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Equivalent Dihedral Angle

Dihedral can be critical to a successful design. Too much dihedral leads to problems with dutch roll and too little makes for tricky trimming and perhaps the ultimate model killer: the spiral dive.

Simple V dihedral is easy to measure as an angle in the front view, but how do you measure dihedral on a Polyhedral or multi-panel wing where there is more than one angle? ‘Equivalent Dihedral Angle’ (or EDA) can be calculated to give the angle that you would find on an equivalent V-dihedral wing. This means a comparison can be made between the dihedral effectiveness of any model, regardless of the panel arrangement. Figure 1 shows three wings, all with the same equivalent dihedral of 15°: a simple V; raised wing tips and flat centre section as might be found on a towline glider; and a six-panel wing as per some tip-launched gliders and CLG’s.

In some disciplines getting the correct dihedral is the key to success, for example in catapult gliders where it is important for a good transition. By using EDA to compare what works and what doesn’t, designs can be improved.

It should be noted that in scale models the fuselage may affect dihedral effectiveness. A high wing model may behave as if it has an extra few degrees of dihedral, where as a low winger may require a degree or two more for similar stability. Significantly swept wings also give some dihedral effect.

The maths behind EDA is a little complex but by far the most convenient method is to use a dedicated calculator. A good one is available on Charles River RC’s site here: www.charlesriverrc.org/articles_modeldesign.htm
(direct link: http://www.charlesriverrc.org/articles/design/eda1.xls)

This simple Excel file allows you to put in the basic measurements of a model and gives you an EDA figure. The ‘Panel Angle Calculator’ enables you to work out the panel angles from the rise under each wing tip or dihedral break - with no protractor and no trig! (But do note that the ‘Panel Angle From Horizontal’ field is a total angle in the front view – each panel angle must be added to the last.)

The EDA calculation is not just an average of panel angles but also takes into account the area of each panel where it is situated. A panel at the wing tip is more effective than one near the centerline. It will provide more roll effect because it acts at a longer lever from the centre of gravity. Figure 2 shows the difference between a raised wing tip and a gull wing configuration. Although the two dihedral panels are the same size and angle the gull wing has a much reduced EDA.

The area of a panel also determines its effectiveness. A bigger panel will have a bigger effect. Therefore tapering the planform on a multi-panel wing reduces the area of the tip panels and reduces its EDA (note this does not affect the EDA of a simple V dihedral wing.) Figure 3 shows that tapering the wing tips on a towline model will require a greater panel angle to maintain the same EDA.

Of course dihedral is only one factor in a model’s flight behaviour. Tail moment arm, fin area and inertia all play a part in spiral stability. But used with this in mind, Equivalent Dihedral Angle is a handy tool that removes some of the guess work we often resort to!

For more on the maths behind EDA see Mark Drela’s lecture notes here:

And Blaine Rawdon’s article here:

Jonathan Whitmore
December 2013