# What causes the secondary effect of rudder, and which direction does it act?

I understand that rudder deflection causes several things to happen. Primarily the aircraft yaws, and for a positive (trailing edge left) rudder deflection there will be a positive side force generated and negative yawing moment to yaw the plane nose left. I also understand that there is a direct secondary effect of rudder in that the side force acting at a distance above the roll axis of the aircraft creates a rolling moment (positive rolling moment to starboard for a positive rudder deflection) and there is a yaw-induced effect where as the aircraft yaws (in the case of positive rudder deflection the yaw is to port) the outer (starboard) wing experiences a greater flow velocity and therefore generates more lift which generates a negative rolling moment (to port).

My question is what is the overall rolling moment for some rudder deflection, is the direct effect stronger or is the yaw-induced effect stronger.

For context I am a third year aeronautical engineering student trying to answer this question: "About which axis does the secondary effect of rudder deflection act? About this axis which direction (sign) would a moment generated from a negative rudder defection act, for a conventional tailplane and rudder (relevant control derivative is positive)? Explain any reasoning behind your answer."

• If you have progressed to the third year of your studies without developing an instinctive feeling for the effects of the rudder being above the roll axis then I suggest you should consider taking up the design of boats. Jan 8 at 0:01
• The total resultant effect on roll from any rudder input, is a complex issue, dependant on several other factors, (AOA, airspeed, wing anhedral/dihedral and sweep, etc.), but generally, it will be in the same direction as rudder input, (right rudder will generate right roll and left rudder, left roll) Jan 8 at 12:19
• It would help a lot to build your own aircraft and try it. Imagine a very tall thin balsa rudder on your glider, then a square one with equal area. Then try varying degrees of wing dihedral. A small hill and some glue is all you need (paper works too). Jan 8 at 13:56
• @CharlesBretana The z axis positive direction is defined down in the kinematic coordinate system. The signs of deflections, forces and moments are correct. Jan 8 at 16:00
• Normally, rolling will be dominated by dihedral. The rudder will have only a minor influence, but it controls the yaw angle which produces the sideslip which in turn is necessary for dihedral to do its job. Jan 8 at 16:10