Choosing the Hilltop: Fourr’s Ranch (Dragoon Mountains)
The question.
Visibility analysis around Fourr’s Ranch identified two feasible hilltops in the Dragoons with respect to the 1890 Army heliograph exercise. Which one carried the Army’s heliograph? The answer comes from combining visibility with the Army’s own azimuth and distance records and a weighted mean center calculation.
The question.
Visibility analysis around Fourr’s Ranch identified two feasible hilltops in the Dragoons with respect to the 1890 Army heliograph exercise. Which one carried the Army’s heliograph? The answer comes from combining visibility with the Army’s own azimuth and distance records and a weighted mean center calculation.
Method
1) Map the candidate hilltops. Run visibility analysis from the hilltops that are required connections. This produced two realistic sites near Fourr’s Ranch from which those other connections can be seen (see the map below).
1) Map the candidate hilltops. Run visibility analysis from the hilltops that are required connections. This produced two realistic sites near Fourr’s Ranch from which those other connections can be seen (see the map below).
Two areas identified by visibility analysis
2) Using the recorded azimuths and distances for the 1890 heliograph exercise, convert those historical bearings to true azimuths. Army notes list magnetic bearings and distances between stations (example: Bowie Peak, 39 miles at 240° 20′ magnetic). Convert each to true using the period declination (e.g., +12° 15′ E in 1890 → 252° 35′ true for that line). Repeat for all connected stations (Rincon, Bowie Peak, Colorado Peak, Fort Huachuca, Mount Graham, Dragoon RR Station). Using the corrected azimuth, plot each endpoint of the azimuths and distance lines from those connected stations.
3) Weight the endpoints by information quality. Field officers used prismatic compasses with ~½° resolution and typically averaged several shots. Because angular error maps to a larger positional envelope with distance, assign each endpoint a weight inversely proportional to distance (nearby ties exert more pull than distant ones):
- 39 miles @ 0.5° → ~1,797 ft lateral tolerance
- 4 miles @ 0.5° → ~184 ft
The inverse of 39 and 4 gives us the weights: W ≈ 0.03 for the far line, W ≈ 0.25 for the near line.
4) Compute the weighted mean center. Load endpoints and their weights into a feature class and run the Mean Center tool. The weighted center represents the most probable location consistent with all azimuth-distance constraints. Compare that point to the two candidate hilltops surfaced by visibility; the hilltop closest to the weighted center is the likely heliograph site. (Screens in the deck also show a “standard circle” overlay to visualize the tolerance zone.)
Source: ESRI
Why this works
- Visibility narrows the terrain to a few physically plausible summits.
- Historical bearings and distances add directional constraints from multiple neighbors.
- Distance-aware weighting reflects instrument limits and practice (half-degree prismatic readings), so closer ties count more than far ones (a great example of Tobler's first law of geography, by the way).
- A single, reproducible statistic (the weighted mean center) resolves ties objectively.
- The “standard circle” validates consistency. A standard distance circle drawn around the weighted mean center summarizes the residual spread of all weighted endpoints. If a candidate hilltop falls inside this circle, it’s within the expected tolerance of the combined azimuth-distance constraints; if it falls outside, one or more constraints are inconsistent there or that hilltop is unlikely.
