# Can the pressure term in the general thrust equation be negative?

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?

• 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? Commented Mar 7, 2019 at 19:10
• 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.
– user93237
Commented Mar 7, 2019 at 19:16
• 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 Commented Mar 7, 2019 at 19:25
• 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. Commented Mar 7, 2019 at 19:49
• 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. Commented Mar 7, 2019 at 19:58