This paper primarily deals with the assessment of tiedown lashings and direct securing measures used to secure cargo on road vehicles. In daytoday practice, extremely simplified mathematical models are used for such an assessment. Such models allow the carrier to determine the amount of securing required and also permit the police to perform inspections and, where necessary, provide an assessment that will stand up in court. Any simplified mathematical model for assessing a cargosecuring arrangement should not only be easy to use, but should above all realistically reflect the actual overall securing effect despite ignoring the small number of less significant side effects.
The current discrepancies between the mathematical models for tiedown lashings in the VDI 2700, Part 2 Guideline and the DIN EN 121951:2004 standard compared with the DIN EN 121951:2011 standard have only arisen over the past decade. The discrepancies result from differences in the simplifications used in the mathematical models. In particular, the DIN EN 121951:2004 standard, which has in fact now been superseded, includes the „k factor“ in the calculation to account for the transmission loss of pretensioning force when tensioners are used on one side only, which leads to a 33% increase in the amount of securing required in order to comply with the standard.
The mathematical models for tiedown lashings have been presented in detail in this paper and compared with the actual securing effect, which is more complex. Some important aspects of the assessment of direct securing measures were also investigated. The results are summarized below:
 The common mathematical models for determining the number of tiedown lashings required ignore side effects of a tiedown lashing that have the nature of direct securing measures and therefore provide inflated results, especially for small coefficients of friction or small resting moment levers in the case of units that are liable to tip. This means that the securing outlay appears to increase disproportionately for small coefficients of friction or small resting moment levers, which does not quite correspond to reality.
 The use of the k factor of 1.5 to mathematically account for the transmission loss of pretensioning force in a tiedown lashing with onesided tensioning, when the DIN EN 121951:2004 standard was introduced in Germany, was by and large accepted, even though there was no recognized evidence for the inadequacy of the previously applicable mathematical model in the VDI 2700, Part 2 Guideline, which did not include the k factor.
 The way in which the new k factor was dealt with in DIN EN 121951:2004 was, on the one hand, inconsistent, because the lateral components that had been made available by the k factor were not taken into account in the sliding balance, although this was done in the tipping balance. In the latter case, they were evaluated in a way that made no physical sense, which led to completely unrealistic results. The reason for this incorrect evaluation was that movement of the cargo was ignored for cargo secured by tiedown lashings, although movements of this sort had always been presumed when assessing directly secured cargo.
 The introduction of the standard tension force S_{TF}, to be determined by prototype testing according to the DIN EN 121952:2001 standard, led to speculation that engagement of the pawl of the ratchet tensioner with the previous tooth of the winding shaft would cancel out the transmission loss in the overall pretensioning force with reference to S_{TF}. This paper, however, demonstrates that this cancelling effect does not occur, but that generally the k factor only rises slightly.
 In the case of direct securing, small movements or deformations of the cargo cause the initial pretensioning force on the side to which the load is applied to rise, allowing the lashing capacity LC of the relevant lashing equipment to be used in calculations. In the case of a tiedown lashing, on the other hand, the pretensioning force on the side to which the load is applied only increases to the extent permitted by the Euler ratio to the simultaneously falling force of the belt on the other side. In any event, however, the resulting configuration of horizontal components is beneficial with respect to securing.
 For the entire range of lashing angles, the actual securing effect of a tiedown lashing against forces in transverse direction and forces in longitudinal direction relative to the vehicle is greater than the securing effect according to the mathematical models in the currently applicable DIN EN 121951:2011 standard and are by and large greater than the securing effect according to the mathematical model in the VDI 2700, Part 2 Guideline. Furthermore, the dependency of the securing effect on the sine of the lashing angle that underpins all the mathematical models to date is unfounded. The actual maximum for the securing effects is achieved with lashing angles of between 60° and 70°, and not at 90°.
 For the entire range of lashing angles, the actual securing effect of a tiedown lashing against moments in transverse direction relative to the vehicle is greater than the securing effect according to the mathematical models in the currently applicable DIN EN 121951:2011 standard and in the VDI 2700, Part 2 Guideline. In this case also, the influence of the sine of the lashing angle that has been claimed is unnecessary.
 For the entire range of lashing angles, the actual securing effect of a tiedown lashing against moments in a longitudinal direction relative to the vehicle is greater than the securing effect according to the mathematical models in the currently applicable DIN EN 121951:2011 standard and in the VDI 2700, Part 2 Guideline if a small degree of tilting of the cargo unit is permitted. Because a tiedown lashing essentially secures a cargo unit directly against tipping in a longitudinal direction if the lashing is arranged laterally, there is a temptation to use the lashing capacity LC as the securing force. It is urgently recommended that this should not be done, because this force is only achieved after the cargo tilts significantly. It should be mentioned that in this case also, the influence of the sine of the lashing angle that has been claimed is unnecessary.
 In the case of a tiedown lashing, the coefficient of friction between the belt and the cargo should be as small as possible, i.e. 0.2 or smaller. This can be achieved using smooth, rounded edge protectors or similar lowfriction materials. The exception to this rule is when securing cargo units that are liable to tip against tipping in a lateral direction, in which case it is more beneficial to have a large coefficient of friction between the belt and the cargo.
 In Germany, discussions have ensued regarding a purported reduction in safety as a result of the introduction of the DIN EN 121951:2011 standard. In this respect, we can say that the new version DIN EN 121951:2011 places more stringent demands on a tiedown lashing than the VDI 2700, Part 2 Guideline, which is still used in parallel. Because this guideline is still recognized as the „generally accepted technical rules“, the arguments against the DIN EN 121951:2011 standard are not consistent.
 The mathematical models in the predecessor standard DIN EN 121951:2004 for transverse and longitudinal securing forces are 17.5% more stringent than those in DIN EN 121951:2011. In the case of tipping loads in a lateral direction, the discrepancies can run to several hundred percent. Aside from these discrepancies caused by a modelling error, the reduction in safety pointed to by critics is only around half the magnitude of the gain in safety resulting from the k factor introduced a few years earlier. DIN EN 121951:2011 thus represents an improvement in safety compared with the VDI 2700, Part 2 Guideline.
 Although the instruments contained in DIN EN 121951:2011 appear to be acceptable on the basis of the findings indicated in points 10 and 11, this is not to say that this standard is not in need of correction and could not be improved. It is not, however, the main purpose of this paper to make suggestions for improvement.
 As has already been noted in point 1 above, the coefficient of friction between the loading surface and the cargo that is chosen plays a key role in the simplified mathematical models for assessing a tiedown lashing used to secure a cargo against sliding. After weighing up the various opinions that are currently in circulation, we can support the proposal made in DIN EN 121951:2011 to use a mean value between the coefficient of static friction and the coefficient of dynamic friction.
 Direct lashing forces are used in the common mathematical models at the value of the lashing capacity LC of the lashing equipment. The movement of the cargo in the direction of the external force that is required in order to achieve this force in the lashing equipment can and should be reduced to a minimum. This can be achieved by aligning the lashing equipment as closely as possible to the direction of the external force, by applying a high pretensioning force to the lashing equipment (although this must not exceed 40% to 50% of the LC) and by choosing lashing equipment with a large elastic constant.
 The common mathematical models for assessing a direct securing arrangement do not take account of the necessary movement of the cargo, which is always present. This means that the results from the mathematical models differ from those of a more accurate calculation. For sliding balances, the discrepancies are on the „safe side“ and for tipping balances, on the „unsafe side“. As a whole, however, they can be tolerated.
 If two or more items of cargosecuring equipment which secure the cargo directly in the same direction and which have different angles, different lengths and/or different elastic constants, are assessed using the common, simplified mathematical models, all the equipment is incorporated in a force or moment balance calculation at its LC. This approach is incorrect. When the item of securing equipment with the most favourable direction of action, the shortest length and/or the largest elastic constant reaches its lashing capacity LC, the other items have still, to a greater or lesser extent, not reached their LC. The securing arrangement is therefore inadequate or it is accepted that the first of these items of securing equipment (the „most rigid“) will become overloaded. Suitable provision should be made in the guidelines and standards to take account of this.
 The rolling factor introduced in the German VDI 2702 Guideline, that was intended to take account of additional tilting moments resulting from rotational accelerations of the loading surface and rotational inertia of the cargo, may have been the victim of misunderstandings during the course of the consultations on the DIN EN 121951:2011 standard. The reduction from 0.2 g to 0.1 g appears to be justified. However, the application criterion for identifying the risk of tipping is not correctly formulated and there is no physical evidence for the claimed dependency of the use of the rolling factor on the pretensioning force.
 The static tipping test for establishing the appropriateness of securing arrangements that cannot be verified using the simplified mathematical models is not completely equivalent to the simplified mathematical models. The use in the test of a coefficient of static friction that has been „arbitrarily“ reduced using a factor of 0.925 as specified causes the coefficient of static friction that actually applies to make it appear that a smaller securing effect would be sufficient than would be required by the mathematical model using the reduced coefficient of friction.
 The standardized driving test that is permitted as an alternative necessarily includes dynamic effects. These effects generally cause greater movements of the cargo with the result that the discrepancy compared with the simplified mathematical model tends to occur on the other side. Thus it is both accurate and explicable that a static tipping test and a dynamic driving test are less equivalent to each other than either of the options are to the simplified mathematical model. The static tipping test, however, is easier to perform and can be done in a more controlled manner, and also corresponds sufficiently to the mathematical model.
 One important insight for tiedown lashings is that any number of mathematical models or accurate coverage of all securing effects are useless and of no predictive value if daytoday practice fails to ensure that the forces from the belts are transmitted to the entire cargo efficiently and across the greatest possible time span. This was clearly illustrated in the example of the hay wagon and the pole along the top which was presented at the beginning of this paper. In the case of normal cargoes on modern road vehicles, edge protectors and pressure distributors should be used for the same purpose. Accessories such as these are integral components of a tiedown lashing concept and should therefore be given a recognized role in assessing a tiedown lashing in the guidelines and standards.
