Ship Resistance, Hull Form and Propulsion
What it costs to push a hull through water: frictional and wave-making resistance, the flow that causes them, and the powering numbers a designer works to.
Key Principles at a Glance 8 points
- Total resistance is the sum of frictional and residual resistance, and frictional resistance is the part that depends on the wetted surface.
- Frictional resistance rises with wetted surface area, so any appendage — bilge keels, rudder, bossings — is paid for twice: once in steel and once in resistance.
- Wave-making resistance is the energy spent making the bow and stern wave systems, and it is the part of the bill that hull form can recover.
- Residual resistance is what is left after friction is taken out, and it is dominated by wave-making at high speed.
- Streamline flow keeps the water in smooth layers; turbulent flow breaks it into eddies, and a hull is designed to delay the transition for as long as it can.
- The after body resists more than the fore body, because separating flow aft has already lost the pressure recovery the bow was given.
- Increasing length at constant displacement reduces wave-making resistance, which is why the fast ship is long and fine rather than short and full.
- The Admiralty coefficient relates displacement, speed and power, and it is used to compare the propulsive efficiency of one hull against another.
13.1 The two resistances
What it costs to push the hull through water, and what the hull form does about it. Part 8 spent engine power making a bow wave; this part is where that bill is broken down — and where the designer learns which part of it can be recovered and which cannot.
13.1.1 Frictional resistance — and the wetted surface it depends on
As a ship moves through the water, the friction of the water acting over the entire wetted surface of the hull causes a net force opposing the ship's motion.
The total resistance is the sum of its two parts:
The frictional part is:
| Term | Value |
|---|---|
| f, coefficient of frictional resistance | 0.01 |
| S | Wetted surface area |
| V | Velocity in knots |
| n | 1.87 |
Everything about this formula points the same way: frictional resistance is a surface resistance. It scales with how much hull is wet and how fast the water moves past it — not with the shape of the bow, not with the fineness of the lines. That is why the wetted surface area of §13.3.1 is a design number in its own right, and why the bulb of Part 8 §8.3.5 pays a skin-friction price for its wave-making saving.
13.1.2 Wave-making resistance
The second major component of hull resistance is the resistance due to wave making. The creation of waves requires energy. As ship speed increases, the height of the waves produced by the ship increases, and therefore the energy required to produce them also increases. This lost energy is referred to as wave making resistance, and it often becomes a limiting factor in the speed of a ship.
That last clause is the operational point. Friction grows steadily with speed; wave-making grows with the height of the waves, which itself grows with speed — so at some speed the wave-making term dominates, and adding power mostly makes bigger waves rather than more knots. The bow wave of Part 8 §8.3.2 and the destructive-interference bulb of §8.3.3 are this resistance being generated and then partly cancelled.
13.1.3 Residual resistance
Residual — residuary — resistance is caused by the distribution of pressure which develops about the hull because of the waves and eddies formed by the ship's motion.
It divides into three components:
- Resistance caused by formation of streamline around the ship due to change in direction of water.
- Eddy resistance due to sudden change in form.
- Resistance caused by formation of wave while passing through the water (wave making resistance).
Note the nesting: wave-making resistance is both a major component in its own right (§13.1.2) and the third component of the residual. The residual is everything left over once the skin friction has been subtracted — the pressure field, the eddies and the waves together.
13.1.4 Frictional against wave-making
The comparison, as the oral puts it:
| Frictional resistance | Wave-making resistance | |
|---|---|---|
| Cause | Friction of water over the entire wetted surface | Energy lost in creating the ship's wave system |
| Depends on | Wetted surface area and speed (Rf = f·S·V^1.87) | Wave height, which grows with speed |
| Character | Steady, present at all speeds | Grows disproportionately; limits the ship's speed |
| Designed against by | Less wetted surface, smoother hull | Hull form, Froude-number choice, bulbous bow |
13.2 The flow around the hull
13.2.1 Streamline
A streamline is a line in a fluid such that its tangent at any point is parallel to the instantaneous velocity of the fluid at that point.
The first component of the residual exists because the water must change direction to get around the hull, and that change of direction is drawn as streamlines. Smooth, attached streamlines cost little; streamlines forced into sudden changes cost eddies.
13.2.2 Turbulent flow
Turbulence flow is fluid flow where the particle motion at any point is rapidly changing both in direction and magnitude.
13.2.3 Forward or aft — which end resists more
The aft portion of the ship has more resistance:
Along the length of the hull, the laminar flow exists for a very small distance and then converts to turbulence flow, which creates the boundary layer.
The mechanism:
- In the forward portion, pressure forces act normal to the surface.
- In the aft portion, the boundary layer reduces the forward-acting component of pressure. This reduction in the forward-acting component results in a net resistance force on the hull — the increase called viscous pressure drag.
So the bow meets clean laminar flow and the stern inherits the turbulent boundary layer the whole forebody has grown. The aft end pays for the friction of the forward end twice: once as skin friction along the hull, once as lost pressure at the stern. That is one reason the Part 9 stern lines are drawn for smooth water flow into and away from the propeller — the propeller must work in the water the forebody has already disturbed.
13.2.4 What increasing the length does
The length of a vessel is directly proportional to its resistance: the longer the vessel, the greater the resistance. As Rf is directly proportional to wetted surface area, increasing the length increases the frictional resistance.
The model-testing law behind that statement is Froude's law of comparison. If the residual resistance varies as the cube of the linear dimension, then speed varies as its square root — the speed-length ratio:
V / √L = constant V1 / √L1 = V2 / √L2
Where Rr is the residual resistance, L the linear dimension and V the speed.
Three readings follow:
- At corresponding speeds the wave-making characteristics are the same.
- At high speed the speed-length ratio is high and the wave-making resistance is large.
- A ship is therefore considered slow or fast in relation to its speed-length ratio — not its absolute speed.
That third line is the design meaning of the Froude number used throughout Parts 8 and 13: "fast" is speed relative to the wave the hull's own length generates, which is why a bulb that pays at high Froude number charges interest at low.
13.3 The powering numbers
13.3.1 Wetted surface area — and its appendages
The wetted surface area of a ship is the area of the hull in contact with the water. It is found by putting the transverse girths of the ship, from waterline to waterline, through Simpson's Rule and adding a small percentage to allow for the longitudinal curvature of the shell. To this area is added the wetted surface area of appendages such as cruiser stern, rudder and bilge keels.
Two approximate equations are carried for it:
Taylor's equation: S = c · √(Δ · L)
Where S is the wetted surface, L the length, d the draught, ∇ the volume of displacement, Δ the displacement and c the Taylor coefficient.
The appendage clause is the part the oral tests: the cruiser stern, the rudder and the bilge keels are all wet, all frictional, and none of them appears in the girth integration — each must be added by hand.
13.3.2 Admiralty coefficient — what it compares
A coefficient used in the preliminary estimation of the power required in a new design to attain the desired speed. Values range from 400 to 600 — the higher the value, the more economical the vessel.
Admiralty coefficient from:
- D = displacement in tons
- V = speed in knots
- P = shaft power in kW
The coefficient compares like with like: displacement and speed achieved against shaft power spent. A 600 ship converts power into transport more economically than a 400 ship, and the designer quoting the number is saying how the new design stands against the fleet before the model tank has spoken. The second treatment of the coefficient in the material is a bare question heading with no text.
13.3.3 Propulsive characteristics and hull form as a design output
From the preliminary design of a vessel due for construction, six outputs are obtained: dimensions, displacement, stability, propulsive characteristics and hull form, preliminary general arrangement and principal structural details. The type of ship decides all six.
That is the closing loop of the part: resistance is not a penalty discovered after the ship is drawn. The power required to push the hull at the contract speed — frictional over the wetted surface, wave-making in the wave system, residual in the pressure field — is one of the six numbers the design starts from, and the hull form is shaped around it.