MnrAq

Annex 1 177
Main engine power output
In steady state (constant speed), the thrust produced by the engine and propeller is in equilibrium with forces
opposing the ship’s motion. These forces include both hydrodynamic and aerodynamic resistance. Both forces
are modified by the weather; e.g. sailing into headwinds or head seas (waves) increases resistance. In both
calm and rough weather, total resistance is dominated by hydrodynamic resistance, which in turn is dominated
by viscous (friction) and wavemaking resistance.
Naval architects have progressed methods for estimating resistance from ship characteristics for a ship in
ideal conditions (negligible wind and waves, clean hull), which reveal that in these conditions, resistance is
strongly related to the speed of the hull through the water. However, in operation, a hull rarely stays “clean”
and the surface properties are modified over time as coatings deteriorate, macro- and microfouling grows on
the hull and the plating deforms through wear and tear. This modification of surface properties can have a
significant impact on viscous resistance and needs to be taken into account in any calculation of operational
fuel consumption.
Further influences to a ship’s resistance and propulsion are its draught and trim, which are in turn determined
by the ship’s loading condition (the amount and distribution of cargo and variable loads). A greater draught will
increase the wetted surface area of the hull and typically increase the resistance (although both bulbous bow
and propeller performance can sometimes counteract this trend of increased power demand with increasing
draught). The approximation used in this model is to represent the effect of draught through the use of the
Admiralty formula, which assumes that power is related to displacement to the power 0.66.
The formulated equation to encapsulate all of these effects on resistance and therefore main engine power is
given in equation (1).
​P​
​P​ t
​ = ​
ref(
__
​t​ t ​
​t​ ref
​) ​ __
( 2 3 )​
___
( ​V​ t ​ n
​
​V​ ref
​)
____________
​η​ w η​ f
​ eq. (1)
In equation (1), P t , V t and t t are respectively the instantaneous power, speed and draught at time t, P ref is
the reference power at speed V ref and draught t ref (both taken from IHSF). n is an index that represents the
relationship between speed and power, and η w is the modification of propulsion efficiency due to weather
and η f is the modification of propulsion efficiency due to fouling (discussed above). For the bottom-up model,
the same assumptions have been used as in the Second IMO GHG Study 2009: that n = 3, an assumption
discussed in greater detail in Section 1.5, and evaluated with respect to quality in Section 1.4.
Auxiliary engine and boiler power demands
The power outputs required by both the auxiliary engine and the boiler are both found using look-ups from
input tables described above in the section “Assumptions for auxiliary and boiler power demands”. The
corresponding mode is calculated for each ship and each hour of operation, from its instantaneous observed
speed.
Emissions subroutine: Emissions_at_op
The emissions produced by machinery are a function of the amount of fuel consumed and the specifics of
that fuel’s combustion. The former (fuel consumed) is found from the power, SFOC and time, and the latter is
found from the use of an emissions factor – in the case of CO 2 , a carbon factor. The calculation of SFOC and
emissions factors is detailed in Section 2 and Annex 6. Given this information, the formulation for this model’s
calculation of emissions of main, auxiliary and boiler machinery is given in equation (2).
CO 2 = P t × sfc × C f × t eq. (2)
In equation (2), P t is the instantaneous power output at time t (obtained from Power_at_op), sfc is the specific
fuel consumption (for a given engine with a given fuel at a given load factor), C f is the carbon factor (for a
given fuel), and t is the length of time the instantaneous power was observed to be constant. The values of C f
specific to different fuels are reported in Section 2.2 along with the other emissions species.
The sfc is found from the combination of a default assumption for a given engine type, size and age, sfc e and
a modifying factor obtained from a look-up table to account for variations in sfc as a function of fuel type and
engine load factor.