originally posted by: Fools
I know that some jet fighters have a service ceiling of 65,000 feet, the F-15 for instance. Altitude.org tells me that "At 65000ft, the standard
barometric pressure is 6 kPa (47 mmHg). This means that there is 6% of the oxygen available at sea level." Ok, so there is a little oxygen to help the
combustion mode. I suppose there is some equation where the mixture of fuel to that oxygen ration allows the engines to still work. However, if you go
to the SR-71's service ceiling of 75,000 feet that brings you down to 4% oxygen. So when reading on some aircraft though it seems they were also
designed to reach 97,000 to 100,000 feet - which brings it down to 1%. Is that all that is needed to provide combustion or is some other fuel brought
along to help out?
I had to go back and re-read some of my old propulsion textbooks from grad school to answer this question.
Various commenters in this thread have contributed elements of the correct answer; I will take a stab at putting them together in a coherent story.
First, It is obviously true that the atmosphere becomes less dense as you go up in altitude. Aerospace engineers typically use the US Standard
Atmosphere of 1976 as the reference model.
This model shows that the density at 65,000 ft is about .07 (7%) as much as the density at sea level.
The single most important parameter that characterizes the performance of a turbojet engine is the mass flow—the total mass of air flowing through
the engine at any point in time. The mass of fuel that is being burned at any point in time is a fairly constant (and very small) fraction of the
total air mass flow so, the greater the mass flow, the greater the fuel burn, and the greater the thrust. Therefore, the amount of thrust a jet
engine produces follows the air mass flow, directly.
The compressor on a jet engine operates at a relatively fixed, constant compression ratio; the rotating machinery of the compressor stage takes air
at the compressor intake face and makes it more dense, by a fixed factor (typically, between 5 and 10) at the point at which it enters the combustion
chamber. If you had a turbojet engine in a test stand at sea level, wound up to max power, there would be a certain air mass flow rate, a certain
fuel flow rate, and a certain thrust level associated with that condition. If somehow—magically—you had a stationary engine test stand at 65,000
ft, and operated that same engine, the air density at the inlet would only be 7% the density at sea level, the flow rate would only be 7%, and the
fuel burn and thrust level would also be only 7% as much as the equivalent sea level values.
But that’s not the condition that a real jet engine installed in a real airplane actually sees. In forward flight, the jet engine is connected to
an inlet that collects the ram air coming toward the airplane and compresses it before it ever enters the turbo machinery. In other words, it is made
denser in two steps; once when it enters the inlet and once again in the turbo compressor. As a result, the mass flow through the engine does not
decline directly with altitude, it declines more slowly than that.
As someone pointed out, the dynamic pressure (due to the ram air, and usually denoted by the symbol “q”) that is needed to provide lift to the
wings is exactly the same dynamic pressure that compresses the air in the intake inlet. If there is enough q to keep the airplane flying, there is
enough q to pre-compress the air before it enters the turbo machinery. In fact, when they are not maneuvering, jet aircraft tend to fly at relatively
constant q. When the air density decreases with altitude the flight speed increases to keep the q relatively constant. It can be shown
mathematically (which I will leave out, unless anyone wants it) that an aircraft flying at 65,000 ft with the same q as it had at sea level would have
a mass flow through the engine of about 25% the amount it had at sea level—about 3.8 times as much as the 7% it would have under static conditions.
It would therefore have 25% the thrust level and 25% the fuel burn. The pressure and temperature inside the combustion chamber would be very similar
to the values at sea level, so no special fuel or fuel additives would be necessary to keep the flame lit.
There’s nothing magical about the 65,000 ft altitude, either. This process continues smoothly as long as you can continue to fly faster and higher.
One limit you might reach is the red line speed limit for the airframe (around Mach 0.7, for the U-2). At that point, you can no longer increase
speed to make up for the declining air density and if you try to go higher, the available excess thrust will quickly go to zero. Alternatively, the
thrust level might continue to decline, until you eventually reach a point where the thrust available is no longer enough to overcome the drag. As I
understand it, the U-2 routinely cruises within a few knots of the speed and altitude where these two curves of declining performance cross—which
leaves almost no room for pilot error.
In summary, the main thing you need for subsonic, turbojet flight at altitudes of 65,000 ft and higher is an engine that has about 4 times as much
thrust at sea level as is needed at the cruise altitude. That’s mainly how the U-2 does it, which explains why it always ascends from take off at
sea level like a homesick angel (flight path angle of 45 to 60 degrees).