Archimedes' Burning Mirror Problem Solved (cont.)
By Christopher Jordan
Parabolic concentrators
The
problem of how to make powerful solar concentrators has plagued
historians and scientists from Archimedes' time to Newton's. The
reasons for this interest are not abstract, but the practical uses of
the ideal curve. A perfect parabola will concentrate sunlight
infinitely, which can be very useful, alas, perfection is impossible
to engineer.
A
hemisphere is easy to make, but it is thought that it proves a poor
parabola. The paper above shows explicitly that if smaller and
smaller sections of a sphere are used, the approximation to a
parabola increases exponentially. If a twentieth of a spherical
surface is used, it concentrates sunlight by several thousand times.
If a hundredth of the surface is used, it has an incredible
concentration ratio of several million. See the math paper for the
detailed calculations.
Concentration ratio for a 1 m dish as the pendulum length increases
The math
that underpins the idea is indisputable, but it is the physical proof
that persuades most people. There is also the matter of whether the
ancients had the technology to build such devices. To address these
issues, the mirrors have to be made, tested, found in the
archaeological record along with explicit evidence of ancient use.
