DIHEDRAL EFFECTS By Bill Meadowcroft, EAA 3052 robably no factor which influences stability is so misunderstood, among homebuilders, as is dihedral. This P stems from the fact that most of us are former model airplane builders, and what we now require in a manned airplane is exactly the opposite of what we required in a model. Dihedral affects a number of stability conditions in an airplane, unfortunately in opposite ways, so that we must choose which stability mode we want to be stable and choose our dihedral accordingly. The primary modes effected by dihedral are spiral stability and dutch-roll. As modelers we were interested in spiral stability so that our pride and joy wouldn't come thundering down in circles of decreasing radii and with increasing airspeed. In a full sized airplane a pilot can easily control this tendency since it comes on slowly. A great many airplanes now flying are unstable in the spiral mode although few pilots realize it. Dutch roll, on the other hand, is completely undesirable because it makes the passengers sick, the performance sick, and the navigation miserable. Airplanes have been built which exhibit dutch-roll and they are no joy to fly. One, a jet fighter in which the dihedral was dictated by the height at which the tip tanks would gravity feed, furnished the author with an unlimited number of sick radar-observers. The effect of excessive dihedral, as you probably suspect by now, is to induce dutch roll while making the spiral stability more positive. A side effect is to make the airplane sensitive in roll with rudder displacement. For those of you who are used to thinking of static and dynamic stability as being different I should perhaps mention that spiral stability is a static action while dutch roll is of the dynamic variety, and in common with many dynamic phenomena is difficult to damp because of its short period. Up to now I have intimated that you can't have both spiral stability and freedom from dutch roll in the same design. As most of you are aware this not the case, if you design carefully and you are lucky you can have both. The converse- is also true if you play your cards right you can end up in misery. The point here is to design toward elimination of dutch roll because you probably will never notice a slight case of spiral instability. Now that we are all confused I'll add to the despair by saying that less criteria exists for choosing dihedral than for probably any other stability factor. In designing the F-104 a pilot flew a simulator while the designers varied the dihedral effect by means of a computer. The result came out with drooping wings. The following is an approximate method suggested by Perkins and Hage which will at least serve as an improvement on the eyeball for dihedral determination. The factors which contribute to effective dihedral and the symbols which will be used here are: geometric dihedral angle (A), tip shape (B), vertical tail effect (C), fuselage interference effect on the wing (D), and wing interference effect on the vertical tail (E). The Air Force usually shoots for an effective dihedral value of: (A)+(B)+(C) + (D) + (E) = -00025 (square root of gross weight) wing span in feet (A) geometric dihedral angle effect
(B) tip shape looking at the wing tip from the front 7
+ .0002
\
—.0002
(C) vertical tail effect a. determine effective tail aspect ratio from: _ height of tail squared Note: squared means A.R. = 1.55 multiplied by itself vert i ca i tail area b. determine slope of tail lift curve a v by using A.R. A.R. aT 1 .028 2 .045 3 .056 4 .064 5 6 7
.070 .073 .075
c. determines height of center of vertical tail area from wing (+ if above wing, — if below wing) in inches d. now _ a v (value from c.) (vertical tail area)____ ~~ (height of vertical tail in inches) (wing area) (D) fuselage effect on wing High wing .0006 Mid wing 0 Low wing —.0008 (E) wing effect on vertical tail High wing .00016 Mid wing 0 Low wing —.00016 Just for practice let's determine what the geometric dihedral angle should be on my airplane, Chinook. 1. Find required dihedral value .00025x(1200#)'/2 — .00346 25' 2. On Chinook the tip shape value (B) is O 3. Chinook is a mid wing so (D) and (E) are O 4. To find the vertical tail effect (C) a. AR= 1.55x32x32= 1.57 1010 This is OK for a conventional tail but Chinook has a "T" tail so we multiply by 1.33 to get 2.09 b. From the chart av=.045 c. The height of the center of tail area above the wing is 11 inches.
5. Now combining the information above and using the Air Force criterion: (A) + (B) + (C) + (D)+(E)=.00346 (A) contains the angle we want (.0138xdihedral angle) +0+. 00904 + 0+0= .00346 dihedral angle =~-°°5,5,8 = —.408 degrees .Uloo
We don't use any geometric dihedral angle and she flies beautifully, demonstrating neither spiral instability nor dutch roll, so apparently if you stay near the suggested value you are within the envelope. Good luck!
(A)=.0138xdihedral angle in degrees SPORT AVIATION
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