Colin Mill - Practical Theories

In the May issue I looked at the way the main rotor reacts in forward flight. We saw that to cope with the different airspeed seen by the blades on the advancing and retreating sides of the rotor disk it was necessary to allow the blades some freedom to flap up and down as they go round. This time we will look at the way the rotor head allows control of the helicopter in roll and pitch. This is done by changing the angle of attack of the blades. To permit the angle of attack of the blades to be varied they are pivoted around an axis that points approximately along the length of the blades. These pivots are called the feathering hinges or feathering shafts. Rolling and pitching control is provided by changing the angle of attack of the blades in a cyclic manner. The angle of attack is increased as a blade passes through some part of its rotation while being decreased when it is on the other side of the rotor. For obvious reasons this is called cyclic control.

At first sight it can seem as if the roll and pitch cyclic controls are crossed over however the following way of looking at things helps overcome that confusion.

In figure 1 we see what happens when a clockwise rotor has cyclic control applied. In this example the control is arranged to increase the angle of attack of the blades at the back of the rotor and reduce it at the front of the rotor. In response to the increase in attack, the blades (which are more or less free to hinge up and down) respond by climbing as they travel around the rear half of the rotor. Conversely, in response to the reduced angle of attack there the blades fall on going round the front half of the rotor. The result of this is for the rotor to take on a tilt with the 'high point' on the left side of the helicopter and the 'low point' on the right. In other words the effect of this particular cyclic control is for the rotor to roll to the right.

We can get another insight into the way the rotor responds by looking at the same situation as seen from behind the helicopter. To keep things simple let us imagine that the helicopter is strapped down preventing it from following the rolling motion. In Figure 2(a) we catch the rotor the instant the control is applied (but before the rotor has had time to respond). Here the different angles of attack at the rotor disk front and rotor disk back resulting from the cyclic input are seen. In Figure 2(b) we see the situation when the rotor disc has had time to tilt over to the right. Notice how the blades are now at the same angle of attack all the way around the rotor. This happens because the tilt of the rotor disc changes the path of the blades through the air but, because we have fixed the helicopter, the head and swashplate (that are responsible for fixing the direction in which the blades 'point') have not tilted and so the direction of the zero-lift line of the blades has not changed. There is a simple relationship between the cyclic pitch and the limit to which the rotor disc will tilt. If the cyclic control increases the angle of attack at the back of the rotor by 5 degrees and decreases it by 5 degrees at the front, the rotor disc will tilt over by 5 degrees relative to the head and stop.

If the helicopter is not strapped down the tilting of the rotor disc will be followed by the body rolling with it. The force that the rotor imparts to the body when cyclic controls are applied comes from three causes. The first source of torque (turning effort) results from the thrust of the rotor no longer acting straight through the helicopter's centre of gravity (C of G). As can be seen from figure 3 the thrust line now passes to one side of the C of G and the resulting torque is equal to the rotor thrust multiplied by the distance between the thrust line and the C of G.

This torque depends on the size and direction of the rotor thrust. In the hover the thrust will approximately equal the weight of the helicopter and the torque will be acting to make the body follow the rotor. In inverted flight however the direction of the thrust is reversed. This reverses the torque that now acts to tip the helicopter in the wrong direction (see Fig. 4). So this torque is de-stabilising for an inverted helicopter and for reasonable stability in inverted flight it is important that the other torques are big enough to overcome this effect. We can minimise this torque by keeping the distance between the rotor head and the helicopter's C of G to a minimum.

The second source of torque between the rotor and the body comes from the head having some sort of damper rubbers or spring plates that resist the free up and down hinging of the blades. As the plane of the rotor tilts relative to the head these come into play and provide a torque tending to roll (or pitch) the body with the rotor disc. Where the damper rubbers are very hard, flexibility of the blades may also come into play.

Finally, if the rotor head has flapping hinges (such as the 'Concept') there is a torque due to the centrifugal force acting on the blades combined with the separation of the hinges. Fig. 5 shows an exaggerated situation where the rotor disc is canted over relative to the head. The uplifted blade on the left is pulling the left hand side of the head up while the blade on the right is pulling the right hand side of the head down. Because the blades are not hinged at the same point but at flapping hinges that are separated the result is a torque that is trying to tilt the head to the right. This force increases with increasing distance between the flapping hinges and with increasing centrifugal force on the blades. The latter means that heavy blades and high rotor head speeds will give an increase in this torque and cause the body to respond faster to rotor disc tilting. Some heads have a single axle and no flapping hinges. In these cases this effect is absent.

Now let us return to the case of our right roll command and see what happens when the helicopter is free to follow the rotor. Because of its inertia the helicopter body initially lags behind the rotor but the torques we have just looked at accelerate the body into the roll and eventually the body 'catches up' with the rotor. If the roll command is held on the cyclic pitch on the blades is maintained because the swashplate moves with the body. Rather than stopping as we had with the helicopter strapped down, the rotor continues to roll and the body goes with it. It is fair to ask how fast the helicopter will roll. However, the answer to this does not rest with the forces we have just been discussing as they do not set the final roll or pitch rate but rather they govern how quickly that rate will be reached.

The speed of response of the rotor to cyclic commands is very important to the controllability of the machine. If the response of the helicopter to cyclic commands is too slow the pilot may, in extreme cases, have insufficient authority to correct for natural disturbances in the helicopter attitude. Conversely, the helicopter may be so quick to respond to cyclic controls that the pilot is unable to react fast enough to maintain proper control. The natural tendency with model helicopters is towards an excessively rapid response. It is generally the requirement that the control system tame this exuberance. So far we have assumed that the cyclic controls are applied directly from the servos to the main blades (well, via the swashplate of course). Without very careful design, this arrangement makes for a helicopter that responds too quickly for a human pilot to control. This is because the main blades respond very quickly to cyclic control inputs. The aerodynamic forces acting on the blades are large (comparable to the weight of the helicopter of course!) On the other hand the blades are relatively light so it is inevitable that the blades will react quickly to any changes in their angle of attack. To get some idea, the two situations shown in figure 2 would typically be separated in time by only a few hundredths of a second. The application of a small, say 5 degree, cyclic control could cause a roll rate of more than 360 degrees per second. This sort of handling characteristic would render the machine almost un-controllable.

While some so called 'flybarless' model helicopters exist they are by no means common, and with very few exceptions are scale types where the choice has been driven by the need for scale appearance rather than by handling characteristics. The vast majority of model helicopters employ a control system, standing between the servos and the main blades, to regulate the response to cyclic controls. These systems vary in many respects, however they all have one feature in common: the flybar, about which more next time.

Last time I touched on the question of the cyclic response of a model helicopter. We saw that the natural tendency is for the main blades to respond too quickly to cyclic commands. This happens because the aerodynamic forces acting on the blades are large compared to the weight of the blades. We can't do much about this because the lift on the blades has to be big enough to support the weight of the helicopter and so we can reduce the forces on the blades only at the expense of not having the helicopter fly at all!

The control systems employed on model helicopters almost without exception employ a flybar to overcome these difficulties.

The flybar as illustrated here consists of a rod carrying small aerofoils (paddles) and is pivoted so that it may rock. The angle of attack of the paddles is set by the cyclic control and they respond in much the way outlined for the main blades last time. Again, to roll the flybar to the right the angle of attack of the paddles is increased on going round the rear half of the rotor and reduced on going round the front half of the rotor. This is simply done by rotating the whole bar around its axis. Because the flybar is not responsible for lifting the helicopter the aerodynamic forces acting on the paddles can be tailored to give the required speed of response. It is best to think of the flybar as a gyroscope that can be steered by the cyclic controls but when not being steered tends to maintain its axis of rotation relative to the ground rather than the helicopter body or the air. The speed of response of the flybar to commands can be adjusted as follows:

This last point was something that Ken Rudd touched on in W3MH some time ago. However its not obvious why this should be the case so let me just give my reasoning for it. If we take one size and weight of paddles and fit them to a flybar that has been lengthened by say 10%. We :-

Now effect 1) acts to slow down the response of the flybar, and it involves a square law so a 10% increase in flybar length increases the torque needed for a given roll rate by about 20%. However, effect 3) also involves a square law so, with the paddles 10% further out they produce 20% more force for a given cyclic pitch. So effects 1) and 3) cancel one another out. This leaves effect 2) which is linear and so a 10% increase in flybar length speeds the flybar up by 10%.

This is the simpler of the two systems seen on models. In this case the cyclic controls are transmitted from the servos to the flybar only. The cyclic pitch variations of the main blades are then controlled entirely by the tilting of the flybar. The sequence of events that follows the application of a cyclic roll control go like this:

The amount of cyclic control applied to the main blades is automatically adjusted so that the correct roll rate is maintained. The more the main rotor lag behind the flybar the greater the cyclic control applied to the main blades and vice versa.

The problem with the basic Hiller control system is the delay it introduces in the response of the helicopter. The pilot must wait for the flybar to respond before his cyclic commands get through to the main rotor. This means that a degree of anticipation is required by the pilot to get the control inputs in slightly ahead of their being required.

The Bell-Hiller system of control addresses this problem and has become almost universal in modern model helicopter designs. In this system the cyclic controls go to the flybar as before. A proportion of the cyclic control is also taken directly to the main blades and mixed with the cyclic control from the tilt of the flybar. The Bell-Hiller mixing ratio determines the proportion of the main blades cyclic control comes directly from the swashplate and how much comes from the flybar. When a cyclic control input is made the main blades now respond immediately to the command. Any tendency for the main rotor to roll too far or too fast is resisted. If the main rotor overtakes the flybar in the roll the control fed from the flybar to the main blades will reduce the cyclic control on the main blades and slow their progress. The beauty of the Bell-Hiller system is the degree to which the response of the helicopter can be adjusted to suit various requirements. For a beginner, the helicopter can be set up so that the flybar roll rate is very slow by using heavy paddles. The resulting machine can still have a quick response to cyclic commands because of the direct element of the main blade control that allows the main rotor to tilt before the flybar has moved. The slowly responding flybar helps in two ways. It limits the initial rotor tilt and acts to help return the rotor level after the command has been released.

So far we have only considered the action of the flybar in the hover but it is interesting to see what happens to the flybar in forward flight.

Normally the paddles of the flybar are set with no collective pitch. In forward flight the helicopter is tilted nose down and there is a net downflow through the main rotor. This means that the flybar paddles are at a negative angle of attack. As a consequence the paddles are pushing downwards. However, when the paddles are on the advancing side they have a higher airspeed and the downforce is greater than on the retreating side. The paddles fall on the advancing side and rise on the retreating side resulting in a nose down tilting of the flybar. If this effect was not opposed the helicopter would take on a steadily increasing nose down attitude and dive into the ground. What opposes the nose down tendency? Previously we saw that in forward flight the greater lift of the blades on the advancing side causes the main rotor to have a nose-up tendency and this requires some forward cyclic control to be used if a constant attitude is to be maintained. The natural nose-down tendency of the flybar will go some way to provide this. A correct balance between the two opposing effects depends on many factors: Flybar length influences the advance ratio of the paddles. Bell-Hiller mixing ratio determines how much the main blade cyclic pitch is changed by the nose-down attitude of the flybar. The stiffness of the damper rubbers, etc. determines how closely the body follows the main rotor attitude. The attitude of the body determines the plane of the swashplate that in turn influences the cyclic pitch of the flybar etc, etc. Down force on the tailplane and drag on the tail rotor and the boom all provide a stabilising influence on the nose-up nose-down attitude of the helicopter. Certainly, this seems to be one aspect of the helicopter where almost every component has some influence.

In the last few articles we have seen how cyclic control of the pitching and rolling motion of the helicopter is accomplished and how Hiller and Bell-Hiller control systems allow the response of the helicopter to cyclic control to be tailored. We saw that, for freely flapping blades the maximum cyclic pitch must be applied 90 degrees before the required high point of the flapping. In other words, for a clockwise rotor a right roll is caused by having maximum cyclic pitch as the blades cross the boom, and nose-down pitching is caused by having maximum cyclic pitch on the retreating side of the rotor.

In the May issue I mentioned (when considering forward flight) that offset flapping hinges and damper rubber stiffness change the way in which the blades flap, and that they could cause a roll tendency in forward flight. Cyclic control response is also changed by flapping hinge offset and damper stiffness. They cause the high point of the flap to occur earlier, that is, less than 90 degrees after the maximum cyclic pitch.

In this illustration we see what happens if we continue to apply the cyclic controls 90 degrees ahead of the required motion. Notice how the right roll command now additionally causes a nose down pitching motion. To combat this the control system needs to feed the cyclic inputs in later in the rotation. This can be done by rotating the swash plate in the direction of rotation. With the cyclic controls retarded in this way the correct response to cyclic inputs is obtained as seen below.

The Hiller and Bell-Hiller control systems have the effect of reducing these cyclic control phase shifts and so many model helicopters make no provision for rotating the swashplate. The flybar in the control system is freely rocking and pivoted on the axis of the main shaft (the equivalent of having zero flapping hinge offset) so it does not suffer the sort of phase errors just described. In the Hiller control system the cyclic control to the main blades comes from the flybar and any tendency for the blades to misbehave (pitch up or down during a roll command for example) is suppressed. This happens because any angle between the plane of the main blades and the flybar causes a correcting cyclic control to be fed to the main blades to make them follow the flybar. If in a roll the main blades start to pitch nose down the nose down attitude of the main blades relative to the flybar will cause some nose up cyclic control to be fed to the main blades opposing further nose down movement. The same happens with the Bell-Hiller system but because a proportion of the cyclic control of the main blades taken directly from the swash plate, the degree of phase error suppression is lower. Where the mechanics provides the facility, residual phase errors can of course be removed by rotating the swashplate as mentioned before.

This is a rather involved topic and here I will be looking at just a few aspects such as the position of the Centre of Gravity, or more strictly Centre of Gyration, the position of the Lead-Lag hinge (i.e. the bolt hole) and the stiffness of the blade.

In the May article we touched on the forces that determine the coning angle but at this point it is worth looking on more detail at the forces acting on the blades. Figure 3 shows how the forces are distributed along the length of a blade. Because most of the lift is generated by the fast moving outer part of the blade the lift acts as if centred on a point some 80% of the blade length out from the main shaft. The blade cones up until the lift is balanced by the component of the centrifugal force that is perpendicular to the blade. The centrifugal force does not act at the centre of gravity but at a point called the Centre of Gyration. The Centre of Gyration differs from the Centre of Gravity because, when considering centrifugal forces weight near the centre of rotation (the main shaft) is moving more slowly and is less important than weight further out along the blade. For a blade that is uniform along its length the centre of gyration is 58% out along the blade. The addition of weight at the tip moves the Centre of Gyration further out. Adding 25 grams of lead right at the tip of a 70 gram blade will result in a Centre of Gyration located at about 70% of the blade length. The Centre of Gravity of this blade will, by contrast, be at about 62%.

Looking now at the chord-wise position of the Centre of Gyration, consider the blade is made from a single piece of uniform density material. The centre of gravity of such a blade will be about 35% of the chord back from the leading edge. If the blade is the same along its whole length (i.e. no weights) then the chord-wise position of the centre of gyration coincides with chord-wise position of the centre of gravity. An aerofoil generates more lift near the leading edge than it does near the trailing edge and as a consequence the centre of lift is only about 25% of the chord back from the leading edge.

This situation as viewed from the end of the blade is shown in Figure 4. Note the centre of gyration lies behind the centre of lift. The lift on the blade, acting at the centre of lift, is balanced by the downward component of the centrifugal force acting through the Centre of Gyration. The distance between the centre of lift and centre of gyration results in a twisting effort or couple that tends to twist the leading edge up and increase the angle of attack. If the blade is flexible to twisting any increase in lift will be accentuated by the increase in lift coefficient resulting from the blade twisting in the nose-up direction. This interaction between lift and twist can set off an oscillation called flutter in which the tip of the blade goes into large torsional vibrations that can make the helicopter uncontrollable or destroy the structure of the blade.

To prevent flutter the Centre of Gyration should be brought forward to a point at, or ahead, of the centre of lift. To this end, wooden blades are made using hardwood at the leading edge and balsa at the trailing edge. Weights added close to the leading edge move the Centre of Gyration even further forward. Weight added near the tip has a greater influence on the Centre of Gyration than weight near the root, so tip weights let into the leading edge of the blade can move the Centre of Gyration significantly ahead of the chord-wise position of the Centre of Gravity.

Figure 5 shows the situation when, by the addition of a leading-edge weight, the Centre of Gyration is ahead of the centre of lift. The twist on the blade is now reversed and acts to reduce the angle of attack of the blade. So, any increase in lift will be accompanied by the blade twisting nose-down to reduce the lift coefficient. This tends to damp out any variations in lift and flutter will not occur. In practice flutter will cease with the centre of gyration still some way behind the centre of lift. The stiffer the blade in torsion the further this will be.

It is interesting to look at the torque that the blades cause around the feathering shafts because this torque must be overcome by the control system and ultimately by the servos, especially the collective servo. This is one area where the design of the head has a great influence on how a given set of blades behave. Initially we will ignore the effect of lag angle. First let us look at the situation with unweighted blades.

Figure 6. Unweighted blade with bolt hole in line with centre of gyration

Figure 6 shows that with the bolt hole (which serves as the lead/lag hinge) in line with the centre of gyration at about 35% chord the centre of lift lies in front of the axis of the feathering shaft. Lift thus causes a torque about the feathering shaft that tends to increase the angle of attack. If there is any slop or sponginess in the collective linkage this can give a rather sharp response to collective control.

Figure 7. Blade with leading edge weight towards tip

In Figure 7 the Centre of Gyration has been moved out and forward by the addition of a leading- edge weight near the tip. Here the centre of lift is now behind the feathering shaft axis and lift causes a torque around this shaft tending to reduce the angle of attack. This makes for more tolerance of slop and 'give' in the linkages and a softer collective response.

Figure 8. Unweighted blade with bolt hole moved towards trailing edge

In figure 8 we see that the centre of gyration usually lies inside the centre of lift. Moving the bolt hole towards the trailing edge angles the blade backwards at the tip and moves the centre of lift backwards relative to the feathering shaft axis. Notice from Figure 7 that the addition of a tip weight moves the centre of gyration out along the blade and towards the centre of lift. This renders the movement of the bolt hole relatively less effective than on an unweighted blade.

Figure 9. Effect of lag angle on the distance between feathering shaft axis and centre of lift.

We now need to look at the effect of lag angle. The lag angle is caused by the torque transmitted by the head through the lead/lag hinge to the blades. We can see from Figure 9 that the lag angle moves the centre of lift back relative to the feathering shaft axis and so promotes a leading edge down torque about the feathering shaft. The lag angle varies from zero (or slightly negative) during autorotation to its maximum values under high load (high g) situations especially where the head RPM (and thus centrifugal force) are low. Here the design of the rotor head comes in because the lag angle depends on the distance between the lead/lag hinges. The greater the distance between these hinges the smaller the lag angle (see figure 10)

To sum up, the distribution of weight within the blade is important because the combination of a rearward Centre of Gyration and a high degree of torsional flexibility renders the blade susceptible to flutter. However, a very forward Centre of Gyration can cause a high load on the collective servo. This is especially so where a small distance between lead/lag hinges causes large lag angles especially under climb or during high g-load manoeuvres.