Theory of Rudder on Ships

The rudder is used to steer the ship. The turning action is largely dependent on the area of the rudder. The required area of the rudder varies with different type of vessels since desired maneuvering ability differs considerably and the general ship design may imposed restriction.

In practice the rudder area is usually relative to the area of the immersed metal plane. The ratio of the depth to width of a rudder  is known as the aspect ratio and its value is generally 2. High aspect ratio is used in large vessels, where depth is not a constraint. Higher aspect ratio reduces the astern torque considerably. 

Aspect Ratio = (Depth of Rudder / Width of Rudder)

The force on the rudder depend on:

1. Area of the rudder
2. The form of rudder
3. The speed of the ship
4. The angle of helm

Force acting on the rudder, F = k A V²

where,

k = Constant depending upon the shape of the rudder, water density, rudder angle. It varies from 570 to 610.

A = Area of rudder in m²

V = Speed of ship in m/s

F acts at a point M, measured from the leading edge of the rudder (where water flow first touches rudder).

M = (0.195 + 0.305 sinθ ) L

where,

θ = Turning angle of rudder

L = Width of the rudder

Area of rudder is 1/60 to 1/70 th of the immersed middle plane area of the vessel. Faster vessels require less rudder area.

Rudder may be hinged on the pintles and gudgeons, or the may turn about an axle which passes down through the rudder. The weight of rudder may be taken by bearing pintles, or by a bearing at the rudder head (rudder carrier), or by a combination of both.

Types of Rudder

Balanced rudder

• When 20% to 37% of the area is forward of the turning axis there is no torque on the rudder stock at certain angles.
• At some angle of rudder, it is balanced. i.e., torque is zero, to keep rudder at that angle.
• Axis of rotation lies between 0.2 L and 0.37 L.

Semi-balanced rudder

• A rudder with a small part of its area, less than 20%, forward of the turning axis.
• At no angle rudder is balanced.
• Axis of rotation lies less than 0.2 L.

Unbalanced rudder

• A rudder with all of its area aft of the turning axis.
• At no angle rudder is balanced.
• Axis of rotation is the leading edge.

Construction of Rudder

• Modern rudders are of stream lined form and are fabricated from steel plate, the plate size being stiffen by internal webs. Where the rudder is fully fabricated, one side plate is prepared and the vertical and horizontal stiffening webs are welded to this plate.
• The other plate often called the closing plate is then welded to the internal webs from the exterior only. This may be achieved by welding, flap bars to the webs prior to fitting the closing plate, and then slot welding the plate.
• The upper face is formed into a usually horizontal flat palm, which acts as the coupling point for the rudder stock.
• A lifting hole is provided in the rudder to enable a vertical inline lift of a rudder when it is being fitted or removed. This lifting hole takes the form of a short piece of tube welded through the rudder with doubling at the side and closing plate.
• A drain hole is provided at the bottom of the rudder to check for water entry when the ship is examined in dry dock. 
• To prevent internal corrosion the interior surfaces are suitably coated, and in some cases the rudder may be filled with inert plastic foam.
• The rudder is tested when complete under a head of water 2.45 M above the top of the rudder.

Rudder Carrier Bearing on Ships

Most of the rudders are supported within the hull. The rudder carrier carries the full weight of the rudder. A rudder carrier may incorporate the watertight gland fitted at upper end of the rudder trunk. 

Why Rudder Angle Limited to 35 Degrees ?

• Beyond 35 degree rudder efficiency is reduced due to formation of eddies on the back of rudder as the flow is no longer streamlined. This is called stalled condition.
• The manoeuvrability does not increase beyond 35 degree, but rudder torque increases and ship’s turning circle increases.

Why Steering Test Rudder angle 35 degree to 30 degree ?

• So that the point at which it is reached can be exactly judged as it crosses 30 degree.
• As hunting gear puts pump stroke to zero, the rudder movement slows down progressively as it approaches 35 degree.

Why Astern Turning Moment much less than Ahead ?

• The propeller thrust adds to the force on the rudder when going ahead, but in astern that thrust is lost.
• The pivoting point (point about which ship turns) shifts aft to 1/3 rd the length from aft. This reduces turning moment greatly.

What is the Pivoting Point for Ships ?

• The ship turns about a point called pivoting point. This is situated about 1/3 rd to 1/6 th of the ship length from forward, depending on the ship design.

Why is Torque on Rudder Stock more on going Astern ?

• While moving astern, trailing edge of rudder becomes leading edge. Center of pressure from turning axis increases.
• Flow of water to rudder is unobstructed causing point of action of force to go closer to the leading edge, 0.31 times the width from leading edge.

Why Rudder is situated Aft of the Ship ?

• To make use of propeller wash for thrust.
• The pivoting point of ship is 1/6 to 1/3 rd of length of ship from bow, the greater the perpendicular distance between point of action of force and pivoting point, the better rudder movement.
• Better protected at astern from damage.
• Drag is reduced if rudder is situated aft.

Why Full Astern Power is usually Less than Full Ahead Power ?

• Propeller blade section is designed for maximum efficiency in ahead.
• In astern direction, angle of attack is high on back of blade.
• Propeller will absorb very little available power, severe eddying occurs on face. Therefore, efficiency is very low.
• Hence, if 80% of full ahead power is available for astern, then boosting it to 100% will have minimal return in thrust from propeller.