Does altitude influence the flight range of an engine driven aircraft?

Question

I'm reading a chapter about flight performance during the cruise phase and the influence of altitude.

My book (Aerodynamica, prestatieleer en vliegtuigtechniek by Bas Vrijhof on page 155, written in Dutch) describes the following:

Naarmate de hoogte toeneemt, neemt de luchtdichheid af. De afnemende luchtdichtheid heeft een effect op het benodigde vermogen, en dus op de prestaties. Om bij een lagere luchtdichtheid te vliegen is meer vermogen nodig. Om bij een lagere luchtdichtheid voldoende lift te houden moet de TAS toenemen, dat kost vermogen.

Translated to English:

Airdensity decreases with altitude. A decrement in airdensity influences flight performance. To fly at a lower airdensity more engine power is needed. To maintain enough lift at lower airdensity the TAS needs to increase, this comes with the cost of engine power.

This is totally clear to me. Then the book says.

Endurance... Meer vermogen betekent een hogere brandstofverbruik. De endurance neemt daarom af.

Translated:

Endurance (amount of fuel per hour), more engine power means a higher fuel consumption. The endurance decreases with an increase in engine power.

Again, this is also clear to me.

Range... De range verandert niet bij toenemende hoogte. De range is niet afhankelijk van de vlieghoogte. Wel neemt de Vmax range toe als de hoogte toeneemt.

Translated:

Range (maximum flight distance, amount of fuel per km) doesn't change with an increase in altitude. However, the Vmax range increases with an increase in altitude.

The last sentence is confusing me. Because my instincts say that a higher fuel consumption comes with a shorter flight distance. So my question is:

Is it really true that the altitude doesn't influence the flight range? Does the book has an error?

Answer 1

Your book may not be wrong, but it is misleading, because the answers depend on the the aircraft type, and the type of engine. (piston, turboprop, turbojet, turbofan)

In general:

All aircraft have the best range at higher altitudes.

Piston powered aircraft have the best endurance at low atitude.

Jet powered aircraft have the best endurance at their optimum altitude. (not too low and not too high)

Answer 2

Jet engines can make the same horsepower/thrust at basically all altitudes due to their compressors, thus the same fuel burn - this lets them take advantage of the less dense air/less drag at higher altitudes, and perhaps take advantage of jet stream tail winds. Well, maybe not the same, see here for more How does turbojet thrust change with altitude?

Smaller planes can be equipped with turbochargers, or turbonormalizers, to make sealevel horsepower at higher altitudes and also take advantage of the thinner air.

Non-turbo engines like mine and most small planes are limited to leaning the mixture to keep the engine from running rich/wasting fuel as (generally) climb above 3000 feet. We can't get fully as high to the thinnest air, but we're also burning less fuel once cruise altitude is reached.

Answer 3

any aircraft has an optimal altitude for cruising. account for burn at takeoff and landing, then the cruising altitude is the one minimizing the costs. since combustible is the main cost, then is easy to determine which altitude is the economical one, even customized for the trip length and wind direction. however, for practical reasons and separation of air corridors, the economical altitude also depends on imposed constraints related to air traffic.

for distances of less than 1000km, the 6000m 675km/h turboprops of small capacity are the most economical. embraer and bombardier are flying those routes. for longer distances, the 11000m 980km/h large airliners are the most economical. for planetary distances, the largest airships are the most economical. the altitude is limited to 11000m.