Ackermann's angles

The steering system of a kart seems at first very simple, but it has been developed from a clever idea from a German, Ackermann, who used it for the first time on carriages. The problem to resolve was the different paths traced by front wheels round corners. The steering system with wheels parallel means tyre wear and power loss caused by to the tread sliding on the asphalt. 

BEHAVIOUR OF KART ROUND CORNERS


The system has two rotation centres that causes vehicle to swerve and make wheels to skid on the asphalt. This means that if the front wheels are parallel, you do not get just one theoretic rotation center when going round corners. By creating a system where leading wheels are not parallel, but have different steering angles, you get only a theoretic rotation centre. In fact, one could think that the tilt (weight transfer) of the kart on its external wheels around corners means that the inside front wheels unloads and thus the sliding effect is limited. However, the big caster angle of modern karts creates a difference of level between the front wheels: the inside goes down while the other lift. So weight is distributed on both wheels, and more, on taking slow corners, the inside front wheel is the one that directs the curve and works more.

For this reason Ackermann steering system is used (patented London 1818), later re-used by French mechanic Jeantaud. The system is known as 'Jeantaud's quadrilateral system'. This is why the spindle arms are tilted inwards to get a different slant respect to the front wheels. To give more progression at the varying Ackermann angles, that is, to vary the difference between between the two steering angles of inside and external wheel while the steering wheel's arem are connected to two different points of the energy-absorbing steering column. This way to the two front wheels change their steering angle in a non uniform way, to suit the path's different curve angles.

To get a theoretic rotation centre using Ackermann's angles, tie internal wheel's steer angle alpha with external wheel's steer angle beta. The relation that binds the two angles is: 

cotg (alpha) - cotg (beta) = t/l

The advantage of Ackermann's system is that it is easy to carry out, but on the other hand there is a fair amount of approximation. What happens is that the aplha and beta angles do not always give a perfect rotation centre, and there is always an error of one of the two angle respect to the value of other. As shown in the illustration we can see that one of the Ackermann's angles is more accentuated (open convergence) and this reduces the error in small steers, so it helps in wide corners with small curving radius, while it accentuates the negative error at large curving angles, that is at sharp corners. 

CURVE ANGLES AND TYRE DRIFT 

We say "theoretic" rotation centre because the vehicle does not really follow the path dicated by its wheels. The drift phenomena intervenes on the path that the kart follows, and it is such that tyre under trasversals bends and no longer moves along the direction given by its axial section, but in a tilled direction respect to it by an epsilon angle, called drift angle. Drift depends on the tyre transversal elasticity that, because of deformability, allows continuous lateral movement during motion. Up to a certain epsilon value (depending on the characteristics of the tyre, on the load acting on the wheel, and on inflation pressure) there is an existing proportionality between transversal force and drift angle. Having reached a certain limit value of force, the angle increases until the wheels skids. As weight on front wheels is different, drift angle should be different, but as the wheels are fixed to the kart, the total angle can be (in effect it is slightly greater) averaged between the values of internal and external wheel. 

EFFECT OF ACKERMANN IN CORNERS 

Ackermann's angle has a relevant effect on taking corners as it accentuates load transfer in diagonal sense, and increases inside rear wheel lift. So there is more precision in taking the corner (also faster). You get the same effect on coming out of the corners with reduced understeering, the kart is slower in the second part of the curve. The Ackermann's angle can be changed by changing convergence, but this also determines a wider front tyre opening and less speed along straights. This is why, if convergence is open toward the front the initial Ackermann's angle increases and viceversa if convergnce tend to close. Ackermann's angle in karts is considered to be a variant that hardly ever needs changing, it is always set by manufacturers to suit more or less all types of tracks.