provided by the lock wall on the barge train during the impact. Note that the mass used to develop the

correlation of linear momentum normal to the wall with values of (*F*w)max is the mass of the barge train

and does not include the computation of any hydrodynamic added masses. However, the values of (*F*w)max

in Table E-1 (which are derived from the field test data) reflect the effects of the external forces of barge

train (due to engine), drag force, and helper boat force acting on the barge train as well as the effects of

the hydrodynamic masses and the inertia of the barge train mass decelerating during impact.

A summary of the values for the maximum impact force normal to the wall (*F*w)max for the eight full-scale,

controlled barge impact experiments shown in Table E-1 compared to the empirical equation is given in

Table E-2. For example, the energy method or the equilibrium with a fixed coefficient of friction value

(= 0.6) for the full-scale, controlled barge impact experiment (No. 29) produces an (*F*w)max value of

1,274.99 kN (286.63 kips), and the best-fit straight line of the empirical correlation produces an (*F*w)max

value of 1,736.49 kN (390.38 kips). This corresponds to a 36 percent overprediction by the best-fit

straight line of the empirical correlation approach. The maximum force normal to the wall (*F*w)max com-

puted using the best-fit straight line of the empirical correlation differs from the maximum force (*F*w)max

values presented in Table E-2 by a 23 percent underprediction to a 36 percent overestimate for these eight

impact tests. Based on the linear regression of the data point in Table E-2, standard error or standard

deviation of the model is 351.4 kN (79 kips). This model variability should be accounted for in the

empirical equation by including a 10 percent coefficient of variation to the linear equation defined

above. Figure E-3 shows the cone-shaped variation in the empirical results that should be included in the

PBIA from 0 to 3,558 kN (800 kips).

29

12.63

2.2

286.63

390.38

36

30

12.19

2.35

369.15

402.69

9

31

10.60

1.61

236.2

240.35

2

37

10.29

1.95

327.27

282.68

-14

38

11.94

1.83

230.29

307.25

33

39

14.12

1.61

271.07

318.74

18

41

8.76

2.86

419.37

353.48

-16

42

17.48

1.83

577.44

446.08

-23

Note: To convert ft/sec to m/sec, multiply by 0.3048. To convert kips to kilonewtons, multiply by 4.448.

E-3

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