# How does an engine work when an airplane has $v=0$ on the ground?

I mean, for a turbofan: $$T= \dot m_{air,h} (1+f) v_{e,h}+ \dot m_{air,c} v_{e,c}- (\dot m_{air,h}+ \dot m_{air,c} ) v_0+ (P_{e,h}-P_{amb} ) A_{e,h}+ (P_{e,c}-P_{amb} ) A_{e,c}$$

but $$\dot m_{air}=\rho Av_0$$

do I have to impose $$\dot m_{air}$$? in this case how the thrust expression change (in particular the terms with $$v_0$$)?

• In your second equation, $v_0$ should be the speed of the air moving through the area $A$, not the speed of the aircraft, right? Jul 30, 2019 at 18:14
• It works the same way as it does in the air. The only difference is that there is no ram air at the intake, the compressor has to suck air in. Jul 30, 2019 at 18:34
• @Bianfable Yes, I think it should. But in my propulsion course we often approximate $v_{inlet}=v_{aircraft}$. I think that my doubt come from this! Jul 31, 2019 at 10:07
• The question you probably should ask when someone says something like "but $\dot m_{air}=\rho Av_0$" is why does that hold? You can turn this question around by asking yourself: what happens if the aircraft is stationary on the ground, pointed directly into the wind, with a wind speed of (say) 30 kt? Now consider the opposite case: what happens if there is no wind (perfectly calm air), but the aircraft is somehow being propelled forward at a speed of 30 kt with no friction losses against the ground? From the aircraft's perspective, what is the difference between the two cases?
– user
Jul 31, 2019 at 16:30
• As a practical example, you might note that somewhat modified jet engines are widely used for electric power generation: en.wikipedia.org/wiki/… Jul 31, 2019 at 17:47

To start the engine, the fan blades have to be spun up. This is typically handled by either blowing air through them from some outside source, and/or by using an APU to generate power to drive the shaft they're connected to.

Once the engine is running, it sucks in enough air to keep going on its own.

• And the airflow has velocity $v_0$ which differs from zero when the aircraft is stationary. Jul 31, 2019 at 5:43
• Therefore, should I impose $\dot m_{air}$ and calculate $v_0$ knowing the intake geometry? In this case I have one more question: $\dot m_{air}$ is fixed with altitude variation or not (or at least is it a reasonable approximation)? Jul 31, 2019 at 10:14

$$v_0$$ is the airflow speed through the engine, not the airspeed. As per @Bianfable’s comment.

How the engine works at standstill: the compressor sucks air into the inlet, it initiates the flow through the engine. Axial compressor blades similar to a propeller, centrifugal compressors by slinging air out towards the compressor outlet.

Maximum thrust at standstill should be a given for the engine under consideration. At standstill, if the exhaust is choked, the mass flow follows from:

• Thrust.
• Speed of sound at the exhaust gas temperature.
• Exhaust pressure and area.
• Bypass ratio.

With the mass flow given, you can compute $$v_0$$