After a bit more digging I figured that the SketchUp North conventions, as of 2016, evidently are as follows:
- Google Maps are aligned with True North, which, given the necessary worldwide coverage, seamless and at all map scales, use a variant of the original Mercator projection that is oriented along the Earth’s polar axis.
- SketchUp’s solid green axis in a model is an immutable “world” axis and will be interpreted as UTM Grid North when geolocating the model. The camera Standard Views (Top, Bottom, etc.) are always with respect to these original world axes. Neither using the Axes tool nor geolocating a SketchUp model affects the original drawing axes or alters their interpretation. Upon geolocating, a North Angle is added which points towards True North.
- Imported Google Maps imagery will be aligned with True North. Location and Terrain image groups will be aligned along the original drawing axes, i.e., UTM Grid North.
- SketchUp solar shadows are calculated and shown correctly with respect to True North. Further, the shadow model evidently and correctly takes into account the equation of time, i.e., the difference between true local solar noon and mean local solar noon which varies through the course of a year by up to about 20 min. This is done at appropriate but not astronomical accuracy. There is no accounting for the added day of a leap year and no input for a year as such. Both aspects give rise to periodic and secular deviations of the local solar azimuth and altitude for a given time of day and day of year.
Going back to the mapping aspects: The deviation of True North from UTM Grid North is the meridian convergence (γ), which is location-dependent. The convergence increases with increasing longitude away from the zone central meridian (Δλ), and with increasing geographic latitude (φ). In a first approximation, not taking into account flattening of the earth, the convergence can be calculated from:
tan γ = tan Δλ × sin φ
Importantly, the meridian convergence jumps sign when the reference location changes from one UTM zone to another. It occurred to me that this is testable as follows: I modeled a roughly 1500 ft. tall solar gnomon and geo-located it at two different locations on the Alaskan coast, chosen for high latitude and thus expected big effect. The locations are a mere 1500 ft. (500 m) apart at roughly the same latitude, but are chosen to lie on different sides of a UTM zone boundary, i.e., in different UTM zones. As expected, after geolocating the resulting imagery is angled towards the right in one model and towards the left in the other. The resulting North angles (as inspected in the Solar North SketchUp extension) are about 2.7° away from 0°, and at different sign, as expected. Both angles agree with the sperical approximation of the meridian convergence (above formula) to within 2×10-4 degrees.
The attached screenshots illustrate the findings. Note how the True North directions (orange) and the solar shadows match up between the two locations, despite the imagery being projected into two differing UTM grid orientations.
Here’s a table for the numbers and intermediate results:
Finally, the camera Standard Views could be more properly called:
- Top
- Bottom
- North
- South
- East
- West
- NW isometric.
All of these could be prefixed by “UTM Grid …”
Hope this helps.
Best, Michael