The top line should be at such a height that it extends past the bottom line plus two inches - including the height of an average flame from said candle.
Why 2 inches?
The centre of a 1320 foot piece of an "ideal" sphere of radius 3,958.8 miles is only about
1/
8 of an inch above a straight line joining the ends.
And on the practical side, Dyneema (Ultra High Molecular Weight PolyEthylene) has close to the best specific strength of any fibre.
Sufix 832 Braid Line-600 Yards is 600 yards is a braided line with 7 Dyneema fibres plus 1 "GORE Performance Fiber".
It has a nominal breaking strain of 20 lbs and the 600 yards only weighs about 5.1 ozs.
The
"Displacement Cable Sag Error Calculator" needs:
the
cable tension in pounds force, so start at
20 lbf, the length in feet,
the length in feet, so
1320 feet, and
the
cable weight per unit length, so use
5.1 oz/(16 × 3 × 600 yards) = 0.000177 lb/foot.
Using these values in the
Cable Sag Calculator the sag in the centre of that 1320 feet is
1.93 ft!
Maybe someone could check these figures.
In practice a 20 lb braid line will commonly not break at under twice the rated strength so let's "stretch the friendship" and put 40 lb tension on the line.
The sag is still
0.96 ft so I don't hold any hope of measuring the "earth's curvature" that way.
And don't think that longer distances will help because over a mile that cable would sag about
15 feet even at the 40 pound load.
Maybe someone could try it out at the 20 pound tension and 1320 feet. The line is $51.40 at
Amazon: Sufix 832 Braid Line-600 Yards.