I had came across a simplified simplified rocket lateral dynamics model seen in this image below: enter image description here

. It has vanes at the exit which generate lift force and can control the rocket orientation- the lift force is actually a ''side force'' which can impose moments about the rockets centre of gravity. The link :https://github.com/build-week/hover-jet/blob/feature/start-design-scripts/design-scripts/jet_vane_speed.ipynb contains more infomation by the author. In it, linear and angular momentum equations are present for the current orientation.

Fj: engine thrust

Lv: lift force

Dv: drag force

rv: Distance from vanes to rocket centre of mass

alpha: vane angle of attack

theta: pitch over angle of the rocket

angular momentum:

$$ L_v r_v = I \ddot{\theta} $$

Linear momentum:

$$ -(F_j - D_v) \sin\theta + L_v \cos\theta = m \ddot{x} $$

I don't seem to understand the sign convention for the lift force generated by the vanes in these equations; at the current angle of attack seen in the image, the lift force Lv would be in a south-west direction. In the equations, it seems the author took it in the north-east direction. In other words, should the equations instead read as:

$$ -L_v r_v = I \ddot{\theta} $$

$$ -(F_j - D_v) \sin\theta - L_v \cos\theta = m \ddot{x} $$ Does anyone happen to know why he made the signs by Lv positive instead? Any advice is appreciated

  • 1
    $\begingroup$ What is the "sign" of $r_v$ ? Maybe the author started from the expression for moment of a force : $r \times f$. $\endgroup$
    – AJN
    Commented Jul 26, 2021 at 4:15
  • $\begingroup$ @AJN thanks for pointing that out, I missed adding info about r_v. I believe it is the distance from the vanes to the rockets centre of mass $\endgroup$
    – Johan M
    Commented Jul 26, 2021 at 7:14
  • 1
    $\begingroup$ for that matter, what is the sign of angle θ, as the diagram uses a most unconventional way of measuring the angle? $\endgroup$ Commented Jul 26, 2021 at 7:40
  • $\begingroup$ @PcMan it seems the author took theta as an acute angle, and manually added the negetive/positive signs $\endgroup$
    – Johan M
    Commented Jul 26, 2021 at 12:22

1 Answer 1


The equations the author gives are correct.

Notice that with the angular momentum equation: $$L_vr_v = I\ddot{\theta}$$ We would expect a positive $L_v$ to increase $\theta$. Similarly with the linear momentum equation, a positive $L_v$ should increase $x$.

Now for the confusion: The author has drawn an $L_v$ vector on his/her diagram pointing in the negative direction! They show the positive direction with that dashed line. This would then be carried through the equations with a built-in negative, giving the same result as your rewritten equations.

This is actually a common convention for body-centered coordinate systems for aircraft: forward (through the nose) and starboard (through the right wing) are taken as positive.

  • $\begingroup$ @A McKelvy thanks for the comment. I can picture what you mean about the angular momentum part when looking at it backwards; the current negative Lv would decrease theta. To be honest I'm still confused about the signs in the linear momentum part. I'm not certain what you mean by built-in negative. I had thought the author meant to explicity state the signs in the equation, such as with Dv being positive and Fj negative. The airfoil lift would have to act in the ''negative'' direction with the pictures orientation, though I'm not sure why he would omit the sign for that only. $\endgroup$
    – Johan M
    Commented Jul 26, 2021 at 21:40
  • $\begingroup$ I see that the answer by @A McKelvy has 4 upvotes. Can some user please advise me why he is correct? or correct my possible confusion in my reply to his answer $\endgroup$
    – Johan M
    Commented Aug 1, 2021 at 10:13

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