A method for obtaining the exhaust gas emission of a ship's main engine

Abstract

The present invention discloses a method for obtaining the emission of waste gas from a ship's main engine, including: S1: obtaining AIS data, interpolating the longitude and latitude, speed and bow in the AIS data; S2: obtaining the marine environment information of the longitude and latitude points in the interpolated AIS data, and correcting the ship's ground speed to the ship's still water speed; S3: estimating the hull fouling factor using the initial roughness of a new ship and the hull roughness during the ship's operation; S4: estimating the load power of the ship's main engine using the corrected speed, hull fouling factor and draft adjustment coefficient based on the propeller law, and comparing it with the actual ship's monitored fuel consumption to verify the accuracy of the ship's main engine load estimation; S5: estimating the pollution emission of the ship's main engine based on the ship's main engine load estimation model and the pollutant emission factor. The present invention improves the estimation accuracy of the main engine load; and achieves accurate estimation of the ship's main engine emissions through the estimated main engine load and emission factor.

Description

Technical Field

[0001] The present invention relates to the field of estimation of exhaust pollutant emission of ship main engine, and in particular to a method for obtaining exhaust gas emission of ship main engine. Background Art

[0002] At present, the emission of ship pollutants is mainly estimated by the "bottom-up" dynamic method, and the main engine pollutant emission is the main emission source. IMO, the United States Environmental Protection Agency (USEPA) and other institutions continue to optimize and update their emission inventory methods, mainly using the propeller method and the naval method to estimate the main engine load. Therefore, the ship speed is an important factor affecting the accuracy of the estimation. However, the speed provided in the AIS data is the speed after being affected by wind, waves and currents. It is necessary to eliminate the influence of wind, waves and currents to obtain the actual output speed of the ship in order to reflect the impact of actual sea conditions and weather conditions on the instantaneous output power of the ship. In addition, changes in hull fouling will cause changes in the instantaneous power of the ship. The fourth greenhouse gas research report of IMO (IMO4) recommends that the hull fouling factor in the load equation adopts a fixed value. However, hull fouling is a biological phenomenon that is difficult to predict and control. The type and severity of fouling are closely related to the type of antifouling coating and the operating conditions of the ship. Hull fouling will cause a significant increase in resistance and power. Therefore, weather, sea conditions and hull fouling are crucial to accurately estimate the main engine load. Summary of the invention

[0003] In view of the shortcomings of the prior art, the present invention proposes a method for obtaining the exhaust gas emissions of a ship main engine, so as to improve the estimation accuracy of the exhaust gas emissions of a ship main engine. To achieve the above-mentioned invention purpose, the technical solution adopted by the present invention is as follows:

[0004] S1: Obtain AIS data and interpolate the latitude, longitude, speed and heading in the AIS data;

[0005] S2: Obtain the ocean environment information of the longitude and latitude points in the interpolated AIS data, and correct the ship's ground speed (navigation speed) to the ship's still water speed (ship speed);

[0006] S3: Estimate the hull fouling factor using the initial roughness of the new ship and the hull roughness during ship operation, and improve the time accuracy to the month unit;

[0007] S4: Based on the propeller law, the ship's main engine load power is estimated using the corrected speed, hull fouling factor and draft adjustment coefficient; and compared with the actual ship's monitored fuel consumption to verify the accuracy of the ship's main engine load estimation;

[0008] S5: Identify the ship status through AIS data and estimate the pollution emissions of the ship main engine based on the ship main engine load estimation model and pollutant emission factors.

[0009] The specific method used in S2 is as follows:

[0010] S21: Assume that the ship speed before the wind is affected is V, the specific method is as follows:

[0011]

[0012]

[0013]

[0014] Where: V SOG Indicates the ship's ground speed in AIS data (m / s); V w represents the wind-induced drift velocity (m / s), θ w Indicates the angle between wind direction and bow direction, V y represents the wind-induced drift speed of the ship when it is stationary (m / s), K is the drift coefficient, and its values ​​are 0.038 and 0.041 when the ship is unloaded and fully loaded, respectively. a is the hull waterline side area (m 2 ), L w is the waterplane length (m), d is the actual draft of the ship (m), V a Indicates wind speed (m / s);

[0015] S22: Assume that the ship speed before the impact of the wave is V, the specific method is as follows:

[0016]

[0017]

[0018] BN=4.21794×H 0.31

[0019] tanker

[0020] Other ships

[0021] Where: θ s represents the angle between the wave direction and the bow direction; μ represents the speed loss coefficient under different angles between the wave direction and the bow direction; △V / V represents the speed loss; BN represents the Beaufort coefficient (dimensionless); H represents the effective wave height (m); C represents the dimensionless parameter: 0.5 for oil tankers and 0.7 for other ships; ▽ is the displacement of the ship (t);

[0022] S23: Assume that the ship speed before the flow is affected is V, and the expression is as follows:

[0023]

[0024] Where: V c Indicates flow velocity (m / s); θ c Indicates the angle between the flow direction and the bow direction;

[0025] S24: Assume that the original ship speed, that is, the speed corrected by wind, waves and current is V, and the expression is as follows:

[0026]

[0027] The specific method used in S3 is as follows:

[0028] S31: The average roughness (k1) of a new ship's hull is about 120μm, and the hull roughness increases by an average of 30μm per year as it ages. The roughness equation that increases with the age of the ship is fitted, and the expression is as follows:

[0029]

[0030] Where: b represents the roughness that increases with ship age (μm); x2 represents the ship age (years); the linear regression equation is fitted with data from Greenhouse gas emissions from global shipping, 2013–2015 (ICCT 2017);

[0031] S32: Establish a functional relationship equation of the change of hull roughness (k2) with the operation time (dry dock interval) during ship operation, and the expression is as follows:

[0032] k2=ax1+b(R 2 =1)

[0033] Where: a represents the average monthly increase of hull roughness by 2.5 μm (ICCT 2017); x1 represents the interval between ships entering dry dock (month);

[0034] S33: The hull fouling factor equation is as follows:

[0035]

[0036] Where: HFF is the fouling factor of the hull; L is the length between vertical lines of the ship; k1 is the initial roughness of the new ship (120 μm); k2 is the roughness of the hull that changes with the operating time (interval time of entering the dry dock) (μm);

[0037] The specific method used in S4 is as follows:

[0038] S41: The draught adjustment factor (DAF) is expressed as follows:

[0039] DAF = (T / T max ) 2 / 3

[0040] Where: T represents the instantaneous draft of the ship (m); T max Indicates the maximum draft of the ship (m);

[0041] S42: Based on the propeller law, the ship's main engine load is estimated using the corrected speed, hull fouling factor and draft adjustment factor. The expression is as follows:

[0042] LF i =(V i / V max ) 3 ×DAF i ×HFF i

[0043] In the formula: LF i Indicates instantaneous host load; V i V represents the instantaneous speed of the ship corrected by wind, waves and currents (kn); max Indicates the maximum design speed of the ship (kn);

[0044] S43: According to IMO4, the equation of fuel consumption rate SFOC and main engine load is established to estimate the main engine fuel consumption FC. The accuracy of the main engine load estimation is verified based on the measured main engine fuel consumption. The main engine fuel consumption estimation expression is as follows:

[0045]

[0046]

[0047] Where: SFOC i Indicates that the host is in LF i Fuel consumption rate under (g / kWh); SFOC baseline Indicates the minimum fuel consumption rate (g / kWh); P e LF is the rated power of the host; i represents the instantaneous host load; t represents the time interval between two consecutive AIS reporting points.

[0048] The specific method used in S5 is as follows:

[0049] S51: The selection of pollutant emission factor (EF) depends on the engine type, fuel sulfur content, etc. The present invention selects the pollutant emission factor proposed in IMO4;

[0050] S52: Calculate the time interval t between two consecutive AIS reporting points based on the estimated host load estimation model and emission factor iThe emissions under the above conditions are added together to obtain the single ship main engine emissions E;

[0051] The emissions E of NOx, CO, PM, HC (CH4 and NMVOC) and N2O are estimated as follows:

[0052]

[0053] The emissions E of CO2, SOx and BC are estimated as follows:

[0054]

[0055] Where: EF e,i EF represents the emission factor of the pollutant based on power (g / kWh); f,i LLAF stands for emission factor of fuel-based pollutants (g / g fuel); i Indicates the emission factor adjustment coefficient when LF is less than 20%; P e LF is the rated power of the host; i Indicates the instantaneous host load.

[0056] The present invention discloses a method for obtaining the exhaust gas emission of a ship main engine, which has the following beneficial effects compared with the prior art: (1) The present application uses real-time wind, waves and currents to correct the ship speed, and fits the function of the hull fouling changing with the ship age and dry dock time; (2) The corrected speed, hull fouling factor and draft adjustment coefficient are used to estimate the load power of the ship main engine, and compared with the actual ship monitoring fuel consumption to verify the accuracy of the ship main engine load estimation; (3) The present application uses a ship main engine load estimation model and pollutant emission factors to estimate the pollution emission of the ship main engine. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is the overall flow chart of the experiment in the present invention;

[0058] Figure 2 It is the plane motion diagram of the ship under the influence of wind and current;

[0059] Figure 3 It is the encounter angle diagram between the ship and the wave;

[0060] Figure 4 This is a comparison chart of HFF in years and months (taking a ship with an age of 12 years as an example);

[0061] Figure 5 It is the instantaneous corrected speed change diagram of ships on each route;

[0062] Figure 6 This is a comparison chart of load estimation between IMO4 and the present invention. DETAILED DESCRIPTION

[0063] In order to make the technical solutions and advantages of the present invention easier to understand, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the accompanying drawings and embodiments. Figure 1 A method for obtaining the exhaust gas emission of a ship main engine is shown, comprising the following steps:

[0064] S1: The present invention takes four voyages of two typical Chinese bulk carriers as examples and uses the cubic spline interpolation method to interpolate the original AIS data with a time resolution of minutes.

[0065] S2: Extract the wind, wave and current information corresponding to the time and longitude and latitude in the interpolated AIS data. The instantaneous corrected speed changes in the four voyages are as follows: Figure 4 As shown, the impact of marine environmental factors on ship speed loss is quantified.

[0066] S21: Assume that the ship speed before the wind is affected is V, and the plane motion diagram of the ship under the influence of wind is as follows: Figure 2 As shown, the specific method is as follows:

[0067]

[0068]

[0069]

[0070] Where: V SOG Indicates the ship's ground speed in AIS data (m / s); V w represents the wind-induced drift velocity (m / s), θ w Indicates the angle between wind direction and bow direction, V y represents the wind-induced drift speed of the ship when it is stationary (m / s), K is the drift coefficient, and its values ​​are 0.038 and 0.041 when the ship is unloaded and fully loaded, respectively. a is the hull waterline side area (m 2 ), L w is the waterplane length (m), d is the actual draft of the ship (m), V a Indicates wind speed (m / s);

[0071] S22: Assume that the ship speed before the wave impact is V, and the encounter angle between the ship and the wave is Figure 3 As shown, the specific method is as follows:

[0072]

[0073]

[0074] BN=4.21794×H 0.31

[0075] tanker

[0076] Other ships

[0077] Where: θ s represents the angle between the wave direction and the bow direction; μ represents the speed loss coefficient under different angles between the wave direction and the bow direction; △V / V represents the speed loss; BN represents the Beaufort coefficient (dimensionless); H represents the effective wave height (m); C represents the dimensionless parameter: 0.5 for oil tankers and 0.7 for other ships; ▽ is the displacement of the ship (t);

[0078] S23: Assume that the ship speed before the flow is affected is V, and the ship plane motion diagram under the flow is as follows: Figure 2 As shown, the expression is as follows:

[0079]

[0080] Where: V c Indicates flow velocity (m / s); θ c Indicates the angle between the flow direction and the bow direction;

[0081] S24: Assume that the original ship speed, that is, the speed corrected by wind, waves and current is V, and the expression is as follows:

[0082]

[0083] S3: The fouling factor estimation method is a function of the average initial hull roughness and the average annual increase in roughness (30μm) based on the ship age classification. The time accuracy is improved to months, which will greatly improve the accuracy of hull roughness estimation and thus improve the accuracy of load estimation.

[0084] S31: The average roughness (k1) of a new ship's hull is about 120μm, and the hull roughness increases by an average of 30μm per year as it ages. The roughness equation that increases with the age of the ship is fitted, and the expression is as follows:

[0085]

[0086] Where: b represents the roughness that increases with the age of the ship (μm); x2 represents the age of the ship (years); the linear regression equation fitting data comes from ICCT2017;

[0087] S32: Establish a functional relationship equation of the change of hull roughness (k2) with the operation time (dry dock interval) during ship operation, and the expression is as follows:

[0088] k2=ax1+b(R 2 =1)

[0089] Where: a represents the average monthly increase of hull roughness by 2.5 μm (ICCT 2017); x1 represents the interval between ships entering dry dock (month);

[0090] S33: The hull fouling factor equation is as follows:

[0091]

[0092] Where: HFF is the fouling factor of the hull; L is the length between vertical lines of the ship (m); k1 is the initial roughness of the new ship (120 μm); k2 is the roughness of the hull that changes with the operating time (interval time of entering the dry dock) (μm).

[0093] S4: Based on the propeller law, the ship main engine load power is estimated by using the corrected speed, hull fouling factor and draft adjustment coefficient, and the fuel consumption is estimated by using the SFOC proposed in the fourth greenhouse gas research report of IMO. By comparing it with the fuel consumption monitored by the actual ship, the accuracy of the ship main engine load estimation is verified. Table 1 is a comparison of the fuel consumption of the present invention, IMO4 and the measured fuel consumption.

[0094] S41: The draught adjustment factor (DAF) is expressed as follows:

[0095] DAF = (T / T max ) 2 / 3

[0096] Where: T represents the instantaneous draft of the ship (m); T max Indicates the maximum draft of the ship (m0;

[0097] S42: Based on the propeller law, the ship main engine load is estimated by using the modified speed, hull fouling factor and draft adjustment factor. The expression is as follows and compared with the IMO4 load estimation method. Figure 3 As shown;

[0098] LF i =(V i / V max ) 3 ×DAF i ×HFF i

[0099] In the formula: LF i Indicates instantaneous host load; V i V represents the instantaneous speed of the ship corrected by wind, waves and currents (kn); max Indicates the maximum design speed of the ship (kn);

[0100] S43: According to IMO4, an equation of fuel consumption rate SFOC and main engine load is established to estimate the main engine fuel consumption FC. The accuracy of the main engine load estimation is verified based on the measured main engine fuel consumption. The main engine fuel consumption estimation expression is as follows:

[0101]

[0102]

[0103] Where: SFOC i Indicates that the host is in LF i Fuel consumption rate under (g / kWh); SFOC baseline Indicates the minimum fuel consumption rate (g / kWh); P e LF is the rated power of the host; i represents the instantaneous host load; t represents the time interval between two consecutive AIS reporting points.

[0104] Table 1 Percent error between estimated and monitored fuel consumption values

[0105]

[0106] As can be seen from Table 1, the average percentage errors of the fuel consumption estimated by IMO4 and the present invention are 19.28% and 11.76% respectively. This shows that the main engine load estimation model using the corrected speed, hull fouling factor and draft adjustment coefficient can accurately estimate the main engine load. Therefore, the main engine load estimation model of the present invention is used to estimate the pollutant emissions of the ship main engine.

[0107] S5: Identify the ship status through AIS data, and use the ship main engine load estimation model and pollutant emission factors to estimate the pollution emissions of the ship main engine.

[0108] S51: The selection of pollutant emission factor (EF) depends on the engine type, fuel sulfur content, etc. The present invention selects the pollutant emission factor proposed in IMO4, as shown below.

[0109] EF SOx (g SO X / g fuel)=2×0.97753×s

[0110] HFO:EF PM10 (g / kWh)=1.35+SFOC×7×0.02247×(s-0.0246)

[0111] MDO:EF PM10 (g / kWh)=0.23+SFOC×7×0.02247×(s-0.0024)

[0112] EFPM2.5 (g / kWh) = 0.92 × EF PM10

[0113] HFO:

[0114] Two-stroke engine: EF BC (gBC / gfuel) = 1.5 × 10 -4 ×(LF -0.359 )

[0115] Four-stroke engine: EF BC (gBC / gfuel) = 2.5 × 10 -4 ×(LF -0.968 )

[0116] MDO&MGO:

[0117] Two-stroke engine: EF BC (gBC / gfuel) = 3.11 × 10 -5 ×(LF -0.397 )

[0118] Four-stroke engine: EF BC (gBC / gfuel)=1.201×10 -4 ×(LF -1.124 )

[0119] Where: s represents the sulfur content of fuel.

[0120] Table 2 NOx emission factors (g / kWh)

[0121]

[0122] Table 3 CO emission factors (g / kWh)

[0123] Host Type HFO & LSHFO MDO Methanol SSD 0.540 0.044 0.054 MSD 0.540 0.046 0.054 HSD 0.540 0.540

[0124] Table 4 CO2 emission factors (g CO2 / g fuel)

[0125] Fuel Type Carbon content <![CDATA[EF f ]]> HFO 0.8493 3.114 MDO 0.8744 3.206 LNG 0.7500 2.750 Methanol 0.3750 1.375 LSHFO1.0% 0.8493 3.114

[0126] Table 5 CH4 emission factors (g / kWh)

[0127] Host Type HFO,LSHFO&MDO Methanol SSD 0.010 0.001 MSD 0.010 0.001 HSD 0.010

[0128] Table 6 NMVOC emission factors (g / kWh)

[0129]

[0130]

[0131] Table 7 N2O emission factors (g / kWh)

[0132] Host Type HFO & LSHFO MDO Methanol SSD 0.031 0.030 0.003 MSD 0.034 0.030 0.003 HSD 0.030 0.034

[0133] S52: Compare the ship speed and the speed limit of the working condition classification to determine the ship's sailing condition and calculate the main engine load. This study selected a Tier 0 ship and a Tier II ship, a total of 4 voyages, and used the estimation model based on the main engine load estimation model and emission factor to estimate the emissions, and calculated the time interval t between two consecutive AIS reporting points. i The emissions under the above conditions are added to obtain the single ship main engine emissions E. The calculation results are shown in Table 9.

[0134] The emissions E of NOx, CO, PM, HC (CH4 and NMVOC) and N2O are estimated as follows:

[0135]

[0136] The emissions E of CO2, SOx and BC are estimated as follows:

[0137]

[0138] Where: EF e,i EF represents the emission factor of the pollutant based on power (g / kWh); f,i LLAF stands for emission factor of fuel-based pollutants (g / g fuel); i Indicates the emission factor adjustment coefficient when LF is less than 20%; P e LF is the rated power of the host; i Indicates the instantaneous host load, as shown in Table 8.

[0139] Table 8 Low load correction factor

[0140] Host load PM NOx SOx <![CDATA[CO2]]> CO <![CDATA[CH4]]> NWVOC <![CDATA[N2O]]> BC <＝2％ 7.29 4.63 1.00 1.00 9.70 21.18 21.18 4.63 1.00 10％ 1.38 1.22 1.00 1.00 1.97 2.18 2.18 1.22 1.00 20％ 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

[0141] Table 9 Pollutant emissions (t)

[0142]

[0143]

[0144] S6: The emissions of the main engines of individual ships can be obtained through S5. The emissions of ships in the selected area are added up to obtain the emissions of the main engines of ships in the area, and a regional ship main engine pollutant emission inventory with three dimensions of time, space and ship attributes is constructed.

[0145] In summary, in the above embodiments of the present application, an accurate algorithm for estimating the ship emission inventory is provided, including: high time resolution interpolation processing of the longitude and latitude, speed and bow direction in the AIS data, using wind, wave and current information to correct the ship's ground speed (speed) to the ship's still water speed (ship speed) and establish a function of the change of hull fouling over time to optimize the ship's main engine load estimation. By comparing with the actual ship's monitored fuel consumption, it is proved that the present invention improves the estimation accuracy of the main engine load; accurate estimation of the ship's main engine emissions is achieved through the estimated main engine load and emission factors.

[0146] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in the field. Although the specific implementation methods of the present invention are described, the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for obtaining the exhaust gas emission of a ship main engine, characterized in that include: S1: Obtain AIS data and interpolate the latitude and longitude, speed and heading in the AIS data; S2: Obtain the ocean environment information of the longitude and latitude points in the interpolated AIS data, and correct the ship's ground speed to the ship's still water speed; S3: Estimate the hull fouling factor using the initial roughness of the new ship and the hull roughness during ship operation; S4: Based on the propeller law, the ship's main engine load power is estimated using the corrected speed, hull fouling factor and draft adjustment coefficient, and compared with the actual ship's monitored fuel consumption to verify the accuracy of the ship's main engine load estimation; S5: Estimate the pollution emission of the ship main engine based on the ship main engine load estimation model and pollutant emission factors; The specific method used in S4 is as follows: S41: The expression of draft adjustment factor DAF is as follows: DAF=(T / T max ) 2 / 3 Where: T represents the instantaneous draft of the ship; T max Indicates the maximum draft of the ship; S42: Based on the propeller law, the ship's main engine load is estimated using the corrected speed, hull fouling factor and draft adjustment factor. The expression is as follows: LF i =(V i / V max ) 3 ×DAF i ×HFF i In the formula: LF i Indicates instantaneous host load, V i V is the instantaneous speed of the ship corrected by wind, waves and currents. max Indicates the maximum design speed of the ship; S43: Establish a main engine fuel consumption estimation equation of fuel consumption rate and main engine load, and verify the accuracy of main engine load estimation based on the measured main engine fuel consumption. The main engine fuel consumption estimation expression is as follows: Where: SFOC i Indicates that the host is in LF i Specific fuel consumption, SFOC baseline Indicates the minimum fuel consumption rate, P e is the rated power of the host, LF i represents the instantaneous host load, t represents the time interval between two consecutive AIS reporting points; The specific method used in S5 is as follows: S51: Select pollutant emission factors; S52: Calculate the time interval t between two consecutive AIS reporting points based on the host load estimation model and emission factor i The emissions under the above conditions are added together to obtain the single ship main engine emissions E; The emissions E of NOx, CO, PM, CH4, NMVOC and N2O are estimated as follows: The emissions E of CO2, SOx and BC are estimated as follows: Where: EF e,i represents the emission factor of the power-based pollutant, EF f,i represents the fuel-based pollutant emission factor, LLAF i Indicates the emission factor adjustment coefficient when LF is less than 20%, P e is the rated power of the host, LF i Indicates the instantaneous host load.

2. The method according to claim 1, characterized in that The specific method used in S2 is as follows: S21: Assume that the ship speed before being affected by the wind is V, and the specific method is as follows: Where: V SOG Indicates the ship's ground speed in AIS data, V w is the wind-induced drift velocity, θ w Indicates the angle between wind direction and bow direction, V y It represents the wind-induced drift speed when the ship is stationary, K is the drift coefficient, B a is the hull side area above waterline, L w is the length of the water plane, d is the actual draft of the ship, V a Indicates wind speed; S22: Assume that the ship speed before being affected by the waves is V, and the specific method is as follows: BN=4.21794×H 0.31 tanker Other ships Where: θ s represents the angle between the wave direction and the bow direction, μ represents the speed loss coefficient under different angles between the wave direction and the bow direction, △V / V represents the speed loss, BN represents the Beaufort coefficient, H represents the effective wave height, C represents the dimensionless parameter, and ▽ represents the displacement of the ship; S23: Assume that the ship speed before being affected by the current is V, and the expression is as follows: Where: V c represents flow velocity (m / s), θ c Indicates the angle between the flow direction and the bow direction; S24: Assume that the ship's still water speed, that is, the speed corrected by wind, waves and current, is V, and the expression is as follows:

3. The method according to claim 1, characterized in that: The specific method used in S3 is as follows: S31: Fitting the roughness equation that increases with ship age, the expression is as follows: Where: b represents the roughness that increases with the age of the ship, x2 represents the age of the ship; S32: Establish a functional relationship equation of the change of hull roughness k2 with the operation time during ship operation, the expression is as follows: k2=ax1+b(R 2 =1) Where: a represents the average monthly increase of 2.5 μm in hull roughness, x1 represents the interval between ships entering dry dock, S33: The hull fouling factor equation is as follows: Where: HFF represents the fouling factor of the hull, L represents the length between vertical lines of the ship, k1 represents the initial roughness of the new ship, and k2 represents the roughness of the hull that changes with the operating time.

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