The formula that you provided will give the different results to the one in the cited eurocontrol document. The result form the sensor (on of the popular Bosh sensors) is a pressure - we convert it to altitude using International Standard Atmosphere model (formula is different than the one presented here). And that result is a proof of beating some World record. There is no other technical way to use different sensor (GPS altitude indication is not correct on these altitudes and also not correct by the definition). radar could not be used same as Lidar or laser measurement. How the formula should be used? 1. conditions at the object take off altitude above mean sea level = 78 m - from digital terrain model temperature measured by termometer in the car 8deg C temperature indicated by the ventusky (weather forecast) 11degC pressure indicated by the ventusky (weather forecast) 1016hPa pressure indicated by one of the altimeters (not conatining pressure sensor that we are talking about) = 1005hPa Which pressure should be used and feed to the formula as p0 (p0 is present in formula presented here as well as in eurocontrol document as pb)? Shall i take pressure at altitude 76m and find pressure at the Mean Sea Level = 0m and use that pressure from mean sea level in the formula or something else. From that what I see the idea is to adjust pressure at the sea level and than calculate altitude. Regarding airplanes yes they switch altimeters around some altitude (i belive 12 000 feet) and switch their mean se level pressure to 1013 hPa in their altimeters. That pressure is different in comparison to the altimeter that has been zeroed at QFE = 1025 hPa theses 12hPa is around 12*9m for low altitudes but for high altitudes it will even more like 12*30m). So from perspective of people thatare setting the "word record " it is very important what to put in the fomula and correct it by ground level. Also theere is one more what if altitude is 11km (tropopause) and accoridng to ISA model the p0 is around 226mbar.
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Also there is a bit different formula in ISA model in this publication: https://www.eurocontrol.int/publication/revision-atmosphere-model-bada-aircraft-performance-model see page 22. these formuals gives different reasult in comparision to one provided in this answer on the top of discussion
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