1.8 m aircraft propeller CFD: cruise and static A first aircraft propeller designed in Heliciel Propeller at take-off: off-design calculation

An aircraft propeller turns engine power into thrust by throwing air backwards; designing one means choosing its diameter, number of blades, blade shape, airfoils and pitch so that every blade section works close to its best angle of attack. Here we look at what the propeller became after 1940: variable pitch, number of blades, airfoils, contra-rotating propellers, vibration, de-icing, the turboprop and supersonic propellers. Every current or future development draws partly on what has already been tried, and the limits our predecessors reached show where the ones we would like to push back lie.

This page continues two others: the brief history of the evolution of aircraft propellers from 1920 to 1940, which explains how we got to the modern propeller, and the tutorial for building an aircraft propeller with Heliciel. We rely heavily on the book by Jean Grampaix cited in the bibliography on propellers, wings and wind turbines, which we have reworded and completed with a few photos and reminders of the physics. The historical figures (powers, masses, speeds) come from that book; we add none of our own, apart from unit conversions.

Contents:

• Aircraft propeller evolution after 1940
• Adapting the aircraft propeller to higher power
• Propeller diameter and blade tip speed
• Blade width and plan shape of aircraft propellers
• Propeller blade airfoil: from the Clark Y to the NACA 16
• Variable-camber propeller (Hamilton)
• Number of blades of an aircraft propeller
• Contra-rotating propellers: advantages and limits
• Propeller vibration: engine, location, unbalance
• Propeller anti-icing and de-icing
• Turboprop propeller: variable pitch, gearbox, coupling
• Supersonic propeller: where do we stand?

1: Aircraft propeller evolution after 1940

Before going into detail, a word of vocabulary. A propeller's relative pitch is the ratio of its pitch to its diameter. Like a screw in wood, a propeller theoretically advances one pitch per turn; a relative pitch of 1.9 therefore means it would advance 1.9 diameters per turn if the air did not give way. We detail this notion in the page on geometric pitch and effective pitch of a propeller.

The speeds and powers of aircraft kept growing. Could the propeller "absorb" these new figures? Yes, and the increase in speed even favoured it: it allows large relative pitches, which reach 1.7 and even 1.9 without the diameter or the rotational speed becoming prohibitive. A relative pitch of 1.9 is chosen in particular in commercial aviation, where economy in cruise comes first.

The propeller is not at the peak of its possibilities, either. If aircraft flew faster still, the propeller rotational speed could rise in proportion. The diameter would then shrink, and so would the weight of the propulsion unit, and with it the weight of the engine and the landing gear. Designers are already moving towards knife-edge airfoils at the blade tips, to cope with the effects of compressibility (air no longer behaves as an incompressible fluid near the speed of sound).

Rising power, on the other hand, posed a hard problem: the mass of the propeller grows with engine power, and faster than the power and mass of the engine itself. Would the propeller reach its limit there?

Two engines of a Super Constellation at take-off: at full power the propellers are just a blurred disc, but that disc passes the whole engine power to the air.

Several solutions were considered:

• Smooth out the engine torque, to reduce by as much the periodic loads the propeller has to absorb.
• Increase the number of blades, which large relative pitches allow. The larger the pitch, the less the air is disturbed when a blade enters the wake of the previous one, and the less the blades interact. The loss of efficiency caused by the larger number of blades is then more than offset by the large relative pitch.
• Split the aircraft's total power between a larger number of engines.
• Use contra-rotating propellers, which we come back to below.

2: Adapting the aircraft propeller to higher power

The large four-engine aircraft built in this period (Super Constellation, DC-7, Superfortresses, Boeing) forced propellers to keep up with the speed and power of their engines. These were piston engines of 3,500 hp, about 2.6 MW (one metric horsepower is about 0.735 kW). That power marks the limit of what the reciprocating engine could deliver.

A propeller in front of its radial piston engine: the cylinders are visible behind the hub.

Turboprops followed, with even higher performance and different operating characteristics. A new range of propeller adaptations came with them. To absorb the new powers, propeller makers worked on six parameters:

• diameters;
• blade lengths;
• the blade shapes, in plan and in section;
• the number of blades;
• the number of propellers on the same shaft (contra-rotating system);
• the rotational speed.

The evolution of these parameters was itself tied to materials, tooling, machining methods, inspection means, and ground and flight test facilities. The general pattern of propeller adaptation is as follows.

When engine power increases, for a given propeller, one can for example increase the pitch angle of the blades (hence the pitch) or the blade area, through either the chord or the diameter. This route has its limits: either change lowers efficiency, and the power needed to vary the pitch becomes prohibitive.

Another solution is a variant of the area increase: add blades. Here too the limits soon appear, with interaction between the blades and a "thickening" of the hub. We end up with similar compromises when speed or altitude must rise.

Manufacturing imposes a compromise as well. For obvious reasons it is attractive to lighten the propeller, strength being equal. But as an order of magnitude, a propeller weighing 200 g per horsepower lasts 7,000 to 8,000 hours of service, whereas one weighing 150 g per horsepower lasts only 4,000 to 5,000 hours. Lightness has a price.

On a piston engine, fitting a damper (an elastic coupling) between the engine and the propeller lets the propeller weight drop by 25 to 30%. The percentage is much lower with a turboprop. The irregularity of a reciprocating engine's torque is indeed the factor that weighs most on propeller strength. The propellers of that era carry a tensile stress, caused by centrifugal force, of the order of 10 kg/mm² (about 98 MPa), and work with a safety factor of 4.

3: Propeller diameter and blade tip speed

High speeds did not frighten propeller makers. They had met the transonic range (the zone near the speed of sound) in the years 1930-1935, with the propulsion units of the Schneider Cup seaplanes. Specialists had established at the time that blade tips cope well with transonic flow provided they are very thin with a sharp leading edge. The results proved them right: a Ratier propeller turned at 345 m/s at the blade tip with an efficiency of 82%. That speed is close to the speed of sound, 340 m/s at 15 °C at sea level.

A Schneider Cup seaplane: its thin two-blade propeller already took the blade tip close to the speed of sound.

One point is worth keeping in mind. The total speed at the blade tip is the resultant of two speeds: the circumferential speed (radius × angular speed, ω·R) and the aircraft's forward speed V. It is written √((ω·R)² + V²). When the aircraft accelerates, the blade tip therefore accelerates too, without any change in rotational speed. Beyond a certain point it was no longer just the blade tip but the whole propeller that risked going supersonic. The propeller had to go back to the drawing board.

A diagram nevertheless offered reassurance. It showed how the drag coefficient of an airfoil varies between 900 and 1,600 km/h (250 to 444 m/s). Apart from a "peak" between 1,110 and 1,300 km/h, which brackets the speed of sound (about 1,225 km/h in the conditions quoted), the propeller would cope fairly well with supersonic flow. The diameter evolved between two opposite solutions:

1. A long, very narrow blade with a very tapered tip. The poor supersonic efficiency then affects only a small area, that of the tapered tip.
2. A short, very wide blade with a square tip. The blade tip, which is asked to do work similar to the other sections, does not operate at very high speeds.

In propeller calculation, the choice of rotational speed therefore sets both the efficiency and the blade tip speed: the two have to be tuned together.

4: Blade width and plan shape of aircraft propellers

Blade width. When high powers appeared, widening the blades was tempting. Designers went easily from 7 to 8% of the blade length to about 10%. Going further, they met two difficulties:

1. flow separation may occur. This can be cured with hollow blades that suck away the boundary layer, centrifugal force helping the suction;
2. a blade that is too wide needs too much power to vary the pitch.

Plan shape. The same engine can drive various types of propeller, all able to absorb its power. They differ greatly from one another, in their blades at least, depending on whether the user wants to favour take-off, cruising speed or economy, or a compromise between them. To fit the engine with a propulsion unit that meets the chosen goals, designers therefore work on the plan shape of the blades, their airfoil, their diameter and their width.

To meet the new requirements after 1940, various blade shapes appeared, from the scimitar to the square-tip blade. The scimitar comes from an aerodynamic analogy with the swept wing. The square tip won out. Created around 1946 by Hamilton Standard, this type of propeller is also recognized by its airfoil, which has a laminar profile: the maximum thickness is moved rearwards and the leading edge is very thin.

Hamilton Standard propellers lined up in a workshop: their wide blades and massive hubs give an idea of the scale of these machines.

From 1920 to jet propulsion, blade shapes varied a great deal. When the turbine arrived, the propeller had to adapt again, first to the high powers of the reciprocating engine, then to those of the turbine, which produced very varied blade shapes. When sonic speeds appeared at the blade tip, designers thinned and tapered the airfoils there, as we saw above.

When aircraft speeds rose further, this remedy was no longer enough. Two answers appeared:

• Hamilton proposed a wide propeller with square-cut blade tips. Unlike the earlier design, the blade tip is part of the active surface, but the diameter is smaller. The circumferential speed drops, and the outer edge of the blade leaves the sonic zone.
• Curtiss transposed to the propeller the design of heavily swept wings, which give the best results at very high speeds. The result was the scimitar propeller.

More unusual shapes were tried, but in the end it was the square-tip propeller that prevailed for high speeds.

A propeller with square-tip blades, seen from the front.

Designers did not worry only about blade shape. At the same time they solved difficult questions of strength of materials, pitch-change controls and manufacturing. Two examples with figures show the scale of the progress:

• the DC-3 propeller, 3 m in diameter, weighs 170 kg and absorbs 1,200 hp (about 0.88 MW);
• the DC-6 propeller, 4 m in diameter, weighs 175 kg, absorbs 2,400 hp (about 1.8 MW) and covers a pitch-change range three times larger.

The DC-6 propeller thus transmits twice the power for practically the same weight. Another example conveys the dimensions reached. In the United States Curtiss-Wright ran the "Octoprop", intended for a 15,000 hp turboprop (about 11 MW), the total power of a Super Constellation. It consists of two contra-rotating four-blade propellers of 5.79 m diameter, with feathering and reversing, and hollow steel blades. According to the author it is the largest aircraft propeller ever built, and it remained a prototype. The largest propeller produced in series is that of the B-36, with the same dimensions as the Octoprop but not mounted contra-rotating.

The Octoprop (figure 63 of the book cited): two contra-rotating four-blade propellers, eight blades in all.

5: Propeller blade airfoil: from the Clark Y to the NACA 16

As long as aircraft speed did not exceed 650 km/h (about 181 m/s), designers used airfoils such as the Clark Y. Between 650 and 750 km/h they developed the Clark Y into an airfoil that is thinned from 85% of the blade radius, with the maximum thickness at about 40% of the chord.

The Clark Y airfoil as the Heliciel airfoil database displays it: slight camber, almost flat lower surface, relative thickness of 0.117, centre of lift at 36.6% of the chord. (Capture from an older version of the interface.)

Later the NACA 16 family became the general base airfoil. These airfoils were at first fairly "worked": double-curved, with a concave lower surface and a slightly raised trailing edge, in the hope of a high lift coefficient. But making them raised serious difficulties. So designers stayed within the NACA 16 family, but chose airfoils with a low lift coefficient.

Flight tests showed that these airfoils suited level-flight speed, but behaved poorly when high speeds were combined with high angles of attack, as imposed by the climb. The climb was improved by widening the blade along its whole length, without appreciably affecting level-flight speed. Research led to propellers that are thin along the whole blade length, light, and give good efficiency in the various flight configurations. From this point of view, modern propellers no longer pose a major problem.

These results had in fact been achieved long ago, with relative thicknesses (thickness divided by chord) of 5 to 5.5% for speeds of 700 to 800 km/h, and 4.5% for 900 km/h.

We deal with choosing an airfoil, its polars and its database in the page on the aerodynamic and hydrodynamic airfoil database.

6: Variable-camber propeller (Hamilton)

In the period 1920-1940, designers studied what could raise propeller efficiency. In practice, only variable pitch took hold. But among the concepts was variable camber, and a version of it appeared at Hamilton in 1960, research on VSTOL aircraft (vertical or short take-off and landing) not being unrelated to it.

The propellers tested at Hamilton were constant-speed doublets, each with 3 or 4 blades. In fact they were two propellers, each with its own hub, mounted one behind the other on the same shaft. The aim was to give the propulsion unit the equivalent of the wing with its camber flap. Such a scheme, fairly easy for a wing, becomes extraordinarily complicated for a propeller because of its high rotational speed. Until then, every solution adding an extra structure on the propeller had failed. Hamilton therefore approached the problem differently.

In its system, the operation of each propeller depends on the other. The pitches vary differentially according to a law that links the surface of the front propeller and that of the rear one, depending on the flight configuration: take-off, climb, cruise. Each pair of blades thus forms, aerodynamically, a single slotted surface. Changing the pitch angle of one blade is then exactly equivalent to changing the camber of the pair, as is done with a wing and its flap. With a conventional propeller, the choice of airfoil is a compromise between the demands of take-off and those of cruise. With the Hamilton propeller, each pair forms an airfoil suited to each configuration.

From one phase to the next, the operation is as follows:

• For take-off and climb, each blade of the front propeller is at fine pitch and the pitch of the rear propeller is larger. Altogether, each pair forms a single highly cambered airfoil, with good efficiency at low speeds.
• As flight speed increases, the front blades move to a coarser pitch. The whole then works at coarse pitch, that of high speeds, the camber decreases and the airfoil of each pair becomes a high-speed airfoil.

Hamilton counted on the following improvements:

• long-endurance aircraft (anti-submarine warfare aircraft, for example): endurance improved by 20%;
• transport aircraft at Mach 0.7-0.8: endurance up 40% and payload up 30%;
• VSTOL aircraft: payload up 50%;
• in general, runway length reduced by 15%.

The Hamilton propeller did not become widespread. It could still appear on turboprops and give them a considerable boost. Either way, this journey around the formula shows the astonishing possibilities of the propeller, whether they assert themselves in the near or the more distant future.

7: Number of blades of an aircraft propeller

Experience shows that the maximum number of blades on the same hub must not exceed a few units (the author hesitates between 5, 6 and 7, and raises the question himself). If it were higher, the hub would grow excessively and need a cowling, which would cancel the whole benefit of the small frontal area the turbine allows. Other problems would also arise:

• interaction between the blades of the propeller itself;
• proper air supply to the turboprop's compressor, which a bulky hub would hinder;
• a lower rotational speed: for a given power, adding blades lowers the rotational speed.

Choosing the number of blades therefore remains a compromise between efficiency, noise, torque and hub size. We treat it in detail in the page number of blades of a propeller: how to choose.

8: Contra-rotating propellers: advantages and limits

For more information, a contra-rotating propeller design tutorial with Heliciel is available.

Contra-rotating systems are the last stage in adapting the propeller to high power. They equipped the Bristol "Brabazon", the Saunders-Roe "Princess" and the Tupolev Tu-114.

The Tupolev Tu-114: each of its four turboprops drives two contra-rotating propellers, eight visible blades per engine.

Two formulas exist: coupled and uncoupled contra-rotating propellers. In the first case, the propellers are linked to coupled free turbines. In the second, they are driven by directly coupled turbines, each propeller having its own turbine.

With piston engines, one early example is worth recalling: Ratier fitted the V.B. 10 fighter (two Hispano-Suiza 12 Z of 1,350 hp each, arranged in tandem) with two coaxial three-blade propellers. The pitch change of the rear propeller was driven by a fixed electric motor, that of the front propeller by a rotating electric motor. In a variant, the pitch change was done by two fixed electric motors. The system reaches its maximum efficiency when both propellers absorb equal torques. To achieve this, the rear propeller must be given a slightly finer pitch than the front one.

The advantages of the system:

• no reaction torque or gyroscopic torque, hence better manoeuvrability;
• straightened wake: the energy lost in spinning the fluid flow is recovered by the second propeller;
• smaller diameters;
• better take-off and climb performance, especially at heavy loads, with little noticeable gain in cruising speed;
• with uncoupled propellers, no asymmetry if one of the two engines fails: one propeller is feathered, the other keeps turning with little loss of efficiency.

The other side of the inevitable compromise has two drawbacks:

• directional instability, caused by the drift effect of the system, which can be compensated by increasing the area of the aircraft's vertical fixed surface;
• greater complexity.

9: Propeller vibration: engine, location, unbalance

The propeller is the seat of vibrations with different sources: one is induced by the engine, another comes from the propeller's location, others are specific to the propeller, and still others have various origins.

The engine

The piston engine generates very large torsional oscillations. These crankshaft vibrations cause considerable alternating loads in the hub and the blades. They made it necessary to strengthen the root sections of the propeller beyond what the calculation of aerodynamic and centrifugal loads required. An elastic coupling can be fitted between the engine and the propeller: it reduces the loads arising in the hub from the irregularity of engine torque and prevents resonance building up between engine vibrations and propeller vibrations. Dampers are also fitted on crankshafts, and the engines are elastically mounted to the airframe.

These vibrations come from the reciprocating system: they do not exist in the turboprop. With turbines, thinner and lighter propellers can therefore be used. The specific weight of turbine propellers is 70-80 g per horsepower for a single propeller, against the 150 to 200 g quoted above for piston-engine propellers.

The location of the propeller

This aerodynamic excitation results from the interaction between the propeller and the engine cowling, the wing leading edge, the landing gear, and more generally any obstacle to the flow of the air the propeller stirs. The whole part of the aircraft affected by the propeller's aerodynamic field must therefore be designed with the propeller in mind. The number of blades can also be changed to act on the frequency of the vibrations coming from the propulsion unit. Finally one must consider the mutual influence of propulsion units placed on the same wing, and the interaction between the propeller and the ground, which once caused blade failures at Junkers.

The propeller itself

The vibrations specific to the propeller come from four phenomena:

• Static unbalance. Due to manufacturing imperfections, it is easily cured by a simple inspection operation.
• Dynamic unbalance. It comes from an uneven distribution of mass in the propeller and can only be detected while the propeller is turning. As a first approximation it is corrected by static balancing at the various pitches of the propeller. A rigorous solution requires very large installations, notably an immense two-part steel shell, between the halves of which there is a perfect vacuum in which the propeller under test turns. Hamilton Standard had such equipment.
• Aerodynamic unbalance. It is caused by small differences in shape or pitch angle between the blades of one propeller, arising from manufacturing or setting tolerances. These blades then give unequal thrusts and absorb unequal torques. Present test equipment can detect these defects, which can then be corrected.
• Internal aerodynamic excitation. These vibrations occur between the blades of one propeller. They have been detected on propellers with four or more blades but not on three-blade ones. They cause no reaction on the propeller shaft.

Vibrations of various origins

These are the ones that occur in chance cases: aerodynamic excitation when passing an obstacle, when crossing a turbulent layer of air or in the wake of any moving body.

10: Propeller anti-icing and de-icing

The propeller's leading edge, like the wing's, is subject to icing. Two schools exist to protect it: anti-icing and de-icing.

Anti-icing is permanent: the system that prevents ice forming is switched on as soon as the aircraft detects the danger. The means tried all pursue the same goal, bringing heat to the leading edge. This is done by electric current (the general case) or, with hollow blades, by circulating hot gas inside the blade.

De-icing, by contrast, acts only after the ice deposit has formed. The chemical method is the most common: a pump delivers glycol into a ring fixed to the propeller hub, from which fine tubes lead to the blade roots. Centrifugal force does the rest, throwing the glycol along the leading edge. This "rain" of glycol makes the ice that has formed fall away.

Electric blade de-icing system: protection strips (blue) cover the leading edge, the heating element (yellow) is connected to the supply by wires.

11: Turboprop propeller: variable pitch, gearbox, coupling

In our time the propeller has gone from the 3,500 hp piston engine to a range of turboprops whose power reaches 7,500 hp, about 5.5 MW (Pratt & Whitney T-34). What were the consequences for the propeller? Four elements need consideration: the pitch change, the gearbox, the compressor air supply and the three systems for coupling the propeller to the turbine.

Pitch change. As on piston engines, propeller pitch variation covers a range from fine pitch to reverse, through coarse pitch and feathering. But a pitch even finer than fine pitch is needed for starting, at least with direct propeller-turbine coupling. A piston engine can start a propeller at take-off pitch. A directly coupled turbine does not have enough power at standstill, its power curve lying below the curve of the power the propeller absorbs. The other two couplings compare with the propeller-piston engine link for the starting phase. For the behaviour of a propeller at standstill, we have devoted a page to static thrust of a propeller at zero speed.

The gearbox. The turbine-propeller gearbox is heavier and more complex than a piston-engine one, which is understandable: the turbine turns much faster than the crankshaft. But the experience gained on very many gearboxes for reciprocating-engine aircraft has made turboprop gearboxes well developed.

The compressor air supply. With the piston engine, fixing various accessories on the engine nose was no major drawback. It is different with the turboprop, whose compressor must be fed properly. Hence a reduction in the height of the blade-root fairings and of the hub arms they contain, a miniaturization of accessories and new cowling designs.

The three propeller-turbine coupling systems. The propeller can be coupled to the gas turbine in three ways:

1. Direct coupling: the turbine drives the compressor and the propeller.
2. Coupling by compound compressor: the first turbine stage drives the free centrifugal compressor; the second stage drives the axial compressor and the propeller.
3. Coupling by free turbine: the first two turbine stages drive the compressor; the third stage drives the propeller.

12: Supersonic propeller: where do we stand?

In the 1930s, in very particular cases such as the Schneider Cup, blade tips "grazed" the supersonic range. Since then, however much aircraft speed has increased, they have gone no further into that zone. The measures described above (tapered tips or reduced diameter) keep the propeller out of supersonic flow.

To our knowledge, no supersonic propeller is in service. The extreme case today, as before, remains a blade tip that grazes this zone. If propeller speed had to increase, the doctrine would be "all or nothing": the whole blade in supersonic flow, or no part of it. It follows that airfoils evolve without being revolutionary. We are at the NACA 16, whose maximum thickness lies at about 50% of the blade chord; the leading edge has become finer, but not yet a knife edge.

On an experimental basis, however, supersonic propellers have been built. We cite as an example tests run at Langley Field under the direction of NACA, using a McDonnell XF-88B (derived from the XF-88A "Voodoo") fitted out as a flying test bed. It had two Westinghouse J-34 jet engines and an Allison XT-38 turboprop that drove the propeller under test, a Curtiss with 2, 3 or 4 blades and a diameter of 3.05 m, 2.15 m or 1.20 m. Electronic equipment recorded the measurements on board. These tests interested all of American technology, since the USAF Propeller Laboratory, the Air Development Center at Dayton (Ohio), the US Navy Bureau of Aeronautics and McDonnell in St. Louis collaborated with NACA.

The McDonnell XF-88B: a jet aircraft turned into a flying test bed, with the test propeller mounted in the nose.

One last reminder links this history to calculation. At high speed it is the blade tip speed (see section 3) that limits the propeller. For a given forward speed, reducing the diameter or the rotational speed lowers the circumferential speed, hence the blade tip speed: this is the lever Hamilton used with its square-tip propeller.

To go further, we can revisit the brief history of aircraft propellers from 1920 to 1940, build our own propeller step by step with the aircraft propeller design tutorial, or compare an Heliciel calculation with wind-tunnel measurements on aircraft propellers in the Heliciel validation on NR640 and DA4002 propellers page.

The difference between cruise and static thrust shows up in simulation: the case study aircraft propeller CFD compares the two operating points on the same propeller.

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