Specific Thrust Calculator

The specific thrust answers the direct question of how much thrust a jet engine can produce per kilogram of air per second. The answer is obtained by dividing the thrust by the mass flow rate of the inducted air. This calculator allows you to find out the remaining values from the entered ones, thus calculating the specific thrust. In addition, based on the desired specific thrust and the mass flow rate of air, you can calculate the required thrust or how much air an engine needs to process to achieve a certain thrust.

What specific thrust measures:

Specific thrust is the ratio of thrust produced by a propulsion system to the mass flow rate of air through that propulsion system per second. The units for this result are newton-seconds per kilogram, which simplifies to meters per second. It's not an accident that dividing thrust by the mass flow rate results in a velocity.

Physically this value represents the increase in speed that the engine imparts to the air. The engine sucks air in at flight speed and expels it at a higher speed. The difference of these speeds, combined with the volume of air involved, is what specific thrust captures. A high number means that a small amount of air is being expelled very quickly. A low number means that a large amount of air is being moved forward slowly. Both can produce the same amount of thrust but the engines are completely different.

The formula for specific thrust is:

The specific thrust is the ratio of thrust to mass flow rate of air.

In this case, I_s is the specific thrust, F is the net thrust, and m with a dot above it is the mass flow rate of air, i.e. the mass of air per unit time. In SI units, dividing the Newtons of thrust by the kilograms per second of mass flow rate gives a specific thrust in meters per second.

Since this equation contains three quantities, it can be rearranged to calculate the missing quantity.

Example calculation:

For example, a military turbofan engine has a rated thrust of 75 kilonewtons and an air intake rate of 250 kilograms per second. The thrust is first converted to base units, which gives 75,000 newtons, then divided by the mass flow rate.

So the speed of the air leaving is about 300 meters per second faster than that of the incoming air. If these values are entered, then the specific thrust field will display 300. Conversely if the thrust is left blank and instead 300 is entered as the specific thrust, the calculator will return the required thrust of 75 kilonewtons for this specific thrust.

Why can it happen with the same motor that 300 or 30 are displayed?

The specific thrust is a value that depends on the flight conditions and can therefore be easily confused. In a static test, the aircraft does not move so the incoming air starts at rest and the velocity gain exactly matches the speed of the jet exhaust. In this situation, the high-bypass turbofan has a figure around 300 meters per second while the turbojet is closer to 800 meters per second.

During cruise flight the airplane is already moving at a high speed so the engine only needs to add a small amount of velocity to the airflow. Even with the same fan, net thrust - that is, the value obtained by subtracting the flight speed from the exhaust speed - will be on the order of tens of meters per second. This is the number often quoted for the engines of large passenger jets. Although it's the same hardware, operating conditions are different. By opening up the "flight speed" section in this calculator you can toggle between these different scenarios based on the relationship "exhaust speed = specific thrust + flight speed."

Why do engine developers value specific thrust?

Specific thrust is one of the first numbers that designers specify and it has far-reaching effects on almost all other aspects. Higher specific thrust leads to a more compact engine with faster response time and supersonic capability, but also higher fuel consumption and noise levels. Lower specific thrust requires a larger fan moving more air, which in turn leads to higher bypass ratio, heavier engine, and significantly lower fuel consumption at subsonic cruise flight.

The bypass ratio is a key lever. A turbofan with a ten to one ratio is on the gentler side while a pure turbojet represents the opposite end of the spectrum. The latter is usually only suitable for military or supersonic applications. The key to this compromise is replacing exhaust velocity with mass flow, and specific thrust is a scale that illustrates this trade-off.

Specific impulse versus specific thrust

Specific thrust and specific impulse are similar concepts that can be easily confused. Specific thrust is the thrust per unit mass flow, so F divided by m-dot, and is measured in meters per second. Specific impulse is the thrust per unit weight flow, so F divided by (m-dot * g), and is measured in seconds. So dividing specific thrust by standard gravity 9.80665 gives specific impulse.

Dividing 300 meters per second by 9.8 gives about 31 seconds, which explains the origin of that small number. A specific impulse of thirty seconds for a jet engine and a specific thrust of 300 meters per second describe exactly the same engine using different methods of measurement. Rocket developers use specific impulse because a rocket carries its own oxidizer and there is no air mass flow to divide by. So, for air-breathing engines, specific thrust is a more natural measure.

Typical values for different engine types:

The following table shows the approximate specific thrust for major engine types at sea level static. In static tests, specific thrust is roughly equivalent to exhaust velocity, so the table ranges from large slow fan units to small fast jets.

Advantages of drive efficiency and low specific thrust:

There is a clever reason why low specific thrust can reduce fuel consumption. The propulsion efficiency of a jet engine - the proportion of the kinetic energy of the exhaust stream that actually goes to move the aircraft rather than mixing up the exhaust - is given by twice the flight speed divided by the sum of the exhaust and flight speeds.

As the exhaust velocity approaches flight speed this value slowly approaches one. A low specific thrust means that the exhaust velocity is only slightly above the aircraft's speed so almost no energy is wasted. This is the fundamental reason why high bypass ratio engines are so efficient and this calculator computes results for various flight speeds.

How to use this calculator:

Enter the thrust and mass flow rate in user-friendly units and read the specific thrust from the results area. The field for specific thrust can be switched between feet per second, miles per hour, knots or kilometers per hour. In the common units area you can display several units at once.

To calculate another quantity simply leave the corresponding field blank. If you enter specific impulse and mass flow rate then the calculator will return thrust. If you enter thrust and specific impulse then the calculator will return the mass flow rate that the engine must process. No mode selection is required as leaving fields blank tells the calculator which quantity to solve for.

Assumptions and limitations:

This calculator uses a simple definition of thrust divided by the mass flow rate, where the mass flow rate is considered to be all factors. In real engines fuel is also burned so that the mass exiting the nozzle is slightly greater than the mass of air entering. Also an accurate thrust equation has a pressure term at the nozzle exit. For engineer specified specific thrust values these corrections are small and the mass flow dominates.

Please note that specific thrust is a value calculated at one particular point in time. Published values are usually measured under standard conditions (sea level and static conditions) so they do not represent what an engine can produce at any given altitude or Mach number. You should consider these values as a way to compare engines, the flight speed calculation will help compensate for those differences.