Propeller Performance: Practical Engineering Applications
This book does not discuss propeller design. Aircraft designers select propellers offered by the manufacturer, mostly off-the-shelf types, unless they are specially designed in consultation with aircraft designers, such as the rubberized turbofan. This section describes considerations that are necessary and appropriate to aircraft designers in selecting an appropriate propeller to match the sized engine in order to produce thrust for the full flight envelope.
Readers may note that the propeller charts for the number of blades use only three variables: Cp, в, and n (the subscriptp is omitted); they do not specify the propeller diameter and rpm. Therefore, similar propellers with the same AF and CLi can use the same chart. Aircraft designers must choose AF or CLi based on the critical phase of operation. The propeller selection requires compromises because optimized performance for the full flight envelope is not possible, especially for fixed – pitch propellers.
Recently, certification requirements for noise have affected the issues of compromise, especially for high-performance propeller designs. A high-tip Mach number is detrimental to noise; to reduce it to n is compromised by reducing the rpm and/or the diameter, thereby increasing J and/or the number of blades. Increasing the number of blades also increases the cost and weight of an aircraft. Propeller curvature is suitable for transonic operation and helps reduce noise.
Figure 10.38. Design CL to avoid compressibility loss
Equation 10.22 gives the aerodynamic incidence – that is, the blade angle of attack, a= (в – ф), where у is determined from the aircraft speed and propeller rpm (i. e., function of J = V/nD). It is best to keep a constant along the blade radius to obtain the best Cui (i. e., a is maintained at 6 to 8 deg). The value of 0.7r or 0.75r is used as the reference point – the propeller charts list the reference radius.
The combination of the designed propeller rpm is matched to its diameter to prevent the operation from experiencing a compressibility effect at the maximum speed and specific altitude. A suitable reduction-gear ratio decreases the engine rpm to the preferred propeller rpm. Figure 10.36 is used to obtain the integrated design Cu for the propeller rpm and diameter combination. The factor ND x (ratio of speed of sound at standard day, sea level to the altitude) establishes the integrated design Cu. A spinner at the propeller root is recommended to reduce loss.
The following stepwise observations and information are important to progress the propeller-performance estimation by using the charts in Figures 10.34 through 10.38 (in the figure fc = aait/aSu, where a = speed of sound):
1. Establish the integrated design Cui using Figure 10.38.
2. A typical blade AF is of the following order:
• Low power absorption, 2- to 3-bladed, propellers for homebuilt flying = 80 < AF < 90.
• Medium power absorption, 3- to 4-bladed propellers for piston engines (utility) = 100 < AF < 120.
• High power absorption, 4-bladed and more propellers for turboprops = 140 < AF < 200.
3. Keep the tip Mach number around 0.85 at cruise and ensure that at takeoff, the rpm does not exceed the value at the second segment climb speed.
4. Typically, for a constant-speed, variable-pitch propeller, в is kept low for takeoff, gradually increasing at climb speed, reaching an intermediate value at cruise and a high value at the maximum speed. Figure 10.32 shows the benefit of в-control compared to fixed-pitch propellers. Although the figure demonstrates the merit of a constant-speed propeller, its constraints render the governor design and в – control as complex engineering, which requires two modes of operation (not addressed in this book). Design of an automatic blade-control mechanism is specialized engineering.
5. The propeller diameter in inches can be roughly determined by the following empirical relation:
D = K( P)025,
where K = 22 for a 2-blade propeller, 20 for a 3-blade propeller, and 18 for a 4-blade propeller. Power P is the installed power, which is less than the bare engine rating supplied by the engine manufacturer. Figure 10.39 provides the statistics of a typical relationship between engine power and propeller diameter. It is a useful graph for making empirically the initial size of the propeller. If n and J are known in advance, the propeller diameter can be determined using D = 1,056V/(NJ) in the FPS system.
Figure 10.39. Engine power versus diameter
6. Keep at least a 0.5 m (1.6 ft) propeller-tip clearance from the ground; in an extreme demand, this can be reduced slightly. This should prevent the nose – wheel tire from bursting and an oleo collapse.
7. At maximum takeoff static power, the thrust developed by the propellers is about four times the power.
Continue separately (in FPS) with propeller performance for static takeoff and inflight cruise.
Static Performance (see Figures 10.34 and 10.36)
1. Compute the power coefficient, CP = (550 x SHP)/(pn3D5), where n is in rps.
2. From the propeller chart, find CT/CP.
3. Compute the static thrust, TS = (CT/CP)(33,000 x SHP)/ND, where N is in rpm.
In-Flight Performance (see Figures 10.35 and 10.37)
1. Compute the advance ratio, J = V/(nD).
2. Compute the power coefficient, CP = (550x SHP)/(pn3D5), where n is in rps.
3. From the propeller chart, find efficiency, nP.
4. Compute thrust, T from nP = (TV)/(550 x SHP), where V is in ft/s.
If necessary, off-the-shelf propeller blade tips could be slightly shortened to meet geometrical constraints. Typical penalties are a 1% reduction of diameter affecting 0.65% reduction in thrust; for small changes, linear interpolation may be made.