Cross-coupling and Cyclic Control Rotor Phasing
Model aviators are very adaptable in the corrective piloting inputs as applied to the radio controlled helicopter. Unlike the fixed wing aircraft a helicopter is subjected to nonlinear dynamic changes as a result of outside forces imposed upon the rotor system. Most of the non-linearities occur any time other than hovering due to different or uneven air flow over and through the rotor disk. A helicopter is not a symmetrical flying device like the fixed wing aircraft for these reasons. Since there are different types of rotor designs and setups, the resulting cyclic corrections made by the pilot will vary somewhat from machine to machine. Going over basic helicopter dynamics written previously others may offer a better foundation for understanding this slightly advanced document. In any event by knowing that certain characteristics exist in different situations should certainly prove very useful during the long model helicopter learning journey.
Two things are often confused when it comes to ill effects during forward flight and sometimes during large stationary manoeuvres like standing flips and rolls. One is called swashplate phasing and the other is cross-coupling. Both these are similar in results yet different in cause. Before I go into detail too much you should understand that the magnitude of phasing effects are masked by the flybar in varying degrees being dependent on the weight of the bar and the mechanical geometry of the mixers. In essence the flybar is free to teeter unaffected directly by restrictive dampers or increased cyclic power supplied by independent offset (outboard) flapping spindles. These items will slightly alter the 1/4 revolution rotor response time. In other words the phasing would be exactly 90 degrees with the flybar if it were to be considered alone and soley by itself as a rotor. Many alterations to the dissymmetry of the helicopter control responses come and go during flight. Some add and some cancel each other depending on what the machine is doing at a particular time. Due to this fact it is presently impossible to mechanically modify the cyclic controls to cover all perspective flight situations and remove cross coupling. Like any other skill the experienced modeler will adapt and anticipate each situation using his best personal setup compromise and pilot judgement. Maybe one day gyro electronics will change this situation making the helicopter more like a plank to fly…..personally I certainly hope not!
To better understand rotor control phasing, think of it as a timing device. If the disk were to initially tip forward and slightly to the left on a CCW rotor with a purely forward cyclic stick deflection we would say it was retarded or happening too late. If it tipped initially to the right under the same control input it would be called advanced by occurring too early. Be cautioned though, what appears on the ground might not be the same case when in the air flying. The reason is that the fuselage is anchored to the ground and not allowed to follow the rotor. This is easily proven through cyclic deflection and observation on the ground and in the air. I first noticed this on a rigid flybar less system when I had adjusted the disk deflection on the ground exactly for a pure cyclic disk response to the stick inputs. This was accomplished using the idler rotation as it was so equipped, but rotating the swashplate non rotating portion or the washout driver will do the same thing. When I hovered this particular helicopter and air taxied around it was no longer “in phase,” so I to returned it to the standard “90 degree prior to” configuration with more sensible results. I have compiled information from extensive research using reputable sources and personal experiences on the matter since my interest was tweaked.
Cyclic control phasing can be changed in addition to mechanically altering the radial position of the swashplate inputs, by changing the stiffness of damper rubbers, using a different type of rotor head or altering the rotor inertia. By using the more elaborate radios the same modified swashplate effect can be established electronically. Again the effect of a flybar will play a very large role here in so far as corrective measures go. In all flight manoeuvres the highly desired 90 degree or 1/4 revolution response time of the rotor will not be available no matter which or how many crafty tricks are applied.
To better separate how the cyclic stick deflects the disk during a roll (as an example) with the free teetering, rigid and offset flapping spindles consider the following facts, again ignoring the flybar corrections. The rigid rotor responds the soonest followed by the offset spindled head, with the free teetering head being the slowest at 90 degrees. By soonest I don’t mean maximum cyclic rate or the cyclic acceleration rate even though the cyclic acceleration rate is in fact truly reflective of this. What I do mean is the actual point of rotation where the disk deflects for a given input when induced by the pilot’s cyclic stick. The diagrams depict the differences in a visual manner which I hope gets the point home better. A key point to remember here is that two forces cause the helicopter to roll and pitch. One is the re-directed rotor thrust or lift vector through tipping of the disk acting upon the fuselage. The helicopter follows or is pulled through the leveraged action of the mast to the c of g of the helicopter and rolls the helicopter. The second is the bending moment applied at the rotor hub through blade flapping which tends to speed up the cyclic. If the rotor is free teetering there will be no such secondary force. Since our models are not free teetering rotors at the center of the mast or rotor hub this will not be the case. This mast following force will still however be dependant on rotor flapping restraint (damper hardness) and rotor head design (offset flapping spindles).
As a brief review I shall cover blade flapping in order to better understand cross-coupling. Blade flapping is controlled by two factors. One is by the model aviator directly through the cyclic controls and the other is through the automated flapping of the disk due to external influences. It must be clearly stated that blade flapping occurs in a delayed order both through the design of the cyclic control inputs and in how the disk behaves to gusts or other outside influences. The angle of attack that a blade sees while being directly related to the cyclic and collective stick position is also related to the relative wind the blade sees at a given point in time.
Here is an important point to store in your mind. When a blade aerodynamically sees a higher angle of attack it will climb in a delayed manner. When the blade responds, so will the disk and hence the helicopter. When a gust enters the disk with the helicopter pointed into wind the rotor will flap aft. This flapping does two things. It will as imagined certainly attempt to pitch the helicopter. Secondly it will damp the external disturbance since the advancing blade is reducing its angle of attack with respect to the relative wind by flapping up and away from it. The retreating blade is doing the opposite by flapping down increasing its angle of attack. Remember think deferral here with the results being fore/aft. This is why auto gyros without a swashplate need larger amounts of blade flapping. Without ample amounts or the correct use of negative “Delta-3” the autogyro would pitch up in forward flight. Now all we have to figure out is when and where the blades see an angle of attack change other than what the pilot has directly commanded. Remember the pilot also controls blade flapping with the cyclic controls and can productively cancel out that which was caused by an outside force if seen as an undesirable.
After reviewing and understanding the article basics on this web site regarding “Delta” we may now expand upon it as it relates to phasing. As stated blade flapping will respond in the approximate belated 1/4 revolution manner. Since the delta effect takes affect as the blade rises or falls its affect upon the disk will lag behind. Since its affect to the disk is behind or dependant upon the blade actually climbing or diving it will impose an uncommanced cyclic factor. Think about a head wind gust, the rotor wants to tip aft as all rotors do. When the rotor tips aft the largest amount delta if so equipped will be fed to the blade pitch change horn. It will have some of its affect upon the disk deflection aproximately 1/4 revolution later resulting in a roll factor. This induced error is a form of acceleration cross-coupling. This is because it happens only during blade flapping. When a cyclic rate is established or in the case where the fuselage has caught up with the rotor, blade flapping is reduced. If flapping at the head is non-existant then delta geometry is doing nothing.
Another way to understand how delta functions at times in a main rotor head is that once the rotor disk becomes parallel to the swashplate tilt, the effects cease. This is because the rotor disk and head are now cyclically aligned to the control input. So really delta 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 as mentioned 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.
Let us take the example of a standing roll. Maximum cyclic blade pitch change is applied over the nose and tail due to the approximate 1/4 revolution response of the rotor disk. The helicopter disk deflects laterally and maximum flapping occurs during this lateral point of rotor rotation. The roll will now be accelerated until the fuselage and mast approach the maximum rolling velocity, at which time lateral flapping will be reduced. Another way to think of it is that the fuselage has caught up with the cyclic. This is because the rolling velocities of the disk and the helicopter are almost matched. Since flapping has in effect ceased at the (selected) maximum roll rate, the rotor head flapping design has little effect upon the maximum rate. It has however a large consequence on the roll acceleration up to this point. Phasing changes (accelerating cross-coupling) due to rigid or offset spindled rotor head flapping design will fade out as the maximum rate is approached. A left or right hand roll will cause a forward or aft tilt of the disk through this cross-couple and this is dependant on what directional rotation the rotor turns but not the direction of airflow (+/-collective) through the disk.
Another thing happens that causes uncommanded pitching to the rotor which is passed along to the helicopter. It is the result of secondary longitudinal flapping caused by the roll independent of what the pilot has inputted. For simplicity this example has ignored the accelerative/ decelerating effect that gravity will have through the fuselage c of g and the mast during a full roll including the application of negative collective when inverted. The reason for this non-commanded pitching (rate cross-coupling) during the roll has to do with the lateral lift imbalance which the rotor sees. Its results are seen in a delayed manner with blade flapping over the nose and tail. This is because one side of the disk is entering the roll with an increased angle of attack while the other side is rolling or attempting to exit from the very air it is trying to accelerate. What the blades see is an increased angle of attack on one side and decreased angle of attack on the other. Again this is observed approximately 90 degrees or 1/4 revolution later by the rotor in an automatic flapping response thus causing a pitching moment. The pilot corrects for this with the longitudinal (fore/aft) cyclic by cancelling out the undesired secondary flapping. This form is called “rate cross-coupling”. Another way to think of the “root” cause is that one side of the disk has the added velocity of the roll while the other side has this same velocity subtracted. We can see why this cross couple is called rate because its effect increases with the speed of the roll.
We now have two major things causing cross-coupling as mentioned earlier and it should be mentioned clearly how they relate to each other. At the initial start of the roll we will have accelerating cross-couple which will fade out upon approaching the maximum (or selected) roll rate where as the secondary fore/aft flapping (rate cross-coupling) will not. These two forms can be similar in nature, so initially they may have a somewhat cumulative effect upon one another in “specific situations” and the reverse in others. This is where the head type and/or dampening might be adjusted for a benefit. Delta might also be introduced to reduce flapping and cross-coupling but only at specific times.
Adjusting the phasing by swashplate/washout rotation should be considered if the cross-coupling is caused primarily by the rotor head and not the aerodynamic secondary flapping. There will also be an overlap factor to consider between two factors which I think should be averaged to a central best cross over point. By this I mean the area where one starts or accelerates a roll verses the other end where the roll is checked and decelerated.
Besides dealing with the type of rotor head, the inertia of the rotor blades can cause “apparent” changes to the amount of cross-coupling. The aerodynamic rate is not affected by the larger rotor blade inertial mass, even though the cyclic stick deflection will be larger for the same roll or pitch rate. What is relative is the ratio between the two, since the larger inertial situation will require more lateral cyclic (for a given roll rate) with the correction for rate cross-coupling being the same as a “lighter” situation. The blades also will not move out of their rotational plane as quickly and supply as large a bending moment to the mast. If we rig the control throws for a larger swashplate deflection to compensate for the heavy rotor, the pilot cross-coupling corrections at the stick will have to be smaller. If we leave the control rigging the same the balance between the two will be altered some.
Another manifestation of cross-coupling occurs from a flight configuration known as transverse flow. Transverse flow happens at low airspeed and is felt as a rolling moment which fades in and then out quickly at low forward airspeeds. The pilot corrects for this with an opposite lateral cyclic stick input as the helicopter tries to roll down into its advancing blade. The direction of rotor rotation will logically dictate the corrective measures required of the pilot. This situation should not be adjusted out with mechanical changes to the helicopter as all single rotor helicopters suffer from this. With transverse flow we have to consider the localized induced velocity at different areas of the rotor disk. Induced velocity is the air that the rotor pulls in which has an effect on the blades angle of attack. Since the model helicopter may complete an inverted landing approach into a stationary hover, transverse flow corrrections by the pilot will be opposite on the sticks. Think of it this way, the air is still accelerating towards the ground but in this respect or relatively speaking, the rotor rotation is reversed.
Overall or averaged induced velocity variance on the other hand is also what causes a higher collective and power requirement to be needed for hovering as compared to maintaining altitude at forward airspeeds. This is called translational lift in the forward flight mode. The same can be noticed in strong winds as the collective pitch and engine throttle opening will be reduced for hovering.
Now back to the localized parts of the disk, as once again induced velocity can be extremely different at various locations on the rotor disk causing an imbalance which must be corrected by the pilot’s cyclic to maintain the desired or current attitude. This transverse effect will vary depending on the machine, setup and flying style but it is notable never the less by keen observation. Basically the higher the induced velocity the lower the angle of attack. In this case the angle of attack will be higher at the front of the disk due to the lower (local)induced velocity as compared to the rear as exampled in the diagram. A vibration is encountered at the fore/aft point of the blades rotation but due to the delaying action (often called gyroscopic precession) the effective moment is felt laterally. The vibration is larger when decelerating towards the hover and can be often heard as excessive blade flapping. The ram air effect into the rotor as airspeed increases quickly removes the phenomenon. Remember, the blade sees air coming at it due to the rotors rotation, the downward induced velocity vectors and in addition to the helicopter airspeed considerations. I shall leave transverse at this for now but more importantly remember the end result will require minor pilot correction.
Cross-coupling occurs between the tail rotor and the main rotor. This is called “Translating Tendency” and is not to be confused with translational lift or picking up translation. The whole helicopter has a tendency to drift in the direction of tail rotor thrust. It is the result of the tail rotor thrust acting upon the helicopter as a whole. Since usually the tail rotor is located above the helicopters c of g its spot will have a small affect too. This situation is normally corrected with lateral swashplate trim thus altering the rotors tip path plane slightly to counteract. Another method is to tilt the mast which I have not personally seen built into a model up to this point in time. The term is rather confusing until you realize that the machine will drift off sideways and enter translational lift…. if it is not compensated for. Chances are it was an early pilot who named it, not fully realizing what it actually was or the confusion the term might cause.
The resultant tail rotor thrust will also have a pitching effect on the helicopter since the countering cyclic roll position that is holding the aircraft stationary against said T/R thrust has also redirected the tail rotor downward. This is because the fuselage and tail boom has followed the main rotor disk deflection. So it can be seen that main rotor stiffness will play a role here. Mentioned earlier was main rotor phasing changes from acceleration cross-coupling. This effect in a very minor state, can show up in the hover when the rotor is not parallel to the helicopter’s longitudinal and lateral axis. So when we add all the little things together we can end up with a noticeable pitching error that should be corrected for during pirouettes. Some people have actually canted their tail rotor gearboxes to try to remove this problem. Doing so will however create other areas to be corrected for. The best thing to do is leave things in one mechanical condition and adapt your flying skills. If we want to nit pick, the height of the tail rotor may affect matters through a leveraged action.
Sometimes the collective can have an impact on the cyclic. This can be perceived when the collective is rapidly lowered in fast forward flight. The nose will pitch down or attempt to tuck under. The reverse is true of a collective increase causing a pitch up. Lucky for us the flybar is there to partially compensate in radical situations. Here is how it works in the case of a collective increase when not compensated for with the cyclic. Since the advancing and retreating sides are receiving the same collective pitch change but at the same time have different air velocities due to forward airspeed, the advancing side with the higher velocity develops more lift. This is seen as an imbalance with flapping occurring 1/4 revolution later up over the nose. This is a gradual out of trim flapping situation in normal smooth manoeuvres and the seasoned pilot subconsciously compensates with forward cyclic. We can see that cyclic trim is a function of forward air speed.
When the collective is moved down rather abruptly, things can become more noticeable. Lets say the machine is in fast forward flight and we decide to do an auto by quickly lowering the left stick before slowing down. The result will be seen as a nose down flapping requiring substantial aft cyclic to compensate. We can use this situation to our advantage should the engine fail. By lowering the collective and pulling more aft on the cyclic we can initiate a high speed flair increasing rotor rpm and also gain altitude until the optimum airspeed is reached for the best rate of descent. Guys flying flybarless model rotor heads, can and should tell you all about this lovely pitching issue!
Since I should have you thinking about relative angles of attack or what the blade actually sees from its perspective I’d like to take matters a step further. The angle you see on your pitch gage will be very different to what the blade actually encounters. We have the downward inflow of air through the rotor which reduces the angle of attack.
Also during a climb or descent the inflow of air will change as can be seen through the diagrams causing again a further reduction in angle of attack. A loose analogy might be a fixed wing propeller taching up at a lower rpm value at full throttle on the ground as compared to the higher in flight rpm situation. Some fixed wing props can have some pretty wild pitch angles. You may also want to consider the benefits of (safe?) run-up stands for model helicopter tuning purposes when you consider that the angle of attack a rotor sees will be less overall in a climb or decent as compared to being secured in position.
Let us consider a swept airfoil and the fact that it was developed to allow higher angles of attack prior to stalling. This includes both a forward and aft swept configuration. Since our helicopters operate in forward flight the disk will see a swept effect except for when the blades are directly over the sides of the machine. The non swept position is after all a very small part of the blades rotational journey. The blade also encounters its maximum cyclic blade pitch angle but momentarily. Because it takes time for an angle of attack instability to develop our rotors can be subjected to much higher angles than say a fixed wind airfoil. Due to the different airflow velocities along the blade, under normal conditions a complete stall will never occur.
Now coming back to the climb/descent diagrams and the auto diagram below it should be noted that due to the fact that inflow has reduced angle of attack it is possible for autorotation even at slightly positive pitch gage indications. We often argue/discuss when the blade stalls and what should be the maximum static blade pitch angle. Well I certainly hope that now you will view the pitch gage and transmitter sticks with a new found interest and respect.
These are but the most common causes of cross-coupling which tend make many of us better coordinated than the planksters on the sticks. The mechanical nature of the machine enables us to become better model engineers and technicians. Generally helicopter people tend to be broad minded, very safety conscious and better suited to improvising, when compared to our stiff winged counterparts. And that one fact of added complexity often separates the two schools unfortunately.
Finally, if you adjust the swashplate phasing, do so in tiny amounts since chances are that the results very well could be made undesirable. Make considerations to your flybar, rotor and your flying style since it is a big part of the end result. The fore mentioned examples are but some of the major forms of control cross-coupling the helicopter pilot must succumb to. The same respective principals can be applied to various cyclic/flight conditions. What you see contained in this text is a result of my past full scale and model knowledge/experience, and adjusted to apply to our hobby as best I could. I still expect to learn more in the future and hope others will write more on these detailed issues. If you want to keep your head buried in the sand….you’ve come to the wrong web site!