アナログ計算万歳

ノモグラムをつくろう！ Draw a Nomogram!

平成28年2月22日 (Feb 22, 2016)

作り方使い方完成品
作りやすい編 下記↓ PDF/PNG PDF/PNG
使いやすい編 下記↓ PDF/PNG PDF/PNG
how to makehow to usefinished
'Easy to make' ver. see below↓ PDF/PNG PDF/PNG
'Useful' ver. see below↓ PDF/PNG PDF/PNG

ノモグラムとは、 平行に並んだ軸に目盛りを打って、 それに定規などの直線を交わらせることで加減算（線形変換）ができる、 という原理で様々な計算ができるよう作られた図である（狭義には）。 乗除算は対数変換で加減算になるので、目盛りの数字を対数で打てば、たとえば
Nomogram is a chart that consists of three or more parallel lines as axes with tics, and that makes us enable to compute addition and subtraction (linear transformation). Multiplication and division are transformed into addition and subtraction by logarithms, therefore, for example, the nomogram can be made that computes

距離 = 速さ × 時間
Distance = velocity × time.

という計算をするノモグラムを作ることができる。 というわけで、作ってみよう。 以下は、速さも時間も距離も 1 から 100 までの範囲のものを作る手順である （対数変換に基づくから、範囲全体が正の数でなければならない）。 精度を高くしたい時は、もちろん図を大きくして目盛りを多くすればいいが、 まずは線を細くするといいかもしれない。 図はクリックすると大きくなるよ！
Here, let's make it! Following pictures indicate how to draw the nomogram in which the limits are 1 to 100 for each all variables (distance, velocity, and time. ranges can not include zero or minus bacause the chart is based on log transformation). Precision of the calculation depends on the number of tics or how large the chart (larger chart can have more tics). But the first thing you may try to make it precise is use thin lines to draw the chart. Click following pictures to enlarge.

その１：作りやすい編

'Easy to make' version

Step 1: Draw axes.
  1. Put three vertical lines.
  2. Lower ends are put at the same height.
  3. Outer two axes are in a same length. Length of the inner axis is the half of those of longer ones.

Step 2: Put tics.

  1. Decide a number of tics, and put same number of tics on all three axes (10 intervals here).
  2. Lengthes of intervals are common to all tics for each axis.

Step 3: Put numbers on tics.

  1. Decide the ranges of axes (0 to 100 here for all axes).
  2. Put numbers to tics of an outer axes as a geomertic sequence. It's common ratio is the range to the power of the reciprocal of the number of intervals (100 to the power of 0.1, or 1.5849 here).
  3. Put same numbers on the other outer and inner axes in the backward order. It's done!

その２：使いやすい編

'Useful' version

Step 1: Draw axes (same as 'Easy to make' version above).
  1. Put three vertical lines.
  2. Lower ends are put at the same height.
  3. Outer two axes are in a same length. Length of the inner axis is the half of those of longer ones.

Step 2: Put tics.

  1. Decide the range for axes (1 to 100 here for all three axes).
  2. Put tics with log-ratio intervals (see the bottom of the picture).
  3. Tics on the short and the right long axes are put in opposite direction to those of the left long axis.

© Daisuke Tominaga, 2023.