back of the envelope look shows a lot of road bikes are around 100cm wheel base. My Motorcycle has a 146cm wheelbase. Obviously a big difference, way bigger then the difference between any two bicycles as long as neither of them is a tandem.

It still has a minimum turn radius of around 9 feet. But it very much exhibits the effects mentioned earlier in the thread. It takes longer to change lean angle then on a bicycle. In order to do something like a 9ft circle you have to make a pretty hard steering input. If you don't, the time required to achieve the lean angle will widen the turn radius by a very large amount. That contributes to it feeling vastly less nimble then a bicycle, even if the turning circles are not really that different. There is actually a lot of fear to overcome to change lean angles that fast at low speed on a motorcycle. Amazingly for sport motorcycles some of the other important geometry figures like rake & trail are not that far off of road bicycles. Certainly way less difference then the wheelbase figure.

[Dave]

I've ridden a sport motorcycle (Suzuki SV650) on the same twisty mountain roads as my bicycle and it felt like wrestling a hog compared to my bike. It sure was easier to go up the mountain quickly, though.

I always disagree with the idea of "momentary" countersteering. Perhaps that's the case if speed is constant, but that's never the case. I couldn't keep a truly constant speed on a bike or motorcycle, if I had too.

[RPS]

....snipped......
Amazingly for sport motorcycles some of the other important geometry figures like rake & trail are not that far off of road bicycles. Certainly way less difference then the wheelbase figure.
Similar applies to bicycles too -- wheelbase length in itself doesn’t seem to affect optimum steering geometry all that much. At the extremes, comparing a road tandem to a road single when both are designed for similar use shows that their steering geometry is not all that different; at least not when compared to their differences in wheelbase. My Cannondale tandem’s wheelbase is nearly double that of my shortest bike, yet HTA is only about one degree off and trail isn’t all that different either. The longer wheelbase of a tandem does make it a lot more stable at high speed though.

[Kontact]

Ah, sorry, I missed meaning of your question.

As mentioned in the wikipedia article, bicycles are maneuvered and turned by countersteering - momentarily steering opposite to the direction of intended travel, in order to establish a lean angle. The rate of change of the lean angle is related to speed at which the front wheel moves laterally (in response to a steering input), and the distance between the front wheel and the CG of the bicycle. To achieve the same lean angle by countersteering, the front wheel of a long wheelbase bike will have to move laterally further than it does for a shorter wheelbase bicycle. This means that at the same steering angle (and laterally movement rate), the long wheelbase bike will change lean angle more slowly, or that to acheive the same rate of lean change the front wheel of a long wheelbase bike will have to be steered at a larger angle.

The upshot is that changes of lean angle (and therefore changes of direction) required less steering input with short wheelbase bikes than for long wheelbase bikes, generally making the short wheelbase bike more agile and manueverable.
For this to be a true and useful statement (along with your previous), two bikes that are identical with the exception of chainstay length (which adds length behind the center of gravity, and modifies it very little due to high rider mass) will handle identically. In other words, the rate of lean change should be identical due to the identical location of rider mass to front wheel, and the assertion that lean angle produces nearly identical turn arcs regardless of wheelbase.

Would you agree with that? Will a 56x56cm, 73/73, 45mm rake bike with 38.5 chainstays handle nearly identically to the same rider on an otherwise similar bike with 43.5mm stays, since they have the same steering geometry and CG to steering distance?

[RPS]

I've ridden a sport motorcycle (Suzuki SV650) on the same twisty mountain roads as my bicycle and it felt like wrestling a hog compared to my bike. It sure was easier to go up the mountain quickly, though.

I always disagree with the idea of "momentary" countersteering. Perhaps that's the case if speed is constant, but that's never the case. I couldn't keep a truly constant speed on a bike or motorcycle, if I had too.
Some would argue that countersteering is a continous process, not momentary. Without countersteering constantly a rider would fall over.

I'm not following why you feel constant speed, or lack thereof, plays a role in countersteering. I know we've discussed this issue many times but don't recall constant versus variable speed being a factor. Can you remind me in what context this is an issue when riding a bicycle?

[RPS]

For this to be a true and useful statement (along with your previous), two bikes that are identical with the exception of chainstay length (which adds length behind the center of gravity, and modifies it very little due to high rider mass) will handle identically. In other words, the rate of lean change should be identical due to the identical location of rider mass to front wheel, and the assertion that lean angle produces nearly identical turn arcs regardless of wheelbase.
I raised this same issue above, but expect that it was meant to be applied to an identical (or same) bike with the rider in a different position as to affect CG.

Would you agree with that? Will a 56x56cm, 73/73, 45mm rake bike with 38.5 chainstays handle nearly identically to the same rider on an otherwise similar bike with 43.5mm stays, since they have the same steering geometry and CG to steering distance?
I'm certain the two bikes you describe would not handle the same. They have different wheelbase and different weight distribution.

[Kontact]

Hey RPS,

Countersteering does not appear to be constant - once in the turn you steer in the same direction that you are turning, which you can look down and see. Countersteering is the impulse that starts the change in lean angle, but doesn't maintain it. Since I like airplanes, I'd compare countersteering to banking a plane - you move the stick laterally to roll into the turn, then center to hold the bank angle. Countersteering is like that.

I think we were responding at the same time, so I didn't see your post. I, of course, agree that the two bikes won't handle the same. But I think it is because of a geometric issue that is difficult to even describe - the top tubes of bikes in turns are not perpendicular to the radius of the turn because of the differing wheel track of the front and rear wheel. And bikes with different wheel bases are pointing in different directions for the same lean angle. But the calculations that talk about lean angle don't really address this, and treat the bicycle like it is a unicycle with lean angle measured in line with the radius of the turn. I think the reality is different.

However, Mark is a smart guy, and I'm not 100%, so I think I'd like to see where his explanation takes us. Wheelbase and lean rates could be the missing factor, but my example should address that since CG to steering distance remains constant.

[bigreen505]

Would you agree with that? Will a 56x56cm, 73/73, 45mm rake bike with 38.5 chainstays handle nearly identically to the same rider on an otherwise similar bike with 43.5mm stays, since they have the same steering geometry and CG to steering distance?

I'm virtually certain that is not true as I am still trying to get the bike with the 41 cm chain stays to handle like the seemingly otherwise identical bike with 39.5 cm stays. Stay length effects rider position/center of gravity between the wheels and weight distribution. In theory I think longer stays put more weight on the front wheel for a given position.

[Kontact]

Just to clarify what I was talking about, I'd like to point out that there are at least three ways one could define the lean angle of a bicycle:

1. The angle of a line running from the CG to the ground through the plane of the frame, but in the same plane as the radius of the turn.

2. The angle of the frame to the ground.

3. The angle a line perpendicular to a line between tire contact patches drawn to the CG.

On a unicycle, all three of these are the same. On a bicycle with a vertical steerer and no rake 2 and 3 are the same. On a bike with trail, none of them are the same.

So when someone says an equation gives "lean angle", I'd ask "which lean angle?" Two dissimilar bikes might have the same lean angle in one way, but that might not be the way that is important to the cyclist.

[slowgoing]

I bet we see fewer questions about frame geometry from now on.

[rice rocket]

I bet we see fewer questions about frame geometry from now on.
And unless you're a framebuilder that iterates these changes in geometry one increment at a time, it's all mental masturbation anyways.

[Dave]

Some would argue that countersteering is a continous process, not momentary. Without countersteering constantly a rider would fall over.

I'm not following why you feel constant speed, or lack thereof, plays a role in countersteering. I know we've discussed this issue many times but don't recall constant versus variable speed being a factor. Can you remind me in what context this is an issue when riding a bicycle?

In theory, if speed is constant, you could momentarily countersteer to initiate a turn and the bike should keep turning until you countersteer in the opposite direction. Countersteering should be done with the same hand as the direction of the turn. Push with the right hand (turning the wheel to the left) to initiate a right hand turn.

If you're descending a mountain you're nearly always accelerating. If you apply the brakes before a turn, then countersteer to initiate the turn, it requires constant countersteering or the bike will straighten up on it's own from the increase in speed. I've deliberately turned corners with one hand, using an open palm, so all I could do was push on the right side to turn right and let off the pressure, to allow the bike to straighten itself. It does not require pressure on the left side to stop the bike from turning, as some people suggest.

I was taught to ride a motorcycle the same way - push on the right side to lean the bike to the right and turn right. Most people accelerate out of a turn, so there is no need to push with the left hand to quit turning. Just quit pushing and accelerate a little. I went from the training course to the twisty mountain roads and always stayed in my lane, so it apparently works.

[RPS]

Hey RPS,

Countersteering does not appear to be constant - once in the turn you steer in the same direction that you are turning, which you can look down and see. Countersteering is the impulse that starts the change in lean angle, but doesn't maintain it. Since I like airplanes, I'd compare countersteering to banking a plane - you move the stick laterally to roll into the turn, then center to hold the bank angle. Countersteering is like that.

Whether to use “momentary” or “continuous” depends on what interpretation a person uses for what countersteering is in the first place. There seems to be two main interpretations of what it is when applied to bicycles, and I can work with either as long as I know which one the person is using.

“Momentary” seems more appropriate when countersteering is viewed as only a deliberate and forceful steering input to initiate a change in direction; particularly when the rider wants to do it very quickly. Seen from this angle it’s a momentary input because it is not required once the proper lean angle is achieved for the turn.

“Continuous” seems appropriate for those who believe that countersteering inputs are inherently required to balance a bike even when trying to ride a straight line. To them it’s all the same except for the magnitudes.

I see no point in arguing which word is best unless we first define which definition of countersteering is being applied. In any case, this is a significant thread drift.

[RPS]

Just to clarify what I was talking about, I'd like to point out that there are at least three ways one could define the lean angle of a bicycle:

1. The angle of a line running from the CG to the ground through the plane of the frame, but in the same plane as the radius of the turn.

2. The angle of the frame to the ground.

3. The angle a line perpendicular to a line between tire contact patches drawn to the CG.

On a unicycle, all three of these are the same. On a bicycle with a vertical steerer and no rake 2 and 3 are the same. On a bike with trail, none of them are the same.

So when someone says an equation gives "lean angle", I'd ask "which lean angle?" Two dissimilar bikes might have the same lean angle in one way, but that might not be the way that is important to the cyclist.
In my opinion you are making this more difficult than it has to be by considering issues that have insignificant effects. If you go down that path there will be no end in sight.

Depending on what problem is being solved, a person may indeed want to define “lean angle” differently if it makes solving the problem easier. Generally I use lean from vertical, but sometimes use lean relative to road if the pavement is banked and I’m trying to solve for traction. The only time I recall using the angle of the frame itself is when trying to estimate pedal-to-pavement clearance.

Because riders outweigh bicycles by 10 times and may not stay centered directly over the bike, I recommend not using the bicycle’s frame as reference other than when estimating pedal clearance or something similar. Normally the combined bike/rider center of gravity is preferred when applying information to physical equations.

[Kontact]

RPS,

My post was simply there to demonstrate that the equations being used may be simplifying the question too far by defining the angle from a reference that obscures actual lean, making a realistic comparison of wheelbases produce weird results. Riders look at lean as frame angle - it defines whether they are going to have a pedal strike or not and where the contact patch on the rear tire is. But the math offered probably uses angle 1., which is shallower than frame angle, and departs from it more the longer the wheelbase is (by quite a few significant degrees). Which would simulataneously explain Mark's POV, and mine.

Countersteering - we see it the same way. I've had people insist that the front wheel is in a countersteer even in a constant corner - wheel pointed out of the turn - and that's what I thought you were saying. Yes, countersteering inputs are being made all the time - no argument. It's what really keeps the bike upright.


I apologize to those who think this question has gone too far afield, but talking about wheelbase's affect on handling almost never happens in concrete terms, so I'm really glad some people want to talk about it. To most of the cycling world, the most important handling bit of geometry is head tube angle, and that seems to be completely backwards.

[RPS]

RPS,

My post was simply there to demonstrate that the equations being used may be simplifying the question too far by defining the angle from a reference that obscures actual lean, making a realistic comparison of wheelbases produce weird results. Riders look at lean as frame angle - it defines whether they are going to have a pedal strike or not and where the contact patch on the rear tire is. But the math offered probably uses angle 1., which is shallower than frame angle, and departs from it more the longer the wheelbase is (by quite a few significant degrees). Which would simulataneously explain Mark's POV, and mine.

Kontact, I’m sorry but I’m going to have to let this go because I can’t follow what you are stating or why you think it’s important, or what weird results you are referring to. :confused: That’s not to say it isn’t important, just that I can’t follow your arguments. When it comes to determining the amount of bicycle lean to use in most equations I’ve always used the plane defined by three points: the combined bike/rider center of gravity and each tire contact point. At the higher bike speeds I’m interested in, turn radii are large enough compared to wheelbase that it all works out without any problems.

No disrespect meant, but it seems we are just going in circles.

Rick