equation solving sans computer, calculator or slide rule richard j. nelson 1 on a boss financed...
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Equation Solving sans Computer, Calculator or Slide Rule
Richard J. Nelson1
On a boss financed Paradise Island vacation
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Situation: The boss will finance an all expense paid two week vacation on a paradise island which doesn’t allow any electronics: Cell phones, computers, internet, etc. Even a slide rule is considered anti-vacation and
not allowed.
• Problem: You have two days of design work on your
electronics circuit design.
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Take Your Pick
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I Need to Solve Design Equations
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Helicopter Requires Minimum Weight
My Equation Solving Constraints Are:
1. No Power Usage.2. No Weight.3. No Electronics.4. No Hope?
Obviously I have to go Old-school
What Method, What Technique, What Aids do I Use?
Hints
“It” is one word starting with a letter early in the alphabet.
“It” fits Into my Shirt Pocket.
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The Solution is to Use Graphical Aids to Solve the Equations
These are also known as:
• Graphs• Nomographs*• Nomograms
• * This is the term I prefer.
Simple Nomograph Equation Example
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Parallel Resistor Nomograph Relationships
1. R1 & R2 Scales are linear at right angles.2. RT scale is 45 degrees linear but different scale.3. Practical scales should cover one decade.4. RT scale easily scaled. Use R1 = R2.5. Scales can be made to accuracy desired.6. Equation is solved for any variable.
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Nomograph Terminology
Nonlinear Scale Example
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Logarithmic Scale Example
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Multiple Equation Example
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Smith Chart
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Smith Chart Usage
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Nomograph Summary
• Very low cost (paper and ink)• Very easy to use, especially for inexperienced practioners• No power required• Very complex equations are easily solvable• Very fast to use
Advantages
Disadvantages
• Tend to wear out• May be difficult to create• Limited accuracy• Highly specialized to few equations
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References1. Excellent Book – Fig. 12. Computer Program http://
www.projectrho.com/nomogram/cad.html 3 Tutorial on the Smith Chart http://www.antenna-theory.com/tutorial/smith/chart.php
Fig. 1 – Nomograph Book details
Is Old-school Graphical Equation Solving Obsolete?
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NO!
Nomographs are still actively being used in:
(a) The Medical Community(b) The Pilot Community(c) The Engineering Community• 1. Chemical• 2. Mechanical• 3. Electrical, esp Smith Chart
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The End