Yellowstone rangers — and tourists, too! — can determine the height of a geyser eruption with some simple trigonometry. (Illustration by Mark Wolfe/Yellowstone National Park).
Yellowstone Volcano Observatory scientists investigate many aspects of the Yellowstone volcanic system, including the incredible geysers that are a highlight of any visit to the park. After witnessing a geyser eruption, many visitors begin to wonder about some aspects of these incredible phenomena. One question –“how tall was that?” — can be answered by anybody with a few simple tools.
Estimating the eruption height while watching a geyser can be difficult for several reasons. There often aren’t any reference objects in the immediate vicinity of the geyser, which can throw our perceptions off. Similarly, while you can get a sense of the height of a skyscraper by how tiny the windows at the top appear to be, the water droplets sprayed into the air from a geyser aren’t nearly as good of a reference. Not to mention the fact the droplets start falling as soon as they reach their peak height and, unlike a building or a tree, the fountain of water doesn’t hold still. However, by borrowing a relatively simple technique used in fields like forestry, astronomy, and geodetics, anybody can measure the height of a geyser eruption with a reasonable amount of accuracy. For those who may have wondered during high school math class when you would ever need to remember and use the phrase “SOH-CAH-TOA,” the time has come!
For this method, the only measurement that must be taken during the eruption itself is called the angle of inclination. This is the vertical angle above the horizon (looking straight toward the horizon is 0 degrees and looking straight above your head is 90 degrees). To get this measurement, you can use a home-made “clinometer” made of a protractor and weighted string, or you can buy one (they are typically used in forestry or surveying). There might even be a clinometer or theodolite app on your smartphone! Whichever instrument you use, make sure it is calibrated before use.
When the eruption begins, point your instrument at the peak of the bursts of water and record the angle. This part can be trickier than it sounds. It’s hard to say what the “peak” of a geyser is as the spray diffuses into small droplets, and billowing steam can obscure your view. Use your best judgement and try measuring multiple “bursts” during the same eruption.
After determining the angle of inclination (α) of the eruption, you just need two more measurements to convert that angle into a height. These are your horizontal distance from the geyser (x) and your vertical distance from the geyser’s vent (y1). Since it would be unsafe (and illegal!) to leave the boardwalk and use a measuring tape, you can use a map to determine these numbers—Google Earth, for example, works very well! A more accurate, albeit expensive, method is to use a device called a rangefinder, which uses a laser (and trigonometry!) to determine both distances. Once you have these numbers, it’s “SOH CAH TOA” time:
height = y2 + y1
(You may want to do some additional measurements and calculations if the spray is leaving the ground at an angle, but we’ll leave that for another time.)
Whatever method you use, it helps to plan ahead—where are you going to stand to view the geyser’s eruption?—so you can be ready with the distance measurements. Keep in mind that you don’t necessarily want to be as close as possible to the geyser to get a good measurement. Stand back a bit so you can easily see the full water column. It also helps to do this on a clear, sunny day, and if it is windy, find a spot upwind of the geyser.
No matter the method, there will always be some degree of uncertainty. More technology could be employed to determine the eruption height, but the increase in precision and accuracy might not be worth the effort.
For example, the first few minutes of Steamboat’s eruptions, it has often been measured as more than 300 feet with a few exceptional eruptions measured by visitors at at more than 400 feet. For comparison, the Lower Falls of the Yellowstone is about 308 ft. and the tallest living tree, a redwood in California, is 380.1 ft.
Get out there and try your hand at measuring some of these incredible features next time you’re in the park. You can practice in advance by measuring a building, a tree, or maybe even fireworks. It’s always good to see if your measurements are reproducible. When you’re in Yellowstone, one of the predictable geysers would be good to try to measure, but you could also try your luck (and patience!) trying to measure the so-called “tallest currently active geyser in the world”—Steamboat Geyser in the Norris Geyser Basin.
Yellowstone Caldera Chronicles is a weekly column written by scientists and collaborators of the Yellowstone Volcano Observatory. This week’s contribution is from Mark Wolfe, seasonal physical science technician with the Geology team at Yellowstone National Park.
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