# Blade profile and blade area

The profile of the blade can be represented by the front and side views of the propeller. The front view of the propeller is seen from the back of the ship to the bow, and the side view is seen from the side of the ship. As shown in Figure 1, a common propeller diagram is shown, and the names and terms of each part of the propeller are indicated on the diagram. The shape and name of the propellers have been described in detail earlier.

In order to correctly express the relationship between the front view and the side view, a generatrix in the middle of the blade surface is taken as the reference line for drawing, which is called the blade reference line or the blade surface reference line, such as the straight line OU in the figure. If the propeller blade surface is a positive helical surface, the reference line OU is perpendicular to the axis on the side view. If it is an oblique helix, the reference line and the vertical line of the axis form a certain angle ε, which is called the longitudinal oblique angle. The projected length of the reference line OU on the axis is called the vertical slope and is represented by z_{R}. The pitch propellers are generally inclined backward, and the purpose is to increase the clearance between the blades and the stern frame or the hull to reduce the hull vibration induced by the propeller, but the pitch should not be too large (generally ε<15°, otherwise the centrifugal force of the propeller will increase the bending stress at the blade root during operation, which is unfavorable to the blade strength).

The projection of the blade on the plane perpendicular to the axis of the blade is called the orthographic projection, and its outline is called the projection profile. The sum of the projected areas of all the blades of the propeller is called the projected area of the propeller, expressed as A_{p}. The ratio of the projected area A_{p} to the disk area A_{0} is called the projected surface ratio, namely:

Projection surface ratio=A_{p}/A_{0}

Projected profiles that are symmetrical to the reference line are called symmetrical lobes. If its shape is not symmetrical to the reference line, it is an asymmetrical lobe. The distance x_{s} between the tip of the asymmetric blade and the reference line is called the side slope, and the corresponding angle θ_{s}. is the side slope angle. The skew direction of the blade is generally opposite to the steering of the propeller. Reasonable selection of the skew of the blade can significantly reduce the hull vibration induced by the propeller.

The projection of the blade on a plane parallel to the containing axis and radial reference line is called the side projection. In addition to drawing the outline of the blade and the position of the reference line OU, the maximum thickness line needs to be drawn. The axial distance t between the maximum thickness line and the reference line OU represents the maximum thickness of the leaf section at that radius. It only represents the radial distribution of the maximum thickness of the cut surface at different radii, and does not indicate the position of the maximum thickness along the chord direction of the cut surface. The maximum thickness of the cut surface connected to the hub is called the thickness of the blade root (excluding the fillets on both sides). The ratio t_{0}/D between the distance t_{0} of the intersection of the radiation reference line and the extension line of the maximum thickness line on the axis and the diameter D is called the leaf thickness fraction. In the process, the thickness of the blade at the blade tip is often thinned into an arc shape. In order to obtain the blade tip thickness, the maximum thickness line of the blade needs to be extended to the tip diameter, as shown in Figure 1a.

The shape of the propeller hub is generally a cone, and it can be seen from the side projection that the diameters are not equal everywhere. The diameter of the propeller hub (referred to as the hub diameter for short) refers to twice the distance from the intersection of the radiation reference line and the surface of the propeller hub (ignoring the corner filler at the blade root) to the axis, and is represented by d (see Figure 1a). The ratio d/D of the hub diameter d to the propeller diameter D is called the hub diameter ratio.

After the tangential planes intersecting the coaxial cylindrical surface at each radius and the blade are developed into a plane, the chord length is placed on the horizontal line of the corresponding radius, and the contour obtained by connecting the endpoints is called the stretch contour, as shown in Figure 1c. The sum of the areas contained in the extension profile of each blade of the propeller is called the extension area, which is represented by A_{E}. The ratio of the stretched area A_{E} to the disk area A_{0} is called the stretched surface ratio, that is

Stretch surface ratio = A_{E}/A_{0}

The wheel obtained by approximately spreading the blade surface on the plane is called the unfolding profile, as shown in Figure 1b. The sum of the areas included in the development contour of each blade is called the development area, which is represented by A_{D}. The ratio of the expanded area A_{D} to the disk area A_{0} is called the expanded surface ratio, that is,

Expanded area ratio=A_{D}/A_{0}

The expansion area of the propeller blade is very close to the expansion area, so it can be called the blade area, and the expansion surface ratio and the expansion surface ratio can be called the disk surface ratio or the blade surface ratio. The size of the disk-to-surface ratio essentially represents the width of the blade. Under the same number of blades, the larger the disk-to-surface ratio, the wider the blade.

In addition, the average width b_{m} of the blade can also be used to represent the width of the blade, and its value can be calculated as follows:

where A_{E} is the extension area of the propeller; d is the hub diameter; Z. is the number of blades.

Or expressed by the average width ratio, that is