Calculation method

Glossary

WAPS

Acronym for Wind Assisted Propulsion System or Wind Auxiliary Propulsion System.

Average power saving

Average power saving at main engine propeller shaft, thanks to the use of wind propulsion.

For active systems, this is the net energy saving. WAPS consumption has been deducted from saving.

The average saving depends heavily on the statistical weather conditions encountered on the chosen route.

Average fuel saving

Value deducted from the average power saving assuming a specific fuel oil consumption of the main engine of 180 g/kWh.

CO₂ emission savings

Reduction of CO₂ emissions, counted from “tank to wake”, so the emission associated with the supply of fuel are not taken into account here.

This value is directly related to fuel consumption. For a typical fuel carbon content of 85%, the combustion of one ton of fuel oil releases 3.1 tons of CO₂ into the atmosphere.

Area

The aerodynamic area of a WAPS is the projected or flat surface of the system. For a rectangular wing, it is the product of span (height) by chord (width). The aerodynamic forces are proportional to the surface.

Apparent wind

The apparent wind is the one seen by the WAPS. This is the combination of the True Wind Speed (TWS) and of the vessel speed.

In the case of wind propulsion, it is important to note that:

The Apparent Wind Angle (AWA) is in front of the True Wind Angle (TWA) and decreases as the speed of the vessel increases. For example, a vessel sailing 15 knots with a true wind of 15 knots from the beam at an angle of 90°, sees an apparent wind angle of 45°.
For a given vessel speed and wind speed, the apparent wind speed is much greater when the vessel is sailing upwind than when she is sailing downwind.

The true wind speed increases with altitude, a sail placed higher on the deck of the ship will benefit from a greater true wind speed.

Aerodynamic Force, Lift and Drag

The aerodynamic force is the one coming from the apparent wind blowing around the WAPS.

Lift is the component of aerodynamic force that is perpendicular to the direction of the apparent wind. The name comes from the early days of aeronautics because it is this component that allows aircraft to fly. For a WAPS, lift is an horizontal forces.

Drag is the component of aerodynamic force that is in the direction of the apparent wind.

In the case of wind propulsion, lift is necessary for the system to be able to develop a propulsive force as soon as the apparent wind is in front of the beam. This is the vast majority of conditions encountered.

Propulsive force [aerodynamic]

Component of the aerodynamic force generated along the direction of advance of the ship. This force reduces the required thrust on the main engine propeller.

Lateral force [aerodynamic], drift and heel

Lateral (or side) force is the component of the aerodynamic force perpendicular to the ship.

The ship need to balance the aerodynamic lateral (or side) force. This induces drift on the hull and may require some dedicated appendages, such as dagger boards. Drift also induces an additional resistance. SimWAPS provide an estimate of the associated power loss.

Criteria are included into SimWAPS to detect potential excessive drift or heel.

Lift and drag coefficient

Lift and drag coefficient reprensent the aerodynamic force expressed in a non dimensionnal form. This allow scaling forces between devices of various size and to carry out wind tunnel test at a reduced scale. These coefficients are a distinctive feature of each technology.

The lift coefficient C_L is related to the lift force and the drag coefficient C_D to the drag force.

Maximum lift, C_Lmax

The maximum lift coefficient is the maximum force per unit of surface that can be developed by the wind propulsion system.

Over a large range of apparent wind angles, the optimum operating point is at maximum lift, which is therefore an essential feature of the wind propulsion technology.

One way to increase the maximum lift of a wing section is to introduce camber, so to move away from the symmetrical section. This asymmetry will increase the deflection of the flow and increase the lift of the profile, until it stalls.

Then, the lift to drag ratio shows the ability of the section to develop lift with little drag. This ratio is important at low apparent wind angles.

Aerodynamic interactions

Each device of a wind propulsion systems change the direction of the wind in its viscinity, both upstream and downstream. Therefore, each device sees its own apparent wind and develop its own aerodynamic force. The deviation of performance from the isolated device is generally a loss of performance. Interactions depend on the number of devices, the spacing between the devices and the operating lift coefficient.

Power at [engine] shaft

This is the power required from the engine at the propeller shaft to sail at the desired speed. Wind propulsion reduces the power demand at the propeller shaft

Propulsive power

This is the product of the propulsion force (of the WAPS or of the propeller) by the speed of the vessel.

The power demand on the engine to generate this propulsive power is obtained by dividing by the efficiency of the propeller.

Passive vs active systems

Passive systems do not require any input of energy other than wind to operate (except for control systems where consumption is assumed to be low).

Active systems require a supply of energy. The Suction Wing has an internal fan and the Flettner Rotor rotates constantly at high speed.

The input of energy in active systems allows to reach very high lift coefficients, much higher than those of passive systems. The power balance must obviously take into account this consumption, which is the case in SimWAPS.

Principles of wind propulsion

The aerodynamic force generated by the wind propulsion system is expressed in the apparent wind coordinate system. The direction of the apparent wind is indicated by the vessel’s wind vane.

The aerodynamic force depends on wing or sail trimming, especially the angle of incidence (replaced by rotational speed in the case of a rotor).

When the apparent wind comes from the front (sailing upwind), lift is necessary to develop a propulsive force. When the vessel is sailing beam wind, the propulsion force is confused with the aerodynamic lift. Downwind, it is the aerodynamic drag that is propelling.

The aerodynamic force is proportional:

on the surface of the system,
Square of apparent wind speed
to the load-bearing coefficient.

Each system has the capacity to develop a maximum lift which depends solely on the geometry of the system (and mainly on the wing section) and can be amplified in the case of active systems.

Besides the propulsion force, the wind propulsion also generates a lateral force that must be balanced by the hydrodynamics of the vessel. This results in a drift and in a rudder angle that are not present in the case of mechanical propulsion alone.

Calculation of energy saving

The process of energy saving calculation in SimSpar is as follow:

Calculation of the propulsive force for a given true wind speed and true wind angle:
- Define the optimum operating point on the aerodynamic polar curve,
- Estimate induced drag on the hull,
Repeat the calculation of propulsive force for a set of wind angle and wind speed
Combine the set of propulsive power with weather statistic matrix

For each wind angle, SIMWAPS calculates the C_L that maximizes the net propulsion energy (minus the energy spent by the WAPS and the energy consumed by the additional resistance due to the lateral force exerted by the WAPS-see below). These polars are based on the background of CRAIN, according to published or internal wind tunnel tests, calculations when they are adapted to technology and validated. These polars correspond to a typical installation on an unobstructed deck, spaced vertically from the deck by no more than 10% of the wing span and sufficiently far away from the deck line so that wall effects are negligible.

Effects taken into account and limitations

SimWAPS calculates the power, fuel and CO₂ saving on a method that takes into account the following effects and parameters :

The aerodynamic characteristics (polar curve) of each type of wind propulsion technology. The definition of these characteristics depends on each technology and is detailed in Wind propulsion technologies,
Maximum lift coefficient : the aerodynamic polar (the value of C_D as a function of C_L) is adjusted depending on the C_Lmax selected by the user.
Device aspect ratio: the aerodynamic polar is also adjusted depending on the aspect ratio of the device.

Note

In the case of atypical installations, we can provide a CFD calculation or a wind tunnel test. Contact us!

Wind gradient : This is the change of true wind speed with the altitude. This effect which has significant importance is modelled by a classical law of proportionality of speed with the power 1/7 of altitude.
WAPS energy consumption. It is important for active systems (rotor and suction wing) and is calculated from an aerodynamic power coefficient C_A and the electromechanical efficiency of active systems. We can adjust these values on request.
Aerodynamic lateral force. It is balanced by the hull, which naturally sets in drift which generates an additional drag of the hull. The additional drag is calculated very simply according to the length and draught of the ship with a conventional formula for low aspect ratio bodies. It is sufficiently accurate when the wind propulsion power does not exceed 30% of the total propulsive power. Beyond that, the additional drag could have a significant impact on the contribution of WAPS and a further work is necessary, taking into account in particular the ship’s appendages.
On request we can provide a numerical simulation or a towing tank test.
Aerodynamic interaction between the devices of a system in the case of multiple installation. The interaction causes changes in the direction of the apparent wind that have an effect on the lift to drag ratio of each wing. These changes are calculated according to a formula from results obtained on typical configurations with a vortex method. This method provides results very similar to those obtained in wind tunnels for wings, sails and rotors. For a user-defined number of devices (up to 6), the devices are positioned to occupy regularly 80% of the deck surface of the ship.