You calculate the lean for a flat road first, by setting the overturning moment caused by centripetal force (h x mv^2/r) against the balancing moment caused by moving the CG horizontally as it leans. When you have the angle relative to horizontal, notice it is the same even if the road banks. So if you want the angle relative to the road, you must deduct the road banking angle.lee23 said:Hi all,
I was wondering if anyone could help me with calculating the angle of lean on a motorbike on a banked curve (with friction). If possible proofs would be very useful.
Thanks
Lee
The angle of lean on a motorbike on a banked curve can be calculated using the formula: tan(theta) = (v^2)/(rg), where theta is the angle of lean, v is the velocity of the motorbike, r is the radius of the curve, and g is the acceleration due to gravity.
The angle of lean on a motorbike on a banked curve is affected by the velocity of the motorbike, the radius of the curve, and the acceleration due to gravity. Other factors such as the weight and size of the motorbike, as well as the friction between the tires and the road, can also impact the angle of lean.
The angle of lean is important for motorcyclists because it determines the stability and safety of the motorbike while going around a banked curve. If the angle of lean is too small, the motorbike may slide outwards and lose traction. If the angle of lean is too large, the motorbike may tip over and cause an accident.
The angle of lean can be adjusted by changing the velocity of the motorbike or by adjusting the banking angle of the curve. To increase the angle of lean, the motorbike can be accelerated or the curve can be banked more steeply. To decrease the angle of lean, the motorbike can be decelerated or the curve can be banked less steeply.
The maximum angle of lean a motorbike can achieve on a banked curve is limited by the coefficient of friction between the tires and the road. This limit is typically around 45 degrees, but can vary depending on the conditions of the road and the quality of the tires. It is important for motorcyclists to stay within this limit to maintain control and stability while riding on a banked curve.