Method of estimating frictional resistance of ship bottom coating film, and a method of evaluating coating film performance using said method and a device for evaluating coating film performance

Abstract

A method of estimating a frictional resistance of a ship bottom coating film, the method including measuring any one of Rz (maximum height roughness), Rc (mean height of roughness profile elements), Ra (arithmetic mean roughness), Rq (root mean square roughness) and RZJIS (ten-point mean roughness) as a roughness height R in a mean length RSm of roughness profile elements in the range of 2,000 to 10,000 m according to JIS B 0601:2001 (ISO4287:1997) on a coating film formed by applying a ship bottom coating paint on a substrate and calculating a frictional resistance increase rate FIR (%) from a mirror surface by the following formula (1), wherein coefficient C is a constant depending on the kind of the roughness height R and a frictional resistance testing method, and is previously determined in such a manner that plural ship bottom coating films each having different roughness are subjected to a roughness measurement and a frictional resistance test in a definite evaluation length, and then the coefficient C is determined by the formula (1) using the roughness height R, the mean length RSm of roughness profile elements and the frictional resistance increase rate FIR (%), which have been measured.

Claims

1. A method of estimating a frictional resistance of a coating film, the method comprising: measuring a roughness height R of a coating film painted on a substrate in an area having a mean length of roughness profile elements RSm of 2,000 to 10,000 m according to JIS B 0601:2001 (ISO4287:1997), wherein the roughness height R of the coating film is at least one selected from the group consisting of a maximum height roughness Rz, a mean height of roughness profile elements Rc, an arithmetic mean roughness Ra, a root mean square roughness Rq, and a ten-point mean roughness RZJIS; and calculating a frictional resistance increase rate FIR (%) of the coating film with respect to a mirror surface by formula (1); $\begin{array}{cc}\mathrm{FIR}\left(\%\right)=C\frac{R^2}{\mathrm{RSm}},& \left(1\right)\end{array}$ wherein coefficient C is a constant predetermined by measuring a roughness within a fixed length of a plurality of test coating films having different roughness to determine a roughness height R and a mean length of roughness profile elements RSm of each of the test coating films, conducting a frictional resistant test on each of the test coating films to obtain a frictional resistance increase rate FIR (%) with respect to a mirror surface for each of the test coating films, and calculating the coefficient C from the roughness height R, the mean length of roughness profile elements RSm, and the frictional resistance increase rate FIR of the test coating films by the formula (1), wherein the roughness height R of the test coating films measured to predetermine the coefficient C is at least one selected from the group consisting of a maximum height roughness Rz, a mean height of roughness profile elements Rc, an arithmetic mean roughness Ra, a root mean square roughness Rq, and a ten-point mean roughness RZJIS, of the test coating films, wherein the coefficient C depends on the kind of the roughness height R and the frictional resistance test conducted to predetermine the coefficient C, and wherein the frictional resistant test to predetermine the coefficient C is carried out by using at least one of a double cylinder device, an in-pipe flow path, and a cavitation water tank.

2. The method according to claim 1, wherein the measuring of the roughness height R is conducted in an evaluation length of 10,000 m or more, and a measurement pitch of 500 m or less according to JIS B 0601:2001 (ISO 4287:1997).

3. The method according to claim 2, wherein the measuring of the roughness height R is conducted by using a high pass filter such that the cut-off value c is 10,000 m or more.

4. The method according to claim 1, wherein, in predetermining the coefficient C, the frictional resistance test is carried out by using a double cylinder device by rotating an external cylinder of the double cylinder device to determine a torque T.sub.0 which works on an internal cylinder of the double cylinder device having a mirror surface and then rotating the external cylinder under the same rotating condition to determine a torque T which works on an internal cylinder on which each of the test coating films is formed, and the frictional resistance increase rate FIR (%) of the test coating films is determined from formula (2): $\begin{array}{cc}\mathrm{FIR}\left(\%\right)=\frac{T-T_0}{T_0}100.& \left(2\right)\end{array}$

5. The method according to claim 1, wherein, in the measuring, the roughness height R and the mean length of roughness profile elements RSm are measured by a stylus type roughness measurement device or a laser displacement type roughness measurement device.

6. A method of evaluating performance of a coating film, the method comprising: measuring a roughness height R and a mean length of roughness profile elements RSm; and estimating a frictional resistance increase rate FIR (%) by the formula (1); $\begin{array}{cc}\mathrm{FIR}\left(\%\right)=C\frac{R^2}{\mathrm{RSm}},& \left(1\right)\end{array}$ wherein C is a coefficient predetermined with regard to a coating film formed by applying a coating paint on a substrate, and wherein the coefficient C is predetermined by a frictional resistant test using at least one of a double cylinder device, an in-pipe flow path, and a cavitation water tank.

7. The method according to claim 6, wherein the roughness height R and the mean length of roughness profile elements RSm are measured on a thermoplastic resin replica taken from an actual ship coating film.

8. A device for evaluating a performance of an actual ship coating film, the device comprising: a stylus type roughness measurement device or a laser displacement type roughness measurement device for measuring a roughness height R and a mean length of roughness profile elements RSm; and a frictional resistance calculating part for calculating a frictional resistance increase rate FIR (%) by the formula (1): $\begin{array}{cc}\mathrm{FIR}\left(\%\right)=C\frac{R^2}{\mathrm{RSm}}.& \left(1\right)\end{array}$

9. The method according to claim 1, wherein the coating film painted on a substrate is a coating film formed on a ship bottom.

10. The method according to claim 6, wherein the coating film is a coating film formed on a ship bottom.

11. The method according to claim 1, wherein the measuring comprises measuring a maximum height roughness Rz of the coating film.

12. The method according to claim 1, wherein the measuring comprises measuring a mean height of roughness profile elements Rc of the coating film.

13. The method according to claim 1, wherein the measuring comprises measuring an arithmetic mean roughness Ra of the coating film.

14. The method according to claim 1, wherein the measuring comprises measuring a root mean square roughness Rq of the coating film.

15. The method according to claim 1, wherein the measuring comprises measuring a ten-point mean roughness RZJIS of the coating film.

16. The method according to claim 1, wherein the measuring comprises measuring a mean length of roughness profile elements RSm of the coating film such that the area having a mean length of roughness profile elements RSm of 2,000 to 10,000 m is determined.

17. A method of estimating a frictional resistance of a coating film, the method comprising: measuring a roughness height R of a coating film painted on a substrate in an area having a mean length of roughness profile elements RSm of 2,000 to 10,000 m according to JIS B 0601:2001 (ISO4287:1997), wherein the roughness height R of the coating film is at least one selected from the group consisting of a maximum height roughness Rz, a mean height of roughness profile elements Rc, an arithmetic mean roughness Ra, a root mean square roughness Rq, and a ten-point mean roughness RZJIS, and wherein the roughness height R and the mean length of roughness profile elements RSm are measured by a stylus type roughness measurement device or a laser displacement type roughness measurement device; and calculating a frictional resistance increase rate FIR (%) of the coating film with respect to a mirror surface by formula (1); $\begin{array}{cc}\mathrm{FIR}\left(\%\right)=C\frac{R^2}{\mathrm{RSm}},& \left(1\right)\end{array}$ wherein coefficient C is a constant predetermined by measuring a roughness within a fixed length of a plurality of test coating films having different roughness to determine a roughness height R and a mean length of roughness profile elements RSm of each of the test coating films, conducting a frictional resistant test on each of the test coating films to obtain a frictional resistance increase rate FIR (%) with respect to a mirror surface for each of the test coating films, and calculating the coefficient C from the roughness height R, the mean length of roughness profile elements RSm, and the frictional resistance increase rate FIR of the test coating films by the formula (1), wherein the roughness height R of the test coating films measured to predetermine the coefficient C is at least one selected from the group consisting of a maximum height roughness Rz, a mean height of roughness profile elements Rc, an arithmetic mean roughness Ra, a root mean square roughness Rq, and a ten-point mean roughness RZJIS, of the test coating films, and wherein the coefficient C depends on the kind of the roughness height R and the frictional resistance test conducted to predetermine the coefficient C.

18. The method according to claim 17, wherein the measuring of the roughness height R is conducted in an evaluation length of 10,000 m or more, and a measurement pitch of 500 m or less according to JIS B 0601:2001 (ISO 4287:1997).

19. The method according to claim 18, wherein the measuring of the roughness height R is conducted by using a high pass filter such that the cut-off value c is 10,000 m or more.

20. The method according to claim 17, wherein the coating film painted on a substrate is a coating film formed on a ship bottom.

Description

BRIEF DESCRIPTION OF DRAWING

(1) FIG. 1 shows a relationship between a frictional resistance increase rate FIR (%) and Rz.sup.2/RSm.

(2) FIG. 2 shows a relationship between a frictional resistance increase rate FIR (%) and a maximum height roughness Rz.

(3) FIG. 3 shows a relationship between a frictional resistance increase rate and a mean length RSm of roughness profile elements.

(4) FIG. 4 shows a roughness distribution of a bottom film of an actual ship (a replica method/evaluation length 30 mm).

(5) FIG. 5 shows an example of roughness acquisition of a bottom film of an actual ship.

(6) FIG. 6 shows an estimation example (FIR (%)=2.62Rz.sup.2/RSm) of a frictional resistance increase rate FIR (%).

EMBODIMENT FOR CARRYING OUT THE INVENTION

(7) The present invention will be described in detail below.

(8) The coating paint for a ship bottom which paint is evaluated in the present invention is a coating paint used for corrosion prevention, prevention of organism adhesion and the like in a ship bottom. The coating paint is mainly a coating paint for a ship bottom of a steel ship.

(9) The present invention may apply to these antifouling coating paints such as a self-polishing type antifouling coating paint and a fouling release type antifouling coating paint.

(10) Regarding to the self-polishing type antifouling coating paint, the coating film is dissolved little by little gradually and simultaneously an antifouling agent which is a component having a distaste for aquatic life is also eluted to prevent adhesion of aquatic organism from the film. Regarding to the fouling release type antifouling coating paint, a coating film having smoothness, water repellency and elasticity makes adhesion of aquatic organisms harder.

(11) Examples of the antifouling coating paints are coating paints disclosed in JP-B-4884107, JP-B-4846093, JP-B-4837668, JP-B-4813608, JP-B-4812947, JP-B-4812902, JP-B-4812895, JP-B-4806769, JP-B-4786053, JP-B-4777591, JP-B-4776839, JP-B-4769331, JP-B-4745351, JP-B-4709370, JP-B-4694583, JP-B-4684465, JP-B-4675624, JP-B-4651792, JP-B-4647060, JP-B-4644238, JP-B-4642204, JP-B-4641563, JP-B-4633224, JP-B-4621901 and JP-B-4610763. These known coating paints can be used without limitation.

(12) In the present invention, the evaluation is carried out on a coating film formed by applying the coating paint for a ship bottom on a substrate.

(13) The substrate is not particularly limited. Usual examples of the substrate are steels such as untreated steels, blast-treated steels, acid-treated steels, zinc-plated steels, and stainless steels; nonferrous metal materials such as aluminum (alloy) materials and copper (alloy) materials; concretes; and plastic materials such as vinyl chloride and the like. The shape of the substrate is not also particularly limited. Usually, a cylinder shape, a boat-like shape, a flat plate-like shape and a tube-like shape are used for evaluation.

(14) The coating film for a ship bottom is formed by applying an antifouling coating paint on the surface of a substrate in accordance with a usual method and then, if necessary, vaporizing and removing a solvent at an ordinary temperature or under heating. The coating method is not particularly limited. Examples of the method are conventionally known methods such as an immersing method, a spray method, a brush application, a roller application, an electrostatic application and an electrodeposition application. The spray method is more preferably used to coat a wide ship bottom uniformly.

(15) The film thickness is not particularly limited. The film may have a prescribed thickness. The film has a usual thickness of from 50 micron meter to 1,000 micron meter, such that the substrate is not shown and the roughness of the substrate surface is not affected.

(16) Frictional Resistance Estimating Method

(17) Regarding a coating film formed by applying a coating paint for ship bottom on a substrate, any of Rz (maximum height roughness), Rc (mean height of the roughness profile elements), Ra (arithmetical mean roughness), Rq (root mean square roughness) and RZJIS (ten-point mean roughness) in a mean length RSm of roughness profile elements in the range of 2,000 to 10,000 m is measured in accordance with the rule defined in JIS B 0601:2001 (ISO4287: 1997) and the frictional resistance increase rate FIR (%) from a mirror surface is calculated by the following formula (4).

(18) $\begin{array}{cc}\mathrm{FIR}\left(\%\right)=C\frac{R^2}{\mathrm{RSm}}& \left(4\right)\end{array}$

(19) In the formula, constant C depends on the kind of the roughness height R and a frictional resistance testing method and is previously determined in such a manner that a roughness measurement and a frictional resistance test in a definite evaluation length are carried out, and then the constant C is determined by the formula (4) using the roughness height R, the mean length RSm of roughness profile elements and the frictional resistance increase rate FIR (%), which have been measured.

(20) RSm is a mean length of roughness profile elements and is represented by the following formula (6) as the mean of each length XS of roughness profile element.

(21) $\begin{array}{cc}\mathrm{RSm}=\frac{1}{m}\underset{i=1}{\overset{n}{.Math.}}\mathrm{Xsi}& \left(6\right)\end{array}$

(22) Rz represents a maximum height roughness and is defined as the sum of the maximum profile peak height and the maximum profile valley depth in a standard length of a roughness profile. Rc represents a mean height of the roughness profile elements, Ra represents an arithmetical mean roughness and Rq represents a root mean square roughness. RZJIS represents a ten-point mean roughness and is defined as the sum of the mean heights of the five highest profile peaks and the mean depths of the five deepest profile valleys. These values are measured in accordance with the rule of JIS B 0601:2001 (ISO 4287:1997)

(23) In evaluating the roughness in the present invention, it is only necessary to measure any one of the Rz (maximum height roughness), Rc (mean height of roughness profile elements), Ra (arithmetical mean roughness), Rq (root mean square roughness) and RZJIS (ten-point mean roughness).

(24) These roughness measurements are conducted by using a contact type, a non-contact type, a manual type or an automatic type surface roughness measuring device. Furthermore, a stylus type or a laser displacement type surface roughness measuring device is preferably used in the standpoint of versatility and easy-to-use.

(25) The resulting data may be saved or analog/digital-treated in the inside of a displacement instrument. For the measurement of the objective roughness, the evaluation length is not less than 10,000 m, and the measurement pitch is not more than 500 m in the present invention.

(26) In the parameter analysis, it is desired to use the primary profile as it is. When a waviness having a wavelength of not less than 10,000 m has an affect on the measurement, the roughness profile can be determined by including a high pass filter having a cut-off value (wavelength) c of not less than 10,000 m in accordance with JIS B 0601: 2001 (ISO 4287: 1997).

(27) In the present invention, the necessary evaluation length and cut-off value c for the accurate roughness evaluation are not less than 10,000 m and the measurement pitch is not more than 500 m. Furthermore, when the measurement pitch is 500 m, the measurable minimum wavelength is 2,000 m but the measurement error of the low wavelength roughness is large. Therefore, the practical measurement pitch is about 250 m. When the measurement pitch is smaller, the measurement takes a longer period of time and influences on the wavelength of the low roughness height which is not related to the frictional resistance increase. Therefore, the measurement distance is preferably not less than 100 m in the practical use. Moreover, when the measurement distance is small, or further the apparent wavelength is small by the small roughness and the noise which do not contribute to the frictional resistance, cut by a low pass filter may be conducted.

(28) Determination of Coefficient C

(29) The gradient C in the formula (4) varies depending to the kind of the roughness height R and the frictional resistance test method. Previously, plural ship bottom coating films each having different roughness are formed on prescribed substrates and then evaluated on frictional resistance thereof by the frictional resistance test to determine the coefficient C in the formula (4). For example, when Rz and RSm are measured in an evaluation length of 50 mm and the frictional resistance test is carried out using a double cylinder device, the coefficient C is about 2 to 3. The frictional resistance test is necessary to be conducted by a method of showing a frictional resistance increase rate of not less than 5% on a coating film having a roughness height R of 100 m and RSm of 2,000 to 4,000 m, which are determined by the above roughness measuring method.

(30) Because this is a frictional resistance increase rate under the condition of a high Reynolds number and a thin viscous sublayer thickness, which correspond to an actual ship, and the tank towing test and the flowing round tank test, which are generally used to ship evaluation, are not appropriate because the velocity is low and the length of a test plate is short and thereby the roughness is in hiding under a viscous sublayer, and as a result, the influence of the roughness is not exerted sufficiently.

(31) In order to realize the viscous sublayer thickness which corresponds to an actual ship, it is preferred to employ a method such that the distance between a main flow and the surface of a wall is short and the flow rate is as rapid as possible. The test capable of yielding these results are conducted by a double cylinder device, an in-pipe flow path or a cavitation water tank.

(32) In the case that the double cylinder device is used, a torque T.sub.0, which acts on an internal cylinder with a mirror surface when an external cylinder is rotated at a prescribed rotation number, is determined, then, a torque T, which acts on the internal cylinder coated with a ship bottom coating paint when the rotation is carried out in the same conditions, is determined, and the frictional resistance increase rate FIR (%) is measured by the following formula (5).

(33) $\begin{array}{cc}\mathrm{FIR}\left(\%\right)=\frac{T-T_0}{T_0}100& \left(5\right)\end{array}$

(34) Next, from the formula (4) showing the relationship of the FIR (%) measured, and R and RSm of the coating film formed on the internal cylinder, the coefficient C is determined.

(35) When the coefficient C is used to the formula (4) and R and RSm are measured, the frictional resistance increase rate of a coating film can be estimated regardless of the kind of the ship bottom coating paint.

(36) As described above, the coefficient C previously determined is used, the roughness height R and the mean length RSm of roughness profile elements are measured with respect to a coating film formed by applying the ship bottom coating paint on a substrate, and then the frictional resistance increase rate FIR (%) is estimated by the formula (4). Thus, the coating film performance of the ship bottom coating film can be evaluated.

(37) When in the ship coating job site of a dockyard, the surface roughness of a ship bottom coating film is measured in the following manner that a thermoplastic resin is pressed against a frame pattern to prepare a replica and the surface roughness is measured, the frictional resistance increase rate of the coating film of an actual ship can be estimated.

(38) Specifically, in order to obtain the sufficient accuracy, the surface roughness of the coating film formed on the internal cylinder was measured by a laser displacement instrument on 10 lines, in which one line is spaced apart from another line at intervals of 25 mm, the measurement of the surface roughness on each line being begun at the lower part of the internal cylinder and continued to the upper part of the internal cylinder, except the part measuring 50 mm from the bottom part of the internal cylinder. The laser displacement instrument is installed on the test device and the cylinder is rotated and then the surface roughness is measured. The displacement data are obtained at intervals of 250 m, and thereby 4,000 data are obtained in the distance of 1,000 mm. The measured data in one line are divided by 20 with an evaluation length of 50 mm and then an approximate profile with root mean square is subtracted from the above value to determine the primary profile.

(39) The device of evaluating coating film performance of a ship bottom coating film according to the present invention, which is conducted by the above estimating method, comprises a measurement part for measuring the roughness height R and the mean length RSm of roughness profile elements, and a frictional resistance calculating part for calculating the frictional resistance increase rate FIR (%) using the formula (4).

(40) The above described roughness measuring device is provided in the measuring part. In an estimating part, the resultant data are monitored and the frictional resistance increase rate can be estimated from the formula (4).

(41) In the ship coating job site of a dockyard, the frictional resistance increase rate of a ship bottom coating film can be easily estimated by the use of this coating film performance evaluation device, and the coating film performance can be evaluated.

(42) Moreover, as the wavelength range of the roughness is limited, the evaluation length, the measurement pitch and the cutoff value c, which are the roughness measurement conditions, can be fixed. Therefore, the coating film capacity evaluation device can be provided at a low cost.

EXAMPLE

(43) The present invention will be described in more detail with reference to the following examples below, and it should not be limited by the examples.

Example 1

Frictional Resistance Test

(44) (i) the Case of Using a Double Cylinder Device

(45) The double cylinder device was used and the relationship of the roughness height R, the mean length RSm of roughness profile elements and the frictional resistance increase rate is evaluated.

(46) In the double cylinder device, a polyvinyl chloride made test cylinder (internal cylinder 310 mm diameter) on which a coating paint was applied by spray coating was set in a stainless steel tank (external cylinder 320 mm diameter) filled with an ion exchanged water (23 C.).

(47) Regarding to the coating paints, BANNOH 500N (manufactured by Chugoku Marine Paints Ltd.) was used as a binder coat, and SEA GRANDPRIX 500, SEA GRANDPRIX 1000, SEAFLO NEO or BIOCLEAN HB (all is manufactured by Chugoku Marine Paints Ltd.) was used as an antifouling coating paint. The total thicknesses of the coating films were 125 m or 250 m.

(48) The external cylinder was rotated at 1000 rpm and a torque which acted on the internal cylinder on which the coating film was formed was measured. Subsequently, the frictional resistance increase rate FIR (%) was calculated, provided that a torque, which acted on a complete mirror surface when the external cylinder was rotated at 1000 rpm, was 6.55 N.Math.m and 6.63 N.Math.m when the film thickness was 125 m and 250 m, respectively.

(49) The frictional resistance increase rate FIR (%) of the internal cylinder on which each coating film was formed was calculated by the formula (5). In the formula (5), T.sub.0 is a torque which acted on the internal cylinder with a mirror surface when the external cylinder was rotated at 1000 rpm, and T.sub.0 was 6.55 N.Math.m and 6.63 N.Math.m when the film thickness were 125 m and 250 m, respectively. T is a torque which acted on the internal cylinder coated with the ship bottom coating paint when the rotation was carried out in the same conditions.

(50) The roughness measurement was carried out on the internal cylinder on which each coating film was formed.

(51) In order to obtain sufficiently high accuracy, the surface roughness of the internal cylinder on which the coating film was formed was measured by a laser displacement instrument on 10 lines, in which one line is spaced apart from another line at intervals of 25 mm, the measurement of the surface roughness on each line being begun at the upper part of a specimen and continued to the lower part of the specimen, except the part measuring 50 mm from. The laser displacement instrument was installed on the double cylinder device and the internal cylinder on which the coating film was formed was rotated to measure the surface roughness. The displacement data were obtained at intervals of 250 m and 4,000 data were obtained in the distance of 1,000 mm. The measured data on one line was divided by 20 in an evaluation length of 50 mm and then an approximate profile with the root mean square was subtracted to determine the primary profile.

(52) With regard to the coating film formed by a spray coating, Rz (maximum height roughness) and RSm (mean length of roughness profile elements) were calculated and as a result, in the evaluation length of 50 mm, Rz was 30 m to 200 m and RSm was 2,000 m to 10,000 m. In order to evaluate the RSm range accurately, the necessary evaluation length and cut-off value c are 10,000 m or more and the measurement pitch is 500 m or less. When the measurement distance is 500 m, the measurable minimum wavelength is 2,000 m, but an error of the measurement of Rz and RSm in a low wavelength will be large. Therefore, it is practically about 250 m. Furthermore, when the measurement distance is small, the measurement time is longer. Therefore, it is practically and appropriately 100 m or more. Moreover, when the measurement pitch is smaller, it is occasionally preferred to conduct cutting by a low pass filter because an apparent wavelength will become small by the influences of a small roughness which does not contribute the frictional resistance and a noise. In the practical evaluation, it is preferred to determine a roughness profile by introducing a low pass filter in a cut-off wavelength s in order to remove the influence of a waviness of a long wavelength. However, in the precisely processed circular cylinder, the primary profile was evaluated as it was because the affect of a waviness of a long wavelength was not observed.

(53) From the primary profile, Rz (maximum height roughness), Rc (mean height of roughness profile elements), Ra (arithmetic mean roughness), Rq (root mean square roughness), RZJIS (ten-point mean roughness) and RSm were calculated.

(54) In the case of the measurement using the double cylinder device, Rz, Rc, Ra, Rq, RZJIS and RSm, and the frictional resistance increase rate FIR (%) were shown in Table 1. The mutual correlation analysis on Rz, Rc, Ra, Rq, RZJIS and RSm was carried out and the results are shown in Table 2. As Rz, Rc, Ra, Rq and RZJIS show a high correlation mutually, the evaluation may be carried out using any one of the roughness heights R. In the case that the relationship of RSm, Rz and FIR (%) is evaluated, when the value Rz.sup.2/RSm obtained by dividing Rz.sup.2 by RSm is taken as a transverse axis and FIR (%) is taken as a vertical axis, a high correlation is confirmed along an approximation straight line as shown in FIG. 1. However, when Rz or RSm is taken as a transverse axis and FIR (%) is taken as a vertical axis, large variation is observed as shown in FIG. 2 and FIG. 3. Therefore, it is preferred to estimate FIR (%) by Rz.sup.2/RSm. In this example, the approximation line is a graph passing through the point 0 and having a gradient of 2.62. Accordingly, FIR (%) can be determined from Rz and RSm by calculating backwards from this numeral formula. As is shown in FIG. 2, Rc, Ra, Rq and RZJIS have a high correlation with Rz and thereby using any of them, the evaluation can be conducted in the same manner. But, the coefficient C has a different value in accordance with the kind of the roughness height R.

(55) TABLE-US-00001 TABLE 1 Roughness height R, RSm, Rz.sup.2/RSm and frictional resistance increase rate FIR(%) (length for evaluation 50 mm) Mean height Mean length Frictional Maximum of roughness Arithmetic Root mean Ten-point of roughness resistance height profile mean square mean profile increase roughness elements roughness roughness roughness elements Rz.sup.2/ rate Rz Rc Ra Rq Rzjis RSm RSm FIR (m) (m) (m) (m) (m) (m) (m) (%) 51.8 22.5 8.5 10.7 33.5 5914 0.45 0.80 18.4 7.1 3.2 3.9 11.1 5917 0.06 1.16 54.3 27.4 9.7 12.1 32.3 8506 0.35 1.21 55.0 27.6 9.9 12.3 33.6 8321 0.36 1.44 58.1 26.4 9.6 12.1 36.3 6694 0.50 1.46 66.2 25.7 9.8 12.7 43.6 4400 1.00 1.57 21.0 8.0 3.4 4.2 13.9 4225 0.10 3.79 99.5 42.9 15.5 19.5 71.3 3927 2.52 5.99 61.3 24.2 9.0 11.4 45.2 3173 1.18 6.30 86.2 35.5 13.0 16.6 59.9 4133 1.80 7.00 84.4 35.9 13.2 16.5 61.1 3838 1.86 7.09 98.7 42.4 15.4 19.4 71.0 4007 2.43 7.87 85.1 36.5 13.4 16.7 62.3 3927 1.84 7.93 103.0 43.0 15.8 19.8 76.9 3244 3.27 8.54 130.9 53.7 19.5 24.8 97 3167 5.41 11.18 161.3 63.4 22.8 29.6 116.1 3096 8.40 21.64

(56) TABLE-US-00002 TABLE 2 Mutual correlation of roughness height R and RSm (length for evaluation 50 mm) Rz Rc Ra Rq Rzjis RSm (m) (m) (m) (m) (m) (m) Rz (m) 1.00 Rc (m) 0.99 1.00 Ra (m) 0.99 1.00 1.00 Rq (m) 1.00 1.00 1.00 1.00 Rzjis(m) 1.00 0.98 0.99 0.99 1.00 RSm (m) 0.57 0.47 0.50 0.50 0.63 1.00

Example 2

Roughness Measurement of a Coating Film of an Actual Ship

(57) With regard to actual ship bottoms (4 ships), Rz, Rc, Ra, Rq, RZJIS and RSm were measured and the results are shown in Table 3. On the ship bottoms of the 4 ships, antifouling paints (a) SEAFLONEO, (b) SEA GRANDPRIX 500HS, (c) SEA GRANDPRIX 500 and (d) SEA GRANDPRIX 1000 (any of the antifouling paints was manufactured by Chugoku Marine Paints, Ltd.) were applied respectively. A replica of roughness of each coating film was taken by a thermoplastic resin and carried back to the laboratory and surface roughness was measured by the laser displacement instrument. The evaluation range was 30 mm30 mm, the measurement distance was 250 m and the evaluation length was 30,000 m. Through this measurement, the roughness profiles as shown in FIG. 4 were able to be measured. Rz, Rc, Ra, Rq, RZJIS and RSm were equal to those in Example 1. From this fact, the measurement in the range of RSm equal to that in Example 1 can be carried out on the coating film of the bottom of an actual ship.

(58) TABLE-US-00003 TABLE 3 Surface roughness analysis example in an actual ship shell plating (Replica method/evaluation length 30 mm) Rz: Rc: Ra: Rq: Rzjis: RSm: 1)-1 43.6 21.0 7.8 9.6 24.3 4798 1)-2 60.1 23.7 10.2 12.7 30.9 4811 1)-3 53.7 28.1 9.6 11.9 26.6 4809 1)-4 52.3 14.1 8.5 10.7 26.1 4198 1)-5 71.1 25.3 12.8 15.8 39.9 4289 1)-6 55.4 11.3 9.0 11.3 25.4 5118 1)-7 57.0 15.7 10.0 12.3 28.0 4870 1)-8 78.2 23.7 11.0 14.6 35.5 5279 1)-9 53.8 22.2 10.1 12.2 27.8 6014 1)-10 52.1 18.7 9.6 11.6 29.1 4211 1)-11 72.9 17.5 12.7 16.0 31.6 6040 1)-12 67.3 13.2 11.9 14.9 29.5 4479 1)-13 73.2 25.2 12.3 15.3 38.6 4466 1)-14 65.6 18.9 11.4 14.2 30.0 4947 1)-15 54.5 31.2 9.8 12.0 28.9 5309 Mean 60.7 20.7 10.4 13.0 30.2 4909 Rz: Rc: Ra: Rq: Rzjis: Sm: 2)-1 120.0 50.0 21.8 27.0 47.7 4727 2)-2 109.3 35.8 17.4 21.9 68.1 3228 2)-3 76.8 22.8 13.0 16.1 45.0 3414 2)-4 65.2 12.6 11.9 14.6 39.8 3762 2)-5 72.5 21.3 13.0 16.0 46.9 4094 2)-6 64.6 33.2 11.5 14.2 38.5 4098 2)-7 79.3 37.1 14.0 17.3 47.7 3832 2)-8 55.3 19.3 9.1 11.2 34.4 3407 2)-9 64.6 33.2 11.5 14.2 38.5 4098 2)-10 101.3 35.7 16.0 20.2 68.9 2823 2)-11 68.6 17.4 11.0 13.9 38.0 3087 2)-12 64.1 34.1 10.2 12.8 41.4 2784 2)-13 94.9 29.5 16.0 19.9 58.2 3263 2)-14 101.3 35.7 16.0 20.2 68.9 2823 2)-15 63.6 30.3 10.1 12.7 42.5 2775 Mean 80.1 29.9 13.5 16.8 48.3 3481 3)-1 74.9 20.4 13.0 16.2 32.7 4318 3)-2 73.4 29.4 12.2 15.2 38.0 3854 3)-3 95.2 44.8 16.2 20.3 57.9 3579 3)-4 107.4 29.2 19.3 23.8 65.2 3488 3)-5 109.4 60.6 20.5 25.2 46.6 4082 3)-6 75.8 57.7 12.5 15.7 46.0 3476 3)-7 80.9 23.5 11.8 15.1 44.0 3636 3)-8 109.1 44.7 18.8 23.2 52.2 4764 3)-9 103.7 37.0 16.7 21.1 61.7 3330 3)-10 68.8 32.8 11.5 14.4 42.3 3537 3)-11 59.3 15.3 10.0 12.3 32.2 3336 3)-12 89.1 84.8 15.6 19.1 50.1 3144 Mean 89.9 38.0 15.2 19.0 48.7 3806 4)-1 82.7 44.6 14.1 17.5 54.6 3733 4)-2 99.8 45.1 18.0 22.3 57.3 5134 4)-3 55.5 26.3 9.7 12.0 34.1 3613 4)-4 60.6 35.1 10.7 13.3 34.6 4643 4)-5 76.9 65.7 14.9 18.2 33.8 7592 4)-6 107.4 32.4 16.4 21.2 48.4 4231 4)-7 82.8 47.5 14.1 17.4 55.9 2597 4)-8 75.8 15.6 14.1 17.2 42.0 3337 4)-9 75.4 47.0 13.9 16.9 45.9 4876 Mean 79.7 39.9 14.0 17.3 45.2 4417 1) . . . (a) SEAFLO NEO 2) . . . (b) SEA GRANDPRIX 500HS 3) . . . (c) SEA GRANDPRIX 500 4) . . . (d) SEA GRANDPRIX 1000

(59) In FIG. 5, the values Rz and RSm are shown by three-dimensional column graph. From the result, it was found that the roughness of the shell plating can be evaluated by the method of the present invention. Furthermore, from the mean values Rz and RSm of each ship, the estimation value of FIR (%) was calculated using the coefficient C of 2.62.

Example 3

A Method of Estimating the Frictional Resistance Increase Rate

(60) The estimation example of the frictional resistance increase rate obtained in Example 1 are shown in Table 6. When FIR (%) was calculated using the coefficient C of 2.62, it is confirmed there is a tendency such that as Rz is larger and RSm is smaller, FIR (%) is larger. From these figures, it can be easily estimated to the roughness range in which FIR (%) increases remarkably. Furthermore, Rz and RSm are introduced into the estimation formula directly and thereby the difference of FIR (%) can be compared.