Standardising shadow length on sundials The sundial is fundamentally flawed in that the length of each hourly shadow changes with the seasons. If the base of the sundial was engineered to move cyclically on an anual basis however, the length could presumably be adjusted so that the shadow lengths were the same for each day. What sort of curve would the base have to follow in order for this to be achieved?
 A: Martin, and welcome to the fun house.
First, the sundial is more flawed than you think, since the earth's orbit is elliptical rather than circular. The combination of tilted axis and eccentricity shows up in shape of the analemma
This particular version was made by taking pictures at a fixed time (probably early morning), at weekly intervals (with 3 points missed due to weather). Note a few things.
1) The apparent horizontal position of the sun at any fixed time varies, so a simple sundial will not produce an accurate time based on shadow angle. As you might guess, this is deterministic and can be compensated for: the compensation is determined by the equation of time http://en.wikipedia.org/wiki/Equation_of_time and a graphic version of the equation is sometimes included on high-quality sundials

2) Except for the equinoxes and solstices, any vertical angle (and consequently the length of the sundial shadow), occurs on two different days. So a simple measurement of the shadow angle will not accurately determine the date.
Of course, this sort of complexity is just a challenge for some folk, and in 1959 Scientific American's "Amateur Scientist", Richard L. Schmoyer, showed how to make a gnomon which will allow a sundial accuracy of 1 minute over the entire year http://www.precisionsundials.com/sunquest%20article/amateur.htm
This gives an idea of how it's done, although the exact shape of the gnomon is not numerically specified, and an armillary sphere is used rather than a standard sundial:

