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yasti yantra [Q&A]


Suhas of Poornaprajna PU College asks, what is the stick machine of Bhaskaracharya?

I had no idea what it was until I looked it up online. There is a nice description in a report by S. Narvekar (Astronomical Instruments of Ancient India, IFToMM 2007) that describes a stick-like device that can be used to measure the heights of nearby objects. Here is a geometrical sketch of the device:

The idea is to mount a stick on a pivot at a height d above the ground, and take sightings of the top and bottom of the object of interest using the stick. The projected length of the stick on a horizontal line at the two sightings, L1 and L2, and the heights to which the stick is raised, h1 and h2, can be marked on an adjoining board. If the overall height of the object is H, and the horizontal line at the height at which the stick is mounted splits it into H1 and H2, the lengths form similar triangles, and we can write

h1/L1 = H1/L and h2/L2 = H2/L,

where L is the distance to the object. Eliminating L from the equations using L = H2 (L2/h2), and since H2=d, we get
H = H1 + H2 = (h1/L1) L + H2 == ( (h1/L1) (L2/h2) + 1 ) d .

The height of the object can thus be determined from the measurable quantities. Note that the requirement H2=d is a pretty strong constraint: it precludes using this method at large distances when the curvature of the Earth becomes significant, or when the object is far enough that it becomes difficult to ensure that H2 stays equal to d. So it is really a short-distance surveying instrument.

While Bhaskaracharya is known to have studied astronomy quite a bit, this so-called yasti yantra has no connection to astronomy. But it will make a nice project for a student looking to build something for a science fair.