# Jet Propulsion/Mechanics

## Engine ratings

Engines are certified to deliver standard thrusts depending upon atmospheric conditions. Thrust is typically measured in kN or lbs.

### 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.

### Specific fuel consumption

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.

### Example ratings

The figure below shows the typical behaviour 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..

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.

## 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. For example an engine that has an SFC of 15mg/N-s will have a specific impulse of 6800s. Current turbofan engines have cruise SFC below 15.

For a chemical rocket the specific impulse ranges to about 500s.

## 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:

${\displaystyle T={\dot {m}}(u_{exit}-u_{inlet})}$

## Performance

### Range

The Breguet Range Equation gives the range achieved by a vehicle. For a constant L/D ratio of the aircraft

${\displaystyle Range=uI_{sp}\left({\frac {L}{D}}\right)\ln \left({\frac {W_{initial}}{W_{final}}}\right)}$

where

R = distance flown (m)

u = velocity (m/s)

Isp = specific impulse (s)

L/D = lift-to-drag ratio (dimensionless)

Winitial = gross aircraft weight at the start of cruise (kg)

Wfinal = gross weight at the end of cruise (kg)

### Example

For an aircraft with 50% fuel, velocity of 600 m/s, an L/d of 10 and engines with a specific impulse of 3000 the range is:

${\displaystyle R=(600m/s)(3000s)(10)\ln(2)=12,477km}$

### Maneuver

Jet Propulsion/Thrust

Jet Propulsion/Drag