# 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? – Bianfable Jul 30 '19 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. – Michael Hall Jul 30 '19 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! – wilove Jul 31 '19 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? – a CVn Jul 31 '19 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/… – jamesqf Jul 31 '19 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. – Koyovis Jul 31 '19 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)? – wilove Jul 31 '19 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 $$v_0$$