Pilot Training - Theory of Flight: Propellers

86. General requirements.-In the design and use of aircraft propellers the main consideration is to obtain the maximum performance of the airplane from the horsepower delivered by the engine under all conditions of operation such as take-off, climb, cruising speed, and high speed. Propellers are classified as the following types :

a. Fixed pitch.-Only one pitch setting due to the type of construction.

b. Adjustable.-Pitch setting adjustable only with tools when the engine is stationary.

c. Controllable.-Pilot can change pitch in flight by manual control.

(1) Two-posit;on.-Only two pitch settings available.

(2) Multiposition.-Any pitch setting possible within limits. d. Automatic.-Pitch setting control by some automatic device. (1) Nonselective.-Entirely independent of the pilot.

(2) Selective.-Pilot can select and control, during flight, the conditions at which the automatic features function.

The main purpose of the following discussion is to explain the simple aerodynamic characteristics of the propeller under widely varying conditions of operation in such a manner as to show the necessity for controllable or automatic pitch propellers on all present day high performance airplanes.

87. Dryewiecki (Jerveski) or blade element theory.--a. The fundamental forces acting on an airfoil in motion with an angle of attack relative to the wind are twofold. A lift force is produced perpendicular to the relative wind and a drag force is produced parallel to the relative wind.

The value of the drag force D= C_Dr/SV_R² where V_R is the velocity of the relative wind in feet per second. C_L and C_D are the lift and drag coefficients and their value is dependent upon the shape of the airfoil section, angle of attack, and also upon the velocity relative to the air provided the speed exceeds 700 feet per second.

At speeds above the velocity of sound (1,120 ft. per. see.) the changes in C_L and C_D with changes  of velocity are very pronounced.

b. If the airfoil sections are operated above the velocity of sound there is a marked increase in the drag coefficient C_D while the lift coefficient C_L drops. This results in a low L/D ratio and decreased efficiency. When an airfoil section is operated at speeds above the velocity of sound there is a great increase of sound energy produced by the passage of the airfoil through the air. This is very objectionable for military airplanes since the enemy can easily locate the airplane by the aid of sound locaters.

c. Figure 73 shows the C_L and C_D coefficients for a typical Clark Y section that is commonly used in propeller blades. It can be seen that the most efficient angle of attack a for maximum L/D is about 10. The characteristic curves shown are for a representative section of a propeller.

d. The blade element theory assumes that the propeller blade from the end of the hub barrel to the tip of the propeller blade is divided into small elementary airfoil sections. For example if a propeller 10 feet in diameter has a hub 12 inches in diameter each blade can be divided into 54 one-inch airfoil sections. Figure 74 shows only one of these airfoil sections located at a radius r from the axis of rotation of the propeller. This airfoil section will then have a span of 1 inch and a chord 0. The chord C at any given radius r will depend upon the plan form or general shape of the blade.

88. Propeller blade reactions under various airplane operating conditions.-a. Static condition.-When the airplane is standing still on the ground and the engine is running there are two components of air velocity relative to the blade which determine the blade angle setting. (Fig. 75.)

(1) The speed of the airfoil section in feet per second due to rotation of the propeller is equal to the circumference of a circle having radius r multiplied by the number of revolutions per second. This is equal to 2prn.

(2) When the propeller is turning there is a stream of air moving at high velocity to the rear of the propeller disk. This stream of air is called the slipstream of the propeller. The air in the slipstream does not gain momentum instantaneously upon striking the propeller blade but gains an appreciable velocity before coming in contact with it. Tests show that the air has gained approximately 31 percent of the velocity of the slipstream by the time it strikes the propeller blade. Since the velocity of the slipstream can be computed, the inflow velocity is obtained by multiplying the slip velocity by 0.31.

b. Take-off and climb condition.-At the time of take-off and during steep climbs the airplane has gained forward speed. (Fig. 76.) There is some decrease in the velocity of the slipstream but the forward velocity of the airplane is sufficient to increase the value of the vector BD. To satisfy this condition of operation the blade angle Q_B must be greater than for the condition shown in figure 75.

c. Level Flight high speed condition.-In level flight at high speed, the forward speed of the airplane has increased to a very high value while the slip velocity has decreased to a very low value. The sum of V+0.31V_s shown by vector BD (fig. 77) has increased materially over that shown for static conditions and take-off and climb conditions and the angle Q_B must also be increased.

d. Power dive high speed conditions.-In a power dive the slip velocity is small but the speed of the airplane is so great that the vector BD will be much greater than for any of the above conditions of operation. The blade angle Q_B will have a very high value.

89. Determination of direction and velocity of airflow relative to propeller blade.-(See fig. 78.) The combination of the velocity due to rotation shown by vector AB and the forward velocity of air relative to the propeller  shown by BD can be replaced by the resultant velocity AD. The direction of the airflow relative to the airplane of rotation is shown by angle Q which is equal to tan^-1 BD/AB.

90. Determination of blade angle for airfoil section.-(See fig. 77.) The airfoil section of the propeller will move along the resultant airflow line. The section of the propeller blade is set at an angle of attack a of about 1° so as to obtain maximum L/D which results in maximum efficiency. The angle of the airfoil section with respect to the plane of rotation Q_B=Q+a. The drag on the airfoil section will be parallel to the direction of the resultant airflow and the lift will be perpendicular to the resultant airflow. The lift and drag forces are combined to give the resultant force.

91. Thrust produced by propeller.-In the study of propellers, it is desirable to break down the resultant force into two components, thrust and torque (fig. 78). The thrust force component is parallel

to the axis of rotation of the propeller and is designated by T. If T is the force in pounds and V is the velocity of the airplane in flight in feet per second, the work done per second will be equal to TV ft. lbs. per sec. The unit horsepower is equal to 550 ft. lbs. per ses. Therefore HP=TV/550 the thrust HP produced by the small section of the propeller blade. The thrust horsepower for the complete propeller is obtained by adding together the thrust horsepower produced by all the element airfoil sections of the blades.

92. Torque absorbed by propeller.-The component parallel to the plane of rotation is the torque component force Q. The velocity of the elementary airfoil section in the plane of rotation is equal to 2 p times the radius of the airfoil section from the axis of rotation times the number of revolutions per second.

The torque HP absorbed by the complete propeller is obtained by adding together the torque HP absorbed by all the small airfoil sections of the propeller blades. For any speed of rotation the torque HP supplied by the engine must balance the HP absorbed by the propeller. If the engine torque is greater than the torque required to drive the propeller the engine will increase r. p. m. until a balance is reached. If the torque required to rotate the propeller is greater than the torque supplied by the engine the engine r. p. m. will decrease until a balance is reached.

93. Fixed pitch propellers.-For the fixed pitch propeller at maximum speed in level flight, a balance is ordinarily reached between the torque horsepower supplied by the engine and the torque horsepower absorbed by the propeller when the engine is turning at its rated speed and delivering its full rated output. In climb, the forward velocity of the airplane decreases, the angle of attack of the relative wind on the propeller blade increases, and the torque horsepower absorbed by the propeller momentarily becomes larger than the horsepower output of the engine. The engine speed then decreases until a new balance is reached between horsepower absorbed by the propeller and the horsepower output of the engine. This decrease in engine speed in climb and the corresponding decrease in horsepower output of the engine result in poor performance in climb of airplanes with fixed pitch propellers.

94. Controllable pitch propellers.-The two-position propeller provides a means of rotating the propeller blades to a reduced pitch angle which permits the, engine to turn at normal speed and deliver its full rated horsepower output to the propeller in climb and thus increase the rate of climb. However, this propeller can be designed to give best performance at only two definite speeds of flight. At other speeds in the cruising range and at take-off, performance can be further improved by the use of a propeller whose pitch can be controlled throughout a wide range of pitch angles and which will permit the engine to operate at constant speed in all conditions of flight.

95. Selection of best diameter for propeller.-The diameter of a propeller required to absorb the power output of a given engine is a function of many variables, among which are forward velocity V, air density, speed of rotation of the propeller, number of blades, plan form, profile section, etc. In general, a propeller will only give its best performance for one particular flight condition. The charts shown in figures 79 and 80 are arranged for the convenient selection of suitable diameters for metal controllable pitch propellers of conventional plan form and airfoil section.

Figure 79 is designed to simplify the calculation of Cs, the propeller speed-power coefficient.

where m. p. h. is the forward velocity in miles per hour, HP is the horsepower input to the propeller, N is propeller revolutions per minute, and a is the density ratio obtained from figure 8.

From figure 80 the - ratio corresponding to the calculated value of C_s may be found, and since V and n are known, D is easily computed. General practise is to use a diameter to the nearest 3-inch step.

Example: Determine the best propeller diameter for maximum efficiency at full horsepower and maximum speed of the following airplane:

550 hp. engine output

1, 750 propeller r. p. m.

200 m. p. h. high speed level flight of airplane

10, 000 ft. operating altitude

3 blade propeller.

Calculation: From figure 79 and formula 49.

From figure 80, for C_s=1.71 we find - = 1.03

Note.-Here V is ft./sec. and n is rev. per sec.

Solving for propeller diameter

96. Efficiency of propeller.-a. Some work done by the engine is lost in the slipstream of a propeller and in the production of noise, etc., which cannot be converted into thrust hp. The thrust hp will necessarily be less than the torque hp. The efficiency of the propeller is the ratio of the thrust hp to the torque hp

b. The maximum efficiency that can be obtained in practice under most ideal conditions is about 92 percent when using thin airfoil sections near the tip with very sharp leading and trailing edges. Such sections are not practical where there is any danger of picking up gravel or water spray.

c. The efficiency of high performance airplane propellers of conventional two- or three-blade design is dependent mainly upon the tip speed in feet per second. The following table of efficiencies shows that it is essential to keep the tip velocity below the velocity of sound which is about 1,120 feet per second. The efficiency of high performance airplane propellers of conventional two- or three-blade design is dependent upon the ratio of tip speed to velocity of sound. The velocity of sound varies with temperature and decreases roughly 5 feet per second per 1,000 feet increase in altitude. At sea level it may be taken as about 1,120 ft./see. The following table of efficiencies is based on a velocity of sound of 1,120 ft./see.

d. To obtain tip speeds below the velocity of sound (1,120 ft. per see.) it is sometimes necessary to gear the engine so that the propeller will turn at a slower rate of speed. For example if an engine is geared in a 3: 2 ratio the propeller will turn at 2/3 the speed of the engine. Since the airfoil sections strike the air at a lower speed they do not do as much work as would be the case with the direct drive propeller. It is therefore necessary to increase the blade area by using  a larger diameter or three or more blades. The efficiency of a propeller is influenced by the ratio of forward velocity to rotational velocity. This ratio is expressed by a quantity called the V over nD ratio, or

V/nD

where V is the forward velocity of the airplane in feet per second, n the revolutions per second of the propeller, and D the diameter in feet of the propeller. A particular propeller is designed to give its maximum efficiency at a particular value of forward speed of the airplane (usually the maximum speed in level flight) and a particular engine speed (usually the speed of rated full horsepower output). At any other condition of flight where a different value of the ratio V/nD exists, the propeller efficiency correspondingly suffers

97. Advantages of three-blade propeller on geared engine-.a. The smaller diameter of the three-blade propeller gives lower tip speeds.

b. For multi-engined airplanes the engines can be moved in nearer the fuselage which improves maneuverability for flying characteristics with one engine dead. For single-engine airplanes, the smaller diameter gives more ground clearance and allows the use of shorter and

lighter landing gears and simplifies the retractable landing gear problem.

c. In the three-blade propeller there is very little interference effect due to the blades being so close together. In the four-blade propeller there is a noticeable loss in efficiency due to the blades interfering with each other.

d. The three-blade propeller prevents the engine from vibrating on the mount to a greater extent than the two-blade propeller. With a two-blade propeller it can be seen that the nose of the engine is not restricted to any great extent from movement at right angles to the axis of the propeller blades. For example if the blades are horizontal the nose of the engine can jump up and down vertically more easily than horizontally. The three-bladed propeller acts more as a flywheel and tends to prevent movement of the nose of the engine in any direction.

98. Computations of blade angles.-a. When adjusting the blade angles of a propeller to meet different flight requirements a definite station on the blade is selected and the angle of attack witth respect to the plane of rotation is computed for the station selected. For propellers up to 12 feet in diameter the 42-inch station is selected as a reference station for setting the blades. For propellers between 12 feet and 17 feet in diameter the 54-inch station is selected.

b. If the total disk area of a propeller were effective, the disk area would be equal to . Since the part of the diskarea near the center of the propeller is blanked out by the propeller hub, it is considered that the effective area of the propeller disk

D is expressed in feet. A_s is expressed in square feet.

c. The velocity of the slipstream to the rear of the propeller is computed by the following formula:

where HP=HP output of the engine and h is determined approximately from paragraph 96.

d. s is the relative density of the air at the altitude at which the airplane will fly and is obtained from relative density curves (fig. 8). V is the velocity in feet per second at which the airplane will fly with HP being developed by the engine.

The blade angle relative to the plane of rotation Q_B=Q+a

Example: Compute the blade angle setting at the 42-inch station for the following airplane engine and propeller combination. Airplane air speed at 15,000 ft.=280 m p. h.=410 ft./sec.

Engine 1,000. HP at 15,000 ft. altitude at 2,200 r. p. m.

Engine geared with a 3/2 ratio.

From figure 8, s at 15,000 ft.=0.625.

Propeller 3-blade, diam. 12 ft. 6 in.

Propeller (geared) r. p. m.= ²/3  x 2,200=1,466 r. p. m.=24.44  r. p. s.

Rotational velocity of propeller tip=2p 6.25 x 24.44=960 ft./sec.

Component of tip speed due to advance of the airplane=410 ft. per sec.

Resultant tip speed== 1,043 ft. per sec.

Assume an efficiency of 84 percent for the propeller from paragraph 96.

From formula 50

The most effective angle of attack a for the section is 1°. (Refer to fig. 73)

Substituting these values in formulas 51 and 52, we obtain the requiped blade angle setting at the 42-inch station.

NOTE.-The slip velocity is very small for the high speed condition of flight. The slip values will be much higher for conditions of take-off, climb, and cruising.

Slight changes of blade angle can be made if the engine does not run exactly at rated speed. For a direct drive propeller a blade angle change of 1° will change the engine speed approximately 70 r. p. m. on the ground and 100 r. p. m. in level flight at wide open throttle. For geared engines the change of engine r. p. m. will be greater and will vary directly with the ratio of gearing.

99. Advantages of controllable pitch propellers.-In paragraph 101 is shown performance data indicating the wide variation of angles required for a modern 4-engine airplane with engines supercharged to 15,000 feet if maximum performance under all operating conditions is to be maintained. If it were necessary to use a fixed pitch propeller for this airplane, the best blade setting would be about 38.6° at the 42-inch station.

a. Improved climb and take-off.-The best condition for take-off would require a blade angle of 16° if it is desired to use 100 percent of rated power for take-off. With a fixed pitch propeller set at 38.6° the angle of attack relative to the airfoil would be at least 38.6°-18°'=20.6°'. By referring to the lift and drag curves (fig. 74), it can be seen that the drag would be very high which means that the torque required to drive the propeller would be much greater than the torque supplied by the engine. This will result in the engine slowing down until a balance of power supplied by the engine and power absorbed by the propeller is reached. In the above case the engine would slow down to about one-half of its rated speed and the power output would be about one-half of full rated power. The 50 percent power that is being absorbed by the propeller is being consumed very inefficiently, as the L/D of the airfoil section is very low and the thrust from the propeller will be, low. By the proper adjustment of the blade, angle for take-off and climb, full engine power can be used with more efficient blade angles of attack so that the airplane will take off in about one-third the distance and climb about twice as fast as with the fixed pitch propeller with a blade angle setting at 38.6°.

b. Improved high speed at sea level.-If a blade angle of 38.6 ° is used for high speed at altitude (15,000) the angle of attack at sea level will be 38.6° - 32.4° = 6.2°. This high angle of attack will result in the speed of the engine being held down until only 80 percent of the rated power can be obtained from the engine. This will result in a loss of 20 m. p. h. in high speed at sea level.

c. Improved fuel economy at cruising speeds.-By adjusting the pitch angle of the propeller and the throttle so as to cruise at the maximum allowable intake manifold pressure a saving of approximately 7 percent in fuel can be realized. Maximum allowable manifold pressure is the intake manifold pressure that will force the largest charge of fuel and air mixture into the cylinder that will burn without detonation or preignition. When the engine is operating under high manifold pressures, greater thermal efficiencies are attained. The lower engine r. p. m. also results in less loss of power due to friction of the moving parts of the engine. If the propeller is to absorb more power at a slower r. p. m, the blade angle must be increased to a value greater than the setting required for high speed. It will be noticed that when cruising with increased propeller pitch and high manifold pressure more throttle opening will be required than is required for cruising with a fixed pitch propeller set for high speed conditions.

d. Increased performance with part of engine plant shut down. - For long range military aircraft about half of the flying will be done under light conditions of load since the bomb load and part of the fuel supply will be disposed of. Fuel economy can be obtained by shutting down two engines as shown in paragraph 101 and feathering the blade on the dead engines. The blades are feathered by increasing the blade angle at the 42-inch station to approximately 87° so that the blade has a very low angle of attack. The drag will be much less than if the propeller were stopped by brakes with the blades set at angles required for flight. It is estimated that about 12 miles an hour could be gained on this airplane by feathering the blades instead of keeping the propellers from windmilling by the use of brakes.

c. Increased ceiling.-When a supercharged engine has passed its rated altitude the power will start to decrease due to the decrease in intake manifold pressure. This results in a decrease in engine speed. The supercharger speed will drop which in turn lowers the manifold pressure, the cycle repeating itself. The ceiling can be materially increased with a controllable pitch propeller by decreasing the blade angle so that the engine will run up to its rated speed which maintains the speed of the supercharger at normal and prevents the manifold pressure and power of the engine from dropping off as rapidly as would be the case with a fixed pitch propeller.

100. Advantages of constant speed propeller.-Reference to paragraph 101 will show that to obtain best conditions of operation the pilot will have somewhat of a problem to select the proper pitch setting. It is also annoying to have to change the pitch to meet all requirements. The constant speed propeller has been developed to select automatically the proper pitch angle for the blades and relieve the pilot of manually changing the pitch setting. The propeller pitch is changed to maintain automatically any desired engine speed. The pilot merely sets the propeller control at the r. p. m. at which it is desired to operate. The throttle is then opened until the desired manifold pressure is obtained. The airplane may then be flown through all types of maneuvers without a change of engine speed of more than 10 or 20 revolutions a minute. If the constant speed propeller control is set to obtain full rated engine r. p. in. the following pitch changes will occur to maintain constant engine speed:

a. At the start of the take-off the pitch will be low to allow the engine to turn at full rated r. p. in. and develop full power.

b. Throughout the take-off and climb the pitch will gradually increase as the speed of the airplane increases so that full engine power will be delivered throughout take-off and climb.

c. As the airplane is leveled off after the climb, the speed of the airplane increases and the pitch automatically increases to prevent racing of the engine and to maintain constant engine speed.

d. In a dive the pitch angle increases to a still higher value to maintain constant engine r. p. m.

e. For cruising conditions the constant speed control is set at the desired r. p. m. required - for cruising. The propeller then automatically regulates the pitch to maintain the selected cruising r. p. m. of the engine. The throttle is adjusted to give the desired manifold pressure.

f. When the throttle is closed the speed of the airplane decreases and the pitch automatically decreases. Low and high pitch stops are usually provided to prevent the propeller from attaining blade angle settings that are too low or too high for flight conditions.

101. Comparison of performance of modem four-engine monoplane at sea level and at 15,000 feet.-Engines: 1,000 hp. each at 2,200 r. p. m. All engines equipped with controllable pitch propellers.

a. At sea level:

Cruising speed, 204 m. p. h. with blade angle of 41.7°  70 percent max. HP at 1,400 r. p. m.

High speed, 230 m. p. h. with blade angle of 32.4°.

Cruising speed with 2 propellers feathered 170 m. p. h. 80 percent max. HP at 1,700 r. p. m. and blade angle of 32.8°.

b. At 15,000 feet:

Cruising speed, 248 m. p. h. with blade angle of 47.4° 70 percent max. HP at 1,400 r. p. m.

High speed 280 m. p. h. with blade angle of 37.7°.

Cruising speed with 2 propellers feathered 206 m. p. h. 80 percent max. HP at 1,700 r. p. m. and blade angle of 38°.

Best climbing speed 160 m. p. h. with blade angle of 26°.