# CALCULATING THRUST DISTRIBUTION

We will now have a look at how the turbo-jet generates thrust loads as the mass airflow passes through the various engine components.

We shall examine the compressor, the diffuser, the combustion chamber, the turbine, the exhaust unit, and the propelling nozzle.

It is first useful to consider the passage of the mass airflow through the engine.

The air first passes through the compressor where its pressure is increased.

The pressure difference across each stage of compression and the reaction to the acceleration of the air in each stage results in a considerable forward thrust force throughout the compressor.

The air exits the compressor at high pressure and passes through the divergent section of the diffuser where it loses velocity and further increases its pressure resulting in an additional forward thrust force.

## The air is heated in the combustion section where it expands rapidly and accelerates rearwards at high velocity.

The reaction to this acceleration produces a large forward thrust force, which acts on all the forward wall areas of the combustion chambers.

The gas then expands through the turbine section where its pressure and temperature drops as energy is extracted as work in the turbines. This produces a considerable rearward acting force.

Leaving the rear turbine the gas passes through the divergent section of the exhaust unit where it loses velocity and regains some pressure.

This produces a forward acting thrust. After passing through the jet pipe, the gas then accelerates through the convergent section of the propelling nozzle to a high velocity in the jet stream at the rear of the engine.

The pressure acting on the internal rear-facing wall of the nozzle produces a rearward force as the gas passes through.

You can see from the above, that forward acting forces are produced in the compressor, diffuser, combustion chambers and exhaust unit whilst the rearward acting forces are produced in the turbines and the propelling nozzle.

If you sum up all the forward acting forces and subtract the sum of the rearward forces you will obtain the resultant thrust value or gross thrust; which is the total static thrust value for the engine.

To calculate the thrust load in a component it is first necessary to establish the conditions at the inlet to the component and then calculate the conditions at the outlet from it.

## COMPRESSOR

The inlet conditions for our compressor when the engine is not moving forwards will be zero. The data for the compressor is:

Exit duct area A = 200 squ. In

Exit pressure P = 100 PSI guage

Exit air velocity V = 350 ft/s

Air mass flow W = 220 lb/s

=(A×P)+WV/g−0

=(200×100)+(220×350) /32 −0

Thrust load22 406.25 lbt (pounds thrust).

### DIFFUSER

The inlet conditions for the diffuser duct are the same as the compressor outlet.

Exit duct area A = 220 squ. In
Exit pressure P = 120 PSI guage
Exit air velocity V = 300 ft/s
Air mass flow W = 220 lb/s

=(A×P)+WV/g−22406.25

=(200×120)+(220×300) /32 −22406.25

Thrust load= 6056.25 lbt (pounds thrust)

#### TURBINE

The thrust load for the turbine will be negative

Exit duct area A = 400 squ. In

Exit pressure P = 25 PSI guage

Exit air velocity V = 900 ft/s

Air mass flow W = 220 lb/s

=(A×P)+WV/g−56 718.75

=(400×25)+(220×900)/ 32 −56 718.75

Thrust load = -49 531.25 lbt (pounds thrust)

#### EXHAUST UNIT

Exit duct area A = 600 squ. In

Exit pressure P = 25 PSI guage

Exit air velocity V = 700 ft/s

Air mass flow W = 220 lb/s

=(A×P)+WV/g−7 187.5

=(600×25)+(220×700)/ 32 −718.5

Thrust load = 12 625 lbt (pounds thrust)

PROPELLING NOZZLE

Gas passing through this duct will exert a negative thrust load. We will use our example turbo-jet gas exit figures at this point.

Exit duct area A = 324 squ. In

Exit pressure P = 6.5 PSI guage

Exit air velocity V = 1 080 ft/s

Air mass flow W = 220 lb/s

=(A×P)+WV/g−19 812.5

=(324×6.5)+(220×1 080) /32 −19 812.5

Thrust load = – 10 281.5 lbt (pounds thrust)

If we now look at each of these loads we can see how the positive and negative loads are distributed through the engine.

If you are still awake we shall add them up and see how they compare with our example turbo-jet.

RESULTANT THRUST

RESULTANT THRUST We have calculated the resultant thrust of each component duct by subtracting its inlet condition from its outlet condition.

We can now do this for the whole engine by adding up all the positive, forward acting thrust forces and subtracting the sum of the negative rearward forces.

Positives                        Negatives

22 406.25                       – 49 532.25

6 056.25                           – 10 281.5

28 256.25

12 625

Subtotal 69 343.75        – 59 812.75

Resultant Thrust = 9 531 lbt

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