# Jet Propulsion/Performance

Engine Performance describes the most important attributes of the engine for the aircraft. These are primarily the thrust available to propel the aircraft, and fuel consumption.

## Fuel Consumption
### Specific Fuel Consumption (SFC)

Typically quoted in mg/Ns for engines. Is usually much higher at cruise than at static. A typical high bypass engine will consume about 8mg/Ns at maximum takeoff and 15mg/Ns at maximum cruise thrust. Typical large engines today have TO thrusts approaching 480kN. Typical cruise SFC is around 15mg/Ns. A low bypass military engine will have TO SFC of about 18mg/Ns which rises to 50mg/Ns if afterburner is used.
Available thrust is usually quoted in kN or lbs. Fuel efficiency is usually quoted as a specific fuel consumption
$SFC={\frac {fuelflow,(g/s)}{thrust,(kN)}}$
SFC can only be directly compared at a specific flight condition, usually a nominal cruise condition.

## Specific impulse

Specific impulse is defined as the thrust (N) divided by the fuel weight flow rate (N/s). The resulting measure is usually quoted in seconds and defines the weight fraction that is necessary to give a particular delta V for a rocket or range for an aircraft with a given lift to drag ratio.
For a jet engine the specific impulse can be determined from the specific fuel consumption. The product of SFC and Specific impulse is one. The conversion factor between SFC (mg/Ns) and Specific impulse (s) is 102,000mg/N (1E6mg kg-1 /9.81N kg$^{-1}$). A high bypass turbofan engines have cruise SFC around 15mg/Ns, and takeoff SFC of 8mg/Ns.
Table 9.2: Specific impulse of propulsion technologies :
| Engine | SFC (mg/Ns) | Specific impulse (s) | Energy Density (MJ/kg) |
| Turbofan (Takeoff, M0.1) | 7.5 | 13,600 | 43 |
| Turbofan (Cruise, M0.9) | 15 | 6,800 | 43 |
| Turbofan (with Afterburning, M1.5) | 30 | 3,400 | 43 |
| Solid rocket (including oxidizer) | 408 | 250 | 3.0 |
| LH2LO2 rocket (including oxidizer) | 227 | 450 | 9.7 |
* Example 9.2: Specific impulse of propulsion technologies
* An engine with SFC of 15mg/N-s will have a specific impulse of 6800s.
An air-breathing jet engine typically has a much larger specific impulse than a rocket: a turbofan jet engine may have a specific impulse of 7000 seconds or more at sea level whereas a rocket would be around 200-400 seconds. Air-breathing engines are more propellant efficient because the actual exhaust speed is much lower, since the air provides the oxidizer and because (inert) air is added to the reaction mass. The actual exhaust velocity is lower and the jet engine uses far less energy to generate equal thrust.
We can also see the effect of an airbreathing engine acting on an infinitely large reaction mass in propulsion impulse figure below. In such a case the entire energy goes into accelerating the vehicle rather than the exhaust from the engine. Thus also explains why the space elevator is much more energy efficient to get vehicles into space since the climbers are close to acting on an infinitely large mass. The energy requirements are still very large. What we can also see from the diagram below is that with increasing speeds the reaction engines become progressively more "efficient", getting closer to the infinite mass case.
* Figure 9.2: Specific Impulse ranges for different kind of propulsion engines compared

## Range

The Breguet Range Equation gives the range achieved by a vehicle. For a constant L/D ratio of the aircraft
$Range=uI_{sp}\left({\frac {L}{D}}\right)\ln \left({\frac {W_{initial}}{W_{final}}}\right)$
where
R = distance flown (m)
u = velocity (m/s)
I$_{sp}$ = specific impulse (s)
L/D = lift-to-drag ratio (dimensionless)
W$_{initial}$ = gross aircraft weight at the start of cruise (kg)
W$_{final}$ = gross weight at the end of cruise (kg)
* Example 9.3: Breguet Range Equation
* For an aircraft with 50% fuel, velocity of 600 m/s, an L/d of 10 and engines with a specific impulse of 3000s the range is:
* $R=(600m/s)(3000s)(10)\ln(100\%/50\%)=12,477km$

## Endurance

The Breguet Range Equation can be modified to give endurance. For a constant L/D ratio of the aircraft
$Endurance=Range/u=I_{sp}\left({\frac {L}{D}}\right)\ln \left({\frac {W_{initial}}{W_{final}}}\right)$
* Example 9.3: Breguet Range Equation
* For an aircraft with 50% fuel, an L/d of 20 and engines with a specific impulse of 3000s the endurance is:
* $Endurance=(3000s)(20)\ln(100\%/50\%)=41588s=11.55hours$

## Thrust

The thrust of a jet engine is determined by the difference in momentum of the fluids flowing in and out of the engine. If the mass of fuel added is negligible then the thrust is:
    $T={\dot {m}}(u_{exit}-u_{inlet})$
Engines are certified to deliver standard thrusts depending upon atmospheric conditions. Thrust is typically measured in kN or lbs.
Engines are certified to deliver standard thrusts depending upon flight conditions. Thrust is typically measured in kN or lbs. A 'rating' is a predefined power setting that the pilot can select which may be appropriate for particular flight conditions. Rating terminology differs between civil and military aircraft, reflecting the different requirements of these types of aviation.

## Aircraft Ratings

The following ratings are typical of commercial airliners. The aircraft/engine manufacturer will have to declare two principal ratings to the certifying authorities, since these define the safe limits of operation of the engine/aircraft - these are the Maximum Take-Off (MTO) rating, and the Maximum Continuous Thrust (MCT or MCN) rating.

### Maximum Takeoff thrust(MTO)

This is the maximum thrust that the engine can deliver for 5 minutes in the take-off envelope of the aircraft. Peak thrust is usually achieved when the engine is static, however the most demanding condition for a modern turbofan engine is end-of-runway or lift-off conditions, typically at about 0.25Mn. This condition usually generates the highest stresses and temperatures in the engine, hence use of this rating is only permitted for up to 5 minutes of operation.
It is used, as the name suggests, for take-off when the aircraft is at its heaviest and has to be accelerated to take-off speed in a finite runway distance. The higher the thrust available from the engine, the shorter the runway can be, or the greater the aircraft payload can be. This affects which airports an aircraft can be operated from, and the economics of operation. As an alternative to payload, a higher thrust rating allows more fuel load to be carried into the air, so extending range of operation. These trade-offs between available thrust, runway length, aircraft weight and range may need to be assessed for each flight, and is part of a commercial pilots preparation prior to take-off. An aircraft may take-off with less than maximum take-off thrust to reduce wear on the engine and extend its life. This is usually termed a 'reduced thrust' take-off, and is used to reduce engine maintenance costs.
It is a condition of certification that an aircraft should be able to take-off if one engine fails at the most critical point in the take-off run, when it is going too fast to be able to come to a safe stop in the remaining runway. In the case of twin engine aircraft, they have to be capable of taking off on one engine, so that in normal operation 'de-rate' is usually applied as an excess of thrust is available.
If an engine exceeds its 'redline' speeds or temperatures when running at MTO thrust, it is no longer considered airworthy.
Sometimes referred to as 'TOGA' thrust, short for take-off/go-around.

### Maximum Continuous thrust (MCT)

Outside the MTO flight envelope, the MCT rating defines the maximum thrust that can be demanded by the pilot from the engine. As such, it has particular significance with respect to engine failure in flight, as the aircraft will have to proceed to its destination or nearest diversion airport at max continuous thrust. If the engine cannot achieve this thrust level whilst staying within it operating limits for engine speed and temperature, (them 'amber line'), it is no longer considered airworthy.

### Maximum Climb thrust (MCL)

This is the thrust rating the manufacturer recommends be used during the climb phase of a typical flight. It may be the same as max continuous thrust, and usually is for a three or four engined aircraft. The top of the climb phase is typically the most challenging condition for a turbofan engine outside the take-off regime, and is a critical design requirement. De-rate can be applied to MCL thrust to extend engine life, but at the cost of a slower time to climb and slightly increased trip fuel consumption.

### Maximum Cruise thrust (MCR)

Sometimes defined, but not a particularly useful rating since in cruise the pilot/autopilot will use the thrust required to maintain constant altitude and air speed to meet with air traffic control requirements.

### Flight Idle

The idle rating is the minimum thrust that can be used whilst the aircraft is in flight. It is largely defined by the requirement to keep the engine running, possibly supplying secondary services to the aircraft such as hydraulic and electrical power, and, especially at high altitude, to supply passenger air at a minimum pressure. The flight idle rating is important in that the lower it is, the quicker the aircraft can descend (without going into a dive). It is often determined by stability considerations such as flutter and surge margin.

### High or Approach idle

In the final phases of approach to landing it is important to be able to provide rapid response to throttle movements, this may require the engine to be running at a higher speed than ideal to be able to provide rapid acceleration if required. There may be a maximum response time requirement to achieve 'TOGA' thrust if a landing is aborted.

### Ground Idle

Used for maneuvering on the ground. Typically defined by the need to keep the engine running and supplying power and services to the aircraft. Generally, the lower this value the better, since brake wear is a significant factor in aircraft running/maintenance costs.

### Example ratings

The figure below shows the typical behavior of a modern turbofan. The orange curves show maximum cruise thrust at altitude. The take-off thrust is about 25% higher than the cruise thrust at sea level since it is permitted for short durations only.

## Military Ratings

Combat aircraft have very different requirements to civil aircraft, and different rating terminology is used, especially for aircraft using reheat or afterburning for thrust augmentation.

### Military Thrust

Typically used to define the maximum available thrust without use of reheat. Sometime referred to as maximum 'dry' thrust.

### Maximum Takeoff thrust

This is the maximum thrust that the engine can deliver for 5 minutes at standard sea level atmosphere. Peak thrust is usually achieved when the engine is static.

### Maximum Climb thrust

This is the maximum thrust that the engine can deliver for 5 minutes at standard sea level atmosphere.

### Maximum Cruise thrust

The thrust allowable for unlimited flight duration at the design altitude.

### Maximum Continuous thrust

Also called the maximum maneuver thrust. Sometimes is same as maximum cruise.

### Example: Installed thrust ratings

The figure below shows the typical behavior of a modern turbofan. The orange curves show maximum cruise thrust at altitude. The TO thrust is significantly higher than the cruise thrust at sea level since it is permitted for short durations only..
* Figure 9.5: Turbofan thrust and SFC under different operating conditions