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In simple words could someone please explain the working principle of a dorsal fin in a two engined propelled airplane?

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Dorsal Fin

It is vertical surface located above the fuselage; it has a low aspect ratio and (usually) a high sweep angle. Such aerofoils inherently have a high induced downwash, which delays their critical AoA to a higher angle. This means that the dorsal fin will stall at higher sideslip angles.

Graph showing contribution of various aircraft surfaces on static directional stability

If an engine failure occurs on a twin-engine aircraft at low airspeeds, the resulting yawing moment can produce large sideslip angles. If the fin stalls under this condition, the aircraft will lose directional stability, and the yawing moment of the live engine will force the aircraft to spin out of control. This is certainly not ideal, and the dorsal fin delays this occurance to a higher slip angle.

At large sideslip angles, the dorsal fin also sheds a strong vortex across the main fin surface (including the rudder). This re-energies the boundary layer, thereby delaying seperation. Not only does this increase the stall angle of the main fin, but it also increases the effectiveness of the rudder - improving its ability to counteract the yaw. This makes the dorsal fin sutable for twin-engine aircraft.

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