Chapter 5

Copy Figure 5.1. (a) Show that when the sun is in $\mathrm{C}$ it is day everywhere within the arctic circle and night everywhere within the Antarctic. (b) Make a model of the earth by finding a globe or making a simple globe by taking a melon and drawing the equator, the tropics and the two polar circles. Take a strong torch and fit it such that its horizontal rays point to the centre of the globe. Give the globe a tilt of about ${23.5}^{\circ }$. Reproduce the beginning of summer, autumn, winter and spring by rotating the globe. Find how the length of day changes.

On good locations in South Morocco and Southern California one finds DNI $\ge 2500$ $\left[\mathrm{kWh}{\mathrm{m}}^{-2}{\mathrm{yr}}^{-1}\right];$ on a horizontal surface this is smaller, at $1440\left[\mathrm{kWh}{\mathrm{m}}^{-2}{\mathrm{yr}}^{-1}\right]$. (a) Convert these values to $\left[{\mathrm{Wm}}^{-2}\right]$ and $(\mathrm{b})$ compare the first value to the total solar irradiance.

A state-of-the-art Dutch windmill, shown on the left of Figure $5.10$ was operating in 1937. The height of its axis was $16[\mathrm{m}]$, the radius of its sails $14.35[\mathrm{m}]$. With a wind velocity of $7.77\left[\mathrm{m}{\mathrm{s}}^{-1}\right]$ it was able to pump an amount of water $34.1\left[{\mathrm{m}}^3{\mathrm{s}}^{-1}\right]$ over a height of $1.67[\mathrm{m}]$. (a) Calculate the pumping power. (b) Calculate the input wind energy. (c) The wind energy entering into the rotation of the wings was measured and a value $c_{\mathrm{p}}=0.17$ was found. Calculate the power taken from the wind. Explain the difference with your result in (a).