In general when there the pitch and roll exist the formula for the aerodynamic load factor should be as follows:
aerodynamic_load_factor = cosf(radians(_ahrs.pitch))/cosf(radians(demanded_roll));
which in case of turns (in the horizontal plane) becomes
aerodynamic_load_factor = 1.0f/cosf(radians(demanded_roll));
formulas can be obtained from equations of balanced spiral:
liftForce * cos(roll) = gravityForce * cos(pitch);
liftForce * sin(roll) = gravityForce * lateralAcceleration / gravityAcceleration; // as mass = gravityForce/gravityAcceleration
see issue #24320 [#24320].
To connect loadFactor to airspeed we can use formula of balancing between lift force and gravity force:
liftForce = loadFactor * gravityForce; on the other hand lift force can be expressed as
liftForce = 0.5 * lifCoefficient * airDensity * sq(airspeed) * referenceArea; minimum airseepd is at loadFactor = 1
and lift force only balances the gravit force, so gravity force (which is same as lift force at minimum airspeed) with minimum airspeed can be expressed as
gravityForce = 0.5 * lifCoefficient * airDensity * sq(airspeed_min) * referenceArea; substituting gravit force in previous formula gives us
0.5 * lifCoefficient * airDensity * sq(airspeed) * referenceArea = loadFactor * 0.5 * lifCoefficient * airDensity * sq(airspeed_min) * referenceArea;
from where we get:
loadFactor = sq(airspeed / airspeed_min);
These changes also require changes in ardupilot/libraries/AP_TECS/AP_TECS.cpp
Line 418 (according to the comments by Peter Hall): _TASmin *= _load_factor; should be changed to _TASmin *= safe_sqrt(_load_factor);
See details here: #24320
This is a rework so that servos.cpp is responsible for setting the
throttle limits under more circumstances and always notifies TECS when
it does so.
Additionally, the TAKEOFF mode has been improved with a new parameters
TKOFF_MODE and TKOFF_THR_MIN that extend the throttle behaviour.
this makes it much easier to do a yaw rate autotune, and also means
you don't need to use the rudder stick at all, as the yaw controller
is already exercised nicely with roll movements, so overall the tune
is faster and more accurate as less cross-axis coupling
this is needed due to the filtering done on the target rate in
AC_PID. With a low filter rate in AC_PID a step in the speed scaler
results in a step in the FF output due to the mismatch in the
instantaneous SS and the filtered target rate
to enable for ACRO mode, set ACRO_YAW_RATE to desired maximum rate in
degrees/second, and set YAW_RATE_ENABLE=1 to enable PID tuning of yaw
rate controller
pair programmed with Andy Palmer and Matthew Hampsey
