The Thrust Equation

• From Newton’s second law: F = d(mv)/dt ( F= ma , for a constant mass )

• In jet engine terms, we can re-write this as:

Where:

F is force in pounds

w is the gas flow in pounds per second

g is the gravitational constant

V1 is the initial velocity of the gas, in ft/sec

V2 is the final velocity of the gas, in ft/sec

• Note that instead of using F = ma, we are re-writing the equation as force equals mass flow per unit time multiplied by velocity change.

• This difference is subtle but essential: Acceleration is not the same as velocity change. Thus force is not equal to mass times velocity change; acceleration is velocity change per unit of time.

• Using F = mass flow per unit time multiplied by velocity change is dimensionally correct.

• This difference is subtle but essential: Acceleration is not the same as velocity change. Thus force is not equal to mass times velocity change; acceleration is velocity change per unit of time.

• Using F = mass flow per unit time multiplied by velocity change is dimensionally correct.

We can re-write the thrust equation to make it more meaningful in the context of a jet engine:

This is called the “net” thrust, because it accounts for the momentum of the incoming air; “Gross” thrust is given by the first term in the equation – which is the force created at the exhaust of the engine.

To compute usable thrust, the gross thrust has to be reduced by the amount of the second term, which is the momentum already existing because of the airplane’s speed.

From the equation, you can see that net thrust is a function of the mass flow rate of the air and fuel passing through the engine, and of the exhaust velocity minus the incoming velocity.

From the equation, you can see that net thrust is a function of the mass flow rate of the air and fuel passing through the engine, and of the exhaust velocity minus the incoming velocity.

Additional Thrust Due to Internal Pressure

• The thrust equation as written is somewhat simplified in that it ignores one more possible component of thrust. That component is thrust due to internal pressure.

• Most of the internal pressure within the engine is converted to velocity of the exhaust gasses, which in turn produces thrust.

• At the exhaust, if the total pressure of the gasses is greater than the total pressure at the intake, this surplus of pressure will produce some additional thrust.

• The thrust equation as written is somewhat simplified in that it ignores one more possible component of thrust. That component is thrust due to internal pressure.

• Most of the internal pressure within the engine is converted to velocity of the exhaust gasses, which in turn produces thrust.

• At the exhaust, if the total pressure of the gasses is greater than the total pressure at the intake, this surplus of pressure will produce some additional thrust.

F = A(exhaust) * { P(exhaust) - P(ambient) }

• This component of thrust is small compared to the thrust due to exhaust velocity, but should not be ignored.

Factors Affecting Thrust:

Air density, a function of temperature and pressure altitude, is a very significant component affecting thrust.

Velocity affects both the momentum and the pressure of the air entering the engine intake.

Increasing aircraft speed increases the momentum of the incoming air, lowering thrust, while at the same time compressing the air at the intake (ram effect) increasing thrust by increasing density. The combined effect is show below.

Increasing aircraft speed increases the momentum of the incoming air, lowering thrust, while at the same time compressing the air at the intake (ram effect) increasing thrust by increasing density. The combined effect is show below.

Other Factors Affecting Thrust

• Bleed air extraction affect thrust.

• Power extraction for hydraulic pumps, electric generators, fuel pumps, etc., affects thrust.

• Humidity has a negligible effect on thrust.Artikel Terkait : Engine Performance Analysis

Reff : Flight Operation Engineering - BOEING

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