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enter image description here

If the figure above represents a missile at the angle of attack and we vector resolution the thrust output from the nozzle, we can see that the thrust is divided into sine and cosine parts. Does the cosine and sine section of thrust cause torque in the rocket about cg? does the cosine part produce nose down pitching moment ?

Edit: In the figure above, sine and cosine are named oppositely

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  • $\begingroup$ "does the cosine part produce nose down pitching moment ?" -- why wouldn't that be exactly cancelled out by an opposite pitching moment from the "sine part"? $\endgroup$ Commented Jun 30, 2023 at 9:35
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    $\begingroup$ I think the answer to your question is no, the vector sum of the two components is along the axis T of the rocket. $\endgroup$
    – Frog
    Commented Jun 30, 2023 at 10:59
  • $\begingroup$ This NASA page should be helpful $\endgroup$
    – sophit
    Commented Jun 30, 2023 at 12:10
  • $\begingroup$ @quiet flyer because the distance between sine part to cg is larger than cosine part . $\endgroup$
    – alireza
    Commented Jun 30, 2023 at 15:56
  • $\begingroup$ @sophit in nasa page sine component of drag produce restoring moment about cg $\endgroup$
    – alireza
    Commented Jun 30, 2023 at 16:00

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The pitching moment from thrust vectoring comes from the trust axis' position relative to the center of gravity of the rocket or aircraft's body. If the rocket motor, or jet engine, is rigidly attached to the body, and the extended line of the thrust axis passes through the body's C of G, there are no rotational moments.

It doesn't matter if the rocket motor is at the front, the back, or on a boom 50 feet ahead or behind. What matters is whether the thrust line passes through the C of G.

Thrust vectoring, by gimbal mounting the rocket motor, or using a vectoring nozzle on a jet engine, moves the thrust line to impart rotational moments about the C of G. enter image description here

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  • $\begingroup$ so in aircrafts why front prpoller engine mounted cause distablizing moment avout cg at angle of attack ? $\endgroup$
    – alireza
    Commented Jun 30, 2023 at 15:46
  • $\begingroup$ @alireza -- are you sure it does? Are you talking about something like P-factor-- in that case the thrust line does not pass through the center of the prop hub and therefore is not in line with the CG of the aircraft. But there's no direct equivalent of P-factor as long as far as pitch dynamics are concerned. Maybe you need to ask a new question about that, if you can sort your thoughts out well enough to ask a clear question -- of course there are effects related to propwash over the horizontal tail, but I don't think that's what you are asking about-- $\endgroup$ Commented Jun 30, 2023 at 16:31
  • $\begingroup$ @alireza you have all kinds secondary effects once you add wings, tail, spinning propeller, etc. As far as the thrust force itself goes, that's how it works. Ppl think jets with tail mounted engines are destabilized by the location of the engines at the back. If the engines are rigidly attached, it makes no difference where they are. $\endgroup$
    – John K
    Commented Jun 30, 2023 at 17:05
  • $\begingroup$ @quiet flyer Yes, the professor of the dynamics and control(flight mechanics) course of the University of India said that if a propeller engine is installed in front of the plane, it will cause longitudinal instability and cause the neutral point to move forward and decreace static margin $\endgroup$
    – alireza
    Commented Jun 30, 2023 at 19:14
  • $\begingroup$ @quiet flyer I am not talking about the p-factor. What was explicitly said was that if a propeller engine is installed in front of the plane and the plane is at the angle of attack, the propeller will produce a vertical force, which is the cosine part of the thrust, and because this vertical force is ahead of the cg , it will cause longitudinal instability. $\endgroup$
    – alireza
    Commented Jun 30, 2023 at 19:21

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