The industry uses propeller charts that incorporate special terminology. The necessary terminology and parameters are defined in this section. Figure 10.30 shows a two-bladed propeller with a blade-element section, dr, at radius r. The propeller has a diameter, D. If ю is the angular velocity, then the blade-element linear velocity at radius r is юг = 2nnr = nnD, where n is the number of revolutions per unit time. An aircraft with a true air speed of V and a propeller angular velocity of ю has the blade element moving in a helical path. At any radius, the relative velocity, VR, has an angle p = tan-1(V/2nnr). At the tip, ptip = tan-1(V/nnD).
D = propeller diameter = 2x r n = revolutions per second (rps) ю = angular velocity N = number of blades
b = propeller-blade width (varies with radius, r)
P = propeller power
Cp = power coefficient (not to be confused with the pressure coefficient) = P/(p n3D5)
T = propeller thrust
Cn = integrated design lift coefficient (CLd = sectional lift coefficient)
CT = propeller thrust coefficient = T/(pn2D4)
в = blade pitch angle subtended by the blade chord and its rotating plane p = propeller pitch = no slip distance covered in one rotation = 2nr tan в (explained previously)
VR = velocity relative to the blade element = V(V2 + ю2г2) (blade Mach number = VR/a)
p = angle subtended by the relative velocity = tan-1(V/2nnr) or tan p = V/пnD (This is the pitch angle of the propeller in flight and is not the same as the blade pitch, which is independent of aircraft speed.) a = angle of attack = (в – p)
J = advance ratio = V/(nD) = ntanp (a nondimensional quantity – analogues to a)
AF = activity factor = (105/16) /010 (r/R)3(b/D)d(r/R)
TAF = total activity factor = Nx AF (it indicates the power absorbed)
However, irrespective of aircraft speed, the inclination of the blade angle from the rotating plane can be seen as a solid-body, screw-thread inclination and is known as the pitch angle, в. The solid-body, screw-like linear advancement through one rotation is called pitch, p. The pitch definition is problematic because unlike mechanical screws, the choice of the inclination plane is not standardized. It can be the zero – lift line (which is aerodynamically convenient) or the chord line (which is easy to locate) or the bottom surface – each plane has a different pitch. All of these planes are interrelated by fixed angles. This book uses the chord line for the pitch reference line as shown by the pitch angle, в, in Figure 10.30; this gives pitch, p = 2nr tanв.
Because the blade linear velocity mr varies with the radius, the pitch angle needs to be varied as well to make the best use of the blade-element aerofoil characteristics. When в is varied such that the pitch is not changed along the radius, then the blade has constant pitch. This means that в decreases with increases in r (the variation in в is about 40 deg from root to tip). The blade angle of attack is:
a = (в-ф) = tan-1(p/2nr) – tan-1(V/2nnr) (10.22)
This results in an analog nondimensional parameter, J = advance ratio = V/(nD) = n tan<p.