# Calculate Jet Engine Net Thrust (F(N))

• v_pino
In summary: Hi Jeff,This is the way the formula is written in my book; however, the initial fuel velocity is different than the initial air velocity. Using the plane as a frame of reference, the initial fuel velocity is zero:
v_pino
I was given some notes on aircraft performance that states the equation for finding the net thrust of a jet engine.

----------------------------------------------------
It states (words in brackets are subscripts):

F(N) = m dot (air) + m dot (j) V(j) - m dot (air) V

F(N) = net thrust
m dot (air) = inlet mass flow
m dot (j) = fuel mass flow
V(j) = final velocity
V = initial velocity
-----------------------------------------------------

How is this equation obtained?

I know that Force = change in momentum / change in time

v_pino said:
F(N) = m dot (air) + m dot (j) V(j) - m dot (air) V
I think this should be:

F(N) = (m dot (air) + m dot (j)) V(j) - m dot (air) V

This is obtained as follows (assumes average accelartion, ..., you'd really need to take the integral sum of all the affected components):

force = mass x acceleration = mass x (Vout-Vin)/(unit time) = (mass/(unit time)) x (Vout - Vin)

Hi Jeff,

If I use F=ma, should I not get this:

( m dot (air) + m dot (j) ) ( V (j) - V )

thanks

This is the way the formula is written in my book;
Gross Thrust (Static) F (gross) = m dot (V2-V1)
V2-V1 Final velocity – initial velocity.
F (net) = F (gross) – F (Drag)
F (Drag) is the ram drag or inlet momentum drag caused by forward speed effect. If engine is not moving forward F (net) = F (gross).
Adding fuel: F (net) = m dot (V2-V1) + m dot fuel V (f)
Note: fuel inlet velocity will be same as engine so no initial velocity. Some formulas do not include fuel flow effects because the effects of air leakage are approximately the same as fuel flow effects.

The fuel is added to mass air flow – if used.

Most nozzles are chocked and there is a formula for that I can give you if you are interested.

It's simple...draw a control volume around an engine. The net force is the sum of all of the outgoing momentum minus the incoming momentum.

v_pino said:
If I use F=ma, should I not get this:
( m dot (air) + m dot (j) ) ( V (j) - V )
Not quite, the initial fuel velocity is different than the initial air velocity. Using the plane as a frame of reference, the initial fuel velocity is zero:

Jeff Reid said:
force = mass x acceleration = mass x (Vout-Vin)/(unit time) = (mass/(unit time)) x (Vout - Vin)

F = mass x acceleration
F = (mass (air))(Vout - Vin)/(unit time) + (mass fuel (j))(Vout - 0)/(unit time)
let m dot = mass / (unit time)
F = ( m dot (air) ) ( Vout - Vin) + ( m dot (fuel) ) ( Vout - 0)

## What is the formula for calculating jet engine net thrust?

The formula for calculating jet engine net thrust (F(N)) is: F(N) = (m dot)(Vj - V0) + (Ae)(Pj - P0), where m dot is the mass flow rate of air through the engine, Vj is the velocity of the exhaust jet, V0 is the velocity of the incoming air, Ae is the area of the engine's exhaust nozzle, Pj is the pressure at the exit of the nozzle, and P0 is the ambient air pressure.

## What units are used to express jet engine net thrust?

Jet engine net thrust is typically expressed in units of force, such as newtons (N) or pounds (lb).

## What factors affect the calculation of jet engine net thrust?

The calculation of jet engine net thrust is affected by several factors, including the mass flow rate of air through the engine, the velocity of the exhaust jet, the velocity of the incoming air, the area of the engine's exhaust nozzle, and the pressure at the exit of the nozzle. Additionally, the type and design of the engine can also impact the net thrust calculation.

## How is jet engine net thrust used in aircraft design?

Jet engine net thrust is a critical factor in aircraft design, as it directly affects the performance and capabilities of the aircraft. It is used to determine the amount of thrust needed to achieve desired speeds and altitudes, as well as to calculate the required amount of fuel for a given flight. Net thrust is also used to determine the maximum takeoff weight and range of an aircraft.

## How does altitude affect jet engine net thrust?

Altitude has a significant impact on jet engine net thrust. As altitude increases, the air density decreases, resulting in a decrease in the mass flow rate of air through the engine. This decrease in air mass flow rate results in a decrease in net thrust. Additionally, at higher altitudes, the ambient air pressure also decreases, which can further affect the calculation of net thrust.

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