There is a discrepancy between the sideways forces induced by the rudder and the forces required for straight and level flight.
Let’s go over the basics. We know all forces act through the center of gravity.
We know in straight and level flight that:
Forces:
-
Thrust = Drag
-
Lift = Weight
Moments:
-
Thrust * Engine displacement = Yaw moment
-
Rudder force * rudder displacement= Yaw moment
Putting these together, we can calculate the rudder force by dividing the engine yaw moment by the rudder displacement.
When banked, a lateral force is induced on the aircraft. This lateral force can be calculated by the Sin(bank) * Lift.
In asymmetric flight, this lateral force is countered by the fuselage and rudder, however as there is 0 sideslip, there is no force from the fuselage and any lateral force has to be balanced by the rudder.
Putting these together, we can calculate the rudder force using the lateral force.
Note:
To simplify calculations, the units are simply pounds force and ft.
Fuel balance is manipulated to remove aileron input.
CG was moved to default position of -3.62 ft
Engine thrust var cannot be read and must be input manually.
Weather: Clear skies, 1000ft over water (no turbulence)
Below we can find an example of asymmetric flight in MSFS.
Calculations:
Rudder force by yaw moments:
Left engine: -75 lbs
Right engine: 365 lbs
Total moment: 2522 ftlbs
Divide that by the rudder arm of 16.38ft. We must have a rudder force of 154lbs.
Rudder force by Lateral force:
Bank: 3.89°
Weight: 3927 lbs
Lateral force: 264 lbs
That’s a discrepancy of 110 lbs. 170% difference between the forces. Can a flightmodel engineer please explain this discrepancy?
Relevant flightmodel data:
-
empty_weight_CG_position = -3.62,0,0.4;
-
vtail_pos_lon = -20 (The tail is 16.38 ft away from the CG)
-
Engine.0 = 0.7, -5.4, 0.1
-
Engine.1 = 0.7, 5.8, 0.1
-
prop_mod_moment_scalar_yaw = 1
Thrust data
Calculations
