What a difficult subject to explain in a short post! It almost requires its own educational video.
Dihedral was initially built into the earliest aircraft as a method of controlling roll as most early attempts at powered and unpowered flight did not understand the need for roll stability and it was only with the Wrights that roll stability and its importance was finally appreciated.
Dihedral uses the generated difference in lift between the 2 wings when the aircraft is rolled away from the horizontal to counter the roll forces and thereby return the aircraft to the horizontal attitude. Unfortunately too much dihedral can introduce dangerous handling characteristics such as Dutch roll where in the extreme the rudder causing the turn and hence the roll effect can and does cause the lower wing to fly too slowly and actually stall. This stall causes a violent roll in the direction of the turn and can be fatal at low attitude.
Polyhedral was investigated as a method of providing the stability of extreme dihedral with a less susceptibility to extreme dutch roll especially in early FF models.
For aerodynamic considerations in real aircraft the purpose of the aircraft and its required flight performance dictated the wing placement and any dihedral etc. The four current stability trends are Dihedral, (including polyhedral), Anhedral, Pendulum, and flight stability controllers. At this time I will not mention Stability controllers as they do not dictate the aircraft desin.
Pendulum stability is where the weight of the aircraft, (its centre of mass is below the centre of lift. as the aircraft rolls the centre of mass is moved in the opposite direction to that of the roll. This higher percentage of the mass being more on the higher wing side of the centre of lift applies a greater share of the gravitational force to the higher wing causing it to be more highly loaded and therefore to start to drop until the wing centre of lift and the centre of mass are once again lined up vertically. Pendulum stability is normally found in parasol and shoulder wing designs.
Mass is the key to current stability design. Where the centre of mass is actually above the centre of lift Dihedral can raise the centre of lift and effectively negate inherent pendulum stability or instability effects Such dihedral can be seen in WWII fighter aircraft where the roll stability was needed to be reduced markedly to enhance maneuverability. Shoulder wing designs, (such as the Harrier, AV-8B), have the centre of mass below the wings and so anhedral was included in the design to overcome the roll stability issues in the design, (such anhedral can also be observed in a number of modern heavy lift high speed military transport aircraft,
Dihedral in model design. As models are far lighter in relative terms in both weight and wing loading it seems that best guess is the normal rule. BUT, If you are not pushing for that scale design normally far less dihedral is required than was used in the real aircraft design and in many cases dihedral can be done away with all together. My FT simple cub easily flies the full length of our field, "Hands Off", without any dihedral due to its inherent pendulum stability. (Mind you an accurate build is required).
If doing your own design I recommend you start without any dihedral unless your design demands it and alter the dihedral after the fl=irst evaluation flights during which you determine the models handling and inherent stability issues. Adding dihedral just because it looks right seems to be the accepted norm.
Have fun!
