Figure 10.37. Four-bladed propellerperformance chart – AF180 (for a highperformance turboprop)

10.10.3 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, β, and η (the subscript p 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 fixedpitch 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 η 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, α= (β – ϕ), where ϕ is determined from the aircraft speed and propeller rpm (i.e., function of J = V/nD). It is best to keep α constant along the blade radius to obtain the best CLi (i.e., α 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 CL for the propeller rpm and diameter combination. The factor ND × (ratio of speed of sound at standard day, sea level to the altitude) establishes the integrated design CL. 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 = aalt /aSL, where a = speed of sound):

1.Establish the integrated design CLi 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, β 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 β-control compared to fixed-pitch propellers. Although the figure demonstrates the merit of a constant-speed propeller, its constraints render the governor design and β-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)0.25,

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 propeller 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 nosewheel 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 × SHP)/(ρn3D5), where n is in rps.

2.From the propeller chart, find CT/CP.

3.Compute the static thrust, TS = (CT/CP)(33,000 × 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 = (550× SHP)/(ρn3D5), where n is in rps.

3.From the propeller chart, find efficiency, ηP.

4.Compute thrust, T from ηP = (TV)/(550 × 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.

10.10.4 Propeller Performance: Blade Numbers 3 ≤ N ≥ 4

Using the graphs, a linear extrapolation can be made for twoand five-bladed propellers with a similar AF. Reference [18] discusses the subject in detail with propeller charts for other AF.

358 Aircraft Power Plant and Integration

10.10.5 Propeller Performance at STD Day: Worked-Out Example

In a stepwise manner, thrust from a propeller is worked out as a coursework exercise. The method uses the Hamilton Standard charts intended for constant-speed propellers. These charts also can be used for fixed-pitch propellers when the pitch of the propeller should match the best performance at a specific speed: either cruise speed or climb speed. Two forms are shown: (1) from the given thrust, compute the HP (in turboprop case SHP) required; and (2) from the given HP (or SHP), compute the thrust. The starting point is the Cp. Typically, at sea-level takeoff rating at static condition, one SHP produces about 4 pounds on STD day. At the first guesstimate, a factor of 4 is used to obtain SHP to compute the Cp. One iteration may prove sufficient to refine the SHP.

Problem description. Consider a single, 4-bladed, turboprop military trainer aircraft of the class RAF Tucano operating with a constant speed propeller at N = 2,400 rpm giving installed TSLS = 4,000 lbs. The specified aircraft speed is 320 mph at a 20,000-ft altitude (i.e., Mach 0.421). For the aircraft speed, the blade AF is taken as 180. Establish its rated SHP at sea-level static condition and thrusts at various speeds and altitudes. All computations are in STD day.

Case I: Takeoff performance (HP from thrust). This is used to compute the SHP at sea-level takeoff. Guesstimate installed SHP = 4,000/4 = 1,000 SHP.

From Figure 10.39, for a four-bladed propeller, the diameter is taken to be 96 inches, or 8 ft. Figure 10.38 establishes the integrated design CLi ; the ratio of the speed of sound at STD day sea level to the altitude, fc = 1.0.

The factor ND × fc = 2,400 × 8 × 1.0 = 19,200. Corresponding to aircraft speed of Mach 0 and the factor ND× fc = 19,200; Figure 10.38 gives the integrated design CLi ≈ 0.5.

Equation 10.44 gives:

CP = (550 × SHP)/(ρn3 D5)

or CP = (550 × 1,000)/(0.00238 × 403 × 85) = 5,50,000/49,91,222 = 0.11

Figure 10.36 (4-blade, AF = 180, CL = 0.5) gives CT/CP = 2.4 corresponding to integrated design CLi = 0.5 and CP = 0.11.

Therefore, installed static thrust, TSLS = (CT/CP)(33,000 × SHP)/ND = (2.4 × 550 × 1,000)/(40 × 8) = 1,320,000/320 = 4,125 lb.

The installed SHP is revised to 970 giving installed thrust TSLS = 4,000 lb. It is close enough to avoid any further iteration.

Taking into account a 7% installation loss at takeoff, the uninstalled TSLS = 4,000/0.93 = 4,300 lb, giving the uninstalled SHP = 1,043. It may now be summarized that to obtain 4,000 lb installed thrust, the uninstalled rated power is 1,043 SHP.

Aircraft configuration must ensure ground clearance at a collapsed nose-wheel tire and oleo. A higher number of blades (i.e., higher solidity) could reduce the diameter, at the expense of higher cost. For this aircraft class, it is best to retain the largest propeller diameter permissible, keeping the number of blades to four or five.

If ground clearance is required, then a 1.5-inch radius can be cut off from the tip (i.e., a 3% reduction to a 93-inch diameter), which requires slightly higher