Category Model Aircraft Aerodynamics

Gyroscopic effects arise from the propeller and rotating parts of the engine. Fortunately on models these are small, but may sometimes be responsible for unexpected behaviour. The propeller on normal models rotates anti-clockwise when viewed from the front. A turn or yaw of the model to the left rotates the gyroscopic axis of propeller and motor. The response is a force tending to raise the nose of the model. This nose up pitch causes a gyroscopic reaction to the right. This yaw or turn to the right causes a nose down pitch and as the model pitches nose down gyroscopic reaction tends to yaw it left, and a nose up pitch follows again, causing a yaw to the right. This sequence is known as precession, and if the effect is noticeable at all, which it may be with a propeller which is heavy and rotating relatively fast, the model may ‘process’ continuously under power, apparently ‘weaving’ slightly: up, to the side, down, to the other side, up, and so on. A spinning top exhibits a similar pattern, and on some early full-sized aircraft with ‘rotary’ engines, the effect was very pronounced and responsible for many accidents. In a model the ‘weaving’ caused by precession may react with torque or other more truly aerodynamic effects, to cause stability problems. The ‘P’ force of a propeller is a case in point. A change of trim to bring the model in for landing causes a yaw due to the ‘P’ effect. This produces a nose-up gyroscopic precession (see also 15.7). In a spiral climb gyroscopic forces are particularly important since the model is turning all the time in one direction, bringing about a nose up or nose down gyroscopic moment. Substitution of a lighter propeller may help the modeller in such a situation. Note, however, that in a straight climb at a constant angle, no gyroscopic reaction arises.

Gyroscopic reactions at take off with ‘tail dragging’ models may cause problems. As the tail wheel or skid comes off the ground, the rotating mass at the nose of the model is forced to change the direction of its axis and responds with the usual leftward rotation, causing the model to swing. A ‘ground loop’ can result. Tricycle undercarriages do not suffer in the same way (although no less affected by slipstream on the fin).

A simple explanation of the cau|e of gyroscopic reactions is given in Figure 14.18. Here an aeroplane is shown in a rapidly changing pitch motion such as during a take-off. The plane of the propeller disc is thus rotated in such a way that each blade, instead of following its usual path, is forced to follow an arc such as A-В, relative to the original disc plane. The mass of the blade resists this change and produces a strong reaction: a force appears which tries to return the blades to their original plane. On one side of the aeroplane this force acts forwards and on the other aft, so the resultant couple yaws the aircraft to one side. With the standard right-handed propellers used on models, the yaw is to the port (left) side.

The take-off phase is particularly tricky for this situation since the rudder control which must be used to counteract the yaw while the wheels are still on the ground may be relatively ineffective due to the low forward airspeed. Full rudder may be needed sometimes, if the propeller is relatively massive and if the change of attitude when the tail comes off the ground is large. Some full-sized fighter aeroplanes have proved almost uncontrollable at this moment

Many models have flown very successfully with ducted fan propulsion instead of propellers. This kind of arrangement is particularly suitable for scale models of jet aircraft Fan design is a highly specialised matter and cannot be dealt with in detail here. In theory the fan can achieve more thrust than a propeller of the same diameter, at low speeds of flight for a variety of reasons. The duct constrains the air so that all the energy from the fan is expended in accelerating the flow. The constriction of the ‘slipstream’ diameter characteristic of propellers does not occur.

The walls of the duct act as endplates to the fan blades, restraining the tip vortices and increasing their efficiency. Because the fan is of small diameter, high rotation speeds are attainable and the number of blades may be increased to create high thrust.

The disadvantages, for models, are that the engine is mounted within the duct and relies on the flow through it for cooling. This increases the drag and reduces thrust The duct walls, which, in scale models, are usually very long relative to the fan diameter, exert drag on the airstream both before and after it passes through the fan. The size of the duct opening and exit are of critical importance and it is often necessary to increase these, departing from scale outlines, in order to achieve adequate thrust Resonance of the blades can also cause trouble (an odd number of blades is necessary).

As has been demonstrated frequently, with careful design and experiment, these problems can be overcome, but there is, as yet no very precise method of designing a model fan which can be guaranteed to equal the thrust from an equivalent (though larger diameter) two bladed propeller and engine.

15

Even if, by careful design and trimming, the drive shaft of the propeller is exactly aligned with the flight direction at some airspeed, in every other trim, such as ‘nose-up’just prior to landing, the propeller will not meet the airflow exactly ‘square’ on. The disc of rotation will be inclined at some angle other than 90 degrees to die approaching flow.

This produces a force component acting at right angles to the drive shaft The explanation is sketched in Figure 14.17. Here the aeroplane is in a ‘nose-up’ trim. The propeller blade on the port side experiences a reduction in angle of attack and the blade on the starboard side an increase. This produces more thrust on the starboard side and less on the other so the’ ‘P’ force tends to yaw the aeroplane to port (left, viewed from aft). Similarly, if the propeller disc is aligned nose-down, the ‘P’ force tends to yaw it to the right and side slipping trims have equivalent nose-up or nose-down force effects.

In normal flight, these forces are trimmed out without any difficulty. That is, part of the exercise of trimming a model for level flight involves use of rudder to counteract any yawing imbalances and elevators to balance the total pitching moments, whatever their cause. Model fliers are thus rarely conscious of the ‘P’ force since this is lost in the general balance equation. However, if there is a change during flight, in the alignment of the propeller axis, the ‘P’ force changes and the balance is upset. However, the reaction of the propeller to such an imbalance is not a simple yawing or pitching force. The ‘P’ force is at right angles to the drive shaft, and the propeller’s reaction, due to gyroscopic precession, is at right angles again to the ‘P’ force, in such a manner as to de-stabilise the aircraft, i. e. to exaggerate the change.

Model internal combustion engines, usually one or two cylinders, tend to transmit their power to the propeller in a series of rapid jolts which cause great stresses in the propeller blade. There is also an aerodynamic effect of almost unknown importance. It may be that the boundary layer is repeatedly stripped off and left behind as the blade accelerates after

the power stroke of the motor, to re-form briefly before the next stroke. Just what effects this has on the efficiency of the propeller is hard to say. So far as known, no serious research has been done on the matter. This effect is not important with electric motors.

The choice of aerofoil section for propellers is also conditioned by structural factors, especially near the. hub, where strength is very necessary and the profile must be thickened considerably. Fortunately, this part of the blade is least important from a thrust

point of view. Because of the high r. p.m. at which the model engines run, Reynolds number effects are less significant, on all but rubber-powered models, than for wings. The blade Re of a model propeller usually is comparable with that of a light aeroplane. Accordingly, aerofoils which are satisfactory on large propellers prove the same on models. Many of the boundary layer flow characteristics that plague model wings tend to disappear with propellers, again except for the rubber driven variety. In addition, the •boundary layer flow on a propeller is very much more complex than on a simple wing. The lowest layers, which are dragged along almost at the same velocity as the blade itself, are accordingly subject to strong centrifugal forces, which extend upwards to the rest of the boundary layer in proportion as the air travels round with the blade rather than staying with the general airflow. Within the boundary layer there are strong cross flows. Small vortices form, which almost certainly turbulate the air and probably prevent laminar flow altogether. Partly for this reason, not much effort has been put into designing very refined, low drag profiles for propellers on model aircraft With rubber driven and indoor types, although there has been much experiment and experience over the years, it cannot be claimed that any very startling improvements have appeared.

The least vortex drag for a wing is found with a perfectly elliptical chord distribution. The equivalent shape for a propeller can be found by calculation but it is not an ellipse. This is because the tips of the blades move faster through the air than the roots, so that, in a given time, more air mass is affected by them. The effect of this and other factors is to require, for least vortex drag, a narrower blade profile near the tips than a purely elliptical form, and, near the blade roots, a somewhat broader than elliptical shape. (This refers to the developed planform, when the chord at each place along the blade is plotted in two dimensions as if the blade were straightened out)

The importance of this discovery, largely due to Eugene Larrabee, may be gauged from the fact that the manpowered aircraft, Gossamer Albatross, which crossed the English Channel, was incapable of staying in the air for more than a few minutes, until Larrabee’s design of propeller was adopted. Unfortunately, model aircraft propellers generally are constrained in design by factors other than aerodynamics, especially the need for strength and stiffness under very high loads, and ease of manufacture.

Like the wing, each blade of a propeller generates upwash and downwash and every blade works in the downwash created by the blade ahead of it and in the upwash of the one behind, as they follow one another round.

The distinction should be made here between blade wake and downwash. The wake of each blade, a greatly disturbed, but relatively thin, layer of air that trails behind the blade from the trailing edge, is carried away from the propeller disc by the slipstream. The profile drag of the blade is measurable as the wake thickness and loss of momentum.

The downwash is induced by the tip and root vortices and this is a general distortion of the airflow, just as with a wing. A tailplane on an aeroplane may lose efficiency by being immersed in the wing wake. But even if the tail is mounted well clear of the wake (as with a T tail), the general downwash effect is still present. With a propeller blade, the downwash of the preceding lifting surface is felt in very much the same way. Also, just as a canard foreplane works in the upwash preceding the mainplane, every propeller blade experiences a certain upwash effect from the blade following it This is more pronounced in propellers with three, four or more blades and tends to reduce their efficiency compared

with a two-bladed propeller. But there are vortex-induced losses with two bladed propellers even so, because there is always a preceding and a following blade: the same one. Even a single bladed propeller, which does gain a little efficiency over the two bladed variety, works constantly in its own downwash and upwash. (Single bladed propellers must be balanced and this usually requires at least a stump, suitably weighted, opposed to the blade. This creates drag, so the full gain in efficiency is not realised in practice.)

Figure 14.13 shows how the aerodynamic angle of attack of a propeller blade is affected by downwash. As with a wing, the effect is a considerable increase in drag for a given lift coefficient. However, because the propeller is turning and the outer segments necessarily move through the air at a greater speed than the inner ones, and the blade itself is twisted, the pattern of the vortices is more complicated than for a wing.

In Figure 14.14, a single blade is shown with a vortex at the outer tip and one at the root. It is assumed for the moment that the blade is of the paddle type so that there is nothing to interfere very much with the formation of the inner vortex. The blade is physically twisted to accord with the constant pitch requirement. The vortex from the outer tip of the blade leaves the tip with the relative airflow there. Since the tip is moving forwards as well as rotating, the vortex forms in a helical fashion behind the propeller. The vortex at the hub end or root also leaves the blade aligned roughly with the relative flow, but here the airstream is almost aligned with the direction of flight and the inner vortex therefore streams more or less directly aft.

If the single blade is now supplemented by a second one in the usual way, a fuller pattern appears. Two outer vortices are produced which trail away helically with the

F:~ ■* л * л w—i:——— x———— :—"

Fig. 14.15 Vortex system: two bladed propeller

general airstream. At the centre, the two inner vortices, which are rotating in the same direction, wind together to form one central vortex which streams directly aft.

The final vortex pattern is thus represented in Figures 14.15 and 14.16. Of course, immediately behind the hub of a real propeller there is usually an aeroplane fuselage or at least a nacelle containing an engine, with, probably, various cooling ducts and cowlings. The hub itself may be faired with a spinner. All these interfere with the central vortex and restrain it, just as. an end wall in a wind tunnel restrains the tip vortex if the test wing entirely spans the gap between the walls. Nonetheless, the propeller produces, as far as it can, a strongly rotating vortex which flows immediately over the parts of the aircraft that lie in its path. The rotation lends its strength to the general slipstream rotation which is caused by the profile drag of the blades and their wakes.

Matching propellers to the power of the engine and to a particular aeroplane is mainly a matter of experience and experiment Engine tests carried out on behalf of model aircraft magazines and published therein usually state a range of propeller sizes and rotational speeds achieved, which form a very useful guide. The test reports also usually include a graph of power against r. p.m. (Power is rated in Watts and Kilowatts in SI units and Horsepower in Imperial measure).

An equation which is of some help in choosing a propeller diameter for a particular engine and application is the following:

where propeller diameter, D, is in centimetres and in Imperial units:

Although based on work done for full-sized aircraft this gives results which seem to be applicable to model engines and propellers, although not necessarily quite accurate in every case. A scientific pocket calculator with a ‘fourth root’ function is required. With a rough idea of the speed of flight to be flown the pitch of the propeller follows approximately from Figure 14.12.

Since the pitch is the distance advanced by a blade in one revolution, the relationship of pitch to RPM and speed is fixed, nominally. This does not mean that fitting a propeller of a certain pitch will mean a model must reach the appropriate speed, because this will depend on the engine’s ability to drive the propeller at the required RPM and the thrust even then may not equal the aircraft drag at the nominal speed. It is nonetheless useful to know the nominal speed for a given pitch/RPM relationship since this can be related to the engine power curve published by the manufacturers or in model aircraft magazine engine review articles. Knowing the RPM attainable with a given propeller, the model flier then can assess the suitability of the propeller for a model which flies at a particular speed, or which is intended for that speed. The chart in Figure 14.12 expresses die pitch-

Fig. 14.11 Layout schemes for varieties of non-constant pitch [nominally rated equal at 75% radius]

RPM – Speed relationship graphically and may be used in several ways. If the engine’s RPM for maximum power is known, the appropriate RPM diagonal may be followed to read off nominal speeds and the pitches required for each. Or the design speed may be the starting point and then a series of RPM and pitch figures may be found. For points out of range of the chart, the formulae shown may be used.

The actual flight speed attained by a model depends on the thrust-drag relationship. The chart suggests not that any particular speed will be attained but only what propeller pitch is appropriate for a particular r. p.m. and speed.

Much of the foregoing may be expressed in a single figure, the advance ratio, represented by the letter J. The formula is:

Advance ratio = J =

where D is the diameter and V the flight speed. As shown above, the angle of attack of the blade, for a constant pitch propeller, depends on the flight speed and rate of rotation. The

remaining variable is the diameter which, at a given RPM, determines the actual speed through the air of the propeller tips and, at a given pitch, has a dominant effect on the power required to drive die propeller at the stated RPM.

To overcome the deficiencies of high speed, coarse pitch propellers at take off or in the climb, in full-sized aviation the variable pitch propeller is widely used. In this a fairly complex mechanism allows the pilot to select the blade pitch required to give efficient propeller performance, and hence good thrust, over the whole speed range. This is done by rotating the blades axially at the hub; it is not feasible to change the twist of the blades themselves. Hence such a propeller will still lose some efficiency at speeds other than the design point, but this detracts only slightly from the all-round improvement in efficiency and safety. Model aircraft have been flown with variable pitch propellers and experimentation continues. The cost is likely to be high if a propeller is broken and the danger of shedding blades requires a great deal of care in design of the hub and gearing. Rubber driven models offer scope for improvement here too, and variable pitch propellers have shown up very well in experiments although not, as yet, widely adopted.

A constant speed propeller is one in which the pitch is varied automatically to maintain a constant engine r. p.m. The engine has a most economical speed and fuel can be saved if the propeller pitch is matched to this under all or most flight conditions.

14.3 THE DIAMETER; PITCH RATIO

Propellers for models are ‘fixed pitch’ and are normally marketed with a stated diameter to pitch ratio. The ratio itself is independent of the units and dimensions used, since a 28 x 18 cm propeller, with D/P ratio of 1.56 is practically the same as an 11 x 7 inch propeller, with die exact ratio of 1.57. A propeller with a diameter of 40 cm and pitch of 26 cm would have a D/P ratio of almost the same value. Since the resistance of a propeller to the air depends greatly on the diameter as well as the pitch, if the diameter is increased, the pitch must be reduced if the engine is to drive the new propeller at the same r. p.m. That is, for a given power input, the diameter/pitch ratio must be increased.