Structural analysis in support of the waterborne transport of radioactive materials Page: 3 of 10
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behavior of a RAM package. The loading condition would be the bow
oC the striking ship on one side of the package backed by the internal
structure of the struck ship or cargo on the other. The potential for
damage to the package depends on the remaining velocity of the striking
ship upon reaching the required depth of penetration (i.e., the package
location) and the relative stiffness and strength of the striking ship bow,
the RAM package, and the supporting structures in the struck ship. The
wotk described in this paper only addresses the first of these two types
of analysis. The analysis of the "local" response of the package is a topic
for future research.
In the next section of this paper past research into the consequences
of ship collisions, and the implications of these consequences to
radioactive material package transportation will be discussed.
Following this a proposed simplified method for determining the
damage as a result of collision will be given. The final section will
discuss the results of detailed finite element calculations to determine
the response of a generic small freighter to impacts from vessels with
varying mass and velocity.
SUMMARY OF GLOBAL SHIP COLLISION MECHANICS AND
Because of the complexity of the deformation processes during ship
collisions, most prediction methods have been based on simplified
methods for estimating the amount of damage to the respective ships.
The methods are normally composed of two main steps. First, the
amount of energy to be absorbed during impact must be computed. This
step is sometimes referred to as the "external mechanics" part of the
problem. The second step is to determine how the struck and striking
ships deform in order to absorb the kinetic energy.
To simplify the ship collision mechanics, only collisions at near right
angles are considered in this program. This seems to be a reasonable
assumption for assessing the safety of RAM transport by sea, since
transverse penetration into the RAM-carrying ship is the primary
concern in a collision and such penetration will be greatest in a right
Calculation of energy to be absorbed is relatively straightforward,
based on conservation of momentum and energy principles for an
inelastic collision of two bodies (Minorsky 1959). First, assume that the
center of gravity of the striking ship passes through that of the struck
ship, such that there is no rotation of the ships during the collision. Also,
assume that the angle between the striking and struck ship, a, is near
90. The mass of the struck ship and striking ship is MA and MB,
respectively, with initial velocities of VA and VB before the collision, as
shown in Figure 1.
Based on conservation of momentum and kinetic energy
perpendicular to the struck ship before and after the collision, the
following expression can be derived for the amount of energy absorbed
by deformation of the ship structures, AEk:
A MB(M +AM) 2
AEk = 2M +M +AM (VBsin a) (1)
As shown, AEk is a function of the masses of the respective ships, the
initial velocity of the striking ship, the angle between the ships just
before impact, and the effective mass of water surrounding the ships that
affects the collision mechanics, AM. The proper value of effective water
Figure 1. Ship Collision Parameters
mass is somewhat uncertain. Based on experiments of a ship hull
vibrating in deep water, Minorsky estimated the effective mass to be
40% of the mass of the struck ship, MA.
It is the second step of the solution process, solving the "internal
mechanics" problem, that is the most difficult. This step requires
estimation of how the two ships deform in order to absorb the required
amount of energy, AEk. One of the earliest methods is an empirical
approach developed by Minorsky in which a linear relationship was
established between the amount of energy to be absorbed and the
volume of material within the ships that is deformed during the
AEk= (414.5RT + 121,900) ton-knots2
RT is known as a resistance factor, and is basically equal to the total
volume of damaged structural materials in the striking and struck ships,
except for the outer hull of the struck ship, which is accounted for in the
constant term. The units of RT are ft2-in. The method for computing RT
is given in Minorsky's original paper. Minorsky studied 26 actual ship
collisions, all of which involved nearly right-angle collisions. From
these collisions, nine were finally used to fit a straight line between the
points of AEk and RT. This line is represented by Equation 2 and is
shown in Figure 2. The remaining collisions were not used since they
involved relatively lower amounts of energy absorption and exhibited
considerable scatter. This so-called "Minorsky Method" has been
widely used and appreciated because of the simplicity that it brings to
this complex problem. However, it does not account for the detailed
mechanics of the collision process and, because of its empirical nature,
it may not be applicable for ship designs and impact velocities that are
outside the range of the parameters for which the method was
There have been some attempts to check the accuracy of the Minorsky
Method. These are documented in papers by (Akita et al.1972a) and
others. Computations of AEk and RT based on additional ship collisions
that, apparently, were not used by Minorsky have been performed
(Gibbs and Cox 1961). The data from the Gibbs and Cox report and for
the collision analyzed by MR&S (M. Rosenblatt & Son 1972) are shown
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Ammerman, D.J. Structural analysis in support of the waterborne transport of radioactive materials, article, August 1, 1996; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc673141/m1/3/: accessed March 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.