1  Investigation of load assumptions

1.2 Cornering

Similar phenomena occur on tight cornering as occur on full braking. In the steady-state phase of cornering, the loading area is inclined laterally by a rolling angle. A rapid buildup in centrifugal force up to its maximum value gives rise to a rolling oscillation with amplitudes which are superimposed on the steady-state rolling angle. The transverse force parallel to the loading area acting on the cargo is therefore made up of:

• centrifugal force component from cornering,
• downhill force arising from the geodetic inclination of the loading area,
• inertial force arising from tangential acceleration from a rolling oscillation.

In this case too, the normal force acting from the cargo on the loading area is reduced by two causes, namely, as a result of the inclination of the loading area, by the

• upwardly directed vertical component of the centrifugal force of cornering,
• reduced normal component of the weight-force.

Figure 3: Cornering with unfavorable inclination b of the road

Unlike in the longitudinal direction, the centrifugal force is oriented horizontally in the geodetic reference system, i.e. not parallel to the inclination of the road. Thus the inclination of the road has a direct impact on the centrifugal force components through the downhill force.

Figure 4: Cornering on a level road with 0.42 g centrifugal acceleration and
0.54 g maximum transverse acceleration, maximum rolling amplitude = 5.8°.

Figure 4 shows the numerical solution of the equations of motion over a period of 6 seconds. The forces acting on the cargo have been converted into units of g.

Maximum centrifugal acceleration was deliberately selected at 0.42 g such that, once the rolling oscillations have subsided, a steady-state transverse acceleration of 0.50 g is established. As a consequence, the first rolling amplitude gives rise to a maximum transverse acceleration of 0.54 g. This value increases if the buildup time is shortened or damping of the rolling oscillations is reduced.

Further simulated cornering maneuvers with other loading area spring constants and with favorable and unfavorable corner inclination of the road reveal comparable profiles. The following general conclusions may be drawn::

• The generally accepted assumption of transverse acceleration of 0.5 g for dimensioning cargo securing against sideways sliding must not be interpreted in such a way that this value could be solely attributable to the centrifugal force. Instead, between 20 and 30% of this value must be reserved for the downhill force from the inclination of the loading area and the tangential forces from superimposed rolling oscillations.
• In steady-state cornering, the inclination of the loading area is still present even after the rolling oscillations have subsided and contributes just about 20% to transverse acceleration.
• The transverse force allowances from the downhill force and tangential forces have nothing to do with the "rolling factor", which is required in VDI Guideline 2700 Sheet 2. The rolling factor takes account of dynamic tipping moments, while the stated allowances are forces acting at the center of gravity.
• In favorably constructed curves (road inclined towards the center point of the curve), the parallel component of the force of gravity is partially offset by the inclination of the road. The opposite applies when the road is inclined unfavorably.
• As previously with full braking, stiffer loading area suspension gives rise to smaller rolling angles and the transverse forces thus approximate to pure centrifugal forces.
• Starting to corner more slowly with buildup times of distinctly more than two seconds allows the superimposed rolling oscillations to become insignificant if damping is adequate, because the initial amplitudes fall within the range of the still increasing centrifugal force.
• The normal force from a given cargo unit is reduced by an order of magnitude of around 5%. This has a negative impact both on friction and on stableness.