Get a long stick, stick it in the ground at an angle so it points to the north celestial pole (the star Polaris is close, it is there even in the daytime). The elevation angle should be the same as your latitude, at azimuth zero degrees true north. Let the stick be able to freely rotate in it's hole but not otherwise move relative to the ground. The stick is now parallel to the earth's rotation axis.
Now fasten a short stick to the side of the long one with a single screw so that it can pivot, such that the short stick is free to point at the sun (there will be only a point shadow on the ground from the short stick). At a later time measure the rotation angle you have to rotate the long stick to again point the short stick at the sun. Divide that angle by 15 to get the elapsed time in hours. It's not the projected angle on the ground you need, it is the rotation angle about the earth's axis that measures time. If you do this using a star (any star) instead of the sun, divide by 15.04.
You could calibrate the projected shadow along the ground to read out in hours if you wanted, it would be different for different latitudes. That is the principle of the sundial.