By Douglas P. Adams
Adams D.P. Nomography idea and alertness (Shoe String Pr Inc, 1964)(ISBN 0208004351)(O)(208s)
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CHAPTER 4 THE IMPERFECT CANONICAL FORM ((C)) • INGENUITY • NETWORK CHARTS DEPENDENT AND INDEPENDENT VARIABLES • COMPOUND DIAGRAMS SUBSTITUnONS • ELEMENTARY DIAGRAMS 4-1. Imperfect Canonical Form. «C». A nomog· rapher may be unsuccessful in attempting to place an equation in canonical-form «C»- However, he may arrive at a stage that is not perfect but lends itself to a practical interpretation. 2Kx2y2-(K-I)y2-(K-I)x 2 -2=O (4-4) B Example 4-1. (See also Problem 4-10). Figure 4-l. The equation IO(W + V - 2U) + (W + V) (U - V) = X2 = y2 Let A A .
PROBLEM 4-7. In Problem 3-6 note that different forms of the diagram imply different variables as dependent variable. Note the changes in the form of the rest of the diagram such as the direction and relative placement of vertical scales. These will be referred to later and used as the means of making one variable or another dependent. Can you reach any conclusions about dependent variables and direction of vertical scales? PROBLEM 4-8. Combinations of Elementary Diagrams. The inductance of a single-layer air core solenoid is given by the formula shown in Figure 4-22.
Letting U and W be plotted uniformly on Cartesian axes and V be family parameter, the ratio of W to U remains constant for constant V and the family of V curves appear as straight lines through the origin. Figure 4-4. 2a. The roles of U and V can be interchanged here with V plotted along the prime axis and constant U lines through the origin. Figure 4-5. 3. Taking logs of U . V = W, log U + log V = log W. Plotting X = log U, Y = log V, then constant W yields X + Y =. log W k = constant. Figure 4-6.