Bicycle stability (2)

[billyk]

I've restarted this thread, originally "Incredibly stable recumbents" (in Riding Techniques) because that one became very long and began to wander ... to say the least.

I'm especially interested in the model Hamish Barker presented, that allows identifying the specific elements that cause a particular bicycle to be more or less stable at various speeds. The model is described in the quite technical paper at
http://rspa.royalsocietypublishing.org/content/463/2084/1955

Hamish posted plots of his solutions to this model in the above thread.

Hamish also posted links to videos demonstrating this stuff. See:
http://bicycle.tudelft.nl/schwab/Bicycle/
These show a regular upright (and riderless) bike pushed to roll freely, wobbling and recovering.

Consider three facts:

1) It's easy to wheel an upright bike holding it by the seat, even turning with fair precision; but it is far harder to wheel a Cruzbike like this. (Possible, but vulnerable to sudden failure!)

2) Many postings here throughout the years have noted a sense of coming close to a wobble at high speed. We control it, but I think this is something most of us have felt. Let's be honest about this.

3) Bicycles are balanced by steering to put the wheels underneath the lean. This is a principal result of the Dutch experiments (see movies linked above), as well as previous studies. It has little or nothing to do with the gyroscopic effect of spinning wheels, and a well-designed bicycle will naturally self-steer and recover it's balance when pushed and let roll freely (see movies). That's what the head tube angle and trail do. This is quite similar to how you balance a broomstick on your hand: move the hand to be always under the CoG of the broom.

Unfortunately I'm reluctant to test the ability of my Quest to recover rolling freely after a push! But I suspect it is not great.

In terms of the model Hamish has shown, what is the fundamental difference between Cruzbikes and uprights?

I think the key difference is that on a CB the mass is much further forward than on a DF: both for the drivetrain/boom assembly, and the rider. The whole drivetrain and its structure is in _front_ of the steering axis, and the rider is nearly wrapped around the steering column.

It therefore seems to me that the essential experiment to be done with Hamish's model is to keep everything else constant and move the mass (frame+rider) gradually forward: How does this affect stability? Which of the terms of the model are affected?

I would speculate that the difference is akin to the difference between balancing a tall broomstick (easy) and balancing a spoon (very difficult): With the CoG of the broomstick far from your hand, it is easy to stay underneath it (upright bike with the mass far from the steering axis); on the other hand, balancing the spoon (Cruzbike with the mass close to the steering axis (?)) is harder. Is the Cruzbike/upright situation analogous to the spoon vs broom?

Hamish found that the "weave mode" (oscillation and recovery as in the movies linked above) of a Cruzbike remains unstable at any speed. This is not fatal; as Hamish noted it just means that the rider needs to actively control the wobble. How does the weave mode change as the mass is moved forward?

Another possibility is "wheel flop", the tendency of the front wheel to want to flop over more than the turning input. It's caused by lowering the CoG when the front wheel is turned (as the ground contact point changes), tending to increase the turn. This tendency is increased with mass further forward, but I can't identify this with any of the eigenvalues of Hamish's model. At least this seems to be the reason it's hard to wheel a Cruzbike by its seat.

My further speculation is that the "incredible stability" we feel is not due to the geometry but to our four points of contact with the steering: a much more immediate and forceful response to wobbles and instabilities.

My applause to Hamish for making a leap ahead. I look forward to his refining his experiments.

Billy K

 

[Kim Tolhurst]

Steering

A DF by the saddle while 'walking it' is just a trick. For safety in public one walks it by steering from the handlebars/top of steering stem.
A CB same for easy handling and safety.

Kim..

 

[Charles.Plager]

For your first point: The

For your first point: The weight of the front end is annoying when pushing the bike. That doesn't translate at all into how the bike handles (as Kim correctly pointed out).

For your second point (stability at high speeds):

• This has a lot to do with the rider. If you're tense at high speeds, you'll wobble. Regardless of the bike.
• This has to do with wheel base and trail/rake of the bike. My understanding is that the Vendetta V1 suffers here a bit compared to the V1.5 and V2/v20.

I've ridden both my Sofrider and my conversion 40 mph (45 mph for the Sofrider) and it was very stable. I don't think there's anything inherently unstable in these bikes.

 

[billyk]

"unstable" and "unstable"

Morning Charles -

Maybe I should clear up the difference between "unstable" as in Hamish's model, and "unstable" as in "likely to fall down". The second is the conversational meaning, but here it means "requires rider control". There is a fairly narrow range of speeds for which a riderless bicycle will remain upright and even recover from jostling (movies linked above); that's the meaning of "stable" here.

Note that "stable" is not necessarily desirable; it can make it hard to induce a turn. Certain professional racer bikes are designed to be less stable to give the rider more control (Wikipedia).

It's somewhat analogous to the conversational vs specialist use of the word "theory". As is "evolution is (just) a theory". But that's "theory" in the sense of "coherent explanation", not theory in the conversational sense of "speculative".

Hamish's model will tell us the role of the fore/aft mass distribution. I hope.

 

[Charles.Plager]

Maybe I should clear up the

Maybe I should clear up the difference between "unstable" as in Hamish's model, and "unstable" as in "likely to fall down". The second is the conversational meaning, but here it means "requires rider control". There is a fairly narrow range of speeds for which a riderless bicycle will remain upright and even recover from jostling (movies linked above); that's the meaning of "stable" here.

O.k. I appreciate this definition much more.

 

[MrSteve]

Stable/Unstable

All bikes are unstable for two reasons.
-All bicycles are single-track vehicles and, therefore, their greatest stability is achieved whilst lying on their sides.
-Almost all bicycles are kept in areas outside stables and are, therefore, un-stable vehicles.

You're welcome.

Carry on.

 

[John Tolhurst]

Actually, I stable my bicycle

Actually, I stable my bicycle every evening safely out of the weather.

The Vendetta 1 has a lower headtube angle. Its a bit like cricket, you win the toss, you think about bowling first, then you bat first. With headtube angles, you toy with the idea it would be nice to lay them back, then you keep them where history dictates they best be. When you lay them back, you reduce the responsiveness at 10kph speeds, and you then at 15kph can't carve curves of increasing or decreasing radii as smoothly as you would like. At 20 to 40 kph, no practical difference in stability that I have been able to observe.

With the notched slider on the yellow Vs (where the steering tube enters) the range of adjustment is dictated by the distance from the notch to the curve of the boom. I wanted more adjustment, so eased the headtube angle back - I courageously decided against the cricket maxim.

 

[hamishbarker]

revised model

I redid the models with measurements from my own vendetta 1.5 and careful weight estimates based on wall thicknesses. Robert also sent me weights for V20 parts and my estimates were close.

The big issue with the model is how much coupling there is between the rider's legs and the front end.

The original curves I put up on the original thread were based on stiff coupling of about half of the rider's legs with the the front end. In those curves the oscillating modes seem to be present at the whole speed range. As Charles notes, if the rider is tense, the bike is unstable. If the rider is tense, the legs are possibly more stiffly joined to the steering front end.

With the revised model, I made it much easier to vary parameters quickly to investigate changes to front end mass, front end center of mass location, front wheel rotational inertia, and handlebar mass (the last item because I wondered if there could be any impact on stability when mounting double water bottles up near the handlebars. I didn't couple the mass of the legs to the steering assembly (boom, fork, steerer tube, chainstays, crankset, handlebar, wheel), on John T's argument (which I agree with, since there are many moving joints between the boom and leg masses, including, bottom bracket and pedal axles (single degrees of freedom each), ankle joints and knee joints (multiple degrees of freedom each.). With that change, the model results look rather similar to those of conventional bikes, although the damped stable speed is higher.


Results:
Revised model: stability above 8.5m/s
Revised model, half front end wieght: stability above 7.5m/s
Resivsed model, one tenth front end weight (obviously hypothetical, just looking at extreme case): stability above 6.6m/s
Revised model, steepen head angle to 80 degrees (from 71): stability above 7.2m/s
Revised, head angle 85 deg. stability above 6.3 m/s (but curves starting to look like could be sensitive to Centre of mass or other parameter variations.
Revised model, move center of mass of front end assy rearward by 100mm : stability above 7.8m/s
Revised model: increase handlebar mass by 2kg: stability above 8.3m/s

So the biggest influence on stability seems to be actually to make head angle steeper. This is a bit different to a normal bike, but the difference is I think because the centre of mass of the steering assy is further ahead of the steering axis than normal bike.

The most important stability mechanism is as investigated by the researchers who put together the equations, that the response of the bicycle to a lean in one direction, is to automatically steer into the lean. The bicycle is an inverted pendulum, so at zero speed will just topple over. At higher speeds, the steering into the lean (due to the combination of geometry/head angle/mass of front end) makes the bike steer its wheels back under the center of gravity.).

The mass of the front end seems a fairly weak influence on stability, partly because although the steering force imposed by the heavier mass ahead of the steering axis wants to flop towards the lean (a good thing, steering the wheels back under the CoG), the increased inertia of the front end delays the steer. Put simply: gravity is the force making the correcting steering input. If gravity doesn't change, neither does the stability.

The head angle has a bigger influence on stability. Not sure why, perhaps it could be that steering inputs may become more direct at a faster rate than the rate at which the flopping steering force decreases (at 90 deg head angle, there is no wheel flop to provide a steering force towards the lean, although there might still be some minor gyroscopic precessional torque, not sure if it's helping or hindering though.).

moving the center of mass of the front end assy rearward appears like it might have a stabilising effect, but I didn't make a full geometric model of the movement, so the result is a little suspect. However, increasing the handlebar mass (think, double waterbottles) also increases stability slightly, so maybe the modelling is correct. Anyway, none of them is as big an influence on stability as the head angle change.

Graphs for the above cases attached below. (with the exception of handlebar mass and moving CoM of front assy cases)

First picture: model as described:

Next picture: with front end mass halved

next picture with front end mass one tenth:

next picture: original masses, steepen head angle from 71 to 80 degrees. (wheelbase unchanged).

head angle 85 deg:

 

[Vargas]

All bikes are unstable for

All bikes are unstable for two reasons.
-All bicycles are single-track vehicles and, therefore, their greatest stability is achieved whilst lying on their sides.
-Almost all bicycles are kept in areas outside stables and are, therefore, un-stable vehicles.

Now I know my bike true nature!

The "un-stable" is hilarious. Pity I can't make the same construction in Portuguese.

 

[Eric Winn]

Hamish, now try working out

Hamish, now try working out the TTRIKE dynamics. Did you see in the video how Maria seemed to get a kick out of riding no-hands?


-Eric