Well of Death: Physics behind it

[haruspex]

The standard way of providing this is with a rider who will steer the wheels right to prevent a rightward tip and steer the wheels left to prevent a leftward tip.

Well, it's not all down to the rider. Bicycles are more rideable than that because of the geometry. The front wheel contacts the ground a bit behind where a straight line down through the steering column does. If you hold a bicycle upright with wheels straight then tip it a bit to one side the front wheel will naturally turn that way. The gyroscopic effect of the front wheel also helps with that.

As an aside, I remember noticing as a kid that if I made a left turn after cycling through a puddle then the track left by my front wheel first went a bit to the right. So I was unconsciously throwing myself a bit off balance to the left, only correcting enough to halt the tipping while executing the turn, then overcorrecting to come back upright.

 

[Lnewqban]

I went through the wikipedia link that you've posted above. However, i couldn't find the term alternating steering input that you've mentioned. Could you kindly let me know what the the term alternating steering input means in the context of the bike.[/B]

I have made that term up, sorry it is confusing.
Alternating steering to one side and the other is what I meant.

Copied from same above link:
"If the steering of a bike is locked, it becomes virtually impossible to balance while riding. On the other hand, if the gyroscopic effect of rotating bike wheels is cancelled by adding counter-rotating wheels, it is still easy to balance while riding."

 

[haruspex]

View attachment 319037

The animation doesn’t look quite right to me. Looks like the bike starts to right itself before the front wheel is sufficiently turned into the fall.

 

[erobz]

As an aside, I remember noticing as a kid that if I made a left turn after cycling through a puddle then the track left by my front wheel first went a bit to the right. So I was unconsciously throwing myself a bit off balance to the left, only correcting enough to halt the tipping while executing the turn, then overcorrecting to come back upright.

Thats the difference between us ( besides a 100 IQ pts ). When I was riding my bike, I was being chased by the neighborhood bully, or I was getting ready to attempt a 360 on the next jump! I still don't know "how" I ride a bike to this day.

 

[Lnewqban]

The lateral balance is disrupted, and the axial roll starts as soon as the radius of the turn is increased.

For a bicycle the roll is quicker (and requires a lower magnitude of steering torque) than for a more massive motorcycle.

Please, see:
https://en.wikipedia.org/wiki/Countersteering

 

[haruspex]

The lateral balance is disrupted, and the axial roll starts as soon as the radius of the turn is increased.

For a bicycle the roll is quicker (and requires a lower magnitude of steering torque) than for a more massive motorcycle.

Please, see:
https://en.wikipedia.org/wiki/Countersteering

If that is in response to post #63, I am just saying it does not look quite accurate. As a cyclist, I have some feel for how far I would need to turn the wheel to get back upright, and the video looks to me like it is understeering. Based on the equation below, it should look better played at higher speed. Increasing v allows larger r for the same tilt.

Wrt bicycles versus motorcycles, I am unsure what you are saying. They both obey $v^2=rg\tan(\theta)$, where r is the turning radius, v the speed and $\theta$ is the angle to the vertical.

 

[Lnewqban]

More examples of stability and turning:
http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/bicycle.html

https://www.comsol.com/blogs/simulating-the-motion-of-a-self-stable-bicycle/

 

[hutchphd]

As an aside, I remember noticing as a kid that if I made a left turn after cycling through a puddle then the track left by my front wheel first went a bit to the right.

I am fond of Veritasium. In particular and, hopefully, on point: https://www.google.com/search?q=ver...#fpstate=ive&vld=cid:acab6797,vid:9cNmUNHSBac

 

[Coffee35]

Homework Statement: What will be the maximum velocity for a bike/car to go around in a well of death, when the wall of well of death is vertical, i.e. at 90 degrees ?
Relevant Equations: $$v_{max} = \sqrt{\frac{rg(sin\theta +\mu cos\theta)}{(cos\theta -\mu sin\theta)}}$$

While studying motion of car on banked curve, I was wondering, what will be the vmax when theta is equal to 90 degrees or is close to 90 degrees as it happens in a well of death which is organised in a village fair.

On a banked road with friction present, vmax is given by:
View attachment 317645
if we put theta = 90 degrees in the formula above, which is the angle in the well of death, then
View attachment 317646
But that is not acceptable, as vmax can't be an imaginary number.

I understand that if theta = 90 degrees, then the minimum value of v i.e vmin is given by:

View attachment 317647
This is understandable.

How do I calculate the value of vmax when theta = 90 degrees ?

View attachment 317649

ReplyForward

I don't think the Vmax will vary very much..considering an ideal condition that there is no object which can help to accelerate the bike in the centre of the circular path..the bike should be moving with constant speed, only if the bike moves up and down slightly in a while can it attain further velocity.
I don't know whether my saying is accurate or not but its a possibility nonetheless. Have a good day.