Parts 7 & 8

More on gyros

Having looked last time at delays in gyros I finished by saying that there were other defects in gyros that I would look at this time (what a fool I am!). In order to see how the defects come about we need to look a little at the ways in which gyros work, so here goes.

Mechanical gyros

The heart of a conventional (mechanical) gyro is a motor driven flywheel or, more typically two flywheels, one mounted at each end of the motor.

This whole assembly is suspended, in balance, from a pair of bearings that permit it to rock about a horizontal axis that's at right angles to the motor shaft. Springs apply a centring force so that it normally sits horizontally. As anyone who has played with a kid's gyroscope will know, if you try to change the direction in which the axis of a gyroscope points, the gyro 'fights' this, not with a force directly opposing the change, but rather by attempting to move in a direction at right angles to the one in which you tried to move it (could one perhaps think of gyros as being 'bloody-minded' ?)

For our tail rotor gyro this means that any attempt to turn it about a vertical axis (i.e. yaw it) will cause the gyro to 'want' to tilt about its horizontal axis (i.e. tilt in its support bearings). If it was not for the springs and limit stops the gyro assembly would continue to tilt until its axis was vertical (aligned with the axis about which it is being twisted). With the centring springs the gyro assembly tilts until the force of the springs arrests it. The greater the yaw rate the bigger the spring force needed and so the more the gyro assembly tilts in its bearings. So, if we arrange to measure how far (and in which direction) the assembly has tilted we have a measure of the rate of yaw. The sensing of the gyro tilt is typically done by a solid-state magnetic sensor called a Hall Effect probe who's output depends on the position of a small magnet attached to the gyro assembly. In an ideal situation the output of the Hall probe would be proportional to the yaw rate so the gyro system would provide a true measure of the helicopter's yaw rate.

Yaw rate sensing limitations

Even if this is so there comes a point as the yaw rate increases at which the mechanical end stops prevent any further tilt of the gyro axis. Any increase in yaw rate beyond this will not give any further increase in the gyro signal. As we will see, this gives rise to some curious behaviour of the gyro gain control. To understand this lets look at some data for a particular gyro, the Futaba FP-G154.

Futaba FP-G154 gyro test data

Here are the maximum servo disk movements, at various gyro gain control settings, that the 154 gyro could produce before hitting the mechanical limit stops.

Gyro gain Max servo disk movement (degrees)
10 (max) 65
8 44
6 30
4 20
2 10
0 0

Notes

We can see from these results that, with the gyro gain set to 7 or more the gyro has enough authority to cancel even the full stick deflection from the transmitter. With this much authority the gyro is always in control of the yaw rate. To see this let imagine we have the gain set to 8 and that the servo is at its mid position (call this 0 degrees) with the heli in a steady fixed-heading hover. If we now bang in full tail rotor command on the stick the servo disk moves to 37 degrees (see note 1 in the data) Now as the yaw rate of the helicopter builds up the gyro output acts against the stick input and brings the servo disk back towards the centre position. Since the gyro is capable, with this gain, of moving the servo disk back 44 degrees its possible for the gyro to remove all the 37 degrees stick deflection and actually drive the servo 7 degrees the other way. The yaw rate rise must stop at a rate below that at which the gyro hits the end stop. Notice that the mechanical limits of the gyro are reached at a quite modest rotation of 102 degrees per second. If the gyro gain is reduced to say 6 we see that the gyro authority over the servo (30 degrees) is no longer able to counter the full stick command (37 degrees) and the maximum pirouetting speed may no longer be under gyro control. This causes the maximum yaw rate to change in a rather curious way with gyro gain as can be seen from the graph below.

How the gyro gain affects the yaw rate /stick deflection relationship

Suddenly, as we reduce the gyro gain below a certain value the maximum available yaw rate goes up dramatically with much of the extra rate coming with the last bit of stick travel.

Motor speed dependence

The amount of gyroscopic effect a flywheel has increases with increasing RPM (this is obvious - if it didn't we wouldn't need to turn the thing at all!) It follows that speed variations of the gyro motor due to battery voltage changes etc. will change the effective gyro gain, with a low battery giving a reduced gain.

Zero Error

The position of the 'zero' on the gyro i.e. the way the gyro sits when at rest or at zero yaw rate depends on the balance of the springs. At first sight it might seem unimportant if the gyro does not sit quite in the correct place as any small error can be accommodated by a change in the trim position on the transmitter or in the linkage. However, If a zero error exists in the gyro, the effect of this will go up and down with the gyro gain. All the gyros I have had apart (I wonder why no one lends me radio gear any more!) have a mechanical adjustment to change the mechanical zero, and its worth checking this adjustment by seeing that your tail rotor trim doesn't change as the gyro gain is varied.

Response time

We touched on the consequences of this last time. The cause in the case of the mechanical gyro comes from the inertia of the gyro motor and flywheel assembly in its support bearings. It simply takes a finite time for the assembly to cant over to the required degree.

Solid state gyros

In some ways these are a bit of a misnomer. They still depend on motion (in the form of a vibration) for their sensing and, to that extent, they are still 'mechanical'.

As far as I am aware, all the current crop of model helicopter solid state gyros make use of the same type of sensor, indeed I believe they all use units from MuRata's "Gyrostar" ENC series. Though not by any means the only type of vibration based angular velocity sensor these are of a particularly interesting construction based on a triangular cross-section metal bar. To this bar are attached three Piezoelectric transducers that are used both to drive and sense the vibrations of the bar.

When in operation the bar is set in vibration as shown above. The vibration is such that the degree to which the two faces carrying the vibration pick-up flex is the same (see the middle diagram below) When the beam is not being rotated the signals coming from the two pick-ups are the same size. However, if the bar is rotated about its axis the tendency is for the direction of the vibration to remain the same in space and, as far as the beam is concerned, to be 'left behind'. As a consequence the two pick-ups see different amounts of vibration as one of the pick-up faces bends more than the other (see the left and right diagrams below) Once we stop rotating the sensor the direction of vibration 'catches up' and the vibration seen by the two pick- ups becomes equal again. So, by looking at the relative size of the two pick-up signals we can measure the rotation speed of the sensor. Smart isn't it!

The Pros and Cons

The big thing about these sensors is their rapid response. Roughly speaking, they respond to a change in rotation speed in about 1/50 of a second. This largely eliminates the gyro sensor itself as a factor in the delay-induced tail wagging problems discussed last time (a serious pro!). On the down side we should remember that these devices are vibration sensitive. JR, for example, obviously take this very seriously as they suspend their solid state sensor in a beautifully engineered anti-vibration mounting. However, the most frequently discussed disadvantage of solid state sensors is one of temperature stability or, should I say, the lack of it. There is potentially about a 20% gain drift with temperature over the likely operating range of say 5 degrees C to 35 degrees C. This is much less significant than the temperature drift in the zero. It's interesting that the sensors used in model gyros were developed for anti-shake video cameras, an application where long-term zero stability is not important. Below is a typical zero drift curve drawn so that the drift can be seen in terms of the apparent rotation of the sensor.

At low temperatures especially this drift is severe. If the sensor is zeroed at 10 degrees C and then cools by only 1 degree C its output will change by the equivalent of a rotation rate of about 30 degrees per second. Since the gyro sensor is otherwise 'blind' it can't tell the difference between output changes due to yaw rates and output changes due to temperature changes.

It's all in the software

Ok, I hear you say, how come there are some quite successful solid state gyros about? The answer lies in using software drift compensation. The first 'trick' is for the gyro electronics to zero when the radio is first powered up. To allow this the gyros must be kept still while their electronics take a reading of the output at zero rotation. A 'look-up table' of correction values against temperature for the sensor may be used if the sensor temperature is continuously monitored. The gyro system may also make some assumption about the long-term average rotation of the helicopter being small simply because we spend a lot of the time flying straight and (unless we are un-reformed control-line fliers) make a similar number of turns to left and right. So, if the gyro system 'sees' a significant long-term average yaw rate it's probably due to sensor drift and an appropriate correction can be applied. This is a very good trick to use as it works really well if the temperature drift is checked 'on the bench' or, of course, the model shop counter (a con?). In the interests of a scientific investigation of the methods used by different gyros I think we should see how well they cope when the 'test bench' goes round a bit. I would be grateful if all you solid state gyro owners would try the following simple experiment for me.

Colin Mill
(Ed: From the rubber room.....)

Part 8

Gyro Drift experiment - the results

Last time you may recall I proposed an experiment that involved refrigerating solid state gyros. Thus far I have had no data come in from this experiment and so I have to make outlandish predictions based purely on the absence of data. I conclude :

All Solid state gyro owners had to pawn their fridges and limos-with-wine-cooler to pay for the gyro. An interesting, little known, but 'scientifically' verified fact.

At least for the moment I think I have spent enough time considering the tail of the model and in order to avoid being suspected of an unfortunate tail-obsession I will this time move to the more honourable topic of the main rotor.

The main rotor

I want to start to look at the factors that influence the design of the rotor head. This article will look at the natural behaviour of the blades so that we can better understand what is required of the control system.

Coning Angle

Because the tips of the blades are travelling through the air faster than the inner parts the majority of the lift is produced towards the outer ends of the blades. However, if you try to lift your helicopter by the ends of the blades you will see that the blades bend up in an alarming way long before the skids come off the ground. Indeed the blades might well break at the root if you did lift the helicopter in this way. From this we see that stiffness of the blades does little to support the weight of the machine in flight. It is centrifugal force acting on the blades and throwing them outwards which balances the tendency of lift to fold the blades up.

You can see how the forces balance out when the blades are inclined upwards towards the tips by the coning angle. The greater the centrifugal force the smaller the coning angle while the greater the helicopter weight the larger the coning angle. The centrifugal force depends on the weight of the blades, the rotor diameter, and the rotor RPM. How the weight is distributed in the blade is also important. Weight at the ends of the blades has more effect than weight near the root.

The centrifugal force is surprisingly high. Taking a typical pair of 30 size blades of about 100 grams on a head running at 1700 RPM the centrifugal force trying to pull the blade off the head is over 100 kgf. (220 pounds force), making the rotor head a highly stressed unit. If this rotor is lifting a 3 kg helicopter (1.5kg per blade) the resulting coning angle is only 0.8 degrees. The tendency of the blades to cone up has to be accommodated either by flapping hinges or flexible plates that permit the blade holders to hinge up or (with a through axle head) by the flexing of the blades.

Since coning looks rather like the dihedral on a fixed wing aircraft it is tempting to think that it has a similar effect as an aid to stability but as we will see its effect in forward flight is undesirable.

Forward Flight

Before we go any further let me explain two terms often used when talking about forward flight.

Advance Ratio
This is the forward speed of the helicopter as a fraction of the tip speed of the blades. Typically this ranges from 0 to about 0.5.

Azimuth Angle
This is used to describe the rotational position of a blade. The zero position is when the blade points down stream (i.e. from the point where it is directly above the boom). The advancing side is from 0 to 180 degrees and the retreating side from 180 to 360 degrees.

In the hover the blades are subject to the same airspeed at all points of their rotation. However, in forward flight a blade experiences a greater airspeed on the side where it is moving forward (the advancing side) than it does on the side where it is moving backwards (the retreating side). On a helicopter with a clockwise rotor head the left side is the advancing side, the right side the retreating side. On the advancing side the forward speed of the helicopter adds to the blade speed to produce an airspeed greater than in the hover while on the retreating side the forward speed of the helicopter opposes the blade speed and the resulting airspeed is lower than the hover value. Near the root , the blade speed is low and the flow actually becomes reversed at the inboard end of the retreating blade. If nothing is done to prevent it, these airspeed changes will cause a lift increase on the advancing side and a lift decrease on the retreating side. The lift distribution for a rigid, constant pitch rotor would be something like this.

Even at a modest advance ratio of 0.3 about 80% of the lift would be generated on the advancing side of the rotor. This lift imbalance would cause a torque (turning effort) in the roll direction, but because of gyroscopic effects would result mainly in a nose up pitching of the helicopter.

The same freedom of the blades to move up and down that allows for coning also provides a solution to this problem. Interestingly it was work, not on helicopters, but on autogyros, carried out by Juan de la Cierva that provided this breakthrough. It was reasoned that if the blades were hinged at the mast so that they were entirely free to flap up and down then they could not transmit a rolling moment to the body of the helicopter. Instead, as the lift on the blade increases on the advancing side the blade simply rises while on the retreating side, where the lift is least, the blade falls.

The act of flapping has an effect on the angle of attack of the blade as seen below.

The vertical motion of the blades reduces the angle of attack where the blade is rising (on the advancing side) while increasing it where the blade is falling. When the blades are free to flap these changes in angle of attack occur naturally and need no special geometry of the head. These cyclic attack angle changes result in lift coefficient changes that eliminate the imbalance in lift between the advancing and retreating sides.

The higher the forward speed of the helicopter the more pronounced the flapping becomes. This results in a diminishing angle of attack on the advancing side and an increasing angle of attack on the retreating side. Interesting the limitation to the forward speed of a helicopter (given enough power) is reached when the blades stall on the retreating side as the down flapping on this side increases the angle of attack beyond the point of stall (say about 12 degrees).

Just imagine you are a fly sitting on a rotor head in forward flight and that you are looking out along one of the blades. You would see that on the advancing side the blade rises and reaches its highest point as the blade is pointing forward (azimuth 180 degrees). The blade falls on the retreating side reaching its low point when pointing rearward (azimuth 360 degrees). Seen from outside this flapping action looks like a rearward tilt of the rotor disc relative to the shaft. So by letting the blades flap freely we have traded a violent rolling moment for a rearward tilt of the rotor disc that can easily be opposed by a suitable forward cyclic control input. It is worth noting that the extra lift on the advancing side (at azimuth 90 degrees) raises the front of the rotor (azimuth 180 degrees), indeed the effect of extra lift at any point in the rotation results in an upward movement in the rotor 90 degrees later. This becomes important when later we are thinking about the effect of cyclic controls.

The simple picture of the flapping rotor head is complicated by several factors.

Firstly, the coning angle causes an imbalance in the lift generated by the blade at the forward and rearward positions. The coning causes the angle of attack of a blade to be greater when pointing along the direction of flight than when pointing rearward So the blade continues to rise as it passes over the nose of the helicopter and to fall as it crosses the boom. In other words the high point of the flapping is on the retreating side (say at an azimuth of 200 degrees). Now the tilt of the rotor disc is not simply backwards but has in addition a sideways component. With a clockwise rotor this tilt will be to the left and would need some right cyclic control input to maintain level forward flight if the machine were trimmed for the hover.

Again in our simple picture we have assumed that the blades are free to flap about hinges and that these hinges are coincident with the main shaft. This gives a blade flapping frequency equal to the rotation frequency of the head. However, this is a somewhat impractical arrangement as the body of the helicopter would be free to swing about below the rotor resulting in poor control of the body attitude. In practice the flapping hinges are often set some way out from the shaft and the flapping is restricted by damper rubbers or spring plates. Both these factors affect the flapping action of the blades and raise the natural flapping frequency so that the blade tries to flap at a frequency greater than the rotation frequency. The end result is that the blade flapping reaches its high point earlier in its rotation (i.e. before the blade reaches the forward position), in other words the high point is slightly on the advancing side of the rotor disk (say an azimuth of 160 degrees). This effect is in opposition to that of the coning angle and may swamp it, in which case left cyclic trim may be needed in forward flight (given a clockwise rotor).

Next time

I have been very busy with the preparations for the Sandown Park show and the new release of the simulator so I will be taking a holiday and will be back with you in two months time when I will look at the requirements for cyclic control of the main rotor. In the meantime, good flying!

Colin Mill

(Parts 7 & 8 Originally published April / May1996)

Copyright Colin Mill and Lance Electronic Publishing 1996/7/8