# Why does Engine Pressure Ratio (EPR) rise as thrust levers are pushed forward?

I'm looking for an answer that at least addresses the fundamental thermodynamics of a jet engine.

Jet engines use a Brayton cycle to get useful work out of a heat source. An ideal Brayton cycle engine has the input and output pressure be the same. If Exhaust pressure is greater than inlet pressure, then that's becoming closer to Diesel cycle further from a Brayton cycle (And to those who feel like correcting this point, a diesel cycle has many forms beyond what is typically thought of as a diesel engine but that's not want I want to talk about. Diesel cycle only cares about adiabatic compressions/expansion, constant pressure combustion, and V1 = V4, but I do not wish to dwell on this).

Also, when looking at nozzle design, we ideally try for the exhaust pressure to be equal to ambient pressure as opposed to an over expanded nozzle where the exhaust pressure is less than ambient or an under expanded nozzle where the exhaust pressure is more than ambient.

Both of these two things together seem to indicate that a jet engine would be designed to have the intake and exhaust pressure be the same (ie the EPR should be 1). Is there something that would make achieving this in the real world challenging? Or are the engine designers not even trying to have the exhaust pressure be equal to the ambient pressure? If the latter is the case, why would you not want to try to have the engine operate as closely to the ideal cycle and nozzle design as you could? If it's the former, what conditions would contribute to this becoming more challenging?

I get that if an engine has fixed geometry, if you change the amount of heat added in combustion, it will change the EPR, but there are plenty of jet engines have variable exit geometry. Therefore, I would think you could vary the geometry to get the ideal exhaust pressure. Even if you couldn't vary the engine geometry and only design for 1 power setting, I would expect that it is most efficient where the engine is expected to be used the most. For example, if I expect my engine to spend most of its time being used at 35,000 ft and generating a specific amount of thrust, I would design the nozzle so that the discharge pressure would be whatever ambient is in those conditions. That would translate in the real world to the engine operating at or very close to EPR of 1 during cruise.

It is my understanding that this is not the case, and if that's a correct understanding, I am missing a piece to the puzzle to make sense of why things are the way that they are.

• Related reading here. Mar 13 at 17:02
• @RobertDiGiovanni Not quite related, this isn't about FPR or BPR but EPR... why all those abbreviations! ;-) FPR and BPR are design parameters, EPR is a control parameter. Mar 14 at 14:43

What makes you think the EPR should be 1.0? Note that we are using stagnation/total pressures to determine the EPR, we are not using the static pressures. Although the nozzle expands to ambient pressure, the total pressure is significantly higher due to the fact that the nozzle is producing a high velocity jet stream. The velocities are quite different from the inlet and exhaust mass flow! If not you do not have thrust. EPR is a measure for how hard the engine is working and from that we can derive how much thrust is generated (or if the thrust level is always the same, regardless of engine condition). The higher the EPR the harder the engine works (more fuel is added the faster the spools spin). In afterburning turbofans the use of EPR can be used in afterburning mode to schedule the nozzle area (EPR is kept constant during AB mode); this basically maximizes the spool speeds of the turbofan to MIL power (if you would not open the nozzle, the fan would stall).

Do note that the EPR is defined as the nozzle exit pressure over the fan intake pressure, but more commonly the mixer (where fan and core flow meet in the afterburner) or HPT turbine exit pressure (both total pressures) is used for calculating EPR, these are more easily measured.

We can experiment with the ideal nozzle expansion using an afterburning turbofan model in a (dry/non-afterburning) simulation.

The latter image shows the representation of Pt6 over Pt2 in the upper part and the Pt9 over Pt2 in the lower part.

The following image shows the EPR values for a deteriorated engine as function of thrust, you see that EPR is a direct measure for the thrust level. A deteriorated engine has less thrust for the same combustor exit temperature, and also lower EPR value. This makes the EPR parameter valuable for engine control purposes.

Keeping EPR constant (at the MIL power setting) and increasing the fuel flow in the afterburner and opening the nozzle (calculated area based on added fuel and constant EPR) you will see the thrust increase the more fuel is added:

• I did not realize that it was stagnation pressure not static pressure, but then adding afterburner would raise the EPR, which it sounds like you're saying it doesn't. The whole point of AB is to raise the heat of the exhaust, which means we can extract more kinetic energy, which means more thrust. But that higher speed of the exhaust will have a higher stagnation pressure than it otherwise would, so the EPR should rise when AB is on when compared to mil power should it not? Mar 15 at 4:37
• @youguysfail No, it would not rise, it is kept constant by opening the nozzle. In fact the whole engine in front of the AB doesn't even realize the AB is on, the engine runs in MIL power setting. If you wouldn't open the nozzle during AB, yes the EPR would rise, but then the fan will stall. In AB the EPR is the same as in MIL power, for every AB setting. Mar 15 at 6:36
• Now I'm even more confused. If the pressure is the same in the exhaust both with and without the AB, then the stagnation pressure with AB MUST be higher with AB than without. This is because stagnation pressure is static pressure + .5*density*velocity^2 [Or it's P(1+(k-1)/2M^2)^((k-1)/k) for compressible flow, either way static pressure goes up as velocity goes up]. Since AB raises the velocity but keeps the static pressure the same, that means the stagnation pressure has to go up too. If the stagnation pressure goes up, so too does the EPR. Where am I going wrong here? Mar 18 at 2:22
• The EPR defined by Pt6/Pt2 is kept constant, as described, how would you measure the pressure at station 9, hence the used EPR metric. Static pressure goes down due to afterburning, see e.g. aviation.stackexchange.com/a/91876, due to heating you introduce an additional pressure loss. I think EPR (if defined as Pt9/Pt2) goes down instead of up, download a simulation program and see for yourself. Mar 18 at 12:39
• The simulation is useful but I'd also like to understand they key general key concepts here. Thanks for your help though it is much appreciated. Mar 20 at 13:47