tTurn Trimming

[AirshipSim]

Hi,

I am reading through the FGTrim code. For tTurn, I see a small coding mistake below as phi is assigned twice the same value:
double phi = fgic.GetPhiRadIC();
and just below again:
phi = fgic.GetPhiRadIC();

jsbsim/src/initialization/FGTrim.cpp

Lines 788 to 813 in 0238e96

	void FGTrim::updateRates(void){
	if( mode == tTurn ) {
	double phi = fgic.GetPhiRadIC();
	double g = fdmex->GetInertial()->GetGravity().Magnitude();
	double p,q,r,theta;
	if(fabs(phi) > 0.001 && fabs(phi) < 1.56 ) {
	theta=fgic.GetThetaRadIC();
	phi=fgic.GetPhiRadIC();
	psidot = g*tan(phi) / fgic.GetUBodyFpsIC();
	p=-psidot*sin(theta);
	q=psidot*cos(theta)*sin(phi);
	r=psidot*cos(theta)*cos(phi);
	} else {
	p=q=r=0;
	}
	fgic.SetPRadpsIC(p);
	fgic.SetQRadpsIC(q);
	fgic.SetRRadpsIC(r);
	} else if( mode == tPullup && fabs(targetNlf-1) > 0.01) {
	double g,q,cgamma;
	g=fdmex->GetInertial()->GetGravity().Magnitude();
	cgamma=cos(fgic.GetFlightPathAngleRadIC());
	q=g*(targetNlf-cgamma)/fgic.GetVtrueFpsIC();
	fgic.SetQRadpsIC(q);
	}
	}

But the real question comes here for psidot calculation:

jsbsim/src/initialization/FGTrim.cpp

Line 796 in 0238e96

psidot = g*tan(phi) / fgic.GetUBodyFpsIC();

psidot is calculated using only fgic.GetUBodyFpsIC(), that is the U velocity. With tPullup, Vtrue is used instead. I can understand that by definition we want to avoid sideslip to have a steady turn, so we decide V == 0. But what about W? Shouldn't you write:
psidot = g*tan(phi) / sqrt( fgic.GetUBodyFpsIC()^2 + fgic.GetWBodyFpsIC()^2);

If the current calculation is wrong, that would also mean that people so far had trouble with JSBSim turn trimming... Any clarification appreciated.

Note: my goal is to understand which variable is needed as user input for each trimming possibility, this is how I stumbled upon this code. I can not test the proper in flight behavior at the moment.

Best

[seanmcleod70]

I haven't looked at the trim code in a long time. So, sort of refreshing on the fly looking at the source code now.

So, it looks like in the tTurn case you get to specify a bank angle $\phi$ as part of the initial conditions, and the trim code assumes a level turn, so calculates the required load factor based on $\phi$.

Then as you pointed out it calculates $\dot{\psi}$ using the bank angle $\phi$ and the $u$ body velocity.

jsbsim/src/initialization/FGTrim.cpp

Lines 773 to 784 in 0238e96

	void FGTrim::setupTurn(void){
	double g,phi;
	phi = fgic.GetPhiRadIC();
	if( fabs(phi) > 0.001 && fabs(phi) < 1.56 ) {
	targetNlf = 1 / cos(phi);
	g = fdmex->GetInertial()->GetGravity().Magnitude();
	psidot = g*tan(phi) / fgic.GetUBodyFpsIC();
	FGLogging log(LogLevel::INFO);
	log << targetNlf << ", " << psidot << "\n";
	}
	}

In updateRates() the code then calculates the required body rates $p, q, r$ based on the calculated $\dot{\psi}$ and assuming $\dot{\phi}$ and $\dot{\theta}$ are 0 using:

Using the following controls and states to achieve equilibrium.

jsbsim/src/initialization/FGTrim.cpp

Lines 874 to 881 in 0238e96

	case tTurn:
	TrimAxes.push_back(FGTrimAxis(fdmex,&fgic,tWdot,tAlpha ));
	TrimAxes.push_back(FGTrimAxis(fdmex,&fgic,tUdot,tThrottle ));
	TrimAxes.push_back(FGTrimAxis(fdmex,&fgic,tQdot,tPitchTrim ));
	TrimAxes.push_back(FGTrimAxis(fdmex,&fgic,tVdot,tBeta ));
	TrimAxes.push_back(FGTrimAxis(fdmex,&fgic,tPdot,tAileron ));
	TrimAxes.push_back(FGTrimAxis(fdmex,&fgic,tRdot,tRudder ));
	break;

To answer your original question I think $V$ (true airspeed) should be used rather than just the $u$ body velocity.

[seanmcleod70]

In terms of having difficulty in getting a trim solution for a level turn I just tried trimming the A4 model in JSBSim at 15,000ft 250KCAS with bank angles from 5 deg to 60 deg in 5 deg increments and JSBSim was able to generate a trim solution for every bank angle.

import jsbsim

AIRCRAFT_NAME="A4"
# Path to JSBSim files, location of the folders "aircraft", "engines" and "systems"
PATH_TO_JSBSIM_FILES="../.."

# Avoid flooding the console with log messages
#jsbsim.FGJSBBase().debug_lvl = 0

fdm = jsbsim.FGFDMExec(PATH_TO_JSBSIM_FILES)

# Load the aircraft model
fdm.load_model(AIRCRAFT_NAME)

# Set engines running
fdm['propulsion/set-running'] = -1

# Initial conditions
fdm['ic/h-sl-ft'] = 15000
fdm['ic/vc-kts'] = 250
fdm['ic/gamma-deg'] = 0

for phi in range(5, 61, 5):
    fdm['ic/phi-deg'] = phi

    # Initialize the aircraft with initial conditions
    fdm.run_ic()

    print(f"Trim solution for phi = {phi} degrees:")

    # Trim
    fdm['simulation/do_simple_trim'] = 5

    print('')
    print(f"V = {fdm['velocities/vtrue-fps']:.2f} fps")
    print(f"u, v, w = {fdm['velocities/u-fps']:.2f}, {fdm['velocities/v-fps']:.2f}, {fdm['velocities/w-fps']:.2f}")

Sample output:

Trim solution for phi = 5 degrees:
  Trim successful
  Trim Results:
       Angle of Attack:   2.82  wdot:  2.82e-04 Tolerance: 1e-03  Passed
              Throttle:   0.62  udot:  4.41e-05 Tolerance: 1e-03  Passed
            Pitch Trim:  -0.13  qdot: -2.56e-06 Tolerance: 1e-04  Passed
              Sideslip:  -0.01  vdot:  1.15e-04 Tolerance: 1e-03  Passed
              Ailerons:  -0.00  pdot:  2.14e-05 Tolerance: 1e-04  Passed
                Rudder:  -0.01  rdot: -4.56e-19 Tolerance: 1e-04  Passed

V = 525.05 fps
u, v, w = 524.42, -0.06, 25.81

Trim solution for phi = 10 degrees:
  Trim successful
  Trim Results:
       Angle of Attack:   2.87  wdot:  2.92e-04 Tolerance: 1e-03  Passed
              Throttle:   0.63  udot:  1.42e-04 Tolerance: 1e-03  Passed
            Pitch Trim:  -0.14  qdot: -4.46e-06 Tolerance: 1e-04  Passed
              Sideslip:  -0.01  vdot:  2.38e-04 Tolerance: 1e-03  Passed
              Ailerons:  -0.00  pdot:  3.83e-05 Tolerance: 1e-04  Passed
                Rudder:  -0.02  rdot:  2.38e-18 Tolerance: 1e-04  Passed

V = 525.05 fps
u, v, w = 524.40, -0.13, 26.26

Trim solution for phi = 15 degrees:
  Trim successful
  Trim Results:
       Angle of Attack:   2.95  wdot:  3.11e-04 Tolerance: 1e-03  Passed
              Throttle:   0.63  udot:  5.10e-05 Tolerance: 1e-03  Passed
            Pitch Trim:  -0.14  qdot: -3.38e-06 Tolerance: 1e-04  Passed
              Sideslip:  -0.02  vdot:  3.72e-04 Tolerance: 1e-03  Passed
              Ailerons:  -0.00  pdot:  3.34e-05 Tolerance: 1e-04  Passed
                Rudder:  -0.03  rdot: -4.08e-18 Tolerance: 1e-04  Passed

V = 525.05 fps
u, v, w = 524.36, -0.20, 27.03
..........
..........

Trim solution for phi = 50 degrees:
  Trim successful
  Trim Results:
       Angle of Attack:   5.15  wdot:  1.43e-04 Tolerance: 1e-03  Passed
              Throttle:   0.69  udot: -5.47e-04 Tolerance: 1e-03  Passed
            Pitch Trim:  -0.27  qdot:  5.93e-06 Tolerance: 1e-04  Passed
              Sideslip:  -0.12  vdot:  9.50e-04 Tolerance: 1e-03  Passed
              Ailerons:  -0.01  pdot: -2.65e-05 Tolerance: 1e-04  Passed
                Rudder:  -0.11  rdot: -2.85e-18 Tolerance: 1e-04  Passed

V = 525.05 fps
u, v, w = 522.94, -1.07, 47.09

Trim solution for phi = 55 degrees:
  Trim successful
  Trim Results:
       Angle of Attack:   5.94  wdot:  6.32e-05 Tolerance: 1e-03  Passed
              Throttle:   0.72  udot:  5.62e-05 Tolerance: 1e-03  Passed
            Pitch Trim:  -0.31  qdot: -1.93e-06 Tolerance: 1e-04  Passed
              Sideslip:  -0.15  vdot:  1.17e-04 Tolerance: 1e-03  Passed
              Ailerons:  -0.02  pdot:  1.85e-05 Tolerance: 1e-04  Passed
                Rudder:  -0.11  rdot:  1.19e-18 Tolerance: 1e-04  Passed

V = 525.05 fps
u, v, w = 522.23, -1.38, 54.33

Trim solution for phi = 60 degrees:
  Trim successful
  Trim Results:
       Angle of Attack:   7.03  wdot:  4.34e-05 Tolerance: 1e-03  Passed
              Throttle:   0.76  udot: -5.94e-05 Tolerance: 1e-03  Passed
            Pitch Trim:  -0.38  qdot: -6.35e-07 Tolerance: 1e-04  Passed
              Sideslip:  -0.20  vdot:  2.95e-04 Tolerance: 1e-03  Passed
              Ailerons:  -0.02  pdot:  1.19e-05 Tolerance: 1e-04  Passed
                Rudder:  -0.12  rdot: -1.10e-17 Tolerance: 1e-04  Passed

V = 525.05 fps
u, v, w = 521.11, -1.87, 64.23

Note the trim solutions have a small amount of sideslip, but vdot == 0.

[AirshipSim]

Thanks @seanmcleod70 ,

To answer your original question I think V (true airspeed) should be used rather than just the u body velocity.
👍

the fact that, in your samples output, you have v close to zero but w definitely far from zero, confirms to me that w should be used in ψ ˙ calculation. Or even Vtrue, of course. I will open a PR this week to clean-up that function.

I have never used JSBSim through Python so far, and it will be a good exercise to retry your test code with w.

[agodemar]

@AirshipSim @seanmcleod70
I confirm that, in general, $u$ and $w$ should be considered in a trimmed turn; also in the particular case of $\beta=0$.
Here is something I wrote on the subject: AIAA-2007-6703-905, DeMarco, Duke & Berndt

[seanmcleod70]

Yep, I actually glanced at that report last night, and noticed that for the steady-state turn you have:

$$\dot{\psi} = \frac{g}{V} \tan{\phi}$$

So $V$ as opposed to only $u$.

The JSBSim trim routine doesn't enforce a coordinated turn, i.e. doesn't enforce $\beta = 0$, rather just that $\dot{v} = 0$.

Ah, I see in your paper you also don't assume a coordinated turn.

These results for the body-axis rates are different from those obtained by Chen and Jeske10 and used by
Duke et al.9 Chen and Jeske assume that the steady-state turn is a “coordinated turn” and that the angle
of sideslip, β, is zero. In our approach, we make no assumption on the angle of sideslip.

[AirshipSim]

Fix merged #1404