Carefully studying the Mackay nomograph uncovered several shortcomings related to its use in modern cartography, the most severe being its inappropriateness for computerized dot mapping where dots are placed randomly with no constraint on the amount of individual dot overlap.
Mackay devised his nomograph for this type of dot placement, and the mathematical nature of pseudo-random packing of circles in a square with maximum overlap constraints was investigated.
Once a dot size has been selected, the dot unit value can be selected either by trial and error, or with the aid of a nomograph devised sixty years ago by J.
Cartographers use the Mackay nomograph to find the number of dots per square inch (or [cm.
The Mackay nomograph has guided cartographers for 60 years of creating maps manually, but it has serious drawbacks in the modern age of computer cartography.
The second drawback to the nomograph is the nature of the "zone of coalescing dots" shown on it.
The third and perhaps most serious drawback to the nomograph is its mathematical basis.
The recommended speed based on the nomograph better reflects driver behavior than that based on the ball-bank indicator.
As mentioned previously, the TDCH nomograph for determining safe curve speed is based on the standard design speed formula using a side friction value of 0.
The nomograph and design speed formula are marginally better than the ball-bank indicator in reflecting driver speed behavior on curves (see table 6), but the current values used for side friction are too conservative.