Photo: A view of a G450's engine, from behind, from Eddie's collection.
The twin-spool, axial flow, computer controlled, high-bypass ratio, fan jet engine is a marvelous creation. Right around 1970 it was truly perfected with the advent of the General Electric CF-6. But, if like me, you were brought up on a lesser jet, you may have had a few failures and fires along the way. Now that they've become so much more reliable, we tend to take them for granted. We may not fully realize why the engine behaves as it does. Engine spool-up time can be life threatening if not understood. (See the case of: Mishaps / Gulfstream 550 N535GA.) Thrust measurement isn't as straight forward as you might think and the proportion of thrust to power level angle isn't linear.
Do you need to know this to fly a jet airplane? No. But knowing more than just "push means fast, pulls means slow" will help you operate more efficiently and to diagnose what ails your engines should that time ever come. Most of this comes from the references listed below. My personal unsourced notes are shown in blue.
Figure: Principles of propulsion, from Hurt, figure 2.5.
[ATCM 51-3, Pg. 105]
F = ma
But what does that really mean? The mass being accelerate aft is fuel and air mixture. The mass is pushing against various components of the engine which in turn push the engine (and therefore the airplane) forward. On some aircraft, like the early KC-135A, water is added to the fuel air mixture to increase the mass being accelerated.
Figure: Centrifugal compressor, from Hurt, figure 2.7 (top).
[Hurt, pg. 109]
Figure: Axial compressor, from Hurt, figure 2.7 (bottom).
[Hurt, pg. 111]
Figure: Combustion chamber, from Hurt, figure 2.8 (top).
[Hurt, pg. 111]
The typical introductory text might leave you to believe this is where thrust comes from: the gas explodes aft, pushing the combustion chamber forward. But most burner cans are hardly the robust structures that can withstand this amount of force. There is something else in play here . . .
Figure: Turbine section, from Hurt, figure 2.8 (bottom).
[Hurt, pg. 113]
The rotating turbine blades are where all the heat and pressure are converted into the mechanical energy used to rotate the forward fan (or propeller), run the accessories, and most importantly to push the center shaft forward. This is where thrust gets transmitted to the airplane and this is another reason the bearings holding that shaft in place are so critical.
Figure: Centrifugal compressor engine, from Eddie's notes.
A centrifugal compressor uses a series of blades mounted on a disk to throw incoming air outboard to a cylindrical shaft which funnels the air aft. The air is thus compressed and made ready for combustion. A centrifugal compressor is relatively cheap to make because the required tolerances between moving parts are not as critical as with an axial flow compressor. The centrifugal compressor, however, is not capable of the high compression rates needed to produce very high levels of thrust. The centrifugal compressor engine as a relatively large front area, increasing parasite drag. The thrust to weight ratio of a centrifugal compressor is much lower than of an axial flow compressor.
Example: The T-37 has two centrifugal compressor engines. Many modern auxiliary power units also use centrifugal compressor engines.
Figure: Axial flow engine, from Emoscopes (Creative Commons).
An axial compressor produces much higher pressure than a centrifugal compressor and therefore makes much higher thrust possible at much higher efficiencies. (You get more thrust for less fuel.) Single-spool axial compressor engines do require complicated blade angle control systems to achieve higher pressure ratios, complicating the design and reducing reliability.
Example: The T-38 has two axial flow engines.
Figure: Twin spool engine, from K. Aainsqatsi (Creative Commons).
A twin spool design normally has the front compressors attached to the rear turbines using an inner shaft, with a higher pressure compressor and a higher pressure turbine connected with an outer shaft. Since the shafts are free to rotate independently, the engine can be designed for even higher compression without the need for complicated automatic blade control systems.
Example: The KC-135A has four twin-spool engines engines.
Figure: Fan bypass compressor engine, from K. Aainsqatsi (Creative Commons).
A fan bypass engine takes some of the compressor or fan air outside of the engine core to bypass the combustion section. The mixing of colder and lower speed air with the hotter and higher speed exhaust allows for higher turbine temperatures and thrust while also serving to lower the noise level of the engine.
Example: The G450 has two fan bypass engines.
Figure: Bypass fan compressor engine, from K. Aainsqatsi (Creative Commons).
A high bypass fan engine normally includes a large first fan surrounded by a separate duct, allowing a majority of the fan air to bypass the engine. The fan acts much like a propeller in a turboprop, without the problems of propeller slipstream and drag.
Example: The Boeing 747 has four high bypass fan engines.
Figure: Engine acceleration times, from Davies, figure 4.11
[Davies, page 59.]
There have been two contrary trends in jet engine design when it comes to spool-up time. Full Authority Digital Engine Control (FADEC) should give you all the power you need as quickly as the engine can tolerate it. But the sheer size of modern engines makes it harder to accelerate from lower speeds just due to the centrifugal mass of the fans and compressors. It has been my experience that the larger the engine, the longer to spool-up time from low RPMs.
This slow spool-up tendency from lower RPMs can have adverse affects on a pilot not ready for it. In a G450, for example, if the flaps are set to less than 22° the engines will not go into "high idle" mode, significantly increasing engine spool-up time. More about this: G450 Systems / Powerplant Control / Idle Thrust Management.
Figure: Rolls-Royce turbofan engine test facility, Derby, UK, from Cherry Salvesen (Creative Commons).
Jet engines are commonly rated in terms of static thrust. The engine is restrained from moving and the "push" is measured with scales. In actual use, the true thrust is normally less than static thrust, since exhaust pressure tends to be constant and input pressure increases with aircraft velocity, so the acceleration goes down. There are no scales to measure this.
We can measure drag in a wind tunnel and when the aircraft is in steady flight we know thrust equals drag and can therefore be approximated.
Engine thrust can also be approximated by the engine's number of revolutions per minute, RPM. These numbers are converted to a percentage of a rated value for ease of reading. For twin spool engines, the inner spool is often connected to the most forward and aft sections and is called N1, the outer spool is called N2. Thrust normally does not vary in a linear relationship with RPM. In a typical engine thrust can be idle around 50%, a quarter of maximum at 90%, half at 95%, and maximum at 100%.
A common method of presenting the pilot with an approximation of engine thrust is EPR, engine pressure ratio. In its basic form, pressure probes are positioned at the inlet and outlet, the outlet pressure is divided by the inlet to determine EPR. This number is not an accurate representation of thrust because the pressure pattern of the exhaust tends to be higher in the center and lower in the outer portions of the airflow. It is, however, good enough since it gives the pilot a way of telling relative power settings from idle to maximum.
Later engines use ambient air pressure instead of air inlet pressure, since it is close enough. Many engines do not measure outlet pressure because the temperatures tend to shorten the lives of probes. Instead these engines choose intermediate stages of pressure, such as aft of the compressor. EPR, then, has very little to do with pressure ratios and is nothing more than a fictitious number designed to give pilots an idea of relative thrust levels.
Regardless of how you measure thrust it is important to realize the metric you are using in the cockpit does not correlate one-to-one with thrust. . .
Figure: Variation of thrust with rpm, from Hurt, figure 2.10 (middle).
[Hurt, pg. 117] The variation of thrust output with engine speed is a factor of great importance in the operation of a turbojet engine. By reasoning that static pressure changes depend on the square of the flow velocity, the changes of pressure throughout the turbojet engine would be expected to vary as the square of the rotative speed, N. However, since a variation in rotative speed will alter airflow, fuel flow, compressor and turbine efficiency, etc., the thrust variation will be much greater than just the second power of rotative speed. Instead of thrust being proportional to N2, the typical fixed geometry engine develops thrust approximately proportional to N3.5. The turbojet engine usually has a strong preference for high RPM to produce low specific fuel consumption.
Figure: Relationship between power lever position and thrust, from Davies, figure 4.10.
Handling the Big Jets was written in 1967 and remains my favorite text on how to fly airplanes. But a lot has happened since then. If you are not flying an airplane with a Fully Automatic Digital Engine Control (FADEC), then all that follows probably applies to you. If you are flying a FADEC-equipped airplane, it might apply to you. I can show you how it works on a G450, below. You will have to research your aircraft to be sure.
[Davies, page 57.] [The figure] shows quite simply thrust lever position against thrust, from full ahead to full astern, for both a piston propeller installation and a pure jet installation. These diagrams do not represent particular installations and the characteristics have been deliberately exaggerated in order to accentuate the differences. The following facts are all important in terms of flight handling qualities:
[G450 Aircraft Operating Manual, §2A-76-30 ¶1.]
Figure: Engine thrust management system overview, from G450 Aircraft Operating Manual, §2A-76-00, figure 2.
This mismatch between power lever angle and actual thrust grew from the limitations of mechanical fuel controls and the inherently nonlinear relationship of thrust to RPM. Modern aircraft can easily fix this with computeried engine control. In the case of a G450, the "Throttle Resolver Angle" is linear to EPR and skewed toward the middle in relation to RPM.
Portions of this page can be found in the book Flight Lessons 1: Basic Flight, Chapter 6.
Air Training Command Manual 51-3, Aerodynamics for Pilots, 15 November 1963
Davies, D. P., Handling the Big Jets, Civil Aviation Authority, Kingsway, London, 1985.
Gulfstream G450 Aircraft Operating Manual, Revision 35, April 30, 2013.
Hurt, H. H., Jr., Aerodynamics for Naval Aviators, Skyhorse Publishing, Inc., New York NY, 2012.