Mathematical model, designed for zero gravity conditions, analyzes dynamic effects of large amplitude fluid motion interior to a rigid body. It has two advantages over other mathematical models:  (1) constrains slosh motion to given region in natural manner, and (2) allows equilibrium position of slosh mass to be anywhere on slosh surface

Flanders, H. A.

English

NASA Technical Reports Server

May 1972	 B72-10182 
•	 NASA TECH BRIEF 
Manned Spacecraft Center 	 W 
NASA Tech Briefs announce now technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Prolate Spheroidal Slosh Model for Fluid Motion 
A mathematical model has been developed to 
analyze the dynamic effects of large amplitude fluid 
motion interior to a rigid body. 
The model is based on defining a slosh surface 
that approximates the locus of the center of mass of the 
fluid. The slosh surface is obtained by assuming a plane 
surface for the fluid and allowing any fluid orientation 
such that the fluid is against the wall of the tank. The 
slosh mass is then idealized as a point mass located on 
the slosh surface. This model allows for any number of 
slosh masses (one per surface) within one rigid body 
simulated in six degrees of freedom. 
This simulation model has two advantages over 
other mathematical models of large amplitude slosh. It 
constrains the slosh motion to a given region in a natural 
manner and it allows the equilibrium position of the 
slosh mass to be anywhere on the slosh surface, thus 
permitting the local acceleration field to vary direction 
in the body system. 
The model was designed for zero gravity condi-
tions. Inclusion of gravity forces is required for terres-
trial applications and .should make this model of interest 
to designers and manufacturers of fluid containers for 
transportation vehicles such as railroad tank cars. 
Note:
Requests for further information may be directed 
to:
Technology Utilization Officer 
Manned Spacecraft Center, Code JM7 
Houston, Texas 77058 
Reference: TSP72-10182 
Patent status: 
No patent action is contemplated by NASA. 
Source: Howard A. Flanders

TRW Systems Group

under contract to

Manned Spacecraft Center

(MSC-13864) 
Category 09 
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
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Prolate spheroidal slosh model for fluid motion

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