### Improving a weird curvy nomogram

Posted:

**Thu Jan 31, 2008 3:21 am**Some more on hand-construction...

Let's imagine you have a nomogram with one curvy scale like I just described. The curvy scale is as good as you can make it (or you need to go back and redo the first stage).

How can you make it a little better? Easy - you can curve one of the other two scales. We had Y, Z and W (and W was curvy).

You have to pick one of the other two scales to change - but which one?

Here's one idea - for each of Y and Z, choose a value near each extreme and one near the middle, and for all six values, find several values (say three) of the other two variables that yield that outcome (from the original equations, of course - not from your nomogram!). Draw in your lines and mark in your crosses. Whichever set of three crosses deviates the most from the straight scale is probably the best one to pick. Let's imagine it's the Z scale.

Now delete that straight scale and go through the same exercise as before when you made W a curved scale. Carefully, since you're introducing error as you go now. You should now have a curvy W scale, a slightly curvy Z scale and a straight Y scale.

If absolutely necessary, Y can also be made curved in turn, but it's unlikely to add much, and the accuracy of reading curved scales is less, so be careful.

Now, of course, the entire technique doesn't HAVE to be restricted to initially straight scaled nomograms at all. If you have a circular nomogram or something, the same trick will work, you just have to take care.

Let's imagine you have a nomogram with one curvy scale like I just described. The curvy scale is as good as you can make it (or you need to go back and redo the first stage).

How can you make it a little better? Easy - you can curve one of the other two scales. We had Y, Z and W (and W was curvy).

You have to pick one of the other two scales to change - but which one?

Here's one idea - for each of Y and Z, choose a value near each extreme and one near the middle, and for all six values, find several values (say three) of the other two variables that yield that outcome (from the original equations, of course - not from your nomogram!). Draw in your lines and mark in your crosses. Whichever set of three crosses deviates the most from the straight scale is probably the best one to pick. Let's imagine it's the Z scale.

Now delete that straight scale and go through the same exercise as before when you made W a curved scale. Carefully, since you're introducing error as you go now. You should now have a curvy W scale, a slightly curvy Z scale and a straight Y scale.

If absolutely necessary, Y can also be made curved in turn, but it's unlikely to add much, and the accuracy of reading curved scales is less, so be careful.

Now, of course, the entire technique doesn't HAVE to be restricted to initially straight scaled nomograms at all. If you have a circular nomogram or something, the same trick will work, you just have to take care.