0
$\begingroup$

For a bike steering with radius of curvature $r$, we have $$\theta = \arctan \frac{v^2}{gr}$$ but you need to know r. I want to calculate the leaning angle from steering angle. It should be just enough so the bike doesn't fall over. Is it possible?

Edit:

Forget to mention that I also want to calculate same thing for monowheel bikes.

Improve this question
$\endgroup$
1

2 Answers 2

Reset to default
1
$\begingroup$

I suppose, by "steering angle" you mean the angle $\alpha$ between the front wheel and the rest of the bicycle as shown in this top view of a curving bicycle.
top view of a curving bicycle
From the right triangle you can derive the equation $$\tan\alpha = \frac{L}{r}$$ where $L$ is the distance between front wheel and back wheel, and $r$ is the radius of the curve driven by the back wheel. Together with the other equation already given in your question $$\tan\theta=\frac{v^2}{gr}$$ you can eliminate the radius $r$ and find

$$\tan\theta = \frac{v^2}{gL}\tan\alpha$$

Improve this answer
$\endgroup$
9
  • $\begingroup$ Thomas what if it's a monowheel bike? Like L is then 0 and formula is screwed up? $\endgroup$
    – John T
    Commented Jul 12, 2021 at 12:12
  • $\begingroup$ @JohnT How would you even define the steering angle for a monowheel bike? $\endgroup$
    – Thomas Fritsch
    Commented Jul 12, 2021 at 12:46
  • $\begingroup$ @Thomas btw i tried you formula with 80km/h, wheel base 1m and steer angle 15. It ended up with 90+ degrees for leaning that can't be right. Or can? $\endgroup$
    – trshmanx
    Commented Jul 12, 2021 at 13:08
  • 1
    $\begingroup$ The 8000 should be 80,000 and then $\tan\theta$ is 13.5 and $\theta$ is 85.8 degrees (with g=9.8) $\endgroup$
    – John Hunter
    Commented Jul 12, 2021 at 13:56
  • 1
    $\begingroup$ @trshmanx Your steering angle $\alpha=15°$ is very large. So you get a very small curve radius $r=L/\tan\alpha=3.7$ m. Driving this tight curve with high speed $v=80$ km/h is insane. So it is no surprise you got an insane leaning angle of nearly $90°$. $\endgroup$
    – Thomas Fritsch
    Commented Jul 12, 2021 at 14:58
1
$\begingroup$

For a monowheel bike there is only leaning angle, steering angle is undefined.

Leaning at an angle $\theta$ will cause the monowheel bike to move in a circle of radius $$r=\frac{v^2}{g\tan\theta}$$

Improve this answer
$\endgroup$
6
  • $\begingroup$ Not sure your claim is right. I just tried it with a real wheel and it doesn't go in curve just from leaning. $\endgroup$
    – trshmanx
    Commented Jul 12, 2021 at 13:22
  • $\begingroup$ @ trshmanx was your wheel also travelling at velocity $v$? $\endgroup$
    – John Hunter
    Commented Jul 12, 2021 at 13:32
  • $\begingroup$ Kind of. I am confused. $\endgroup$
    – trshmanx
    Commented Jul 12, 2021 at 13:39
  • 1
    $\begingroup$ @ trshmanx the diagrams on the top right of this link en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics show leaning causing the turn of a bike $\endgroup$
    – John Hunter
    Commented Jul 12, 2021 at 13:48
  • $\begingroup$ I just ride a bike. Leaning it causes me to steer at same direction to not to fall. So steering still happens becouse of my hand force and not just becouse of leaning. $\endgroup$
    – trshmanx
    Commented Jul 12, 2021 at 13:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.