"The Physics Problem"

A good point made here chagrin but the Constants Such as the tyre Radius when Bike is upright & when the Bike leans Can be very easily measured and input into a variable & the acuter met thee accelerometer can easily make out that How much the Bike is leaning So as to Consider that tyre's Radius along its width.

Mad Scientist, hope you remember to put centripetal force in there? It's a biggie on a 500+ lb bike cornering at high speed.

I'm amazed there's no gyroscope/accelerometer to give warnings to the rider that they've about to hit point of no return...

some kind of buzzer to alert the rider....

Usually the point where you have to lift the inside foot because the peg is scraping provides a clue that that's all the lean you're going to get. On my bikes I could lean less to the right because the pipes scraped a bit sooner.

Human gyro/accelerometer is feeling where the G's are pushing. It should be directly into the seat but you can shift it a bit to get the bike more upright if you can lean yourself more into the turn which is hanging over the line just a bit btw.

The accident was determined by the entry speed to the turn. Warnings after that just let you choose to go down or leave the road on the outside of the turn.

Mad Scientist, hope you remember to put centripetal force in there? It's a biggie on a 500+ lb bike cornering at high speed.

Centripetal force is there indeed. What I didn't include was friction and normal force. For a thin wheel, one can approximate they lie on the origin of axes (as i draw them), which is exactly crossed by th wheel longitudinal axis (hence they don't enter into the moment calculation). But for a broad wheel like there are on motorbikes, the point of application will be obviously offset. This is not difficult to include conceptually, but that gores up (does that word exist?) the formulas a bit.

Note that, with my formula, phi always has a solution, which means the bike wheel can be at equilibrium at any lean angle. This is obviously not true in reality (the bike falls), where more stuff (see previous post) must be taken into account.

It's actually a bit more complicated about the point where your knee, foot, ankle or part of the side of the bike fulcrums support for the mass of the bike.

Models are fine as models but reality has ALL the details.

The formula is simple with the 3 variables I mentioned. You cannot find the constant using math. It's much better to find it experimentally for the specific rider and bike you want.

Yup. Make a good run and collect data then work it through some math and say “that’s what it must be!”.

@ s bright 33 ,yup! true , my Math is good Including being the best at trignomity.

But physics is something I left studying very early so Im loose on various points of understating.

Im presently studying the Bike physics page suggested to me by madphysicist.

NI$HANT: If you see the following video >> BMW S1000RR CRASH - http://youtube.com/watch?v=_A_PFBRAx9w

You will see that the riders AT A CERTAIN SPEED , WITH A GIVEN WEIGHT , ALONG WITH A CERTAIN ANGLE OF TILT goes down as the gravitational pull acts like that(may be I don't know better)

I actually wanted to know that one can know using physics that he can calculate that how much he can successfully tilt the bike like in the video GIVEN (he knows the weight of the vehicle in total (including him) + knows the Gravitational pull + the speed )

Assumptions can be: a) The road is not wet. b) Normal sunshine is there making the road a normally hot

He pushed the bike a bit more than the tire friction could take and down he went. That is one of the variables that can be a bit harder to control. A drop of oil/water/spit/snot at just the right spot and the traction picture can change just enough to drop you on your side like that. The opposite can happen also. Your are in the slide and all the sudden you have traction. WHAP!!! and you go down even harder on the opposite side. First crash is a low side, second type is a high side.

cjdelphi: I'm amazed there's no gyroscope/accelerometer to give warnings to the rider that they've about to hit point of no return...

some kind of buzzer to alert the rider....

Like he really has the time and spare thinking power to pay attention to some sensor. When you are laid over like that at speed you are putting every bit of spare processing power into feeling what is happening in real time, and the time to process some number on a display would only be letting you know why you went down, not that you were nearing the edge. What got this guy in trouble was that he didn't quite read the bike right and was just a hair fast.

A drop of oil/water/spit/snot at just the right spot and the traction picture can change

Assumptions can be: a) The road is not wet. b) Normal sunshine is there making the road a normally hot

atleast such sort of calculation will definitely help, it will not take away rider's judgment completely but will Supplement what he thinks he's doing and coupled with All that Math and Rider's judgment/experience this may wholly be a great riding experience which is also secure upto some extent.

More complete explanation with pictures and diagrams here:

http://www.stevemunden.com/leanangle.html

Here's the formula BUT....

.067 v2/r = tana

the constant 0.067 depends on many difficult to measure things like rider weight/geometry, bike weight/geometry, tire dimensions/u, street surface, how the rider is sitting or hanging off. 0.067 is anything but constant. You can't calculate it, you have to measure the 3 variables first. The maximum lean angle is much easier all you need is u=tana.

0.067 is anything but constant. You can't calculate it, you have to measure the 3 variables first.

sort of empirical determined variables, most important to determine is how the original variables influence "the constant", linear exponential quadratic chaotic etc. If that is determined one can derive formulas and calculate it.

This is sometimes trivial, but often rather complex as the variables you start with and measure may not be the "root" variables but depend on an underlying mechanism. Furthermore the "root" variables may change in time which causes the need to recalculate the "constant" constantly. Rules of thumb and approximations maight become the only workable solutions.

And note that the speed you can take a certain radius turn will be different in a level turn vs a descending or rising turn.

Racers learn the course before trying for maximums. A good rider knows how far he or she can lean and still there is no guarantee of safety. What margin you give is the margin you get. Just because someone has killed a tiger with a stick doesn't mean to approach tigers with sticks.

0.067 is anything but constant.

This Constant is a Constant problem.

Actually the lean angel WITH RESPECT TO GRAVITY, does not depend on the road surface banking angle. I may have mistakenly included a few variables in my list that do not change the constant, but some of them do.

yes I understand the explanation on that page was Really precise. the only thing now holding me back is how can I get the Radius 'I was banking Upon accelerometer to get the tilt & its corresponding Radius by forming a look-up table.

There’s no cheap way to measure tilt. You’d need an expensive Gyro because of the vibration. Accelerometers are useless of course. The only way I can think of to measure radius is predetermined based on the road, or GPS.

And where would you take the angle measure? Bike and rider tilt WRT each other, helmet tilts and turns. I leaned inside of hard turns and lifted the inside leg to let the peg fold up. Helmet always turning, I needed to keep awareness high. What's your tire-patch angle on a high crown road as opposed to a low crown road? I once went into a T at 45 mph on a bike with low center stand and slid a ways on the crown with the back wheel off the ground before getting back on two wheels and continuing along my way. I was already letting off the throttle, the back wheel didn't torque me and it's the front wheel that keeps you up. A little instinct with a lot of practice behind it, just hang in there and such minor events won't end your happy day. My accelerometer and gyros are built-in and pre-wired.

A little instinct with a lot of practice behind it, just hang in there and such minor events won't end your happy day. My accelerometer and gyros are built-in and pre-wired.

perhaps thats the reason such system isn't integrated yet.