On GPS accuracy

Accurate coordinates are essential for shadow calculation. The accuracy of the GPS device in your iPhone is limited. It will almost never be below 5 meters (in the ShadowCalc application this means you usually see at most 5 out of 6 bars in the accuracy indicator). This, unfortunately, is a serious restriction for direct usage of the inbuilt GPS when distances are small.

Indeed, the quality of the shadow calculation is proportional to the quotient r/d, where r is the limit for the accuracy of your GPS (say r=5 meters) and d is the distance between the obstruction and your location (say d=20 meters). This is intuitively clear and it means that the smaller the distances are, the more accurate the location data have to be to get good results. As a rule of thumb r/d shoud be approximately 0.05 (or smaller). For more details see the ShadowCalc User Guide

To overcome this problem you may

• » either use an excellent GPS and take care that enough satellites are available;
• » or work with relative instead of absolute locations.
The second strategy is more reliable, very effective and cheaper because it makes accuracy irrelevant: Take only one location using a GPS and calculate all others relative to this one (see example).

Using maps

Using relative locations is an excellent method for small scale calculations but not on a large scale. That's because it's difficult in this case to estimate distances correctly. You usually have to resort to maps then. But how do you find the correct locations on a map?

It can be easy if you know e.g. that the sun vanishes behind a clearly outlined building far away. But usually if you only see the sun setting behind a mountain ridge, it's very hard to find the exact point responsible for obstructing the sun in a certain direction. In this case a satellite picture from Google Earth is virtually useless. You need a topographical map of the area and sometimes you may have to play around a bit until you get the desired result (if you know it for a specific location and time); then you you're in a position to forcast shadow at any time (see example).

Export your locations fom the map using e.g. Garmin Basecamp and they are available for ShadowCalc 2 whenever you need it.

Import of locations marked on maps is supported with ShadowCalc 3!

How to work with relative locations

I recommend you first draw a sketch of the relevant locations:

It's enough to take the GPS coordinates for one location (say "N" - the north end of the house); coordinates for all other points of interest (like "M" or "C") are calculated relative to this location providing directions and distances (you may use the calculator). If possible work with relative direction too, i.e. if you know a location is at a right angle to a given direction (like C relative to line N,M in the sketch), then use this knowledge instead of the compass.

M, for example, is 10 meters away from N in direction 185°, C 12m from M in direction 275°. Therefore if your GPS tells you coordinates of N are

lat 47.110000°, long 8.150000°,

then the calculated coordinates of M are

lat 47.109910°, long 8.149988°.

Based on these coordinates location C is calculated:

lat 47.109919°, long 8.149830°.

Finally the coordinates of S, the south end of the house, which is 20 m from N in direction 185°, are

lat 47.109821°, long 8.149977°.

Shadow calculation at C with an obstruction (N,S) that is 10 meters high produces a perfectly reasonable picture.

Unfounded expectations

The last example shows that shadow periods are not necessarily longer in winter than in summer! This is what most people would expect, but the sun might not even have risen to produce a shadow.

Another example of a common expectation that is not justified in general concerns the position of the sun at a given time. Most people think the sun on its daily path moves uniformly and shines from every direction between east and west, passing either south or north depending on the hemisphere. This should be true at least in summer. But, in general, it is not so. Contrary to what you might expect, it usually takes not 6 hours for the sun, starting in the east, to reach its highest point. For an example, in New York in June the sun stands in the east around 9 am and midday is around 1 pm. And in Harare, the capital of Zaire, the sun will move end of January in 24 hours between 95° and 265° - never reaching east or west at all.

Don't be too surprised if you don't see the shadow of some obstruction at the time you might expect it.

The swimming pool in Vík, South Iceland

A good example for the best use of maps is the swimming pool in Vík, South Iceland. Here the sun sets in early March behind a mountain ridge around 5 pm. (Try it, if you don't believe me.)

If you look at the Google Earth map and switch on the sun you notice first of all that the shadow painted on the map is far away from the swimming pool (Sundlaug). This is simply wrong. Also, it's almost impossible to define the actual mountain ridge.

On a topographical map on the other hand it's much easier to recognize the ridge (although on this map it's a queer coast line, the relative locations are ok). Indeed, using the locations on the map you get the correct result:

Building Project in Munich-Obersendling

New apartment builings are planned on the former site of Siemens-Hofmannstraße in Munich Obersendling. Details may be found on the page of the city administration Munich.

With ShadowCalc it's easy to calculate the shadow from the new buildings on virtually any location on the former Siemens site and in the neighborhood. For this purpose I created a GPX file with the coordinates and heights of the planned buildings.

Have a look at this map:

The points A1,A2,A3,A4,...,G1,G2,G3,G4 mark the seven planned apartment buildings that are almost 40 meters high. I picked a few locations on the site and in the neighborhood that might be of interest; they are marked by little blue flags. Then I created a GPX file with the coordinates and heights of all theses locations and calculated the shadow to expect at various dates of the year. In my calculations I always assumed that the buildings are 36.4 meters high and that all locations of interest are on ground level (0 meters elevation). Only shadow from respectively one high building is taken into account for each location of interest; e.g. for location "Saeumestr (1)" the coordinates and elevation of C1, C4 and C3 define the possible obstruction.

Here are some screenshots that show results:

To summarize, there is little to fear as regards clouding from the new buildings in the neighborhood (locations Saeumestr, Hofmannstr etc.); only in the winter months there will be some shadow in the morning. The situation might be different for the planned apartments that are not in the high buildings: Possible buyers should take a closer look at the situation (see e.g. locations P1, P2,...). To this end download and save the GPX file on your disk; load it via iTunes into ShadowCalc and calculate shadow for whatever locations you are interested in: