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L= Clq(TAS)^2*S/2 D= Dlq(TAS)^2*S/2

Some say it is due to lower friction drag due to lower density. However if our weight does not change, that means lift does not change as well. So when air density decreases with increasing altitude, TAS increases to maintan required lift force, thus dynamic pressure remains constant. This leads to the fact that drag must not change as well (keeping in mind that Dl and S are constant). What do i miss?

Julious
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  • Lets say you wanted to go somewhere at 700 knots, it would take a lot more fuel to fly that 700 knots at 10,000 feet than it would at 35,000 feet. Yes, drag matches thrust in both situations but it would be a lot more drag and a lot more thrust (and fuel) at the lower altitude. Hopefully somebody can put numbers and explain how your equation works with that. – Ron Beyer Oct 26 '18 at 23:33
  • See https://aviation.stackexchange.com/questions/24641/what-is-the-relation-between-an-airplanes-altitude-and-the-drag-it-is-experienc?rq=1 – Pilothead Oct 26 '18 at 23:56

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Because while the dynamic pressures of air reacting on the wings at those altitudes remains the same, the speed of the relative winds, and, as a consequence the aircraft’s ground speed is much higher at higher altitudes than near sea level. This is as a consequence of the air density being much lower at high altitudes than down low. Cold thin air facilitates true airspeeds 100-300 knots higher than indicated airspeed does. Therefore per unit of fuel consumed to overcome drag, the airplane travels much farther and consumes less fuel over the course of the flight.

Example: jet airplane flying at a pressure altitude of 37,000 ft, Outside ambient temperature is -47°C. If the calibrated airspeed the pilot reads in the cockpit is 300 KCAS, the true airspeed is 575 KTAS.

Add to this that these altitudes do allow the aircraft to access the upper level winds of the jet stream, which range between 30 to over 160 knots on certain days, which can facilitate a healthy tailwind for eastbound flights around the globe. It is not uncommon for commercial aircraft to log over 650 knots groundspeed in these conditions, further reducing fuel consumption.

As the speed of sound varies proportionally with temperature, compressibility limitations prevent this form being used beyond Mach .8 - Mach .9 due to Cp movement and control buffeting, depending on the aircraft. There also is a point in the flight envelop where the Stall speed Vs corresponds with the maximum Mach number - see “Coffin Corner” for further details - so this limits the maximum operating altitude based upon outside air temperature as well. Nonetheless, high subsonic air travel remains one of the most efficient means of moving large numbers of people and cargo quickly around the globe.

Romeo_4808N
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  • Just to add. Engines also benefit from very low temperatures at high altitudes. https://aviation.stackexchange.com/questions/1609/why-do-jet-engines-get-better-fuel-efficiency-at-high-altitudes – Electric Pilot Oct 27 '18 at 01:11