# Why is thrust said to be constant over speed for a jet engine?

I'm just interested in some basic facts regarding flight. On reading the rather "low level" book "Understanding Flight, David F. Anderson, Scott Eberhardt), I recently came up to the following diagram:

Why is thrust approximately constant with speed for a jet engine? Everything gets mixed up in my head as follows:

Thrust is approximately $$F_t=\dot m \cdot \left( v_{gas}-v_a\right)$$, where the speeds are outlet speed on the nozzle and true airspeed, respectively.

https://en.wikipedia.org/wiki/Turbojet#Net_thrust

So there are really a lot of parameters. What of them are assumed to kept constant in the right diagram and what are changing? Without that information, the diagram seems meaningless for me. For my naïve opinion, a change of thrust is controlled by changing the thrust lever and thereby changing the fuel content within the combustion chamber. Lets say the lever is at its max or a fixed position (whatever this means). Then while increasing speed the factor $$v_{gas}-v_a$$ gets smaller, assuming the outlet speed is constant.

So to have still the same thrust there are three possibilities':

• outlet speed increases
• mass stream increases
• both of them increase

I can imagine that mass stream increases "somehow" with airspeed (keeping fuel injection constant), so there might be some cancellation of the speed factor. .But is this the whole story? Why is it canceling completely?

On writing this question another question arises:

Considering an ideal engine without losses, total power is

$$P_{tot} = \frac{1}{2} \dot m \cdot (v_{gas}^2-v_a^2) = \frac{1}{2} \dot m \cdot (v_{gas}-v_a)(v_{gas}+v_a) = \frac{F_t}{2}\cdot (v_{gas}+v_a)$$

Lets say, the power lever is on a fixed position. Is this position an indicator for the total power of the engine? In other words: is total power to the engine constant, when the lever is on a fixed position? I ask, because when assuming constant thrust this formula would mean, that total power (as well as propulsive power) must also increase, because at higher TAS of the plane, gas outlet speed would (up to my poor understanding) rather increase instead of decrease. So what happens, when the thrust lever is on a fixed position? Could it be, that there is a governor behind, taking control of thrust? In this case the right picture has no meaning at all, because while increasing TAS the governor automatically injects more fuel.

There are so many questions and in fact no understanding of anything...

• mass flow and outlet speed increasing with airspeed has made sense for me. – Abdullah Oct 2 '20 at 15:26
• see if this helps – Abdullah Oct 2 '20 at 15:29
• yes, it is exactly what I'm asking for. – MichaelW Oct 2 '20 at 18:15