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DisasterMan
Nomographic Accuracy
Nomographs have slide-rule type accuracy. Nomographs constructed in
the original French style originated by d'Ocagne have poorer accuracy as the
number of variables increases. However, Professor Brodetsky (Reference 2)
of Leeds University in England developed a method for preserving accuracy
no matter how many variables are involved. For example, a nomograph for
the multiplication of (X) and (Y) in the French style results in the product
answer (XY) on the inside being at half-scale. The English method would put
the answer on the outside at full scale. Similarly, the multiplication of (X),
(Y) and (Z) in the French style ends up with the (XY)Z answer on the inside
at one-quarter scale. The English method preserves full scale accuracy for
the answer on the outside. Division is handled in a similar fashion.
An example of seven variables illustrates how powerful this English
method is. Professor Brodetsky also suggested starting with the evaluation
of the denominator fi rst in the sequence of calculations. Hence in the
design of a nomograph for A = XYZ / PQR, what we actually do is consider
this to be A = ( (X / (PQ) R) Y) Z and begin with PxQ, then (PQ) x R, etc.
Logarithmic Vs. Linear Scales
Some nomographs may be easier to use if made with linear rather than
logarithmic scales. The nomograph for X = YQ / Z can be designed for either
logarithmic or linear scales as illustrated.
Examples
A nomograph which could be used in search and rescue
operations for planning the number of aircraft required to search
an ocean area for an aircraft forced down at sea is based on the
following expression given by Morse and Kimball (Reference 3):
p = 1 -- e--
(WLN / A)
where p = the percent chance of detection; W = sweep
width in miles; L = length of search track; N = number of search aircraft; A
= area to be searched in square miles.
The target strength of fi sh as a function of size (length, actually) and
sonar frequency is based on the following expressions developed by Love
(Reference 4).
T
D
= 19.1 log L + 0.9 log w -- 34.2
T
S
= 22.8 log L -- 2.8 log w -- 32.4
where T
D
= target strength in dB for dorsal aspect; T
S
= target strength
for side aspect; L length of fi sh in feet; and w = wavelength of sound in
feet.