# Arduino Forum

## Community => Bar Sport => Topic started by: Nishant_Sood on Jul 11, 2013, 12:42 am

Title: "The Physics Problem"
Post by: Nishant_Sood on Jul 11, 2013, 12:42 am
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
Title: Re: "The Physics Problem"
Post by: John_Smith on Jul 11, 2013, 02:48 am
His back wheel lost traction and slid out, its not very mathematical as rubber " marbles" , oil, or a damp patch, can cause it.

You only find where the limit is when you have hit it, which can be expensive   :-(
Title: Re: "The Physics Problem"
Post by: sbright33 on Jul 11, 2013, 04:00 am
There is a formula with 3 variables and a constant.  They are speed, radius, and lean angle.  The constant only depends on the tires, bike, rider geometry/mass.
Title: Re: "The Physics Problem"
Post by: N_Tesla on Jul 11, 2013, 06:29 pm
There is a typical undergrad problem involving an inclinated wheel travelling on a circle.

I did the quick back-of-the-envelope travel agency paper calculation (attached). On this extremely simplified example, you basically have to equate two torques : one from the inclination of the wheel (which tends to make it fall) and one from the change of wheel rotation vector due to orbital movement (which tends to set it back upright). (I neglected precession -due to the rotating wheel inclination- as wheels on a bike are much more constrained; the front one is free but controlled by the driver and the rear one is fixed. I didn't checked if the effect is actually negligible, but it seems an honest approximation, espically for a bike.) Note that for this example, the normal and friction forces can be made irrelevant by choosing the origin of axes at the contact point, but these simplifications most probably won't be possible when you fully consider the bike.

I probably made some calculation mistakes (i make mistakes virtually all the time), but the answer for the equilibrum lean angle seems, at least, reasonable. It only depens on the whell mass and radius, its speed and the radius of the big circle it travels (i left the rotational speed versions of these, but it's the same thing).

What changes for a full bike ? Obviously the center of mass vector won't be as simple (depends on the bike mass distribution) ; the inertia moment (but i left I anyway) ; and finally the radius R is to be changed with the curvature radius of the bike's path (which is now a function of theta) ; plus some other things (like neglected friction or what the driver does with the front wheel).

But to answer your initial question, yes it is possible even for a real bike, and solving everyting numerically should be easier in this case.

edit: On the lowest line, i wrote dr/d(theta), it's of course d(u_r)/d(theta), the unit vector. But that's what i meant on the next step.
Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 11, 2013, 07:02 pm
Thanks all specially Mad physicist I check it out deeply in sometime
Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 12, 2013, 01:23 am
Title: Re: "The Physics Problem"
Post by: N_Tesla on Jul 12, 2013, 02:12 am
Yeah sorry, that was really back-of-the-envelope. I'm typing a PDF version right now, aslo corrected from the mistakes I previously made (including quite stupidly calling theta both the coordinate and the lean angle :smiley-roll-sweat:). It'll be ready soon.
Title: Re: "The Physics Problem"
Post by: N_Tesla on Jul 12, 2013, 03:15 am
Hi,

While typing, I found this wesbite, which presents a simpler way of doing it : http://www.real-world-physics-problems.com/bicycle-physics.html, but they say they have "neglected 3D effects". My answer is the same as their (given that R*Omega^2 = v^2/R), if you neglect the 2*R*I*Omega*omega term.

Anyway, here is the PDF. I actually made two sign mistakes in my first thing, but they cancelled each other! How lucky, why doesn't this happen at exams ?
Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 12, 2013, 05:45 am

hehe, Sometimes teachers while checking offer discount.

what I now want is that the gravitational(gravity Sensor) quantities & Speed derived from a electronic circuitry of mine along with Constants fed into the Final Equation and get the angle,all this need to be calculated in c/c++ with available moth functions library, how to go about that?
Title: Re: "The Physics Problem"
Post by: cjdelphi on Jul 12, 2013, 07:01 am
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....
Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 12, 2013, 07:54 am
@ cjdelphi

The gyro/ accelerometer is needed to note the angle Not a Buzzer at all as these Super Sport or sports Bikes make a lot of noise So most Probably an LCD indication.
Title: Re: "The Physics Problem"
Post by: Chagrin on Jul 12, 2013, 01:32 pm
I think you're going to get a lot of error in your calculation due to the leaning tire and how its grip of the road will change. With the bike and rider you've got ~700 lbs of force (guessing) on a ~40 PSI tire and a footprint of (700/40) 17.5 square inches. But because you're sitting more on the sidewall of the spinning tire that rubber footprint is moving at different speeds across its width and gripping the road much differently than if the bike was upright.
Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 12, 2013, 01:40 pm
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.
Title: Re: "The Physics Problem"
Post by: GoForSmoke on Jul 12, 2013, 08:52 pm
Mad Scientist, hope you remember to put centripetal force in there? It's a biggie on a 500+ lb bike cornering at high speed.

Quote

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.

Title: Re: "The Physics Problem"
Post by: N_Tesla on Jul 12, 2013, 09:07 pm
Quote

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.
Title: Re: "The Physics Problem"
Post by: GoForSmoke on Jul 12, 2013, 10:28 pm
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.
Title: Re: "The Physics Problem"
Post by: sbright33 on Jul 14, 2013, 01:39 am
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.
Title: Re: "The Physics Problem"
Post by: GoForSmoke on Jul 14, 2013, 05:30 am
Yup. Make a good run and collect data then work it through some math and say "that's what it must be!".
Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 14, 2013, 02:57 pm
@ 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.
Title: Re: "The Physics Problem"
Post by: kf2qd on Jul 15, 2013, 08:04 pm

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.
Title: Re: "The Physics Problem"
Post by: kf2qd on Jul 15, 2013, 08:09 pm

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.
Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 16, 2013, 04:37 pm
Quote
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.
Title: Re: "The Physics Problem"
Post by: GoForSmoke on Jul 16, 2013, 05:08 pm
More complete explanation with pictures and diagrams here:

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

Title: Re: "The Physics Problem"
Post by: sbright33 on Jul 20, 2013, 10:19 pm
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.

Title: Re: "The Physics Problem"
Post by: robtillaart on Jul 21, 2013, 12:33 pm
Quote
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.

Title: Re: "The Physics Problem"
Post by: GoForSmoke on Jul 21, 2013, 02:35 pm
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.

Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 21, 2013, 07:48 pm
Quote
0.067 is anything but constant.

This Constant is a Constant problem.
Title: Re: "The Physics Problem"
Post by: sbright33 on Jul 23, 2013, 05:45 pm
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.
Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 26, 2013, 03:35 am
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.
Title: Re: "The Physics Problem"
Post by: sbright33 on Jul 29, 2013, 09:39 pm
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.
Title: Re: "The Physics Problem"
Post by: GoForSmoke on Jul 29, 2013, 11:19 pm
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.

Title: Re: "The Physics Problem"
Post by: Nishant_Sood on Jul 31, 2013, 05:52 am
Quote
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.
Title: Re: "The Physics Problem"
Post by: GoForSmoke on Jul 31, 2013, 06:17 am
Mine are inner ears and kinesio sense I was born with and trained.
Unfortunately they are not calibrated, nor are my eyes and ears, etc.
All are Mk I OEM wetware parts though the eyes have manufacture defects.