# Overall pressure ratio

In aeronautical engineering, overall pressure ratio is the ratio of the stagnation pressure as measured at the front and rear of the compressor of a gas turbine engine. Generally speaking, a higher overall pressure ratio implies higher efficiency, but the engine will usually weigh more, so there is a compromise.

## History of overall pressure ratios

Early jet engines had limited pressure ratios due to construction inaccuracies of the compressors and various material limits. For instance, the Junkers Jumo 004 from World War II had an overall pressure ratio 3.14:1. The immediate post-war SNECMA Atar improved this marginally to 5.2:1. Improvements in materials, compressor blades, and especially the introduction of multi-spool engines with several different rotational speeds, led to the much higher pressure ratios common today. Modern civilian engines generally operate between 30 and 40:1. The three-spool Rolls-Royce Trent 900 used on the Airbus A380, for instance, has a pressure ratio of about 39:1.

## Advantages of high overall pressure ratios

A high overall pressure ratio permits a larger area ratio nozzle to be fitted on the jet engine. This means that more of the heat energy is converted to jet speed, and energetic efficiency improves. This is reflected in improvements in the engine's specific fuel consumption.

## Disadvantages of high overall pressure ratios

One of the primary limiting factors on pressure ratio in modern designs is that the air heats up as it is compressed. As the air travels through the compressor stages it can reach temperatures that pose a material failure risk for the compressor blades. This is especially true for the last compressor stage, and the outlet temperature from this stage is a common figure of merit for engine designs. For civilian engines, the pressure ratio can be adjusted as the aircraft climbs, allowing it to offset some of the heat load through the lowered pressure and temperature of the high-altitude air. This is one of the many reasons airliners climb to high altitude as quickly as possible.

Military engines are often forced to work under conditions that maximize the heating load. For instance, the General Dynamics F-111 was required to operate at speeds of Mach 1.1 at sea level. As a side-effect of these wide operating conditions, and generally older technology in most cases, military engines typically have lower overall pressure ratios. The Pratt & Whitney TF30 used on the F-111 had a pressure ratio of about 20:1, while newer engines like the General Electric F110 and Pratt & Whitney F135 have improved this to about 30:1.

An additional issue is weight: a higher compression ratio implies a heavier engine, which in turn costs fuel to carry around. Thus, for a particular construction technology and set of flight plans an optimal overall pressure ratio can be determined.

## Examples

Engine Overall pressure ratio Major applications Notes
General Electric GE90 42:1 777
General Electric CF6 30.5:1 747, 767, A300, MD-11, C-5
General Electric F110 30:1 F-14, F-15, F-16
Pratt & Whitney TF30 20:1 F-14, F-111
Rolls-Royce/Snecma Olympus 593 15.5:1 Concorde The Concorde's Olympus engines received additional compression from its supersonic inlet, yielding an effective overall pressure ratio of 80:1.[1]

## Differences from other similar terms

The term should not be confused with the more familiar term compression ratio applied to reciprocating engines. Compression ratio is a ratio of volumes. In the case of the Otto cycle reciprocating engine, the maximum expansion of the charge is limited by the mechanical movement of the pistons (or rotor), and so the compression can be measured by simply comparing the volume of the cylinder with the piston at the top and bottom of its motion. The same is not true of the "open ended" gas turbine, where operational and structural issues are the limiting factors. Nevertheless the two terms are similar in that they both offer a quick way of determining overall efficiency relative to other engines of the same class.

The broadly equivalent measure of rocket engine efficiency is chamber pressure/exit pressure, and this ratio can be over 2000 for the Space Shuttle Main Engine.

## Compression ratio versus overall pressure ratio

For any given gas mix compression ratio and overall pressure ratio are interrelated as follows:

 CR PR 1:1 3:1 5:1 10:1 15:1 20:1 25:1 35:1 1:1 4:1 10:1 22:1 40:1 56:1 75:1 110:1

The reason for this difference is that compression ratio is defined via the volume reduction,

$CR=\frac{V_1}{V_2}$,

Pressure ratio is defined as the pressure increase

$PR=\frac{P_2}{P_1}$.

From the combined gas law we get:

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \Rightarrow \frac{V_1}{V_2}=\frac{T_1}{T_2} \frac{P_2}{P_1} \Leftrightarrow CR=\frac{T_1}{T_2} PR$

Since T2 is much higher than T1 (compressing gases puts work into them, i.e. heats them up), CR is much lower than PR.