How The Surveyor's Wheel Works
The surveyor's wheel is marked in fractional increments of revolution from a reference position and its current position can be represented as of a revolution from this reference, where a and b are integers. In the figure on the right, the blue line is the reference starting point. As the wheel turned during measurement, it is shown the wheel sweeps out an angle of radians or turns. In this situation, the fraction, would be the relevant ratio. The usefulness of this ratio becomes clear after further consideration of the equation for the arc length of a circle.
This equation is
,
where is the arc length, is the angle, in radians, of the circle swept through and is the radius of the circle. Now, substitute into the arc length equation the conversion from radians to revolutions to obtain the form,
.
The equation for the circumference of a circle, can clearly be seen and simplifying gives,
.
Thus showing that the base unit of measurement of the surveyor's wheel is determined only by the circumference of the wheel attached.
Read more about this topic: Surveyor's Wheel
Famous quotes containing the words wheel and/or works:
“Let go thy hold when a great wheel runs down a hill lest it break thy neck with following; but the great one that goes upward, let him draw thee after.”
—William Shakespeare (1564–1616)
“Piety practised in solitude, like the flower that blooms in the desert, may give its fragrance to the winds of heaven, and delight those unbodied spirits that survey the works of God and the actions of men; but it bestows no assistance upon earthly beings, and however free from taints of impurity, yet wants the sacred splendour of beneficence.”
—Samuel Johnson (1709–1784)