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Discussion Starter #1 (Edited)
For drivers who live in the more mountainous regions, and for those at lower elevations who occasionally venture there, the following material may be of interest. I've had some experience of driving at higher elevations since I've driven on the Mount Washington, NH (elev. 6288.3') auto road several times.

The greater the density of the intake air ingested by the engine, the greater the BHP output. Three factors that affect air density are elevation, intake air temperature and moisture content or water vapor pressure. Considering ONLY the effect of elevation, an increase in that parameter causes a corresponding decrease in air density that results in a BHP reduction. In fact, the output is almost directly proportional to the density of the atmosphere which itself is directly proportional to the barometric pressure.
Reference:
High Speed Combustion Engines, 16th Edition, by P. M. Heldt, pages 638-9

In a normally aspirated engine the resulting drop in BHP at any given rpm is approximately 3% for each 1,000 feet (304.8 meters) of elevation above sea level.
Reference:
Auto Math Handbook by John Lawlor, chapter 4, Brake Horsepower & Torque, Effects of Elevation, pages 28-30

Lawlor provides the following formula for calculating the reduction of BHP as a function of increasing elevation:
BHP loss = (elevation, in feet/1,000) x (.03 x BHP, at sea level)
or,
BHP loss = (elevation, in meters/304.8) x (.03 x BHP, at sea level)

The following sample calculations are based on the above formulas and are for the current (2019+) Mazda3 2.5 L engine with a rated sea level output of 186 BHP @ 6,000 rpm:
@1,000' - BHP loss = 5.58; BHP output = 180
@5,000' - BHP loss = 27.9; BHP output = 158
@10,000' - BHP loss = 55.8; BHP output = 130

Sample calculations for the current (2019+) SkyActiv-X engine with a rated sea level output of 178 BHP @ 6,000 rpm:
@1,000' - BHP loss = 5.34; BHP output = 173
@5,000' - BHP loss = 26.7; BHP output = 151
@10,000' - BHP loss = 53.4; BHP output = 125

For those who hate math, don't despair. A convenient online calculator allows one to plug in the BHP and elevation figures and get an instant result.
The Wallace Racing-Braking HP Loss at Altitude Calculator:
www.wallaceracing.com/braking-hp.php

Of course, it goes without saying that as air density decreases with elevation, the MAF, IAT, barometric pressure and O2 sensors maintain the proper A/F ratio so the engine continues to run as designed albeit at reduced output. One of the major benefits of electronically-controlled fuel injection systems.

In the next post, although completely unnecessary for calculation purposes, I'll present some material for those who may want to learn more about atmospheric effects on engine output.
 

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Discussion Starter #2
Atmospheric Effects on BHP Output

International Standard Atmosphere
(ISA): It was the basis for the older (now obsolete) SAE Standard J607 which was in effect until June 1990 and is still currently in use to measure aircraft piston engine performance as the ISA also contains density/altitude data necessary to determine aircraft engine performance at various altitudes. The air temperature of 59 deg F (15 deg C) is taken as the mean temperature of the earth at sea level.
Intake air temperature: 59 deg F (15 deg C)
Barometric pressure: 29.291" Hg (101.325 kPa)
Relative humidity: 0%
Air density: .0765 lbs./cu. ft. (1.225 kg/cu. meter)

For a chart of the Standard Atmosphere, go to:

Society of Automotive Engineers (SAE) Standard J1349: The current standard used to determine SAE net BHP, in effect since June 1990. It is the standard on which all advertised BHP ratings are based. Its parameters are:
Intake air temperature: 77 deg F (25 deg C)
Barometric pressure: 29.235" Hg (99.001 kPa)
Relative humidity: 0%
Air density: .0722 lbs./cu. ft. (1.157 kg/cu. meter)

For those wondering about the variation of sea level barometric pressure, the discrepancy is due to the different air temperature standards. Inches of Hg, although considered a pressure unit, changes with temperature; it expands as it gets warmer. For our Forum members who use SI measurement units, the Pascal (Pa) is the fundamental unit of pressure. Since it's such a small unit, the kPa is commonly used in its place.

Finally, I discovered a really cool website that presents pressure units in every possible way. Check it out, you'll be glad that you did.
Conversion of Pressure or stress Units:
www.sengpielaudio.com/calculator-pressureunits.htm

For all you high flyers, clear skies and happy landings.
 
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