In the general thrust equation, it looks like the pressure term can be negative if the ambient pressure is greater than the nozzle exit pressure:

$$F=\dot m\cdot V_\mathrm e+\left(p_\mathrm e-p_\mathrm0\right)\cdot A_\mathrm e$$

However, this has some obvious and strange implications. Lowering mass flow to zero and increasing the exit area of the nozzle I can optimize thrust in the opposite direction and create a rocket engine that can accelerate backwards at ludicrous speeds.

Can the pressure term become negative in real-world applications? Are there limitations to how negative it can become?

  • $\begingroup$ If the ambient pressure is greater than the nozzle exit pressure, doesn't that mean your rocket engine is sucking in air through the nozzle? $\endgroup$
    – PM 2Ring
    Commented Mar 7, 2019 at 19:10
  • $\begingroup$ You should define all the terms in the equation. Also, I googled "general thrust equation" and it appears that it applies not to a rocket with an ambient pressure of Po as implied by the question but to a jet engine with an inlet pressure of Po. $\endgroup$
    – user93237
    Commented Mar 7, 2019 at 19:16
  • $\begingroup$ Pe is exit pressure and P0 is ambient pressure. Here are a couple of references showing the equation used for rockets: grc.nasa.gov/www/k-12/airplane/rockth.html braeunig.us/space/index.htm $\endgroup$ Commented Mar 7, 2019 at 19:25
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    $\begingroup$ The term for this is an overexpanded nozzle, and if you push too far in that direction the flow becomes unstable. (This is probably a good starting point.) If you keep pushing, if I understand correctly, this is often associated with catastrophic self-disassembly by the engine. $\endgroup$ Commented Mar 7, 2019 at 19:49
  • $\begingroup$ Thanks! That's good to know: > Slight overexpansion causes a slight reduction in efficiency, but otherwise does little harm. However, if the exit pressure is less than approximately 40% that of ambient, then "flow separation" occurs. This can cause jet instabilities that can cause damage to the nozzle or simply cause control difficulties of the vehicle or the engine. $\endgroup$ Commented Mar 7, 2019 at 19:58


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