Perhaps you are aware, but it is very simple to calculate.

(90-your latitude) + tilt of the earth (23.5 degrees) = maximum height of the sun during the year

(90-your latitude) - tilt of the earth (23.5 degrees) = minimum height of the sun during the year.

Effectively this means if your latitude is 23.5 or less, you get the sun directly overhead at some time during the year. If your latitude is above 67.5, you get polar night as the sun doesn't rise above the horizon (short one at 67.5, but as you go further toward the pole ever longer)

For Seattle, (90-47)+23.5=66.5 maximum. (90-47)-23.5=19.5 minimum.

Calling these the "maximum height" and the "minimum height" of the sun during the year makes it sound like the height of the sun will always lie between those two figures. That can't be the case -- they have night in the tropics too. Are these what I might call the "high maximum height", the yearly maximum of the maximum height of the sun on any given day, and the "low maximum height", the yearly minimum of the daily maximum height of the sun?

It’s the minimum and maximum angle between sun and horizon at midday on the solstices.

Yes, you are correct. My phrasing was unclear, especially in terms of "minimum".

The numbers are for the highest angle of Sun toward the horizon in a single day. This happens at solar noon (solar noon is the moment that Sun passes your local meridian/north south line).

Maybe minimum and maximum daily peak?

At my school we had this weird climbing frame called the "Pipehenge". I climbed on it for years before we eventually did a class on it and learned that it was an astronomic map: https://www.youtube.com/watch?v=BM4d02tjTqk

Looks they are no longer made, or are they?

I’d love to make one of those

Very much agreed. Things get weirder and weirder as you get towards the poles. At the poles themselves the sun spends half the year hidden, and the other half spiraling up and then down! But never gets very high above the horizon.

I've been thinking a lot about this lately and was thinking of making some educational YouTube videos about it!

If you haven’t looked at that sort of thing on YouTube, don’t. Make your own videos first.

SunCalc (http://suncalc.net) has a visualization for sun position throughout the year and time of day. Another great app is Sun Surveyor for Android, which gives an augmented reality view of the sun's position and trajectory.

The free, cross-platform program Stellarium [0] will show that (among other things).

[0] http://stellarium.org/

> I've come to realize that the sun is never directly overhead, not even in summer

It's only ever directly overhead in the tropics.

.. which is defined to be between the tropic of cancer and tropic of capricorn; 23°26′12.2″ north and south of the equator respectively.

Which is because the earths axial tilt is that angle:

Earth's mean obliquity is currently 23°26′12.2″ (or 23.43672°) and decreasing.

https://en.wikipedia.org/wiki/Axial_tilt