Chapter 7: Numerical Calculations
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Engineering Mathematics: A Series of Lectures Delivered at Union College |
| Year | 1911 |
| Section ID | engineering-mathematics-chapter-06 |
| Location | lines 21989-25587 |
| Status | candidate |
| Word Count | 7123 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 0 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER VII. NUMERICAL CALCULATIONS. i6o. Engineering work leads to more or less extensive numerical calculations, when applying the general theoretical investigation to the specific cases which are under considera- tion. Of importance in such engineering calculation^ are : (a) The method of calculation. (5) The degree of exactness required in the calculation. (c) The intelligibility of the results. (d) The reliability of the calculation. a. Method of Calculation. Before beginning a more extensive calculation, it is desirable carefully to scrutinize and to investigate the method, to find the simplest way, since frequently by a suitable method and system of calculation the work can be reduced to a small frac- tion of what it would otherwise be, and what appear to be hopelessly complex calculations may thus be carried out quickly and expeditiously by a properSource-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Complex quantities
Section titled “Complex quantities”... ansmission line can be simplified by approxima- tion, as discussed in Chapter V, paragraph 123, to the form. + ^/o 1+- ZY + F^oU+^^ (1) where Eo, h are voltage and current, respectively at the step- down end, El, I\ at the step-up end of the line; and Z = r—jx = Q^—\Zbj is the total line impedance; Y = g — jh= —0.0012/ is the total shunted line admittance. Herefrom follow the numerical values : ZY (60-135.f)(-0.0012i) ■^2 2 = 1 - 0.036./- 0.081 = 0.919 - 0.036/; ZY 1+- g- = 1 - 0.012/- 0.027 = 0.973 - 0.012/; ryi Z ...Field language
Section titled “Field language”... iations of the length of air gap, so small as to be beyond the limits of constructive accuracy, and a calculation exact to a fraction of one per cent, while theoretically possible, thus would be practically useless, The calculation of the ampere-turns required for the shunt field excitation, or for the series field of a direct-current generator needs only moderate exactness, as variations in the magnetic material, in the speed regulation of the driving power, etc., produce differences amounting to several per cent. (c) Exact engineering calculation ...Transients / damping
Section titled “Transients / damping”... esist- ance, a;= 135 ohms inductive reactance, and 6 = 0.0012 conden- sive susceptance, for various values of non-inductive, inductive, and condensive load. Starting with the complete equations of the long-distance transmission line, as given in "Theory and Calculation of Transient Electric Phenomena and Oscillations," Section III, paragraph 9, and considering that for every one of the various power-factors, lag, and lead, a sufficient number of values 249 250 ENGINEERING MATHEMATICS. have to be calculated to give a curve, the amount of work ...Ether references
Section titled “Ether references”... regulation of the line at constant current output for varying power-factor. b. Accuracy of Calculation. 162. Not all engineering calculations require the same degree of accuracy. When calculating the efficiency of a large alternator it may be of importance to detcTmine whether it is 97.7 or 97.8 per cent, that is, an accuracy within one-tenth per cent may be required; in other cases, as for instance, when estimating the voltage which may be produced in an electric circuit by a line disturbance, it may be sufficient to NUMERICAL CALCULATIONS. ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
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| Ether | 7 | seeded |
| Light | 4 | seeded |
| Arc lamp | 2 | seeded |
| Frequency | 2 | seeded |
Chapter-Local Glossary Hits
Section titled “Chapter-Local Glossary Hits”| Term Candidate | Hits In Section | Status |
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| ether | 7 | seeded |
Equation Candidates
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Figure Candidates
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Hidden-Gem Quote Candidates
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Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.
- Field language: Read for whether field language is mechanical, geometrical, causal, descriptive, or simply a convenient engineering model.
- Transients / damping: Separate the temporary term from the final steady-state term and compare with differential-equation response language.
- Ether references: Verify exact wording before drawing conclusions. Ether language must be separated from later interpretive systems.
- Magnetism: Track flux, reluctance, permeability, magnetizing force, and loss language against modern magnetic-circuit terminology.
Ether-Field Interpretive Boundary
Section titled “Ether-Field Interpretive Boundary”- Field language: Field-pressure or field-gradient interpretations can be explored here only after the explicit source passage and modern engineering translation are kept distinct.
- Transients / damping: Transient collapse, impulse, and surge behavior can be compared with alternative field language, but only as a clearly marked reading.
- Ether references: If Steinmetz mentions ether, quote only the verified source words first; any broader ether-field synthesis belongs in a labeled interpretive layer.
- Magnetism: Centrifugal/divergent magnetic-field readings are interpretive overlays, not automatic historical claims.
Promotion Checklist
Section titled “Promotion Checklist”- Open the full source text and the scan or raw PDF.
- Verify the chapter boundary and surrounding context.
- Promote exact quotations only after checking the source image.
- Move mathematical candidates into canonical equation pages only after formula typography is corrected.
- Move diagram candidates into the diagram archive only after image extraction, crop verification, and manifest creation.
- Keep Steinmetz wording, modern translation, and ether-field interpretation in separate labeled layers.