Voluntad política que marcó el camino de la integración

and interpretation

The calculation of securing forces is time- consuming, unless an automated algorithm is applied. The calculation shall include vertical lashing angle α, longitudinal lashing angle βx and transverse lashing angle βy. Lashing angles have crucial impact on the lashing means restraining force FR [7]. Their values can be measured practically, or calculated using appropriate mathematical tools.

The method of calculation can be confirmed in an example based on a model application. The task is to secure, e.g. a light amphibious tracked combat vehicle with high mobility and armour protection of BVP-2 type. For the haulage of heavy wheeled and tracked vehicles without limitation, a modernised version of a four-axle flat wagon of Smmps line, design group 54, technical interval 4728, without side stakes (hereinafter referred to as “wagon Smmps 54”), is utilised.

Basic technical parameters of wagon Smmps 54 are as follows:

- loading length – 14,000 mm; - loading width – 3,100 mm [6];

- wagon width (w) – 3,100 mm;

- distance of lashing points from side edges of the railway wagon (bo) – 200 mm.

Basic technical parameters of BVP-2 are as follows:

- weight – 14,300 kg;

- width – 2,700 mm (distance from wagon edges 200 mm from each side); - height – 1,600 mm;

- length – 6,720 mm (distance of points from the end of the railway wagon – 3,000 mm);

- height of attachment points

on the vehicle (v) – 1,600 mm;

- distance between lashing points on a vehicle and a side edge of the railway wagon (bv) – 350 mm; - distance between attachment points on

a vehicle and the plane of lashing points on the railway wagon (z) – 3,000 mm.

The task is to calculate FR, in order to prevent sliding of land military equipment on a wagon during transport, using formula (3), and to determine the minimum lashing capacity (LC) of each of the four straps.

𝐹𝑅 = 𝑚 ∙ 𝑔 ∙_{2 ∙ (cos 𝛼 ∙ cosβ}(𝑐𝑥,𝑦− 𝜇 ∙ 𝑓𝜇∙ 𝑐𝑧)

𝑥,𝑦+ 𝜇 ∙ 𝑓𝜇∙ sin 𝛼) [𝑁] (3)

For this purpose, parameters from standard [1] must be applied:

- gravitational acceleration – g = 9.81 m∙s-2;

- the coefficient of acceleration in longitudinal direction in case of railway transportation – cx = 1.0; - the coefficient of acceleration

in vertical direction in case of railway transportation – cz = 1.0;

- conversion factor for friction – fµ= 0,75;

- friction factor (combination

of materials on the contact surface

– planed wooden loading area of the railway wagon, rubber or a steel belt) – µ = 0.30 for tracked vehicles; µ = 0.60 for wheeled vehicles.

The friction factor μ depends on the type and texture of the surfaces. The equation (3) implies that the higher the value of μ (friction force between land military equipment and the wagon deck) is, the lower the requirements for further securing of load against sliding are. A table stating friction factor values for certain couples of materials is provided in standard [1].

95 In order to determine vertical lashing

angles α1, α2, α3, longitudinal lashing angles βx1, βx2, βx3 and transverse lashing

angles βy1, βy2, βy3, goniometric functions and Pythagoras’s theorem should be applied.

The calculation of lashing angles for crossed diagonal lashing – index 1:

𝑥1 = �𝑣2 + (𝑤 − 𝑏𝑜 − 𝑏𝑣)2 [𝑚𝑚] (4)

where x1 is a (diagonal) distance between an attachment point on a vehicle and the point of intersection of the planes of the railway wagon deck, vehicle front and an opposite lashing point on the railway wagon.

𝑦1= �𝑣2+ 𝑧2+ (𝑤 − 𝑏𝑜 − 𝑏𝑣)2 [𝑚𝑚] (5)

where y1 is a (diagonal) distance between an attachment point on a vehicle and an opposite lashing point on the railway wagon (corresponds to the length of the lashing strap).

tan 𝛼1 = 𝑣 �𝑧2 _{+ (𝑤 − 𝑏𝑜− 𝑏𝑣)}2 = 1,600 �9,000,000 + 2,5502 => 𝛼1 = 22,11° tan 𝛽𝑥1 =𝑥_{𝑧 =}1 �1,600 2_{+ 2,550}2 3,000 => 𝛽𝑥1= 45,10° cos 𝛽𝑦1= 𝑤 − 𝑏_𝑦𝑜− 𝑏𝑣 1 = 2,550 �1,6002_{+ 3,000}2_{+ 2,550}2 => 𝛽𝑦1= 53,13°

The calculation of lashing angles for slope lashing (in longitudinal direction) – index 2:

𝑥2 = �𝑧2+ (𝑏𝑣− 𝑏𝑜 )2 [𝑚𝑚] (6)

where x2 is a (direct) distance between an attachment point on land military equipment and the point of intersection of planes of the railway wagon loading area, land military equipment front and an adjacent lashing point on the railway wagon.

𝑦2 = �𝑣2+ 𝑧2+ (𝑏𝑣 − 𝑏𝑜 )2 [𝑚𝑚] (7)

where y2 is a (direct) distance between an attachment point on land military equipment and an adjacent lashing point on the railway wagon (corresponds to the length of the lashing strap).

tan 𝛼2 =_𝑥𝑣 2 = 𝑣 �𝑧2_{+ (𝑏𝑣− 𝑏𝑜 )}2 = 1,600 �9,000,000 + 22,500=> 𝛼2 = 28,04° cos 𝛽𝑥2= _𝑦𝑧 2 = 𝑧 �𝑣2_{+ 𝑧}2_{+ (𝑏𝑣− 𝑏𝑜 )}2 = 3,000 �11,582,500 => 𝛽𝑥2= 28,18°

96

cos 𝛽𝑦2= 𝑏𝑣_𝑦− 𝑏𝑜

2 =

150

�11,582,500 => 𝛽𝑦2= 87,47° The calculation of lashing angles for V-shaped diagonal lashing – index 3:

𝑥3 = �𝑣2+ (𝑤_{2 − 𝑏}𝑜 )2 [𝑚𝑚] (8)

where x3 is defined analogically to x2.

𝑦3 = �𝑣2+ 𝑧2+ (𝑤_{2 − 𝑏}𝑜 )2 [𝑚𝑚] (9)

where y3 is defined analogically to y2. sin 𝛼3 =_𝑦𝑣 3 = 𝑣 �𝑣2_{+ 𝑧}2_{+ (}𝑤 2 − 𝑏𝑜)2 = 1,600 �13,382,500=> 𝛼3 = 25,94° tan 𝛽𝑥3= 𝑥_{𝑧 =}3 �𝑣2_{+ (}𝑤 2 − 𝑏𝑜)2 𝑧 = �4,382,500 3,000 => 𝛽𝑥3 = 34,91° tan 𝛽𝑦3= √𝑣 2_{+ 𝑧}2 𝑤 2 − 𝑏𝑜 =�11,560,000_1,350 => 𝛽𝑦3= 68,34°

The restraining forces are calculated by supplying the variables into equation (3). The forces are then equal to inertial forces acting during transportation.

The slope (direct) lashing cannot be applied to land military equipment on railway wagons, even though it is

the most convenient method

in the longitudinal direction (LC value is the lowest), as it would be impossible to secure land military equipment in transverse direction, due to assumed equipment width (refer to the high value of FR2y= 13,586 daN).

The diagonal lashing method

– crossing prevents both sliding and tipping over. It is important that the crossing is located above the land military equipment centre of gravity and in the middle of the lashing line length. If the crossing is closer to the equipment, the securing stability decreases, and the possibility of swaying increases. This

method is permitted and can be applied; it is, however, less convenient than V-shaped diagonal lashing. Crossed diagonal lashing is more convenient for transverse securing. In railway transportation, the inertial forces are relatively small in transverse direction in comparison with longitudinal direction. The value of longitudinal inertial force is primarily affected by shocks during shunting.

As the most convenient, the securing method least straining lashing straps can be selected, i.e. the V-shaped diagonal lashing method, where maximum inertial force acting on lashing straps corresponds to the value of FR3x = 6,629 daN.