The Phalaka-yantra is an Indian instrument which allows the reading of astronomical time by noting the sun's shadow length, as well as other astronomical measures like Hrti, Antya, Cora, etc. It is periodically used to measure planets and stars.
For an equinoctial shadow of 1", the cara- segments are 10, 8, and 3/10 inches. The latitude is assumed to be that of the city of Ujjain, where the equinoctial shadow is 4-30. The cara-segments for that latitude are 45, 36 and 15, and cara-segments for any other place are derived from these.
Since an asu is very small, its R sine will be the same. For a radius equal to 3438, the cara is given by the above segments, what will be cara for 30 X 6 asus, then 3438 divided by 30 x 16 is 19, approximately.