TVC applies gimbal moments without the matching lateral thrust force

[thc1006]

Summary

The TVC path reduces axial thrust and applies the moments of a deflected thrust vector, but the lateral components of that same vector never reach the translational equations.

In rocketpy/simulation/flight.py, u_dot_generalized:

thrust3 = effective_thrust * np.sqrt(
    1 - np.sin(gimbal_angle_x * pi/180) ** 2 - np.sin(gimbal_angle_y * pi/180) ** 2
)
tvc_lever = self.rocket.nozzle_to_cdm
M1 += np.sin(gimbal_angle_x * pi/180) * effective_thrust * tvc_lever
M2 += np.sin(gimbal_angle_y * pi/180) * effective_thrust * tvc_lever

R1 and R2 only ever accumulate aerodynamic contributions (R1 += X, R2 += Y from the surfaces). I could not find T*sin(x) or T*sin(y) being added anywhere, and the body-axis equations use R1 and R2 as they stand while the axial one adds thrust3.

So a gimbal command produces a moment and a reduced axial force, but no lateral force on the centre of mass. The same physical force cannot do one without the other.

Numbers

With a 15 degree limit on each axis, commanding both at once:

omitted lateral force	0.366 * T
thrust3	0.931 * T
actual combined deflection	21.47 degrees

That last row is worth noting separately. Two independent 15 degree axes reach a combined deflection of 21.47 degrees, so a parameter documented as a maximum gimbal angle does not bound what the model actually applies.

There is also a domain problem at larger limits: sin(x)^2 + sin(y)^2 > 1 makes the square root argument negative, which happens once both axes exceed 45 degrees. Nothing validates that when the actuator range is configured.

Is it deliberate?

I considered that TVC might be intended as a pure control-moment actuator. If it were, thrust3 would not be reduced by the deflection. Reducing it is what says the code means to model a real deflected vector, so this reads as an oversight rather than a modelling choice.

Suggestion

Build the body-frame thrust vector once and use it for both sides:

F = effective_thrust * Vector([sin(x), sin(y), sqrt(1 - sin(x)**2 - sin(y)**2)])
# translational: add F
# rotational:    add r x F

That keeps the force and the moment consistent by construction rather than by two formulas that have to be kept in step, and it removes the question of which convention each one follows.

Worth deciding at the same time whether the configured limit is per axis or a total cone angle, and validating the two-axis domain so the square root cannot go negative.

A regression test could assert that the force norm equals the effective thrust, that both lateral components are non-zero for a two-axis command, and that the moment matches r x F.

Context

Found while reviewing the TVC integration in BalloonPoppingChallenge, which pins this code. It does not affect that competition's fairness, since every entrant runs the same model, and I am not proposing to change it there before their release. Raising it here because it is a physics question rather than an integration one.

[zuorenchen]

The only thing missing here is the lateral forces on R1 and R2. The others are correct as designed (but not well documented).

Modelling concept:

The thrust on the nozzle is separated into 3 components: longitudinal z-axial force and two lateral forces aligned on X and Y axis.
The forces on X and Y axis are independent, magnitudes are given by sin(x) and sin(y). Thus, the remaining force on z-axis is sqrt(1 - sin(x)**2 - sin(y)**2)

The two lateral force components on x and y axis creates moment on M1 and M2. But missed on R1 and R2.

Reply the questions:

That last row is worth noting separately. Two independent 15 degree axes reach a combined deflection of 21.47 degrees, so a parameter documented as a maximum gimbal angle does not bound what the model actually applies.

As explained above, this matches the modelling concept. The max deflections on x axis and y axis are independent. It is normal that the total combined deflection will be larger.

There is also a domain problem at larger limits: sin(x)^2 + sin(y)^2 > 1 makes the square root argument negative, which happens once both axes exceed 45 degrees. Nothing validates that when the actuator range is configured.

Similarly, this matches the modelling concept: both x axis and y axis at 45 deg means that there is no more longitudinal z axis thrust component.

[thc1006]

Sorry for the slow reply, and thank you for the modelling explanation. That settles two of the three.

The combined 21.47 degrees and the square root domain both follow from independent axes, so they are the model rather than a defect in it. I was reading max_gimbal_angle as a bound on total deflection, and it is a per-axis one. Worth a line in the docstring at some point so the next reader does not make the same assumption, but nothing to fix.

The third one is still there at 473447d, in both places the thrust is assembled:

# flight.py, u_dot_generalized and u_dot
thrust3 = effective_thrust * sqrt(1 - sin(x)**2 - sin(y)**2)   # axial, reduced
M1 += sin(x) * effective_thrust * tvc_lever                     # pitch moment
M2 += sin(y) * effective_thrust * tvc_lever                     # yaw moment
# R1 and R2 get nothing

So the nozzle takes thrust out of the axial direction and turns the rocket with it, and the sideways component of that thrust is never applied as a force. Some of the momentum leaves the model.

With scenario 1's numbers, 1080 N at full throttle and 86 kg at ignition:

gimbal	missing per axis	as acceleration
5 deg	94 N	1.09 m/s2
10 deg	188 N	2.18 m/s2
15 deg, the configured maximum	280 N	3.25 m/s2
both axes at 15 deg	395 N	4.59 m/s2

Liftoff thrust to weight is 1.28, so at full deflection this is a meaningful fraction of what the vehicle has to work with, not a rounding term.

The part I would rather you decided than me: fixing it moves every controlled trajectory, so it invalidates the current leaderboard and both golden-master baselines. You mentioned wanting to change the rocket parameters once the qualifying round is over. If the two go together, the baselines are regenerated once and competitors see one change rather than two. If it should go in sooner than that, say so and I will send it with the baselines updated in the same PR.

Either way the round that is about to be announced runs on the physics as it is, and everyone gets the same physics, so the ranking is not the thing at stake here.