Plane: Fixed formulas for load factor and roll, also corrected _TASmin in AP_TECS accordingly #29101
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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 ArduPilot#24320 [ArduPilot#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: ArduPilot#24320
…r the load factor 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); and_TASmin should be _TASmin *= safe_sqrt(_load_factor);
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This is a rebase of #24509, see also #24320 and #29092
Were were passing about the sqrt log the laod factor. This changes to the standard definition. There should be no change in behavior.