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Diagram of turning vehicle. On wheeled vehicles with the common type of front wheel steering (i.e. one, two or even four wheels at the front capable of steering), the vehicle's turning diameter measures the minimum space needed to turn the vehicle around while the steering is set to its maximum displacement from the central 'straight ahead' position - i.e. either extreme left or right.
The relationship between speed and tilt can be calculated mathematically. We start with the formula for a balancing centripetal force: θ is the angle by which the train is tilted due to the cant, r is the curve radius in meters, v is the speed in meters per second, and g is the standard gravity, approximately equal to 9.81 m/s²:
Ackermann geometry. The Ackermann steering geometry (also called Ackermann's steering trapezium) [1] is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii.
The term scrub radius derives from the fact that either in the positive or negative mode, the tire does not turn on its centerline (it scrubs the road in a turn) and due to the increased friction, more effort is needed to turn the wheel. Large positive values of scrub radius, 4 inches/100 mm or so, were used in cars for many years.
A steering ratio of x:y means that a turn of the steering wheel x degree(s) causes the wheel(s) to turn y degree(s). In most passenger cars , the ratio is between 12:1 and 20:1. For example, if one and a half turns of the steering wheel, 540 degrees, causes the inner & outer wheel to turn 35 and 30 degrees respectively, due to Ackermann ...
This formula also shows that the radius of turn decreases with the angle of bank. With a higher angle of bank the radius of turn is smaller, and with a lower angle of bank the radius is greater. In a banked turn at constant altitude, the load factor is equal to 1 cos θ {\displaystyle {\frac {1}{\cos \theta }}} .
β° = Breakover angle; C = Underside of chassis; W = Wheel; G = Ground; M = Midpoint of wheelbase Example of a vehicle at a significant breakover angle.. Breakover angle or rampover angle is the maximum possible supplementary angle (usually expressed in degrees) that a vehicle, with at least one forward wheel and one rear wheel, can drive over without the apex of that angle touching any point ...
A variation of the Nadal formula, which does take these factors into consideration, is the Wagner formula. As the wheelset yaws relative to the rail, the vertical force V is no longer completely vertical, but is now acting at an angle to the vertical, β. When this angle is factored into the Nadal formula, the result is the Wagner formula: [3]