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Using a Slide Rule

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					    Using a Slide Rule




Everybody chill the %&*$& out -
           I got it!
      8 + 6 = 14




Can do addition!        But what about
                        Multiplication?
                        Division?
     And subtraction!   Square roots?
                        Exponents?
                        Sine/cosine?
                        Etc?
               Log scale: “addition” → multiplication
                         “subtraction” → division




2   x 3   =6
                                               Stock


• Pickett Microline 160-ES                      Slider

                                                Cursor
• Very basic rule
  – Multiplication, Divison   More sophisticated rules have
                              more scales!
  – Square, square root
  – Cube, cube root           Duplex rule: printed on both sides
  – Common logs (base-10)
• Only calculates mantissa, not exponent
   – Mentally find order of magnitude                X
                                                    2.437 x 1023
   – Get a “feel” for the sizes of things!
• 2-3 sig figs
   – Use interpolation                                3.141592653589793
   – Each digit is harder to get than the last!                vs.
                                                      3.1415926535897932
   – Get a “feel” for what accuracy means!
                                                                   Factor of 10!
• Multiple operations in one “step”                                Not just “one
                                                                   extra digit”
   – 2/ , 1/sin(xy) , (ab)3
   – 2.134 x 3.57, 2.134 x 4.37, 21.34 x 437
• Need to be aware of properties of trig functions, logs, exps
   – Must apply identities, etc.
• No addition or subtraction
   – Do that by hand!
• Longer learning curve
   – You get better with practice!
     • Commonly used scales:                                                 Most important scales!
             –   C,D: base scales: Multiplication, division
             –   CF, DF: scales folded at : Operations involving  in one step!            Also CIF, DIF
Reads
from right   –   CI, DI: inverted scales: Reciprocals in one step!                          sometimes
to left!
             –   Trig:         Problem: trig functions cover >1 order of magnitude
               • S: sine 5.7 <  < 90
                         cos 0 <  < 84.3 red scale on S       0.1 < sin,cos() < 1

     uses      • T: tan 5.7 <  < 45 (use CI for 45< <84.3)                 C: 0.1 < tan,cot() < 1
sin()  tan()          cotan: reverse use of C, CI from tan                CI: 10 > tan,cot() > 1
               • ST: sin,tan for  < 5.7 (cos/cot for large )
                       – Alternate: use sin,tan()   (with R marker) for smaller angles
             –   A,B: doubled scales: squares, square roots
             –   K: tripled scale: cubes, cube roots
             –   L: log scale: 10x or log10(x) (Ln: natural logs)
             –   LLn, LL0n (or –LLn): log-log scale LL0: e0.001x
                  • Natural logs / exponents                   LL1: e0.01x
                  • Arbitrary exponents: yx                    LL2: e0.1x
                                                               LL3: ex
                  • Sometimes seen as ZZn, ZZ0n…
                                                               LL0n: e-…x (i.e. 1/LLn)
         Slide rule simulator!
• http://www.antiquark.com/sliderule/sim/

				
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