What is Delta Hinging?
A rotor disk will react from outside influences such as a gust of wind in a precessed manner. A gust of wind over the nose (head wind gust) will cause the main rotor rotor disk to tip aft because the advancing blade flaps up 90 degrees later from this increase in lift. On the other side of the disk a corresponding decrease in lift over the retreating side will cause the blade to dip low. This is called blade flapping. Blade flapping also allows a disk to tilt somewhat independently. Flapping aids in combatting dissymmetry of lift since an upward flapping advancing blade reduces its angle of attack with the relative wind. The downward flapping blade on the retreating side over the tail (90 degree thing again) will increase its angle of attack with the relative wind. This is automatic and self correcting lift wise. This has nothing to do with pitch change or feathering since the key word is relative wind, unless something else called “delta” or “offset pitch horn hinging” is implemented. These are two different forms of a flapping hinge and as usual with things in life there are possible hybrids of the two.
“Dis-symmetry of lift” is caused by the forward motion of the helicopter or airspeed. One half of the rotor has rotational velocity plus air speed, the other side has rotational velocity minus forward airspeed. While the blade is on one half of its rotation it is said to be advancing and on the other half of its journey retreating. Unless something is done there will be a lift imbalance.
Dis-symmetry of lift affects main and tail rotors a like. From the above we can correctly assume that if the blades and head are rigid a bending moment will be imposed on the mast or tail rotor output shaft. This bending moment will in the case of the main rotor cause the fuselage to follow the rotor.
For the main rotor, the swashplate normally compensates for dis-symmetry of lift through pilot cyclic commands. However transient changes to the airflow through the disk from a gust of wind or unanticipated manouevre can change the helicopters heading or attitude. Blade flapping freedom or delta will automatically help to offset these quick and short outside influences. Since the amount of delta is small its influence is also small. The fact that it (negative delta) may alter a cyclic command makes large amounts of it undesirable. It can however help fine tune a marginal setup or personalize the feel of the helicopter controls.
Often we find ourselves reading about things containing the word “delta”, delta three, delta tail rotor, delta this and delta that. This word “Delta-three” is properly used to describe a type of rotor hinging. It is related to the flapping or teetering hinge. Its main purpose is to enhance the automatic equalizing results that normal flapping offers in compensating for dissymmetry of lift. It can also be considered a flapping damper because in effect it tends to reduce flapping. A normal flapping hinge is located 90 degrees to the feathering axis and a delta hinge is not. This hinge is actually moved back opposite the direction of rotation. Through this geometry the flapping action will impart a rolling motion to the rotor hub and blade assembly as a whole.
What this means is that a properly delta hinged rotor does not have to flap as far as a standard flapping hinge to equalize rotor disk lift imbalances. In other words when it flaps, pitch is rolled out of the upward flapping advancing blade and into the retreating blade without any actual feathering movement between the hub and blade grip. This is not without possible cost though since it alters the rotors responce phasing slightly. With this system damper hardness will play a part in the amount of flap reduction compensation. This is again termed negative delta. By strict definition according to some books, negative delta is when the blade pitch angle is reduced, subtracted, or pulled out with flapping (up) towards the direction of rotor thrust and thus makes the best sense to me. Other books term the same process positive delta. Confusing, yes it is, but so long as you understand the process, that is the important thing. Either positive or negative delta may be used to actually shift a poorly phased main rotor into a better condition dependant of course where the problem area may be.You will normally find the negative method used on the tail rotor at the hub centre. Some full scale use an offset delta hinge on each T/R blade but I have yet to see this on a model. One thing both negative and positive delta do is shift the rotors natural flap frequency and damp or reduce flapping by shifting it away from a resonant condition.
With a rigid tail rotor, lift imbalance will try to bend the shaft aft in forward flight which mechanically loads up the bearings and hub/grips. We can remove some of this loading through delta hinging or normal flapping, which will make life easier for the structural integrity of the tail rotor system. This can be a good idea and several machines are currently reaping such benefits. It is not absolutely necessary with many models because nowadays most are built very, very strong. Be cautioned, some manufacturers with this system employed have warned users of hub failures occuring from installing heavier TR blades and removing all flapping action.
Now for the offset pitch horn, which is an entirely different delta type beast. With some models this is used on the main rotor head. The same self balancing (lift) benefits may be enjoyed, but with reduced flapping. What happens is that the axis where normal flapping is located and centred to the mast, is not the same as compared to the axis of the more outboard blade pitch horn. When the advancing blade flaps up a feathering action between the grip and the head spindle will occur. This reduces the amount of lift produced by this blade. The further outboard the pitch horn from the flapping axis, the larger the reduction of pitch with upward flapping. Certainly the reverse is true concerning the retreating blade. With this system damper hardness will play a part in the role of corrective compensation. Some machines even have a provision for moving the location of the ball on the pitch horn or the mixer assembly as a whole. By moving the mixer, mixing ratios are preserved. The advantage of this method of flap reduction might be noticed in forward flight as it has an opposition factor to those pitch up tendencies we often see. Less flapping with more compensation means that the rotor disk is not disturbed as much and fed back through the fuselage. Many manufacturers prefer to have the pitch horns leading so that any geometric flapping interaction (negative delta) will work for you rather than against so far as blade flutter goes. It is also common to have the pitch horn in line or very close in line with the teetering or flapping axis of the head, thus avoiding any interaction by depending solely on normal flapping in itself.
We have another option with independent blade spindles. The flapping hinges can be located outboard with respect to the pitch horns. As the blade flaps up, pitch will be feathered out (negative delta) if the pitch horn is trailing in the direction of rotor rotation. The same applies to the offset mixer/ pitch horn if used in this configuration.
If you have a rigid or very stiff flapping head, delta offset does not generally matter. If however you are experiencing pitching in fast forward flight with any rotor head, that is further aggravated by lower flybar weight and/or soft damping, you might want to think in this direction. Tracking or blade flutter issues may also be corrected with the proper use of negative delta. Some single spindle models which have trailing pitch horns have exhibited this property. The corrections or errors induced, depending on proper application are small, but they are part of the rotors geometry and should not be dismissed so quickly. One machine covered on this web site had blade flutter problems (the earliest Raptor Version I) although the manufacturer has presently fully corrected the issue on the latest Version II. By flipping the blade grips on the V-I, blade flutter has been removed. Manufacturers such as Bergen, Miniature Aircraft and Vario all have or at least lay claims to negative delta rotor heads. The former two are adjustable while the latter is not. It can be stated that negative delta makes for a more stable rotor disk.
What many people fail to understand about delta employed into a main rotor head is that once the rotor disk becomes parallel to the swashplate tilt the effects cease. This is because the rotor is now cyclically aligned to the control input. So really its effect can be said to be somewhat transient in nature occurring during the initial control input or when ever the rotor is disturbed by an outside influence. There is also a cyclic phase error when delta is effective. This is because of the delayed 1/4 revolution rotor response. Max delta feathering occurs at maximum flap, maximum delta induced flap occurs 90 degrees later. The delta phase error can be used as a corrective measure in rotors exhibiting a natural out of phase condition during cyclic acceleration. There needs to be alot for it to be felt in a model and quite frankly the heads are so stiff these days that flap/feather coupling is minimal at best.
With helicopters many things are going on and sometimes one item can compensate for another with a net benefit. This however is not the most efficient way, even though it does work. This might be the case of using stiff damping when the flapping geometry is not co-operating. It might make the machine too crisp in cyclic control for some peoples liking. Keep this in mind when trying to understand your heli and eventually differing designs will make more sense. It’s all part of the attraction! The diagrams represent no machine in particular and were constructed purely as a very basic instructional tool.
While we are on the subject of rotor hinging, I would like to bring to your attention a nifty method which directly affects the dynamic balance of the two bladed main rotor system. The system is called “underslinging” and there is a special article dedicated to it on this very web site. It is nothing more than a geometric mass correction for blade flapping which is accomplished by mounting the feathering axis below the teetering or flapping axis. By using this system, rotor dampers are not required except as a flapping restraint to encourage the fuselage to follow the rotor tilt better. A side effect of non-underslung blade flapping, Coriolis effect can induce a spanwise mass imbalance. The Coriolis diagram will explain fully. This system only works in a correcting manner under positive “G’s” or with the airflow through the rotor in the conventional direction. Well I hope you liked this, if not, remember what a tangled web our helis can weave. The next article in this series will include the finer points of delta and how it can relate to control cross-couple, so have a look. The term delta is often used as a marketing tool so judge your purchases wisely. Delta is used for various reasons, some of which you may not aware of. The links and quotes should below should tweak your interest.