A chart for measuring angle and distance

This chart
works like Angle Cards.

But instead of using your arm measurement to choose among different cards, here you simply fold the chart.

This can be more convenient than the cards when you are, for instance, calibrating a bunch of peoples' thumbs. But its main motivation was...

Simplifying distance estimation for targets of accurately known size

The chart was motivated by a reader's interest in determining the distance to archery targets of known size. With the Angle Cards, if you know the target is say 1.16 yards tall, it takes some work to tell the difference between a 23 and a 25 yard distant target.

With this chart, if you know the size of the target, and the target is about one yard big (or meter, or whatever), then you can simply look up its size in a table, get a "compensating arm length", fold the chart in a slightly different place, and then hold up the chart and just read the distance off the "x" numbers. Just as if the target was exactly 1 yard big.

To create your own "compensating arm length" table,
enter your true eye-to-chart length here:
cm
The table is just compensating arm length = real arm length * ( actual target size / 1.0 ).
[cm = inches * 2.54]

If you are going to be repeatedly dealing with targets of the same size, you might want to take the "compensating arm length" and get, or make, an angle card for it.

The chart graphs (actual height on paper = arm length / the x number). This version was quickly hand drawn, so there may be a bit of sloppiness.

Links

Angle Cards - A "business card" for measuring angle and distance
Measuring Angle and Distance with your Thumb

Thanks to a reader, Lamar Fussell, for motivating this page.

Comments encouraged - Mitchell Charity <mcharity@lcs.mit.edu> 

Notes:
  Here is the xfig source for the first draft chart.

Doables:
  Cleanup chart (generate with PS).
    Add url.
    Variant explicitly targeting archery?
    Extend to low x numbers?  Nice to be able to use meters indoors.
    Add degrees and rad?  In color?
  Add support for imperial units (arm inches)?
  Search engine fodder: range finder.
  CGI draw
    an "x" rule given an eye-to-ruler distance.  See cards.  But bigger.
    a distance rule given an eye-to-rule distance and object height.

History:
  2001-Nov-07  Added name to credit.
  2001-Aug-14  Created.  Ripped from Thumb.