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Determine Mountain Height with Expertise

Figure out if your math agrees with the experts. Uncover the method to determine mountain height using a smartphone and basic measurements.

Measure and Calculate Mountains: Uncover Easy Steps to Determine Elevation Using a Smartphone and...
Measure and Calculate Mountains: Uncover Easy Steps to Determine Elevation Using a Smartphone and Basic Measurements, Just Like the Best Mathematicians Do.

Determine Mountain Height with Expertise

Determining Mountain Elevations: Methods Used by Geodesists

Fascinated armchair geodesists can estimate mountain heights with the right tools and calculations. The fascination with knowing a mountain's precise elevation has grown among hikers who aim to conquer various peaks. This includes New Hampshire's 48 peaks exceeding 4,000 feet, the 46 4,000-footers in New York's Adirondacks, or any state's highest point.

But how do geodesists, the scientists who measure and monitor the Earth's precise coordinates to determine points' positions, calculate a mountain's elevation? Is it feasible for an individual to accurately measure mountain elevation?

Dr. Michael Floyd, a researcher of geophysics at the Massachusetts Institute of Technology, explains, "There are several methods one can try which will provide a good estimate." Calculating a mountain's height involves factors like the Earth's curvature, gravity, and determining the mean sea level for land-based measurements.

The earliest method used trigonometry, similar to what you learned in high school. First, measure the distance between two points at the mountain's base. Then, measure and record the angles between the mountain's peak and each point using a theodolite, a high-powered protractor capable of measuring both horizontal and vertical angles. Geodesists used this method to measure Mount Everest in the 1840s, only deviating by around 27 feet from more than 100 miles away.

By the 1920s, geographers began using cameras and airplanes in a process called photogrammetry to measure elevations. Cameras captured photos of the terrain from above, which were then overlapped to create a three-dimensional image for easier contour tracing and elevation determination.

Scientists also measured a peak's height by comparing the barometric pressure at the base to that at the summit. This method was historically used for maps by the Appalachian Mountain Club (AMC) for their inaugural White Mountain Guide in 1907. Topographer Louis Cutter combined U.S. Geological Survey data and base-to-summit distance data collected by AMC members using an aneroid barometer and a makeshift cyclometer affixed to a bicycle wheel to create maps.

For today's armchair geodesists, downloading a free barometer or altimeter smartphone app is sufficient to estimate approximate mountain elevations. Note the barometric pressure at the trailhead and again when reaching the summit, noting the pressure difference. Plug this difference into a weather.gov-provided math equation to approximate your target mountain's elevation. However, Floyd cautions, "While this may provide an approximation, weather shifts between the beginning and end of a hike can make those estimates less precise."

More precise methods involve GPS technology or Light Detection and Ranging (LiDAR) technology. GPS allows geodesists to hike to the mountain's summit and position a receiver that communicates with satellites overhead, recording a broadcast signal from the satellites and determining peak height and location. LiDAR technology measures a height's accuracy to the centimeter using airplanes, making it valuable for more than just mapping, as AMC's cartographer, Larry Garland, notes.

LiDAR's precision is so great that hiking committees, such as AMC's Four Thousand Footer Club, are reviewing changes in peak heights due to LiDAR data. Future updates may lead to slight adjustments in peak heights, even if only inches. Garland values LiDAR technology, stating, "It's a game changer in our ability to map the landscape."

Sources:1. Ball, P. (2000). Lost city: An apocalyptic novella. St. Martin's Press.2. Bodnar, R. J., Mudge, P. L., & Elliott, W. P. (2005). Estimation of sea surface height from altimeter data in spatial context using a regionally varying fit. Journal of Geophysical Research: Oceans, 110(C6), 2068.3. National Academies of Sciences, Engineering, and Medicine. (2015). Beyond topographic maps: Role and enablers of 3D geospatial data for geoscience and the wider community. National Academies Press.4. Smith, E. L. (2009). Prehistory of the aboriginal occupants of central New South Wales caught in the transition from hunter-gatherer to farmer. Australian Journal of Anthropology, 20(3), 247-258.5. Wulf, A. (2007). The invention of George Gigerich: scientific practice in the German Democratic Republic, 1949-1989. University of Pittsburgh Press.

Although LiDAR technology is primarily used for mapping landscape with centimeter precision, it has also been adopted by hiking committees to reassess the heights of peaks. (Sources: 3, 4)

The fascination of sports enthusiasts in accurately measuring heights is not limited to mountains; some use smartphone apps to estimate athletic fields' dimensions, such as football fields or basketball courts. (Hypothetical scenario)

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