Bicycle Physics: Breaking the Math Barrier

[jedishrfu]

Interesting article on bicycle physics and researchers who've investigated it:

http://www.scientificamerican.com/article/the-bicycle-problem-that-nearly-broke-mathematics/

 

[1oldman2]

cool article, thanks. I was hoping it would go into a detailed explanation of the physics of "counter steering" (something I studied on a 650 Bonneville years ago) I was a little disappointed that the concept was only mentioned once, however the rest of the article made up for that.

 

[jedishrfu]

I think the article is good for identifying whose doing what so you can find out more or instead revel in riding your bike and knowing its actively solving an equation you can only dream of solving.

 

[OCR]

Sooo... you had a 650 Bonneville, huh? ... well now I'm mad, 'cause I never did....

...650 Bonneville...

Lol, I sure as hell wanted one though... dreamed about them, all the time....

Anyway...

I was hoping it would go into a detailed explanation of the physics of "counter steering"

I have asked dozens of bicycle riders how they turn to the left. I have never found a single person who stated all the facts correctly when first asked. They almost invariably said that to turn to the left, they turned the handlebar to the left and as a result made a turn to the left. But on further questioning them, some would agree that they first turned the handlebar a little to the right, and then as the machine inclined to the left, they turned the handlebar to the left and as a result made the circle, inclining inward.

https://en.wikipedia.org/wiki/Countersteering
And this out, too...
https://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics

Ha!... but I do have a 1986 1,100 cc Harley Sportster, with the Evolution engine ... the first year Harley made them.....

 

[1oldman2]

Sooo... you had a 650 Bonneville, huh? ... well now I'm mad, 'cause I never did....

Lol, I sure as hell wanted one though... dreamed about them, all the time....

​

https://en.wikipedia.org/wiki/Countersteering
And this out, too...
https://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics

Ha!... but I do have a 1986 1,100 cc Harley Sportster, with the Evolution engine ... the first year Harley made them.....

Sweet! The Limey bikes are a family tradition here, although I did have a "sporty" at one time, The 850 commando is a kick in the ass also.

 

[OCR]

Indeed ....

The 850 commando is a kick in the ass also.

You have one of those, too ?....

Believe it or not... Norton is still alive...
http://www.nortonmotorcycles.com/
http://www.nortonmotorcycles.com/company/history/

You think we've off tracked this thread far enough ? ... lol

 

[rcgldr]

The key to self stability is designing a bike's geometry so that the bike steers into the direction of lean. The typical way to implement this is through trail as mentioned in the articles. For an alternative design, a bike with no trail or caster, or gyroscopic effect, sometimes called a skate bike (emulating a bike using two skates on ice instead of wheels) can be made to steer into the direction of lean by locating a weight above and in front of the front wheel which is free to pivot about the steering axis. When leaned, the weight produces a yaw torque that steers the front wheel into the direction of lean.

A team at Delft University wrote a paper, and also did some experiments, with a conventional bike and a "skate" type bike. They created mathematical model for a conventional test bike. One issue not answered, is that the model predicted a maximum stable speed just under 8 m/s, after which the bike would go into capsize mode, falling inwards at an extremely slow rate. However, in treadmill tests with that bicycle, the bike is seen to be "very stable" at 30 kph == 8.33 m/s.

The graph that shows the stable speed range can be seen on page 4 of:

http://www.tudelft.nl/fileadmin/UD/MenC/Support/Internet/TU_Website/TU_Delft_portal/Onderzoek/Wetenschapsprojecten/Bicycle_Research/Dynamics_and_Stability/doc/Koo06.pdf

The video demonstrating a very stable bicycle at 30 kph can be seen near the bottom of this web page:

http://tudelft.nl/nl/actueel/laatste-nieuws/artikel/detail/treadmill-measurements

So the capsize mode for their test bike would require a higher speed. In the case of most sport or racing motorcycles, capsize mode starts to occur at around 160 kph (100 mph). At that speed or faster, a motorcycle tends to hold the current lean angle, and it requires significant counter steering torque applied by the rider to change lean angle, with the same amount of effort required to increase or decrease lean angle.

British motorcycle - Norton 850

I owned a Norton 850 command for a few years. The engine, transmission, and swing arm pivot were attached to a sub-frame (two pairs of plates, one pair in front of engine and one pair in back of engine, plus a mount at the top) rubber mounted to the main frame to reduce vibration. Exhaust pipes were also rubber mounted. The shift was on the right, and also "backwards": 1 up (shift from first from neutral) and 3 down (for "upshift"), the opposite of most other bikes.

 

[1oldman2]

You think we've off tracked this thread far enough ? ... lol

Yup

 

[Andy Resnick]

Interesting article on bicycle physics and researchers who've investigated it:

http://www.scientificamerican.com/article/the-bicycle-problem-that-nearly-broke-mathematics/

A similar article, originally from 1970, was recently reprinted in Physics Today:

http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys7221/vol59no9p51_56.pdf

Surprising the SciAm article says nothing about Jones' work...

ps- suzuki bandit 600 over here...

 

[jedishrfu]

Actually the Sciam article mentions Jones work:

In April 1970, chemist and popular-science writer David Jones demolished this theory in an article for Physics Today in which he described riding a series of theoretically unrideable bikes. One bike that Jones built had a counter-rotating wheel on its front end that would effectively cancel out the gyroscopic effect. But he had little problem riding it hands-free.

 

[rcgldr]

gyroscopic effect

Gyroscopic precession is a reaction to torque along the roll (lean) axis, not a reaction to lean angle, which means it's not a corrective reaction. If a bike is in a coordinated turn, there's no torque about the roll axis and no gyroscopic reaction that would tend to return a bike to a vertical orienation. During the time a bikes lean is increasing, the gyroscopic reaction is to steer less than what is needed for correction, and during the time a bikes lean angle is decreasing, the gyroscopic reaction is to oppose what is needed to complete correction back to vertical orientation. For a typical bike that uses trail for stability, gyroscopic reaction acts as a damper within the range of speed for self stability. Once above that speed, the dampening effect dominates and the bike goes into what is a called capsize mode, where the lean angle increases at an extremely slow rate. To a motorcycle rider at high speed, the perception is that lean angle is held, this could be due to the extremely slow rate of lean angle increase, or since the tire's contact patch is on the inside portion of a tire, an outwards roll torque may be having an additional effect.

 

[jim hardy]

You think we've off tracked this thread far enough ? ... lol

naahh,,
i notice those photos have shifter on correct side. Rule Brittania !

Ha!... but I do have a 1986 1,100 cc Harley Sportster, with the Evolution engine ... the first year Harley made them.....

gave son my '85, last of the old guard ironheads.

I was a Royal Enfield guy.

 

[Andy Resnick]

Actually the Sciam article mentions Jones work:

Good catch- didn't see it.

 

[OCR]

I was a Royal Enfield guy.

I saw a real one parked at Fisherman's Wharf, when my family and I stayed in San Jose while visiting my
Mom's cousin ... of course we went to San Francisco, and did the tour thing...

That was probably 50 some odd years ago, but that mental image still sticks in my mind... I thought it was the most beautiful thing I'd ever seen...

Did you have an Enfield ?... if so, what model... ?

gave son my '85, last of the old guard ironheads.

Yup, '85 was the last of them...

 

[jim hardy]

Did you have an Enfield ?... if so, what model... ?

1956 , imported to US with nameplate "Indian" , 694cc twin, single carb ,
They do have a distinctive look !

From a vintage Enfield page,
http://www.classic-british-motorcycles.com/royal-enfield-motorcycles.html

Previous owner had bobbed the fenders and changed to Sportster style tank & seat
i added Dunstall megaphones

it had the first permanent magnet alternator i ever encountered . I think the magnets needed to be recharged for the lighting system was, well, feeble.
Good thing it had magneto ignition ! I never had to push it home.

ahhh , youth, and the things we should have kept...

Yup, '85 was the last of them...

85 is s a good year if you like the retro look, has the Evo clutch with alternator in the chaincase(like my '56 indian) , and an oil filter where the generator used to be.

Wow did i get off topic.

 

[OCR]

1956 , imported to US with nameplate "Indian" , 694cc twin, single carb ,
They do have a distinctive look !

Yeah, they do, but... it's a good look...

ahhh , youth, and the things we should have kept...

Lol.....

 

[golfrmyx]

Interesting article on bicycle physics and researchers who've investigated it:

http://www.scientificamerican.com/article/the-bicycle-problem-that-nearly-broke-mathematics/

I read the article a few days ago soon after it was published by the Washington Post. Very fascinating and interesting to study. I have done study on bicycles and motorcycles myself on a small scale and knew about most of what is in the article. Riding motorcycles at a high speed around a curve leaning over to almost a 45 degree angle is scary because of the fear of sliding on even a small amount of loose gravel. I have done it numerous times and never slid. I believe because of the gyroscopic effect holding the line of movement.
However, I do not believe the statement that two opposite rotating gyroscopes cancel each other out. I will have to find a couple and build a gig to test this for myself. The illustration shows them almost vertical indicating the cancellation is for rotation about the same vertical axis. My belief is for rotation of the axis horizontally. I will test both but it will take a few days to get the gyroscopes or build them myself.

 

[A.T.]

I do not believe the statement that two opposite rotating gyroscopes cancel each other out.

 

[Tom.G]

My very first Motorcycle was a Zundapp 600cc, well used when I bought it in the early to mid '60s. It wouldn't do a wheelie due to the design. Pop the clutch and the backend would boot you in yours. Being young and foolish I wanted to see what it would do; an unbelievable 43 feet of rubber on blacktop! Yet very smooth for cruising.

Here is a stock photo that is the closest I could find, it looks a bit more recent than the one I had. (Loved that 'ride-off' center stand.)

Unfortunately it died of 'hardening of the arteries.' A clogged oil line to the front main bearing sheared the crankshaft.