{ "schema": 1, "pack_id": "contour-school", "checked_at": "2026-10-02", "lessons": [ { "id": 1, "title": "One line, one elevation", "body": "A contour connects equal heights. Travel along a 1100 m contour and the modeled elevation stays 1100 m, even when the line curves. It is an imaginary line, not a path.", "exercise": "hill", "source": "usgs-symbols" }, { "id": 2, "title": "Count the interval", "body": "The interval is a vertical difference, in metres here. At 20 m, successive lines can be 1080, 1100 and 1120 m. Our heavier index lines mark every fifth interval. A smaller interval adds lines without adding terrain detail.", "exercise": "slope", "source": "usgs-symbols" }, { "id": 3, "title": "Read the inside of a loop", "body": "On this hill, labels rise inward. Closed contours can also surround a depression; its elevations fall inward, often with short inward ticks called hachures. A loop alone does not prove a summit.", "exercise": "hill", "source": "usgs-depressions" }, { "id": 4, "title": "Spacing tells you steepness", "body": "Compare lines on the same map and at the same interval. Tight spacing means a steep slope; wide spacing means a gentle one. Grade = vertical rise ÷ horizontal run × 100%. A 20 m rise over 100 m is 20%, about 11.3°, not 20°.", "exercise": "slope", "source": "usgs-symbols" }, { "id": 5, "title": "A valley bends uphill", "body": "In the teaching valley, contours bend toward higher ground at the valley floor. The north–south profile confirms the direction. Water would tend downhill across the contours; this diagram maps no actual stream.", "exercise": "valley", "source": "original-math" }, { "id": 6, "title": "A ridge bends downhill", "body": "The ridge has high ground along its spine and lower flanks. Its contour nose points downhill. Similar-looking bends need elevation labels and surrounding context before you name the landform.", "exercise": "ridge", "source": "original-math" }, { "id": 7, "title": "A saddle has two readings", "body": "Pass a section through the same center in two perpendicular directions. One profile makes a hollow; the other makes a crest. At the exact saddle elevation, a level set can touch itself. Our fixed triangulation makes that special case explicit.", "exercise": "saddle", "source": "original-math" }, { "id": 8, "title": "Aspect is the downhill direction", "body": "Aspect is the direction of steepest descent: 0° north, 90° east, 180° south, 270° west. This kit uses grid north, not a magnetic compass bearing. Aspect at a perfectly flat or symmetric critical point is undefined.", "exercise": "slope", "source": "landfire-aspect" }, { "id": 9, "title": "A profile is a slice", "body": "A–B is a straight horizontal sampling line. The chart plots distance along it against elevation. Move the section and you sample different ground. It is not a hiking route; no path length or trail difficulty follows from the section.", "exercise": "bryce", "source": "original-math" }, { "id": 10, "title": "Stretch the view, keep the numbers", "body": "At 3× vertical exaggeration, a 20 m height difference is drawn three times as tall relative to horizontal distance. The stored heights, contour interval and calculated slope stay unchanged. Return to 1× before judging shape; even then, a sampled grid omits small and hidden features.", "exercise": "bryce", "source": "usgs-ve" } ], "exercises": [ { "question": "What do the nested rings tell you?", "prompt": "Follow one line around the hill. Move the section away from the center and watch the summit disappear from the profile.", "choices": [ "Every ring is a different height", "Every ring is a trail", "The center must be a hollow" ], "answer": 0, "explanation": "These labeled rings rise inward toward a summit. Closed rings alone are not enough: descending labels or inward hachures can identify a depression.", "reading": "A circular hill rises from about 1001 m at the corners to 1180 m at its center. The central west–east profile rises and falls symmetrically.", "lessons": [ 1, 3, 9 ], "id": "contour-school-hill", "shape": "hill", "name": "A rounded hill", "evidence_class": "illustrative", "formula": "1000 + 180 exp(−(x² + y²) / 60000)", "bounds": { "xmin": -400, "xmax": 400, "ymin": -400, "ymax": 400, "min": 1000.8690309988897, "max": 1180 }, "map": "hill-map.svg", "surface": "hill-surface.svg" }, { "question": "Does changing the interval change the slope?", "prompt": "Switch from 20 m to 10 m contours. The extra lines describe the same ground. Inspect the center to read its slope and downhill aspect.", "choices": [ "Yes, the land gets steeper", "No, only the drawing changes", "The elevation doubles" ], "answer": 1, "explanation": "The surface is unchanged. Here each 100 m east adds 20 m of elevation; each 100 m south adds 10 m. The steepest slope is about 12.6° (22.4%), down toward 297° from grid north.", "reading": "Parallel, evenly spaced contours cross a tilted plane. Elevation increases eastward and southward. The west–east center profile rises from 1020 m to 1180 m.", "lessons": [ 2, 4, 8 ], "id": "contour-school-slope", "shape": "slope", "name": "An even slope", "evidence_class": "illustrative", "formula": "1100 + 0.2x + 0.1y", "bounds": { "xmin": -400, "xmax": 400, "ymin": -400, "ymax": 400, "min": 980, "max": 1220 }, "map": "slope-map.svg", "surface": "slope-surface.svg" }, { "question": "Which way does the contour bend point?", "prompt": "Compare the north arrow with the bends. Use a north–south section through the center to find the uphill direction.", "choices": [ "Downhill, toward the south", "Uphill, toward the north", "Every bend points east" ], "answer": 1, "explanation": "In this valley the contour bends point north, toward higher ground. A contour is not a stream: the valley floor descends southward across the contour lines.", "reading": "Rounded V-shaped contours point north. Each side is higher than the valley floor. A north–south profile along the center falls from 1152 m to 1008 m.", "lessons": [ 5, 9 ], "id": "contour-school-valley", "shape": "valley", "name": "A valley", "evidence_class": "illustrative", "formula": "1080 − 0.18y + 0.0007x²", "bounds": { "xmin": -400, "xmax": 400, "ymin": -400, "ymax": 400, "min": 1008, "max": 1264 }, "map": "valley-map.svg", "surface": "valley-surface.svg" }, { "question": "How is this bend different from the valley?", "prompt": "Look at the shape first, then confirm with the numbers. Compare the center section with a section near either side.", "choices": [ "It points toward lower ground", "It always points upstream", "It proves a cliff is present" ], "answer": 0, "explanation": "This ridge nose points south, downhill. The crest is higher than the land on either side. Read the labels to distinguish a ridge from a valley.", "reading": "Contours bow south around a crest. The center is high compared with its east and west flanks. The central west–east profile rises to 1230 m and falls again.", "lessons": [ 6, 9 ], "id": "contour-school-ridge", "shape": "ridge", "name": "A ridge", "evidence_class": "illustrative", "formula": "1230 − 0.18y − 0.0007x²", "bounds": { "xmin": -400, "xmax": 400, "ymin": -400, "ymax": 400, "min": 1046, "max": 1302 }, "map": "ridge-map.svg", "surface": "ridge-surface.svg" }, { "question": "Can one point be high and low at the same time?", "prompt": "Keep the section centered. Switch between west–east and north–south, and compare the two profiles through the same point.", "choices": [ "No: one of the profiles is wrong", "Only if the units change", "Yes: it depends on the direction" ], "answer": 2, "explanation": "At 1160 m the center is lower than its east and west shoulders, but higher than the north and south approaches. The exact critical-level contour touches here; real map generalization can hide this special case.", "reading": "The center is a low point on a west–east section and a high point on a north–south section. The saddle has no single downhill aspect exactly at its center.", "lessons": [ 7, 8, 9 ], "id": "contour-school-saddle", "shape": "saddle", "name": "A saddle", "evidence_class": "illustrative", "formula": "1160 + 0.0007x² − 0.0007y²", "bounds": { "xmin": -400, "xmax": 400, "ymin": -400, "ymax": 400, "min": 1048, "max": 1272 }, "map": "saddle-map.svg", "surface": "saddle-surface.svg" }, { "question": "What can this Bryce grid actually show?", "prompt": "Trace a section from the plateau toward the intricate terrain below. Compare 1× and 3× height, then return to true vertical scale.", "choices": [ "Every overhang and hidden rock wall", "Sampled ground elevation and broad landform", "Current trail access and stability" ], "answer": 1, "explanation": "This 768 m square comes from an existing USGS bare-earth terrain derivative, sampled every 8 m. Thin fins and steep breaks can be simplified. It cannot recover hidden rock faces, establish a route or replace a ground-level scan.", "reading": "An irregular plateau edge gives way to steep, closely spaced contours and lower branching terrain. Heights in this crop range from 2286.5 m to 2468.1 m NAVD88. The cut boundary is editorial.", "lessons": [ 4, 9, 10 ], "id": "contour-school-bryce", "shape": "bryce", "name": "Below Sunset Point", "evidence_class": "derived", "formula": null, "bounds": { "xmin": 0, "xmax": 768, "ymin": 0, "ymax": 768, "min": 2286.5, "max": 2468.1 }, "map": "bryce-map.svg", "surface": "bryce-surface.svg" } ], "sources": [ { "id": "usgs-symbols", "title": "USGS · US Topo Map Symbol Guide", "url": "https://www.usgs.gov/ngp-standards-and-specifications/us-topo-cartographic-specifications-map-symbol-guide", "use": "Contour and index-line symbols; reference only." }, { "id": "usgs-map-reading", "title": "USGS · Finding your way with map and compass", "url": "https://pubs.usgs.gov/publication/fs07999", "use": "Equal-elevation lines, contour intervals and close spacing on steep slopes; factual reference only." }, { "id": "landfire-aspect", "title": "LANDFIRE · Aspect", "url": "https://landfire.gov/topographic/aspect", "use": "Downslope aspect definition; reference only." }, { "id": "usgs-depressions", "title": "USGS · Depression contour symbols", "url": "https://carto.nationalmap.gov/arcgis/rest/services/contours/mapserver/34", "use": "Depression hachures; reference only." }, { "id": "usgs-ve", "title": "USGS · Vertical Exaggeration", "url": "https://water.usgs.gov/nrp/gwsoftware/ModelMuse/Help/vertical_exaggeration_dialog_box.html", "use": "Vertical versus horizontal display scale; reference only." }, { "id": "usgs-rights", "title": "USGS · National Map data terms", "url": "https://www.usgs.gov/faqs/what-are-terms-uselicensing-map-services-and-data-national-map", "use": "Public-domain elevation data and requested attribution." }, { "id": "nps-sunset", "title": "NPS · Sunset Point", "url": "https://www.nps.gov/places/000/sunset-point.htm", "use": "Place context only; no page photograph copied." }, { "id": "original-math", "title": "Original analytic teaching surfaces", "url": "./assets/park-packs/contour-school/methods.html", "use": "Equations, triangulation, units and calculation limits." } ] }