In this appendix, an empirical correlation between the maximum force normal to the wall and the linear

momentum normal to the wall is presented. The maximum force *F*w used in this correlation was obtained

from the models presented in Chapter 5 of Arroyo, Ebeling, and Barker (2003). Recall that no damage

occurred to the barge and no lashings failed during impact testing for the eight impact experiments used

to derive the empirical correlation described in this appendix. The experiments were also conducted to

eliminate both the transverse velocity component *V*0*y *and the rotational component. These both were

negligible in the results from the data processing.

wall given in the last column of Table E-1, a best-fit straight line was calculated for the eight experiments.

The velocity *V*0*x *listed in the third column of Table E-1 acts in the local barge x-axis. This approach

relates the *F*w obtained from the energy method directly to the linear momentum. Figure E-1 shows the

velocity vector transformation from local (barge) axis) to global (wall) axis used for the experiments. It is

important to mention that only one data point of the whole *F*w time-history for each of the eight

experiments was used to develop this empirical correlation. The velocity normal *V*norm and velocity

parallel *V*par shown in Figure E-1 relate the coordinate system of the barge train to the coordinate system

of the wall.

eight data points (for the eight impact experiments) for the Figure E-2 empirical correlation. The line was

assumed to start at the origin (i.e., no intercept term was used for the linear equation). The resulting best-

fit equation for this set of eight data values is (*F*w)max = 0.435**m***V*0*x**sin θ, where *m *is the mass in tons.

That is, a coefficient times the linear momentum normal to the wall determines the maximum force

normal to the wall.

29

12.63

2.2

1,865.59

286.63

897.42

30

12.19

2.35

1,865.59

369.15

925.73

31

10.60

1.61

1,865.59

236.2

552.52

37

10.29

1.95

1,865.59

327.27

649.84

38

11.94

1.83

1,865.59

230.29

706.32

39

14.12

1.61

1,865.59

271.07

732.74

41

8.76

2.86

1,865.59

419.37

812.59

42

17.48

1.83

1,865.59

577.44

1,025.48

2

2

Note: To convert kip-sec /ft to MN-sec /m, multiply by 0.135. To convert k-sec to MN-sec, multiply by 0.004450 MN-sec.

E-1