11-1: The most obvious advantage is that we normally view the world in 3-D. Our experience in that mode allows us to recognize features both by their shape and their depth, or their variation in height. This is especially helpful when our vantage point is from above. If we were to fly over an area at low altitude, but well above the surface (to avoid collision), we can separate mountains from valleys by their relief (differences in elevation) and thus identify each landform type. Three-dimensional viewing permits us to determine whether a building is tall or low. From both a practical and a scientific outlook, in geology, for example, knowing whether a rock type is a ridge or a depression tells us something about its relative hardness or resistance to weathering, and hence aids us in identifying it. BACK

11-2: The sum of the highest and lowest points is 65200 feet or, dividing by 5280 ft/mile, 12.35 miles. Dividing this latter number by 3980 miles and multiplying by 100 gives 0.31%, a small variation indeed, so that the Earth's surface at full scale is almost smooth, and its radius varies by about 1 part in 320. BACK

11-3: This notation can be read as "latitude 34 degrees, 12 minutes, and 31 seconds south, longitude 77 degrees, 3 minutes, and 41 seconds east" Each degree consists of 60 minutes, so that in decimals 12/60 = 0.2; each minute consists of 60 seconds, so that 31/60 = 0.052; the latitude can then be expressed as lat 34.2052° N, and so forth. The length of a 1° latitude varies slightly, from 68.704 miles at the equator to 69.386 miles at 80°. The length of 1° of longitude ranges from 69.172 miles at the equator to 12.051 miles at 80° latitude and 0 miles at the pole. This is in the nature of spherical geometry in which the longitudinal lines are great circles and latitudes become successively smaller circles poleward. BACK

11-4: Looking down on your head, someone would see a series of concentric near-circles, whose spacing varies (the top of your head is really not a hemisphere). Dare you to try this! Might start a craze, at least in college ranks. BACK

11-5: In the rare, but real, instance in which the top of a cliff overhangs the lower part (unstable, but can occur where stream undercutting is active), the upper contours will cross over lower ones. BACK

11-6: The second scene in Section 6 covers the folded Valley and Ridge province in central Pennsylvania, including State College, home of the Penn State Nittany Lions (Coach Paterno's football team). BACK

11-7: (1800/4000) x (40/6) = 3.0 (Vertical exaggeration is threefold). BACK

11-8: A peak near the lower right corner. BACK

11-9: The layers are inclined downward towards the upper right. BACK

11-10: The central hill is a bit lower than the high points on the anticlinal rim. BACK

11-11: It is necessary first to convert inches on the photo to feet on the ground. Divide 3600 by 12, so that the scale can be stated as 1 inch = 300 feet. Then d becomes 150 ft and r becomes 900 ft. Substituting in the equation h = Hd/r = (1800 x 150)/900 = 300 ft. BACK

11-12: h = (2000 x 0.4)/(70 + 0.4) = 800/70.4 = 11.36 meters. BACK

11-13: Susanville lies on the east side of the Sierra Nevada Mtns., about 45 miles almost due east of Mt. Lassen (a volcano active early in this century), at an elevation of 4200 feet. What you see are mountains in light gray and valleys in dark gray to black. Individual mountain rises occur over most of the map. A large valley occupies center right. A more continuous mountain range, dissected by a stream's headwaters, is located in the lower left. BACK

11-14: The key to quick location is the Big Horn Mountains, a slightly curved range that is found at the top center of the Wyoming map. That curvature aids in finding its equivalent in the U.S. map. To the east of the Big Horns is an isolated rise, the Black Hills. BACK

11-15: This is a toughie. But look at the snow pattern on the North Rim. There is a south-pointing lobe (the first in from the right) separated by a large north-pointing canyon indentation to that rim, and then a second snow-covered lobe. This second lobe makes up the light pinkish-brown plateau surface that occupies the upper left corner of the perspective view. That same kind of surface appears on the South Rim in the lower right corner. It shows in the Landsat as a distinctive brown pattern.BACK

11-16: The more expensive models of automobiles, such as Cadillac, now offer built-in GPS-based locator systems. Eventually, most cars will have this capability. Pleasure boats also utilize GPS navigation. And, anyone hiking in the wilderness would benefit from a hand-held locator - at least one would know where one is lost. BACK

11-17: The key word, given at the beginning of the page, is "narrow foot-paths". Altimeters send down a narrow beam that effectively shows the topography as a profile. To make a high quality topographic map, one must have data on elevations spread rather evenly over the two-dimensional surface. Orbits of spacecraft are usually set far apart, so that the distance between successive paths is typically in 10s to even 100s of kilometers. The orbits do drift over time so that the "footprints" tend to spread out but there still are gaps even after long periods. However, over the years, and with a series of orbiting satellites, there should eventually be enough close-spaced orbits so, with suitable extrapolation, detailed and highly accurate maps of the Earth's surface - widespread enough to eliminate the present deficiencies shown in the graph at the top of the page - will evolve. Meanwhile, the altimeter data serve to produce exceptional control profiles that "calibrate" other methods in use. BACK

11-18: Depends on what you are using the stereo for. A high VE helps the eye and mind to see differences in relief that are useful in studying landforms, urban infrastructure, and forest cover. Small variations in relief are especially detectable when the exaggeration is pronounced. A low VE tends to present the surface features and scenery is a more realistic mode. Calculations of slope angles and strata dips are affected by the value of the VE and generally must take that into account for accurate results. BACK

11-19: The Panamint Range, near the bottom, is higher than the Funeral Mtns to the north. BACK

11-20: The plateau is in the lower half of the photos. BACK

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Primary Author: Nicholas M. Short, Sr. email:

Collaborators: Code 935 NASA GSFC, GST, USAF Academy,
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Last Updated: July '99

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