# Using a Slide Rule

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```					    Using a Slide Rule

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

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
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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 views: 47 posted: 4/17/2011 language: English pages: 7