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An introductory look at jet engine performance may be had in a cursory but intuitive way with the aid of diagrams and photographs which show features that influence the performance. An example of a diagram is the [[velocity triangle]] which in everyday life tells cyclists why they struggle against wind from certain quarters (and where head-on is worst) and in the engine context shows the angle air is approaching compressor blades (head-on is best for low losses). The use of velocity triangles in compressors and turbines to show the all-important angle at which air approaches the blading goes back to early steam turbines.<ref>https://arc.aiaa.org/doi/abs/10.2514/1.9176?journalCode=jpp,"Ideas and Methods of Turbomachinery Aerodynamics: A Historical View", Cumpsty and Greitzer, Fig. 1</ref>
Photographs show performance-enhancing features such as the existence of bypass airflow (increased [[propulsive efficiency]]) only visually obvious on engines with a separate exit nozzle for the bypass air. They are also used to show rarely seen internal details such as honeycomb seals which reduce leakage and save fuel (increased thermal efficiency), and degrading details such as the rub marks on centrifugal impeller blades which indicate loss of material, increased air leakage and fuel consumption.
Jet engines perform in two basic ways, the combined effect of which determines how much waste they produce as a byproduct of burning fuel to do thrust work on an aircraft.<ref>An engine applies a thrust force to a stationary aircraft and thrust work is done on the aircraft when it moves under the influence.</ref> First is an energy conversion as burning fuel speeds up the air passing through which at the same time produces [[waste heat]] from component losses (thermal efficiency). Second, part of the power which has been given to the air by the engine is transferred to the aircraft as thrust work with the remaining part being [[kinetic energy]] waste in the wake (propulsive efficiency). The two efficiencies were first formulated in the 19th century for the [[steam engine]] (thermal efficiency <math>\eta_{th}</math>) and the ship's propeller (propulsive or Froude efficiency <math>\eta_{pr}</math>).
A visual introduction to jet engine performance, from the fuel efficiency point of view, is the Temperature~entropy (T~s) diagram. The diagram originated in the 1890s for evaluating the thermal efficiency of steam engines. At that time entropy was introduced in graphical form in the T~s diagram which gives thermal efficiency as a ratio of areas of the diagram. The diagram also applies to air-breathing jet engines with an area representing kinetic energy<ref name="Propulsion and Power">{{Cite journal |last1=Kurzke |first1=Joachim |last2=Halliwell |first2=Ian |date=2018 |title=Propulsion and Power |url=https://link.springer.com/book/10.1007/978-3-319-75979-1 |journal=SpringerLink |language=en |doi=10.1007/978-3-319-75979-1|isbn=978-3-319-75977-7 |url-access=subscription }}</ref> added to the air flowing through the engine. A propulsion device, a nozzle, has to be added to a gas turbine engine to convert its energy into thrust. The efficiency of this conversion (Froude or propulsive efficiency) reflects work done in the 1800s on ship propellers. The relevance for gas turbine-powered aircraft is the use of a secondary jet of air with a propeller or, for jet engine performance, the introduction of the bypass engine. The overall efficiency of the jet engine is thermal efficiency multiplied by propulsive efficiency ( <math>\eta_o = \eta_{th} \eta_{pr}</math>).
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Thrust is generated inside a jet engine by internal components as they energize a gas stream.<ref>{{Cite web |date=2023-10-24 |title=Jet engine {{!}} Engineering, Design, & Functionality {{!}} Britannica |url=https://www.britannica.com/technology/jet-engine |access-date=2023-11-16 |website=Britannica |language=en}}</ref>
Fuel energy released in the [[combustor]] is accounted for in two main categories: acceleration of the mass flow through the engine and residual heat.<ref>{{Cite book |url=http://archive.org/details/sim_journal-of-aircraft_september-october-1966_3_5 |title=Journal of Aircraft September-October 1966: Vol 3 Iss 5 |date= September 1966|publisher=American Institute of Aeronautics and Astronautics |via=Internet Archive |language=English}}</ref>
Acceleration of the flow through the engine causes simultaneous production of kinetic energy accompanying the thrust-producing backward momentum. The kinetic energy is left behind the engine without contributing to the thrust power<ref>'Jet Propulsion For Airplanes', Buckingham, NACA report 159, p. 85</ref> and is known as residual velocity loss. The thrust force from a stationary engine becomes thrust power when an aircraft is moving under its influence.
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