14
CHAPTER 1. INTRODUCTION
Theorem 1: If there is a discrepancy between a theory and the
experiment carried out to verify it, it is likely to be due to
inaccuracies in the experiment.
Theorem 2: It is far more difficult to make good experiments
than it is to make good theories.
Theorem 1 is a warning against overconfidence in experimental results, particularly when errors are introduced because the experiment conditions do
not conform to theoretical assumptions. Theorem 2 evolves from experience
and from seeing Theorem 1 repeatedly proven!
1.5.5 Some Definitions...
Several terms related to physical modeling have been used throughout this
chapter, and hopefully their meaning was evident either from the surrounding text or from the reader’s previous encounters with these terms. The
more important terms are briefly defined below.
• Prototype: The situation which is being modeled, either at the same size, or more often, at reduced scale.
The prototype condition does not necessary have to be
a “naturally-occurring” physical phenomenon.
• Scale: Constant proportions of measurable characteristics
between model and prototype (Yalin 1971). Scales are ratios between the prototype value and the model value of a
given parameter.
• Similitude (or Scaling) Criteria: Formal mathematical
conditions that must be met by the scale ratios between
prototype and model. These criteria can be determined
from mathematical representations of the physical properties, but they are only as good as the representation itself
(Yalin 1971).
• Similarity: A condition that exists when a model gives
a similar response as the prototype, even if the model is
not in strict similitude with the prototype. It is possible
to have model similarity without meeting similitude criteria when some macroscale feature of interest (e.g., beach
profile) is satisfactorily reproduced in the model.
• Scale Effects: Differences between the prototype and
model response that arise from the inability to simulate all
relevant forces in the model at the proper scale dictated
by the scaling (similitude) criteria.
CHAPTER 1. INTRODUCTION
Theorem 1: If there is a discrepancy between a theory and the
experiment carried out to verify it, it is likely to be due to
inaccuracies in the experiment.
Theorem 2: It is far more difficult to make good experiments
than it is to make good theories.
Theorem 1 is a warning against overconfidence in experimental results, particularly when errors are introduced because the experiment conditions do
not conform to theoretical assumptions. Theorem 2 evolves from experience
and from seeing Theorem 1 repeatedly proven!
1.5.5 Some Definitions...
Several terms related to physical modeling have been used throughout this
chapter, and hopefully their meaning was evident either from the surrounding text or from the reader’s previous encounters with these terms. The
more important terms are briefly defined below.
• Prototype: The situation which is being modeled, either at the same size, or more often, at reduced scale.
The prototype condition does not necessary have to be
a “naturally-occurring” physical phenomenon.
• Scale: Constant proportions of measurable characteristics
between model and prototype (Yalin 1971). Scales are ratios between the prototype value and the model value of a
given parameter.
• Similitude (or Scaling) Criteria: Formal mathematical
conditions that must be met by the scale ratios between
prototype and model. These criteria can be determined
from mathematical representations of the physical properties, but they are only as good as the representation itself
(Yalin 1971).
• Similarity: A condition that exists when a model gives
a similar response as the prototype, even if the model is
not in strict similitude with the prototype. It is possible
to have model similarity without meeting similitude criteria when some macroscale feature of interest (e.g., beach
profile) is satisfactorily reproduced in the model.
• Scale Effects: Differences between the prototype and
model response that arise from the inability to simulate all
relevant forces in the model at the proper scale dictated
by the scaling (similitude) criteria.