First we made a little compass by magnetizing a needle and allowing it to hang freely in a glass mug. We did this to orient our shadow board. Our homemade compass shouldn't be trusted to shoot an azimuth, but it does point in a general northerly direction.
We placed a screw partially into a wooden board in order to trace the screw's shadow throughout the day. Once we get a protractor we'll be able to determine the sun's horizontal heading over the (almost) summer solstice (and within some margin of error...).
To determine the vertical angle we used a large stick and measured it's shadow. A large stick, rather than the screw used for the horizontal direction, reduces some of the impact of measurement errors. As the shadow got shorter in the middle of the day, or measurement errors increased. According to the Navy's Sun or Moon Altitude/Azimuth Tables, our calculations were pretty close to accepted values in the morning and evening, but midday we were off by a couple of degrees. For instance, at 1:30 we determined an angle of 75.5 deg. compared to the Table value of 73.1 deg. Earlier in the morning, and later in the afternoon, our calculations were within a degree of the Table values.
Even the cat strolled by to offer assistance
We'll do this again near the equinox, and during the winter solstice. The internet is a much easier way to find an answer, and it's cool that so much information is so easily accessible, but sometimes you just need to take a few measurements and observe in order to have a greater appreciation. Of course, my boys are a little young to understand trigonometry, but the day's lesson was observing the sky and shadows.