ETL 1110-2-563
30 Sep 04
d. The maximum normal force (Fw)max by the empirical correlation is equal to the reaction force
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 (Fw)max is the mass of the barge train
and does not include the computation of any hydrodynamic added masses. However, the values of (Fw)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.
E-3. Summary of Results
A summary of the values for the maximum impact force normal to the wall (Fw)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 (Fw)max value of
1,274.99 kN (286.63 kips), and the best-fit straight line of the empirical correlation produces an (Fw)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 (Fw)max com-
puted using the best-fit straight line of the empirical correlation differs from the maximum force (Fw)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).
Table E-2
(Fw)max Empirical Correlation (Mass = 1865.59 k-sec2/ft)
Approach Angle
Velocity
Measured (Fw)max
Empirical
Percent
Exp No.
deg
V0x, ft/sec
kips
(Fw)max kips
Difference
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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