Wednesday, March 31, 2021

Learning more about altimeters...

After the flight of the Shell Shocked on March 13, I got to thinking about the data provided by the Flight Sketch Mini it carried to just over 300 feet. The day had been warm for mid March - 71 degrees - and I wondered how far off the altimeter altitude was from the actual value. I knew there would be some difference because

  • All hobby altimeters use the same mathematical model to convert pressure to height, and
  • They all assume a temperature of 59 degrees (15 degrees Celsius) in the model. Warmer temps mean that the altimeter readings are low, but flying on a cold day gives readings that are too high. It is a simple matter to calculate the correction by using the formula

    where T is the temperature in degrees Celsius.

So computing the altitude the Shell Shocked actually reached was very quick. 71 degrees Fahrenheit = 21.9 degrees Celsius, giving a correction factor of 1.024. The Shell Shocked actual peak altitude was 1.024 x 319 = 327 feet.

Easy peasy. Can do it on an iPhone calculator...

However, I soon wondered what the model used by the altimeters was; I figured it was a pretty simple model, probably based on the U.S. Standard Atmosphere. A bit of internet searching proved me correct - the bottom two lines in the below slide are the basic equations. The altimeter measures pressure, so all you have to do is solve the equations for altitude in terms of pressure and Voila! You have the math model used to calculate altitude by the altimeter. The only difference is that the 2116 in the pressure equation is replaced by the pressure measured by the rocket on the pad. This gives you the altitude relative to your pad, which is what you want.

Please ignore the primitive English units - I particularly hate mass measured in slugs; it is just wrong!

So I had the model, and me being me, I had to check it out by taking the altimeter pressure numbers, setting the temperature to 59 degrees, and seeing if the altitudes I calculated matched the altimeter's. Sure enough, they did.

Altimeter readings versus model calculations (Click to enlarge).

Immense satisfaction. Putting in the actual temperature of 71.4 degrees (21.9 Celsius) produces a plot like

Altimeter readings corrected for the actual temperature (Click to enlarge).

Peak altitude is 327 feet, matching the hand calculated correction.

I love math...

3 comments:

  1. For the metric-minded: https://www.grc.nasa.gov/www/k-12/airplane/atmosmet.html

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  2. Hi, Bill, This is some good stuff to know. Thanks for doing the research and posting this!

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