Wednesday, September 3, 2014

Using Trig to Estimate Height of Small Slope Soaring Hill

As Paul Naton said in his first soaring video “there are a lot more small slopes than large slopes”, that is sure the situation where I live. With the availability of small foam ready-to-fly gliders such as the UMX ASK-21 and UMX Radian I have been having a great time flying several small slopes and always looking for more to try.  I have been curious to just how tall these slopes were and was thinking that by using trigonometry an approximate height could be arrived at.

Hill to Estimate Height

Slope Flying UMX Radian 

Using the Estes AltiTrak device that I had purchased for computing the apogee of model rocket launches I was able to measure the angle of the face of the slope  (22 degrees), no doubt some type of carpentry level could be used as well. Then I measured the length of the slope using a tape measure (39 feet), this would be the length of the hypotenuse of a right triangle which is the basis of trigonometry. 

Measuring  Face of the Hill - Hypotenuse

Estes Alti - Trak to Find Slope of Hill

For myself math skills become rusty because I do not use math enough, I posed the scenario of what I was trying to calculate on model aviation listserve and someone provided an example of the correct trig function to use; the sine function. Sine = Opposite / hypotenuse so the height of the top of the hill would be the opposite side of the right triangle. Rearranging terms the height of Slope =sin(angle)*hypotenuse or   =sin(22)*39ft = 0.375*39ft= 14.6ft  the height of the slope.

There are other small slopes that I would like to compare to this one as to available lift. It would be interesting to see if there was significantly greater lift from a slope that was 30 feet tall compared to 15 feet. No doubt there are many more variables to the lift than slope height. My guesses to slope height tend to be rather optimistic, this slope I thought was close to 25 feet tall.

Bill Kuhl

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