S Villette
email: s.villette@agrosupdijon.fr

; E Piron

; R Martin

; D Courreau

; D Miclet

; C Gée

Impact recording system to characterise centrifugal spreading

Keywords: Centrifugal spreading, fertiliser, two-dimensional mass flow distribution, impact recording

This paper presents a new method to measure simultaneously the horizontal and vertical distribution of the mass flow in the vicinity of the spinning disc of fertiliser centrifugal spreaders. The method consists in recording granule impacts on a cylindrical vertical screen placed around the disc. Algorithms have been developed to process the impact recording band taking into account its location with respect to the spreading device. The distribution of the mass flow has been studied for three fertilisers. Our findings show that the horizontal and vertical distributions of the mass flow are similar for ammonium nitrate and NPK, while they are different for KCl. For each fertiliser, the horizontal distributions deduced from impact records are in accordance with results deduced from a traditional compartmented ring. This new method is useful to study the vertical distribution of fertiliser granules and paves the way to design simple test and diagnostic tools.

Introduction

Several methods have been proposed to measure the fertiliser distribution obtained with centrifugal spreaders. The most traditional method consists in measuring the transverse distribution by using collection trays lined perpendicularly to the travel axis of the tractor. This requires large test halls and high amounts of fertiliser for each test. In field, transverse distributions can also be measured to evaluate the distribution uniformity and adjust spreader settings, but these measurements are tedious and rarely carried out by operators in practice. Concerning the understanding of the centrifugal spreading process, the transverse distribution curve results from the combination of all spreading parameters and it does not facilitate the study of the influence of each parameter such as: outlet velocity, outlet angle, horizontal and vertical mass flow distributions, fertiliser granule ballistic properties... Considering the mass flow distribution around the disc as one of the results of the fertiliser acceleration, several authors suggested the use of a compartmented ring placed around the disc to study centrifugal spreading [START_REF] Colin | Etude du procédé d'épandage centrifuge d'engrais minéraux[END_REF][START_REF] Olieslagers | Fertilizer distribution modelling for centrifugal spreader design[END_REF]Reumers et al., 2003a)), assess mechanical models [START_REF] Van Liedekerke | DEM simulations of the particle flow on a centrifugal fertilizer spreader[END_REF], or characterise fertilisers [START_REF] Miller | The Measurement and Classification of the flow and spreading characteristics of individual Fertilizers[END_REF][START_REF] Dutzi | Measurement of physical characteristics of fertilisers and their influence on handling and application[END_REF][START_REF] Miller | Procedures for classifying the physical qualities of fertilisers[END_REF]. The measurement of the mass flow distribution around the disc also provides a useful input parameter for ballistic flight models that can be used to predict the distribution pattern deposition on the ground. Thus, some authors [START_REF] Miller | The Measurement and Classification of the flow and spreading characteristics of individual Fertilizers[END_REF][START_REF] Reumers | Experimental characterisation of the cylindrical distribution pattern of centrifugal fertiliser spreaders : towards an alternative for spreading hall measurements[END_REF] suggested using this piece of information to develop an alternate method to traditional measurements of deposition pattern on the ground. Although numerous authors have carried out the measurement of the horizontal distribution of the mass flow, few authors addressed the problem of measuring the vertical distribution. [START_REF] Mennel | The theory of the centrifugal distributor. III : Particle trajectories[END_REF] measured the amount of particle leaving a spinning disc and passing through an opening windows. Using a compartmented ring [START_REF] Olieslagers | Fertilizer distribution modelling for centrifugal spreader design[END_REF] measured the percentage of the particle flow passing through the square entrances of compartments. Reumers et al. (2003a) equipped a compartmented ring with a vertically adjustable screen and deduced the horizontal and vertical distribution of the mass flow from a set of successive tests. Some negative values obtained by the authors in the distribution measurements reflected the difficulties to carry out an accurate method using successive vertical screen positions in front of collection compartments. The aim of this work is to propose a new approach to simultaneously measure the horizontal and vertical distribution of the mass flow in the vicinity of the disc by recording granule impacts on a cylindrical screen placed around the disc.

Materials and methods

Recording fertiliser impacts

In this study, the measurement method of the mass flow has been developed using an experimental spreading device built to study centrifugal spreading process and assess characterisation methods. The mechanical part of the system is made up of elements similar to those found in a traditional centrifugal spreader. For this study, a flat disc was equipped with two radial vanes. The vanes were 325 mm length and had a U-profile whose inner height was 28 mm. The spinning disc was driven by an electric motor whose rotational speed is set by a programmable power supply.

The experimental arrangement used to record fertiliser impacts around the spinning disc (Fig. 1) consists of a vertical and cylindrical sheet of iron placed on an adjustable stand. This cylindrical screen was centred on the spinning disc axle at 600 mm from the disc centre. The screen was covered with a paper band, a carbon film and a protective coat so that fertiliser granule shocks against the screen produce impact marks on the recording paper band. The horizontal and vertical location of the paper band was measured with respect to the disc so that the height of the impacts was known relative to the disc plane and the angular location around the disc was known relative to the mechanical frame of the spreading device. In particular, a horizontal line was drawn on the paper band before each use as a reference line. The vertical height of this line was measured with respect to the disc plane and the intersection of the reference axis of the mechanical frame was reported on this line to create the abscissa reference of the band. This line will be used in further data processing. The exposition time of the recording paper to granule shocks was controlled by the total fertiliser amount placed in the hopper before shutter opening. When the shutter was opened, the size of the orifice at the bottom of the hopper was the same for all tests.

Processing impact records

First, vertical segments were drawn along the reference line crossing the line each 250 mm. The locations of these segments are known with respect to the reference axis of the mechanical frame of the spreading device. Second, the impacted paper band was digitalised section-by-section using a traditional desk scanner so that each section image showed two vertical segments along the reference line. Third, an automatic image processing was used to build a digital image of the whole band. The main steps of the algorithm are as follows:

(1) Using the Hough Transform [START_REF] Hough | Methods and means for recognizing complex patterns[END_REF][START_REF] Duda | Use of Hough transformation to detect lines and curves in pictures[END_REF] the reference line is automatically identified in each individual image and its inclination is measured relative to the pixel lines of the image. The image is then rotated so that the reference line becomes (after rotation) parallel to the pixel lines of the digital image. Note that this image-processing step perfectly locates the reference line in the image.

(2) The vertical segments crossing the reference line are automatically detected along the reference line. Their location is used to truncate the right and left sides of each section and to compute the pixel-millimetre conversion factor. The location of the segments along the reference line also ensures the horizontal angular positioning of the recorded data around the spinning disc.

(3) The digital image of the whole recording band is automatically built by assembling each section so that the vertical location of the reference line in the global digital image of the whole band is the same for all sections. In order to make possible comparisons between measurement systems, the angular mass flow distribution has to be computed at the outer extremity of the vane. Assuming that granules follow straight trajectories during their short ballistic flight, the angular distribution at the extremity of the vane is deduced from the measured angular distribution, the inner radius of the measurement device and the horizontal outlet angle of granules. The horizontal outlet angle out θ is the horizontal angle between the fertiliser granule trajectory and the tangent to the disc. This angle is measured using a digital camera placed vertically above the granule output flow. A specific image processing was used to deduce the outlet angle from motionblurred images on which granule trajectories are identified. The imaging technique is detailed in [START_REF] Villette | Centrifugal spreading of fertiliser: Deducing three-dimensional velocities from horizontal outlet angles using computer vision[END_REF].

Measurements with a traditional compartmented ring

In order to assess the impact recording method concerning the horizontal angular distribution, some mass flow distribution measurements have been carried out using a cylindrical compartmented ring (Fig. 2). The ring consisted of 22 compartments of 10° eac h and its inner radius was 400 mm. The horizontal angular mass flow distribution was deduced from weighing the fertiliser amount collected by each compartment.

Results

Three different types of mineral fertilisers have been used in this study: ammonium nitrate, a compound fertiliser NPK 17-17-17 and potassium chloride KCl. These three common fertilisers are chosen to be compared because of their differences in granule shape, rounded in the case of ammonium nitrate and NPK but angular in the case of KCl.

Two-dimensional representation of the mass flow distribution

Setting the radius of the cylindrical screen at 600 mm, three impact bands have been recorded for each fertiliser: ammonium nitrate, NPK and KCl. For each fertiliser, Fig. 3 shows an example of digitalized impact band represented in the same reference frame and millimetre-graduated scales. The vertical scale is exaggerated with respect to the horizontal scale to improve readability. Note that the abscissa axis is graduated from the left to the right, while the rotation direction of the vane is from the right to the left with the experimental spreading device. Thus, the beginning of the ejection is at the right side of the paper band and the end is at the left side.

Fig. 3. Examples of binary digital images of the impact bands obtained after assembling each band section in the same reference frame for the three fertilisers. Vertical scale is exaggerated to improve readability.

While the impact bands seem similar for ammonium nitrate and NPK, a simple visual observation reveals that the impact distribution of KCl is horizontally shifted towards negative values. Regarding the experimental set-up, this means that the horizontal KCl distribution is shifted in the direction of the disc rotation. Granule impacts are more dispersed at the beginning and the end of the spreading sector. This corresponds to granules whose freedom of vertical motion is higher on the vane. Moreover it seems that vertical dispersion of the impacts is more important in the case of ammonium nitrate or NPK than in the case of KCl. The shape of the granules could also explain this. The rolling motion of rounded granules probably provides more diversity in the granule trajectories on the vane. Note that most of the "pop-corn granules" are not recorded on impact band because of their lower velocity and thus their lower kinetic energy. These granules bounce off the vane or the disc and are not accelerated in the vane before ejection.

Assuming that the surface of impact marks in one area of the paper band is proportional to the fertiliser granule mass intercepted by this area on the screen, the percentage of the fertiliser mass intercepted in an area can be computed relative to the total fertiliser amount intercepted by the screen. In practice, the surface of impact marks lying on a specified area is simply obtained as the number of marked pixels in this area. For instance, sampling the screen into blocks of 5 mm height and 25 mm wide, Fig. 4 presents the two-dimensional distribution of the mass flow for each fertiliser. The grey level of each sampled block corresponds to the percentage of the impact density relative to its maximum value. For each block, this can be transformed into the intercepted amount fraction relative to the total intercepted amount on the whole screen. The most impacted block (5 × 25 mm) corresponds to 1.27%, 1.17% and 1.33 % of the total intercepted amount for ammonium nitrate, NPK and KCl respectively.

Measurements of the horizontal distribution

In order to characterize more accurately the horizontal distribution of the three fertilisers, the binary digital image of the impact bands have been processed by summing vertically the number of marked pixels along an horizontal axis with a sampling interval of one millimetre.

Then taking into account the radius of the impact screen and the value of the outlet angle of fertiliser granules, the horizontal mass flow distribution has been computed with respect to the angular location of the vane. The mean value of the outlet angles deduced from blurredmotion images were: 40.1° for ammonium nitrate, 39. 5° for NPK and 34.8° for KCl.

For the three studied fertilisers, distributions deduced from impact recording bands have been compared to distributions measured with the compartmented collection ring. Figure 5 shows the distribution histograms obtained by both methods for the three fertilisers.

The impact distributions presented in Fig. 5 result from the three impact bands for each fertiliser type. To make possible the comparison, impact distribution data have been classified into the 22 angular sectors delimited by the ring compartments and transformed into angular vane location sectors. Table 1 presents the characteristic parameters of the distribution computed from each recording band (three bands for each fertiliser) and the mean values deduced for each fertiliser. It also presents the characteristic parameters of the distributions measured using the collection ring. The histograms and the distribution characteristics deduced from the impact recording method are in good accordance with those deduced from collection ring measurements. In particular, both methods demonstrate that the horizontal angular distribution is similar for ammonium nitrate and NPK while the distribution is shifted in the direction of the spinning disc for KCl. This confirms the previous qualitative visual appreciation regarding the impact 2D-distribution on the paper band. For instance, note that the difference observed in the angular mean value of the distribution at the extremity of the vane between ammonium nitrate and KCl corresponds to a difference of 160 mm on the cylindrical screen (radius: 600 mm).

Tab. 1. Characteristic values of the horizontal angular distributions deduced from the impact recording method and from the compartmented ring method: µ θ , mean value; σ θ , standard 1), variability appears in the mean values and standard deviations computed from the successive impact recording bands. This could result from fertiliser variability. Moreover, since each impact band measurement only corresponds to a small amount of material (530 g in the present tests), this could increase the sensibility of the method to fertiliser and spreading variability.

Measurements of the vertical distribution

To characterise the vertical distribution of the mass flow, the binary digital images of the impact bands have been processed by summing horizontally the number of marked pixels along a vertical axis with a sampling interval of one millimetre. Table 2 provides height values measured in millimetres on the screen with respect to the disc plane altitude. Height mean values are at least the height of the vane, which is 28 mm. This needs some comments.

Although a flat disc is used, the fertiliser particles do not follow horizontal trajectories in the vane. During their motion along the vane, fertiliser particles move to the upper fold of the vane so that their outlet heights are displaced toward the top of the vane and their trajectories are tilted up. This phenomena probably depends on the mass flow rate but is observed in this study for low rate.

Regarding Table 2, the outlet height of ammonium nitrate or NPK appears higher than the one of KCl. This is due to the rolling motion of the rounded particles (i.e. ammonium nitrate and NPK) on the vane, which yields more vertical motion and variations in the orientation of the trajectories at the extremity of the vane. The standard deviation values (Tab. 2) also demonstrated that the vertical dispersion of ammonium nitrate and NPK is higher than the one of KCl. In order to estimate the angular standard deviation of the flow vertical distribution, it is necessary to consider the height distribution of the particles on the screen and the length of the ballistic flight between the vane and the impact screen that are respectively 337 mm, 338 mm and 352 mm for ammonium nitrate, NPK and KCl.

Considering that the fertiliser flow leave the vane from only one point at the extremity of the vane, the angular standard deviations σ θv of the vertical flow distribution are respectively 1.35°, 1.39° and 1.10°. This means that more than 9 9% of the mass flow leaves the vane with an upward or downward vertical angle of 4.05°, 4.18° and 3.30° for ammonium nitrate, NPK and KCl respectively. Few studies addressed the measurement of the vertical distribution of the fertiliser mass flow around a spinning disc. For vanes with U-profile, [START_REF] Mennel | The theory of the centrifugal distributor. III : Particle trajectories[END_REF] reported that less than 25% of the particles left the disc with a vertical angle comprised between 3° upward and 3° d ownward. These findings are in complete disagreement with those obtained in the present study. The wide vertical dispersion observed by Mennel and Reece is probably due to the fact that individual particles were accelerated one by one on the spinning disc. In opposition, the present study examined the vertical distribution of an entire particle flow.

Using polypropylene particles and U-profile vanes of 40 mm height, [START_REF] Olieslagers | Fertilizer distribution modelling for centrifugal spreader design[END_REF] reported that the amount of particles not captured between 4° upward and 4° downward were respectively 11.2% when the vanes were 280 mm length and 24.8% when they were 150 mm length. These results are much more in accordance with above-mentioned findings.

Various parameters can explain discrepancies. In particular, differences have to be noted in the dimension of the vanes (length and height), in the disc rotational speed and in the particle nature. Reumers et al. (2003a) presented some 2D-distribution measurements around the spinning disc but do not provide any more accurate characteristics concerning the vertical distribution.

In the previous analysis, we assumed that fertiliser granules leave the vane at the same point on the vertical wall on the vane extremity. [START_REF] Mennel | The theory of the centrifugal distributor. III : Particle trajectories[END_REF] or [START_REF] Olieslagers | Fertilizer distribution modelling for centrifugal spreader design[END_REF] implicitly used the same approach to transform height standard deviation into vertical angular standard deviation. In practice, this seems not realistic since granules can be at various heights in the U-profile when they leave the vane. Moreover the shape of the vertical distribution of the mass flow at the extremity of the vane probably depends on the mass flow rate and the resulting vertical occupation of the vane. Thus, a better estimation of the vertical angular distribution can be obtained by measuring the distribution at two different distances from the spinning disc axle. For ammonium nitrate, the distribution has been measured with the same method but with a cylindrical screen radius set at 945 mm. At this radius, the mean value of the standard deviation of the impact height distribution is 13.81 mm. Combining the height standard deviations measured at these two different radii and taking into account the corresponding flight length between these radii, the vertical angular standard deviation is 0.92°. This value is logically lower than the one d educed from the first analysis. Considering this approach, 99% of the mass flow leaves the vane with an upward or downward vertical angle of 2.76° for ammonium nitrate.

Conclusion

The study demonstrated that recording impacts of fertiliser granules against an interception screen provides a new technique to instantaneously record the two-dimensional distribution of the mass flow around a centrifugal spreading device. A specific image processing has been developed to perform an accurate analysis of impact recording paper bands and compare findings to other distribution measurement devices. For three different fertilisers, the horizontal angular distributions deduced from the impact recording method are in agreement with those deduced from a traditional compartmented ring. In particular, impact records show that the distribution obtained for ammonium nitrate is close to the one obtained for NPK while the distribution obtained for KCl is clearly shift in the direction of the disc rotation. The study also demonstrates that impact recording is an efficient technique to measure the vertical distribution of the mass flow. Findings clearly show that the vertical standard deviation observed for KCl is lower than the one observed for ammonium nitrate or NPK. For research work, the method can be used to study the centrifugal spreading process, characterise fertiliser mechanical behaviour or provide input data for ballistic flight model in order to predict the distribution pattern deposition on the ground. Adapting data acquisition and data processing, the study opens up the possibility of designing new simple tests and diagnostic tools to help users in setting their machine.

Fig. 1 .

 1 Fig. 1. Photograph of the cylindrical impact screen placed around the spinning disc

Fig. 2 .

 2 Fig. 2. Photograph of the compartment ring placed around the disc.

Fig. 4 .

 4 Fig. 4. Two-dimensional distribution of the mass flow. The grey scale corresponds to the fraction intercepted by the block (in percent) relative to the maximum intercepted amount by a sampled block (5 × 25 mm).

Fig. 5 .

 5 Fig. 5. Horizontal angular distributions of the mass flow deduced from the compartmented ring (light grey bars) and from impact records (deep grey bars) for three fertilisers.

Author-produced version of the paper presented at AGENG 2010 Conference, Septembre 6-8 2010, Clermont-Ferrand, France


S Villette
email: s.villette@agrosupdijon.fr

C Gée

E Piron

R Martin

D Miclet

M Paindavoine

Centrifugal fertiliser spreading: velocity and mass flow distribution measurement by image processing

Keywords: Centrifugal fertiliser spreading, velocity, mass flow distribution, Hough transform, image acquisition

This paper investigates the use of a new imaging system to measure the velocity and the mass flow distribution of fertiliser granules spread by a centrifugal device. The new acquisition system consists of a digital camera placed above the disc so that its view axis corresponds to the disc axle. This provides useful geometrical properties to develop a simple and efficient image processing. The technique provides a global estimation of the spreading characteristics for the whole fertiliser flow using a global analysis of an image rather than identifying individually each trajectory in the image. The new technique is compared to a previously assessed imaging method. Concerning the mass flow distribution, results deduced from both imaging methods are also compared to those deduced from a compartmented collection ring.

Introduction

In Europe, the application of mineral fertilisers is mainly performed by centrifugal spreaders because of their robustness, simplicity and low cost. The uniformity of the application rate in the field depends on the spreading width and on the overlaps resulting from the parallel passes. Consequently the quality of the spreading in the field depends on the outlet velocity and on the angular mass flow distribution around the spinning disc. In practice, the value of these parameters result from fertiliser physical properties and machine characteristics. Thus, the setting of the spreader with respect to the mechanical behaviour of the fertiliser is crucial for the quality of the spreading. Unfortunately, because of difficulties in adjusting the machines, major differences in the quality of the spread pattern deposition are observed in the field and numerous studies have reported a lack of fertiliser uniformity [START_REF] Ziani | Qualité de l'épandage d'engrais -Enquête auprès des agriculteurs du Val d'Allier[END_REF][START_REF] Sogaard | Yield reduction resulting from uneven fertilizer distribution[END_REF][START_REF] Tissot | Tolerance of wheat crop towards the spreading heterogeneity of nitrogen manure[END_REF][START_REF] Leterme | Précision des épandages : une situation contrastée[END_REF]. This adversely affects not only the crops but also the environment [START_REF] Tissot | Uniformity of N-fertiliser spreading and risk of ground water contamination[END_REF], especially in the case of nitrogenbased fertilisers. Nowadays, economic and environmental considerations call for improvements in the quality of fertiliser spreading and there is a need to better characterise centrifugal spreading and develop autonomous feedback systems for automatic uniformity control. Some works addressed the problem of measuring the outlet velocity of fertiliser granules in the vicinity of the spinning disc. A technique based on the ultrasonic Doppler frequency shift was developed [START_REF] Hofstee | Handling and spreading of fertilisers : Part 3, Measurement of particle velocities and directions with ultrasonic transducers, theory, measurement system, and experimental arrangements[END_REF] using one transmitter and three receivers arranged in a threedimensional configuration. The ultrasonic measurement cell opening was 20 × 20 mm. An optical sensor was developed [START_REF] Grift | Measurement of velocity and diameter of individual fertiliser particles by an optical method[END_REF] using two photosensitive arrays, placed perpendicularly to the radius of the disc. The radial component of the outlet velocity was derived from the time difference corresponding to a particle passing each sensor array. The orifice of the measurement unit was 3 cm. These techniques were limited to a narrow investigated space, and required the displacement of measuring cells in the material flow.

Another approach consists in using imaging systems. These systems have the advantage to cover the whole angular sector of spreading around the spinning disc, and avoid any contact with fertiliser granules. Nevertheless, PIV (Particle Image Velocimetry) techniques, or fast imaging systems are inadequate because they are expensive, complex and difficult to adapt to agricultural machines. Some stroboscopic imaging systems were proposed [START_REF] Cointault | Photographic imaging systems to measure fertilizer granule velocity during spreading[END_REF] to measure the outlet velocity in the case of a flat disc only. In contrast to the stroboscopic approach, a low-cost acquisition system and an automatic image processing were developed [START_REF] Villette | Optimizing Hough transform for fertiliser spreading optical control[END_REF] to derive the outlet velocity from motion-blurred images on which granule trajectories appear as straight streaks. The technique was first available for flat discs, assuming that the particle trajectories were parallel to the image plane to avoid any bias on distance or angle measurements. Then, the technique was extended [START_REF] Villette | Centrifugal spreading of fertiliser: Deducing three-dimensional velocities from horizontal outlet angles using computer vision[END_REF] to deduce the three-dimensional velocities from the horizontal outlet angle of fertiliser trajectories in the case of a concave disc. The main drawback of the method was that each trajectory has to be identified individually in the Hough space. This was time consuming and do not have the robustness of a global analysis of the whole image to provide a global outlet velocity estimation for the whole fertiliser flow. Concerning the measurement of the angular distribution of the fertiliser mass flow around the spinning disc, the traditional method consists in placing a compartmented collection ring around the disc [START_REF] Colin | Etude du procédé d'épandage centrifuge d'engrais minéraux[END_REF]Olieslagers, 1997;[START_REF] Reumers | Experimental characterisation of the tangential and cylindrical fertiliser distribution pattern from a spinning disc : A parameter study[END_REF]. Using this collection device the horizontal angular distribution of the fertiliser flow is deduced by weighing the amount of material collected by each box of the ring. At the present time, no imaging system is proposed in the literature to estimate the angular distribution of the fertiliser mass flow. The objective of the work is to develop cheap, fast and robust vision systems to measure the outlet velocity and the angular distribution of the fertiliser mass flow around a spinning disc. This article compares two imaging systems based on the use of motion-blurred images. It presents developments to provide a global estimation of the spreading characteristics for the whole fertiliser flow using a global analysis of an image rather than identifying individually each trajectory in the image. The study investigates an imaging system in which the camera is placed above the disc so that its view axis corresponds to the disc axle.

Materials and methods

Experimental arrangement

The study is carried out in laboratory conditions using an experimental spreading device made up of elements similar to those found in a traditional centrifugal spreader. The disc is driven by an asynchronous AC motor and a programmable power supply. Fertiliser granules are stored in a hopper at the bottom of which a shutter sets the fertiliser flow. Under the shutter, a delivery pipe adjusts the feeding point of the granules onto the disc Fig. 1. An imaging system was developed to capture an image of the trajectories followed by the fertiliser granules in the vicinity of a spinning disc. The system is made up of a monochrome digital camera placed vertically at approximately 1 m above the spinning disc or above the fertiliser flow in the vicinity of the disc (Fig. 1). The disc rotational axle and the camera optical axis are vertical. A particular acquisition situation is obtained when the camera view axis corresponds to the disc rotation axle. The camera is equipped with a 8.5-mm-focal-length lens that provides a field-of-view of approximately 1×1 m 2 to capture a wide angular range of spreading. Two spotlights are used to illuminate the granule lengthways during their motion at the beginning of their ballistic flight. The camera exposure is set long enough (e.g. 35 ms) so that images are composed of streaks associated to the motion of fertiliser granules after their ejection from the disc (Fig. 3). These images, called 'motion-blurred images', show the trajectories of fertiliser granules in the vicinity of the spinning disc.

Mechanical model

The velocity measurement is based on the analysis of fertiliser granule streaks observed in motion-blurred images (Fig. 3). The outlet velocity is deduced from the horizontal outlet angle θ out which is the horizontal angle between the fertiliser granule trajectory and the tangent to the disc. The cinematic analysis [START_REF] Villette | Centrifugal spreading of fertiliser: Deducing three-dimensional velocities from horizontal outlet angles using computer vision[END_REF] of the fertiliser motion on the spinning disc demonstrated that the three-dimensional components of the outlet velocity were deduced from the horizontal outlet angle θ out as follows:

-radial component of the velocity:

tan 1 tan tan vane out R out r v α ω θ θ = + (1)
-tangential component of the velocity:

tan R T out v v θ = (2)
-vertical component of the velocity:

tan cos R k v v α Ω = (3)
where r vane is the radius of the vane, ω is the rotational speed of the disc, α is the horizontal angle of the vane and Ω is the vertical angle of the vane.

Geometric considerations concerning image acquisition

In the case of a concave disc, fertiliser granule trajectories are not parallel to the image plane and there is an angular bias ε between the apparent observed angle θ out_im in the image and the real horizontal outlet angle θ out . This angular difference ε increases with the distance between the trajectory and the view axis of the camera. Fig. 4 illustrates this phenomena and the influence of the distance between the view axis and the spinning disc centre in the image. In the particular case where the view axis corresponds to the disc axle, the angular bias ε remains constant whatever the location (and the orientation) of the trajectory in the image assuming the vertical outlet angle is constant.

Image processing

After filtering the original motion-blurred image, the binary image of trajectory axes is analyzed by identifying the location of peaks in a parameter space resulting from the Hough transform [START_REF] Hough | Methods and means for recognizing complex patterns[END_REF].

The method consisted in computing the Hough transform in polar coordinates (θ H , ρ H ) (Duda and Hart, 1972) with respect to the disc rotation axle. Considering the normal representation of a line (i.e.

cos sin

H H H x y ρ θ θ = +
) each pixel (x,y) of the image is transformed into a sinusoidal curve in the (θ H , ρ H ) -parameter space. When several pixels lie on the same line in the original image, they provide several curves passing through the same point in the Hough space. The location of this intersection point in the Hough space gives the polar parameters of the corresponding line in the image.

In order to optimize the method we chose the origin of the coordinate system at the disc centre.

This reduces the range of relevant values that have to be considered for ρ H and limits the number of judicious pixels considered in the image (pixels lying on a ring centred on the disc centre are only considered). Two methods have been developed to analyse the Hough space in order to characterise the spreading parameters (i.e. the horizontal outlet angle and the angular distribution of the mass flow around the disc).

Method 1: Iterative identification of individual peaks in the Hough space

When the camera axis does not correspond to the disc axle, a satisfying peak extraction from the Hough space requires an iterative process: identifying the global maximum, deducing the quantified values of the line parameters, adjusting the values with the real location of the trajectory in the image and subtracting from the Hough space the Hough transform of the corresponding segment [START_REF] Villette | Optimizing Hough transform for fertiliser spreading optical control[END_REF][START_REF] Villette | Centrifugal spreading of fertiliser: Deducing three-dimensional velocities from horizontal outlet angles using computer vision[END_REF]. The apparent outlet angle was then deduced for each trajectory. Taking into account the location of the trajectory in the image, this angle was finally corrected to provide each horizontal outlet angle without bias. The angular distribution of the mass flow around the disc can be deduced from the location of each identified trajectory in the image. This method has already been assessed [START_REF] Villette | Centrifugal spreading of fertiliser: Deducing three-dimensional velocities from horizontal outlet angles using computer vision[END_REF] to measure outlet angles and outlet velocities of fertiliser granules leaving a spinning disc. In this study, it is considered as a reference method for the measurement of outlet angles and outlet velocities.

Method 2 : Global analysis of the Hough space when the camera axle corresponds to the disc axis

In order to avoid individual identification of trajectories, the second method takes advantage of the geometrical properties that occur when the view axis of the camera corresponds to the disc rotation axle. In this situation, the angular bias ε measured in the image is constant (Fig. 4).

Consequently, assuming that the mean value of the horizontal outlet angle of fertiliser granules remains constant for the whole angular sector of spreading, the radius parameter ρ im (Fig. 3) of the trajectories (in the image) is also constant whatever the trajectory location around the disc.

The hypothesis concerning the invariance of the mean outlet angle along the angular sector of spreading is supported by previous works [START_REF] Villette | Centrifugal spreading of fertiliser: Deducing three-dimensional velocities from horizontal outlet angles using computer vision[END_REF].

Thus, the horizontal outlet angle θ out for the whole angular sector of spreading can be deduced from the mean value of the ρ im -parameter deduced from the whole Hough space.

Combining the mechanical model, the pinhole camera model, and the specific location of the camera axis, the horizontal outlet angle is directly deduced from the radius parameter ρ im as follows:

( )

2 2 arctan tan 1 cos vane conv im out im vane conv r f p r f f ρ θ ρ α     -   =     ∆ Ω +           (4)
where f conv is the meter per pixel conversion factor, ∆p the pixel size and f the focal length.

The value ρ im of the parameter that describes the best the outlet angle for the whole angular sector of spreading is deduced from the Hough space. This value corresponds to the maximum of the vote number (after filtering) projected on the ρ H -axis. A robust and representative value of the outlet angle is then deduced for the whole spreading sector.

Assuming that the mass flow is proportional to the trajectory density in the image the angular distribution around the disc is also deduced from the Hough space very easily. Since the mean value of the ρ im -parameter remains constant for all trajectories whatever their orientation in the image, the relevant peaks in the Hough space are approximately distributed along the line of the Hough space corresponding to ρ H = ρ im . Consequently, the angular distribution of the mass flow is deduced from the angular location θ H of not null values along the line defined by ρ H = ρ im in the Hough space.

Results

Both analysis methods (methods 1 and 2) have been compared on two sets of 25 images obtained with the same centrifugal disc and when the camera view axis corresponds to the disc axle. Two fertilisers have been used: ammonium nitrate and potassium chloride (KCl).

For an image of these sets, Fig. 6 presents the Hough space (after filtering), and its projection on the axis of the ρ H -parameter. This projection is used to measure the relevant value of the ρ im - parameter that characterise the whole motion-blurred image (Fig. 3) using the global analysis (method 2). The locations of the peaks individually detected by the iterative analysis (method 1) are also marked on the Hough space.

a.

Outlet velocity

For the two studied fertilisers, Table 1 provides the mean values of the outlet angles θ out and the outlet velocities v out calculated on the 25 images using the global analysis of the Hough Space and the iterative method based on individual peak identifications in the Hough space. Table 1 demonstrates that both methods provide very close results.

Angular distribution of the mass flow

The reference method used for the measurement of the angular distribution of the mass flow consists in collecting fertiliser granules around the spinning disc using a compartimented ring divided into 22 adjacent compartments of 10° each. The fertiliser amount contained in each compartment is weighted to provide the angular distribution of the mass flow. Regarding the global location of the histograms it appears that the distributions deduced from the imaging methods are in agreement with those deduced from the compartmented ring.

Considering a Gaussian fitting of the distributions, the mean value θ flow and the standard deviation σ flow of the distributions are as provided in Table 2. Regarding the values of the distribution parameters (θ flow and σ flow ) differences are enhanced between findings deduced from the imaging methods and the reference method. The main difference concerns the estimation of the standard deviation of the mass flow distribution that is overestimated using the imaging methods.

Discussion

Concerning the outlet angle and the outlet velocity of the fertiliser granules when they leave the spinning disc, the values obtained with the global analysis of the Hough space are very similar to those obtained with the iterative analysis that can be considered as the reference method.

Concerning the characterisation of the angular distribution of the mass flow, the mean values of the distributions deduced from imaging methods are in agreement with those deduced from the compartmented ring. Nevertheless, differences appear for the estimation of the standard deviation of the distribution. Compared to the reference histograms (Fig. 7 and8), histograms deduced from the Hough space show saturation in the central region of the spreading pattern.

In this spreading sector, fertiliser granules actually leave the vane with an overlapping in the vertical plane. This leads to a saturation phenomenon. As the granule output flow is captured with a camera placed above the fertiliser flow, upper trajectories (associated to visible granules) are only counted while the downer ones are hidden. This yields to an over-estimation of the standard deviation when imaging methods are used. Future work will be devoted to improve the characterisation of the angular distribution.

Regarding the outlet velocity values and the angular mean values of the mass flow distribution, findings obtained with the vision system clearly show the differences in the mechanical behaviour between the fertiliser types used in this study. The outlet velocity and the outlet angle are higher for ammonium nitrate than for potassium chloride while the mean value of the angular distribution of the mass flow around the disc is higher for potassium chloride than for ammonium nitrate. The shape of the fertiliser granules could explain these observations. In the case of ammonium nitrate granules, which are rounded, the higher flowability of the fertiliser on the vane leads fertiliser granules to reach a higher velocity on the vane and be ejected more rapidly (i.e. at a lower angle value of the vane location). This demonstrates that the vision system presented in this article is of particular interest to characterise the spreading and adjust the machine setting with respect to the real mechanical behaviour of fertilisers.

Algorithms have been developed under Matlab v6.1 and run using a computer with an Intel Pentium III 4.3 GHz processor and one core. The computational times are: 3.7 s for the Hough space building (associated to an angular region of 150°, with a sampling step of 0.15° corresponding to a quantification step of 2 pixels); 21 s to analyse the Hough space based on the iterative method which identifies each trajectory and less than 0.2 s to analyse the Hough space using the global method described in this article. Increasing the sampling step and the space quantification can reduce the computational time of the Hough transform.

The imaging method based on the global analysis of the Hough space is not time-consuming and takes advantage of the global information provided by all the trajectories to improve the robustness of the outlet angle estimation. At the present time, the main drawback of this approach is that it requires placing the camera just above the spinning disc. This is possible for experimental spreading devices specifically built to study the centrifugal spreading process but this is not possible to measure spreading characteristics with a real spreader. Consequently, a new approach is now being studied to make possible a global analysis of a specific parameter space although the view axis of the camera does not correspond to the disc rotation axle.

Conclusion

Two image acquisition and processing methods have been compared to deduce spreading parameters from "motion-blurred images" in which fertiliser granule trajectories appear as streaks. The study demonstrates that a simplified analysis can be used when the camera view axis corresponds to the rotation axle of the spinning disc. This geometrical situation provides useful advantages to improve the robustness of the image processing and reduce computational constraints. Concerning outlet velocities and the mass flow distributions, the study shows that findings deduced from the simplified analysis are similar to those deduced from the reference image analysis in which each trajectory is identified individually in the image. Concerning mass flow distributions, both imaging methods overestimate the standard deviations of the distributions with respect to values deduced from a traditional compartmented ring. At the present time, the main drawback of the simplified analysis method is that the method can only be used when the camera is placed above the disc. This camera position is possible for experimental spreading devices but is not possible for traditional centrifugal spreaders. Future work will be dedicated to improve the precision of the information related to the angular distribution of the granule flow and to adapt the imaging technique to the construction constraints of traditional centrifugal spreaders.

  Fig. 1: Experimental arrangement

  Fig.3: Motion-blurred image (left) and geometric characteristics of a trajectory (right): ρ im is the perpendicular distance of the trajectory from the disc axle; θ out_im is the apparent outlet angle in the image.

  Fig. 4. Simulation of the three-dimensional scene and image acquisition (left); resulting image when the camera view axis does not correspond to the disc axle (middle) and when the camera view axis corresponds to the disc axle (right).

Fig. 6 .

 6 Fig. 6. Hough Space and its projection (right) on the ρ H -axis for an image obtained for potassium chloride (a) or ammonium nitrate (b). The line parallel to the abscissa axis of the graphics corresponds to ρ H = ρ im . The locations of the peaks detected by the iterative analysis are indicated ( ) on the Hough space.

Figure 7 Fig. 7 .Fig. 8 .

 778 Fig. 7. Angular distribution of the mass flow deduced from the image by identifying each peak individually in the Hough space (grey) and collection ring (white) for potassium chloride (a) and ammonium nitrate (b).

Table 1 .

 1 Mean values of outlet angles and velocities for two different fertilisers: ammonium nitrate (Am. Nit.) and potassium chloride (KCl).

		Global analysis of the	Iterative analysis of the
	Fertiliser type	Hough space θ out v out (m.s -1 )	θ out	Hough space v out (m.s -1 )
	KCl	34.7°	33.1	34.2°	32.9
	Am. Nit	40.5°	35.8	40.3°	35.7

Table 2 .

 2 Values of the distribution characteristic parameters deduced from the imaging methods and the reference method for ammonium nitrate (Am. Nit.) and potassium chloride (KCl).

			Imaging methods		Reference method
		Iterative analysis θ flow σ flow	Global analysis θ flow σ flow	Compartmented ring θ flow σ flow
	KCl	72.6°	28.1°	71.1°	25.2°	70.3°	17.2°
	Am. Nit.	57.7°	27.0°	60.2°	27.1°	56.5°	18.7°


Pierre Cariou
email: pierre.cariou@euromed-management.com

Francois-Charles Wolff

Ship-owners' decisions to outsource vessel management

Shipping companies frequently outsource the management of their vessels. In this paper, we use data from Lloyd's Register Fairplay (2009) on 45,456 vessels belonging to 9,580 different shipowners to investigate the extent of outsourcing in shipping and to identify key factors affecting the likelihood of outsourcing. The results of our econometric analysis indicate that ship-owners' decisions to outsource are explained by the characteristics of the vessels in question (age, type, size) and the characteristics of the ship-owner (country of domiciliation, number of vessels). In addition, a specific country effect is identified for Greek ship-owners, which is in line with the findings of previous studies.

Introduction

Over the last decade, outsourcing has become a predominant strategic option for firms. Eighty-two percent of logistics and supply chain managers of 60 large US manufacturers made use of third-party logistics services in 2004 (Lieb and Bentz, 2004;[START_REF] Langley | Third party logistics: Results and findings of the 10 th annual study[END_REF]. Increasingly, companies are moving into foreign markets and globalizing their supply chains and sources of materials [START_REF] Anderson | What drives the choice of third party logistics provider? Social Science Research Network[END_REF]. Similarly, the outsourcing of vessel management has become an option considered by most ship-owners [START_REF] Sletmo | Shipping's Fourth Wave: Ship Management and Vernon's trade cycles[END_REF], as ship ownership and operation are complex activities for which specific expertise is needed (Drewry Shipping Consultants, 2004).

Although outsourcing is a strategic choice that is growing in importance, the extent of outsourcing and the reasons behind the adoption of an outsourcing strategy are not well documented in shipping, at least on the global level, for several reasons. First, the extent of outsourcing is generally difficult to capture, as a variety of activities can be outsourced -transport management, warehousing, distribution or even the management of the entire supply chain [START_REF] Patterson | How different is carrier for third party logistics companies?[END_REF]. Second, statistics on potential "shareholding ties" among the various stakeholders involved in the provision of shipping services are not readily available, which makes the identification of the extent of outsourcing difficult [START_REF] Mitroussi | Third party ship management: the case of separation of ownership and management in shipping context[END_REF]. Despite these difficulties, this article attempts to provide an original contribution in the form of a global analysis of the extent of vessel management outsourcing and an examination of the key factors affecting the likelihood of such outsourcing.

The remainder of this paper is organized as follows. The literature on factors that influence the decision to outsource the management of a vessel are reviewed in the next section. Section 3 presents the dataset, which covers the world fleet as of June 2009, as well as some preliminary statistics concerning the intensity of outsourcing. In Section 4, we discuss results from Probit models and estimate separate regressions for various types of vessels. We then investigate the influence of a ship-owner's country of domicile. The last section provides conclusions and suggestions for further research.

Literature review

Logistics outsourcing is commonly adopted by companies as a means to obtain a competitive advantage [START_REF] Hoffman | 3PLs maturing fast[END_REF][START_REF] Hoffman | 3PLs reach record revenue[END_REF][START_REF] Quinn | 3PLs hit their stride[END_REF][START_REF] Gourdin | Global logistics management. A competitive advantage for the 21 st century[END_REF][START_REF] Parashkevova | Logistics outsourcing -A means of assuring the competitive advantage for an organization[END_REF][START_REF] Marasco | Third-party logistics: A literature review[END_REF].

Outsourcing provides companies with opportunities to focus on core competencies, to access best management practices and to increase competitiveness in implementing new technologies developed by third-party service providers. Furthermore, through relationship learning, outsourcing enables customers and suppliers to identify ways of removing redundant costs, improve quality and reliability, and increase speed and flexibility [START_REF] Selnes | Promoting relationship learning[END_REF][START_REF] Selviaridis | Benefits, risks, selection criteria and success factors for third-party logistics services[END_REF]. At the same time, the potential for a loss of control, uncertainties about the quality of service and questions concerning the true costs of using a third party remain [START_REF] Gourdin | Global logistics management. A competitive advantage for the 21 st century[END_REF].

According to Lieb and Bentz (2004), the most frequently used third-party logistics services in 2004 were direct transportation services (67%), custom brokerage services (58%) and freight payment services (54%). Although the reasons for outsourcing these activities are often similar, differences remain in terms of the motives, extent and context within which such outsourcing takes place [START_REF] Peters | The use of third-party logistics services by European industry[END_REF][START_REF] Lieb | The use of third-party logistics services by large American manufacturers[END_REF][START_REF] Silver | How 3PLs can help manage the increasing complexities of transportation[END_REF][START_REF] Tompkins | The business imperative of outsourcing[END_REF][START_REF] Hannon | Choose wisely: Not all third-party logistics are the same[END_REF][START_REF] Fugate | Operational collaboration between shippers and carriers in the transportation industry[END_REF].

In the shipping sector, outsourcing provides access to cost-efficient factors of production, such as vessel crews, and access to the specific technical expertise of large ship management companies, which offers economies of scale, marketing and bargaining power [START_REF] Sletmo | Shipping's Fourth Wave: Ship Management and Vernon's trade cycles[END_REF][START_REF] Schulte | Third party management moving forward and adapting to change[END_REF][START_REF] Ebsworth | International Ship Management: Profit or Loss from Shipping's Revival, Lloyd's Ship Manager and Shipping News International Conference[END_REF][START_REF] Richards | Reducing ship investments risks. The ship manager's role[END_REF][START_REF] King | Globalisation of logistics management: present status and prospects[END_REF][START_REF] Gunton | Ship management[END_REF]. Access to potential tax exemptions is another likely motive [START_REF] Stopford | Maritime Economics[END_REF].

Outsourcing involves both a choice with regard to the activities to outsource and the selection of an appropriate service provider to handle those activities [START_REF] Anderson | What drives the choice of third party logistics provider? Social Science Research Network[END_REF]. In vessel management, outsourced activities primarily concern commercial and/or technical elements. In 2003, the management of 1,500-1,700 vessels (out of 23,000 vessels) was outsourced to technical managers, while 4,500-5,500 vessels were outsourced to specialized crew management companies (Drewry Shipping Consultants, 2004). A 6-8% increase in the fleet managed by professional ship managers is expected over the long term, mainly driven by two factors: the growth of new shipping/exporting nations without shipping expertise, and changes in traditional shipping nations that support the outsourcing of vessel management. Examples of the latter include the new generation of Greek shipowners, who are moving away from the family "tradition" of small fleets that are managed in-house, and Japanese ship-owners who appear ready to open up to international ship managers.

Although many studies about the extent of outsourcing and the choice of third-party ship managers exist [START_REF] Panayides | Professional Ship Management: Marketing and Strategy[END_REF][START_REF] Panayides | The vertical disintegration of ship management: choice criteria for third party selection and evaluation[END_REF][START_REF] Mitroussi | Third party ship management: the case of separation of ownership and management in shipping context[END_REF]Mitroussi, , 2004aMitroussi, , 2004b)), they have been carried out on a case-to-case basis through surveys, and they often focus on differences in behaviour between Greek and UK ship-owners. [START_REF] Panayides | Professional Ship Management: Marketing and Strategy[END_REF] and [START_REF] Panayides | The vertical disintegration of ship management: choice criteria for third party selection and evaluation[END_REF] surveys of 48 ship management companies and 36 Greek and UK owners show, for instance, that the primary criteria considered by a ship-owner in the selection of a third-party ship manager is technical ability, followed by the experience and qualifications of personnel, while price is not a decisive criteria. Another motive is the need to benchmark the ship-owner's own vessel management performance. Finally, the authors suggest that outsourcing is more likely for liner shipping companies operating a large number of vessels. [START_REF] Mitroussi | Third party ship management: the case of separation of ownership and management in shipping context[END_REF] highlights four elements that lead a ship-owner to use third-party ship managers.

These factors are company size, company type (private/family or public), company age and technological change. In its investigation of the impact of these attributes, Mitroussi's survey (2004aMitroussi's survey ( , 2004b) ) of 46 Greek and 20 UK ship-owners identifies distinct profiles. For instance, while 55% of the UK based companies use third-party management companies, only 8.3% of Greek companies use the same services. Crew and technical management are the activities that are outsourced the most often, while the choice of flag of registry, maintenance and commercial matters often remains the owner's responsibility. Furthermore, the primary reason for outsourcing is flexibility, followed by access to technical expertise. In contrast, existing in-house expertise (for 98% of Greek ship-owners), the need for control (89%) and the cost of outsourcing reduce its likelihood. With regard to the latter, Drewry Shipping Consultants (2004) estimates the fee of a third-party ship manager at USD 100,000 to USD 175,000 per year and per vessel, while [START_REF] Justad | Taking delivery: how to achieve lasting value from outsourcing, Eitzen Maritime Services ASA[END_REF] estimates the cost at 5% of annual operating costs.

Ship-owner's characteristics also have an impact on the choice to outsource (Mitroussi, 2004b). Small and large companies outsource in similar proportions (around 16%). This similarity is explained by the need for expertise for the former and by the need for a reduction in administrative costs for the latter.

The age of the company is also a significant factor. Firms controlled by at least third-generation owners are more likely to outsource. Greek family-owned companies maintain control over the majority of their vessels (86.7%), while private UK companies use third-party managers (53.9%) more extensively. Finally, 53% of owners outsource 100% of their fleet, while 26.7% of owners outsource less than 25% (Mitroussi, 2004a).

This literature review makes it clear that previous research has dealt with the identification of factors affecting the decision to outsource vessel management. However, their scope remains limited to case studies comparing Greek and UK ship-owners. Therefore, we attempt to enlarge the comparison by considering a sample of 45,456 vessels from a range of countries operating in the world fleet in 2009.

Data

Lloyd's Register Fairplay database

We investigate the extent to which ship-owners outsource the management of their vessels using the Lloyd's Register Fairplay (LRF) database. This database distinguishes between the registered owner, defined as the legal owner of the vessel as indicated on the ship's registration documents; the operator, defined as the company responsible for the commercial decisions concerning the employment of a ship; the ship manager, who is designated by the shipowner or charterer as responsible for the day-to-day running of the ship; and the technical manager, who is specifically responsible for technical operations and acts as superintendant of the ship. Information is also available on the country of domicile for the various entities and on the vessels' characteristics, such as the type, building year and size. The data extraction was undertaken in May 2009 and led to the identification of 110,384 different vessels.

We then limit our attention to the management structure of merchant vessels involved in international trade. As a consequence, we remove the "miscellaneous" category of vessels (42,906 vessels) from the original LRF sample. 34.1% of these are fishing vessels and another 28.2% are tugboats. We also exclude vessels of less than 1,000 gross tons, as these are typically not involved in international trade (classification retrieved from UNCTAD, 2009). This reduces the sample size by 21,044 observations. Finally, we drop 978 vessels for which either the owner or the manager of the vessel are unknown.

Hence, our final sample comprises 45,456 vessels belonging to 9,580 different shipowners and operated by 10,186 different managers.

The sample exemplifies the complexity inherent in attempts to identify the level of outsourcing in ship management when dealing with such a large dataset. For instance, Cosco is the largest shipowner in dry bulk markets, where the two largest managing companies are Shipping Co Ltd and Cosco Bulk. In fact, a majority of Cosco's fleet is managed by Cosco Bulk, although the two companies have different names. However, the situation is different in other sectors. In tanker markets, for example, the largest managing companies are Thome Ship Management Pte Ltd, Anglo-Eastern Ship Management and Fleet Management Ltd-HKG. These companies are usually viewed as professional ship managers that are independent of ship-owners.

The LRF database provides another example of this complex situation. The five most important managing companies in 2009 were AP Moller, Zodiac Maritime Agencies Ltd, MSC Mediterranean Shipping Co., Fleet Management Ltd-HKG and NSB Niederelbe. The numbers of vessels managed and owned by each of these companies are presented in Figure 1. Interestingly, both AP Moller and Zodiac own almost all of the vessels that they manage. However, in many publications, Zodiac is presented as one of the leading professional ship managers (Lloyd's Ship Manager, 2003), while AP Moller is not. In contrast, MSC manages 145 vessels, 144 of which are owned by companies not registered as MSC. In fact, MSC is structured in such a way that each vessel it manages is owned by an individual company with a unique name.

Insert Figure 1 here Similar problems occur when analysing the situation for technical managers (Figure 1). In terms of the number of vessels managed, Fleet Management Ltd-HKG is the number one company, followed by Anglo-Eastern Ship Management Ltd, Wallem Shipmanagement Ltd, Moller-Maersk A/S and Thome Ship Management Pte Ltd. Very few vessels are owned by Anglo-Eastern Ship Management or Thome Ship Management Pte Ltd, while the reverse is true for Moller-Maersk A/S and Zodiac Maritime Agencies Ltd. The latter owns 97 of the 105 vessels it manages. V. Ships, which is known as one of the leading technical management firms in shipping, is registered under various names in the LRF database (V. Ships UK or V. Ships Ltd for instance) rather than as a single entity.

These examples illustrate that the identification of independent professional ship managers is difficult, as "shareholding ties" may exist between ship-owners and managers. However, managing companies are neither systematically related to a specific owning group nor do they exclusively work for a certain group. When defining outsourcing as a situation in which the names of a vessel's manager and owner are different, it should be kept in mind that this definition does not correspond to the industry's typical understanding of management outsourcing to independent professional ship managers. As stated above, given the legal and operational complexities found in company structures in shipping, shipowners often outsource the management of vessels to subsidiaries with different names. This may lead us to consider a company as a third-party manager even when it is either directly or indirectly related to the owner of the vessel. This might increase the statistics related to the proportion of outsourcing activities and make comparisons with previous studies difficult.

Another limitation of the initial dataset is related to information on the registered shipowner and the country of domicile. The registered ship-owner might actually be the true owner/manager. However, in other situations, a number of entities might be created to legally "own" the ship in order to limit potential liability, to benefit from offshore tax laws or to fulfil a ship registration requirement for specific flags. The latter is clearly the case with Panama, one of the leading countries in terms of number of registered owners and in terms of flag of registry, but not in terms of controlled fleet (UNCTAD, 2009). These shortcomings must be kept in mind when interpreting our results. Our calculations thus provide an upper bound for the outsourcing rate.

Descriptive statistics

Using the available information, we focus on several characteristics to explain the probability that a vessel will be managed by a company other than the owner: size, type (bulker/combination, container, dry cargo, offshore, passenger/ferry, reefer, roro, tanker), and age. One interesting feature of the LRF data is that it is a matched sample of owners, managers and vessel characteristics, which allows us to study the magnitude of vessel management outsourcing from various perspectives. Starting with the vessel sample of 45,456 observations, we construct two sub-samples: one at the shipowner level (9,580 observations) and one on the manager level (10,186 observations).

1 The distribution of vessels in terms of owners and managers is shown in Figure 2.

Insert Figure 2 here

The analysis highlights the fragmentation in terms of number of companies and the concentration in terms of ownership. In 2009, more than half of all owners (57.7%) owned one ship, while 91.4% owned less than 10 ships. At the same time, owners owning more than 50 vessels represented 1.2% of all owners. These owners owned 28.8% of all vessels. The largest owner was the Chinese government (1,498 vessels), followed by COSCO, Mitsui OSK Lines and China Shipping Group.

Vessels owned by the Chinese Government are managed by a number of small domestic shipping lines. A similar pattern holds for managers. Less than 1% of companies managed more than 50 vessels in 2009. However, these companies operated 28.8% of all vessels.

In terms of vessels,2 around 50% are less than 16 years old and 30% are more than 25 years old. The mean age is 15.9 years. Of these vessels, 38.7% are less than 5,000 gross tons and 28.5% are above 25,000 gross tons. Dry cargo (24.3%), tanker (23.9%), bulker (18.2%) and container (11.3%) vessels are the most common. A closer look at the data highlights differences in the structure of the fleet by country of domicile. On average, Japanese owners operate a relatively young fleet of larger vessels. The German fleet is characterized by a predominance of containerships. 3 The Chinese fleet is relatively old and small, with a high proportion of dry cargo and bulk carriers. Greek owners are active in dry bulk markets and generally operate older vessels. In terms of the number of registered owners, Panama and Greece are the two largest countries but owners in these countries are relatively small in size with 1.5 vessels on average in Panama and 5.2 in Greece. Given the importance of the Chinese government, China is the country in which the mean fleet size of owners is the highest (16.4 vessels).

Table 1 presents some statistics on the extent of outsourcing. For 55% of the vessels in our dataset, the owner differs from the manager. This is nearly twice the proportion reported by Drewry Shipping Consultants ( 2004) in a survey that considered only a limited number of large third-party ship managers. Our analysis includes all ship managers and subsidiaries of ship-owning companies.

Insert Table 1 here

The magnitude of the outsourcing rate is significantly influenced by a vessel's characteristics. The older the vessel, the more likely it is to be managed in-house. One explanation for this finding could be the fee charged by ship managers, which represents a burden for older vessels generating lower earnings. Another finding is that the proportion of outsourced vessels is much higher for larger vessels. Furthermore, we observe significant differences across vessel types. The management of offshore, roro and tanker vessels is outsourced more often than it is for reefers and, to a lesser extent, passenger/ferry and dry cargo ships.

Figure 3 highlights the major differences in outsourcing rates by the ship-owner's country of domicile.

Shipowners from the UK and Panama outsource extensively, while those from Indonesia, Russia and Greece do not. Our results for companies based in the UK and Greece are in line with Mitroussi (2004a). A last finding is that there is a non-linear relationship between the outsourcing rate and owner size (Figure 4). On the one hand, companies with less than two vessels outsource more than companies with three to five vessels. On the other hand, the outsourcing rate is much higher among large companies.

Insert Figure 3 here Insert Figure 4 here

Econometric analysis

The determinants of outsourcing

An econometric analysis allows us to further investigate the roles played by the owners' and vessels' characteristics in determining the extent of outsourcing. We define a latent variable,

* ji DIF , which
indicates the propensity for a vessel i belonging to an owner j to be managed by a company other than the owner. As this latent variable is unobserved, let (1) where ji X is a set of explanatory variables related to both the vessels and the ship-owners, and is a vector of associated coefficients. The term j a picks up unobserved heterogeneity related to the ship-owner j and ji is a vessel-specific random term. We suppose that the perturbations are normally distributed such that 2.

Insert Table 2 here

We first control only for vessel characteristics (column 1 of Table 2). The probability of having a vessel managed by a company different than the owner depends, to a great extent, on the age of a vessel.

The profile is non-linear in this respect. Compared to the reference category of vessels less than five years old, the probability of outsourcing management is reduced by 20 points for vessels older than 35 years, while it increases by 10 points when the vessel is between 15 and 24 years of age.

Outsourcing is more likely for larger vessels, especially those between 10,000 and 50,000 gt. Our findings may be explained by the impact of the fees charged by ship managers, which are often set in proportion to operating costs and, therefore, increase with size and age. Finally, outsourcing is more likely for offshore, tanker and, to a lesser extent, dry cargo and container vessels, while the reverse pattern holds for reefer and passenger/ferry vessels.

We add the owner's country of domicile and fleet size as covariates in column 2 of Table 2. Notably, the addition of the owners' characteristics does not significantly change previous estimates on the influence of vessel characteristics. Owners registered in the UK, Panama, Norway and Germany outsource more often. Conversely, owners from Indonesia, Russia and Greece are more likely to manage vessels in-house, with the probability increasing by more than 60 points. Our econometric estimates confirm findings from [START_REF] Panayides | The vertical disintegration of ship management: choice criteria for third party selection and evaluation[END_REF], [START_REF] Mitroussi | Third party ship management: the case of separation of ownership and management in shipping context[END_REF]Mitroussi ( , 2004aMitroussi ( , 2004b) ) and Drewry Shipping Consultants ( 2004). Although outsourcing is significantly different from one country to another, our results also indicate that this is not solely the result of differences in fleet structures, as we control for age, size and type of vessels in our regressions.

A non-linear pattern between the propensity to outsource and the size of the ownership is also evident. Compared with owners of a fleet of only one or two vessels, the probability of having a vessel managed in-house increases by nearly 20% when the fleet encompasses between three and five vessels. This probability decreases as the size of the owner's fleet grows. As indicated by Mitroussi (2004b), various factors may explain this result. Smaller companies may need technical expertise, while medium-size companies may need a way of benchmarking their own management performance. Finally, the high marginal effect for larger companies is the result of the overrepresentation of container lines among firms operating more than 25 vessels, as they are characterised by higher outsourcing rates [START_REF] Panayides | The vertical disintegration of ship management: choice criteria for third party selection and evaluation[END_REF].

In Table 3, we estimate separate regressions for three types of vessels with high rates of outsourcing: container (57.6%), dry cargo/bulker (54.3%) and tanker (60.1%) vessels. Our main results are the following. First, we observe a weak correlation between the probability of outsourcing and the size of a vessel. Most coefficients for the quintile of gross tons for each vessel category are not significant.

There is no clear relationship between age and outsourcing, except for dry cargo/bulker vessels. For this category, vessels from 5 to 30 years of age are, on average, outsourced more often.

Insert Table 3 here

Second, we observe that the owner's country of domicile has a strong influence. Norwegian, Chinese, US, Panamanian and Dutch ship-owners outsource more than Greek shipowners. For dry cargo/bulker vessels, owners registered in Indonesia, Greece and South Korea manage their vessels in-house more often. In tanker markets, US and Chinese ship-owners outsource more often than owners registered in Indonesia, Turkey, Greece and Russia.

Third, mixed results emerge in relation to owner's size. On the one hand, the probability of outsourcing increases by more than 15% for dry cargo/bulker and tanker companies with more than 25 vessels, while containerships are more likely to be outsourced when the owner's fleet numbers one or two vessels. The importance of ship funds in the container business may explain the high rate of outsourcing for smaller owners without expertise and critical size.

Cross-country differences in outsourcing

As discussed previously, a ship-owner's decision to outsource the management of a vessel involves a set of characteristics related to both the vessel and the owner. Among the latter, the country of registration for a ship-owner's domicile is a decisive factor (Drewry Shipping Consultants 2004;[START_REF] Mitroussi | Third party ship management: the case of separation of ownership and management in shipping context[END_REF]Mitroussi , 2004aMitroussi , 2004b;;[START_REF] Panayides | The vertical disintegration of ship management: choice criteria for third party selection and evaluation[END_REF]. This element is the focus of this section, although the limitations related to registered ship-owners and the true nationality of owners should be kept in mind.

When considering two countries of ownership, we study whether differences in observed country outsourcing rates may be explained by either the structure of fleet by country or by other factors, such as the way companies registered in that country operate. Let us first consider the latent unobserved variable * SAME . Denoting A and B as two different countries, the difference

B B A A B A X X SAME SAME * *
may be expressed as:

) ( ) ( * * B A B A B A B A X X X SAME SAME (2)
This Oaxaca-Blinder decomposition (Oaxaca and Ranson, 1994), which is applicable for continuous dependant variables, indicates that the total difference * * B A SAME SAME may be expressed as the sum of two terms. The first,

A B A X X ) (
, is the difference in the structure of each group in terms of observable characteristics. The second,

) ( B A B X
, is the difference in the returns to the covariates. One difficulty is the fact that our dependent variable, SAME , is not continuous but discrete. We thus rely on a decomposition of the difference in probability in the first moment [START_REF] Yun | Decomposition moment in the first moment[END_REF]. Let

) ( ) ( ) ( ) ( B B A B A B A A B A X X X X P P (3)
The first term in Equation 3 reflects differences in vessels' characteristics, while the second term measures the differences from covariates. We apply these estimations to a cross-country comparison of Japan, Germany, China, Greece, USA and Norway, the six largest countries in which owners are registered. The estimates are reported in Table 4.

Insert Table 4 here

Let us first consider the case of Japan and Germany, the two largest countries in terms of shipowners with 4,003 and 3,897 vessels registered, respectively. The rates of outsourcing are 66% and 53%, respectively. The total difference in probability is, therefore, equal to 13 points. The decomposition shows that 53.8% (0.070/0.130) of this difference is due to the fact that vessels in the two countries have different characteristics, while the rest (46.2%) is explained by a country-specific effect.

A global analysis of results leads to the following conclusions. First, there are limited differences in the outsourcing rate among countries in many cases. For instance, the gap is close to zero when comparing the US and Japan, Japan and Norway, and Norway and the US. Second, the probability of outsourcing is often explained by differences in a country's fleet structure. For instance, for the US-China comparison, the difference in the outsourcing rate is 16.4%, but 93.3% of this gap stems from differences in covariates. In fact, the result is mainly explained by the number of offshore vessels operated by US owners, which is presumably influenced by US laws on maritime operations and cabotage (e.g., the Jones Act) and by the number of large ship-owners in China. This similarity in outsourcing rates is, therefore, more explained by a specialisation in different market segments than by a similarity in ship-owners' outsourcing behaviour.

Third, we observe a difference between Greek ship-owners and ship-owners from other countries.

This difference in the outsourcing rate reaches more than 50% with China. Furthermore, the component stemming from differences in the structure of the fleet is extremely low at 7.4% for Japan-Greece, 1.6% for Germany-Greece and 15.6% for China-Greece. In other words, Greek ship-owners have a lower propensity to outsource the management of their vessels, a feature mostly explained by a country-specific effect. These findings are in accordance with the previous contributions of Mitroussi (2003, 2004a, 2004b) and [START_REF] Panayides | The vertical disintegration of ship management: choice criteria for third party selection and evaluation[END_REF] on differences in the rate of outsourcing between Greek and UK shipping companies.

Conclusion

Different behaviours are evident in this analysis of ship-owners' decisions to outsource the management of a vessel. These differences are explained by characteristics related to the vessel (age, type, size) and to the owner (country of domicile and size). Such differences have been stressed in former studies and are confirmed in this paper. The novelty of our contribution is that we consider a much larger sample of data to investigate these issues although limitations arising from the composition of the LRF dataset should be kept in mind. This paper offers suggestions for further studies. The first is the need for better identification of the links between ship-owners and ship management companies, which would provide a more accurate means for comparing our estimates with former studies focusing on outsourcing to third-party ship managers. A second possibility would be to increase the number of parameters considered. Some factors, such as the history of a company [START_REF] Panayides | Professional Ship Management: Marketing and Strategy[END_REF]Mitroussi, 2004b) and the ways in which the decision to outsource changes over time, could be investigated. The latter issue is worth studying over periods during which a financial or shipping crisis is likely to affect the level of outsourcing and have an effect on company performance. This effect is likely to be magnified for companies serving global markets (Gourdin, 2006, p. 241). A final possible extension of this study would be to compare our results with the extent and forms of outsourcing observed in other industries [START_REF] Marasco | Third-party logistics: A literature review[END_REF] Results from decomposition analysis. The country of reference is in row. For instance, the outsourcing rate is 13% higher in Japan than in Germany. 7 points are explained by differences in characteristics and the 6 remaining points by differences in returns to these characteristics.

  company owns and manages the vessel, and 0 otherwise. By definition,

  j a and ji are independent, the corresponding specification is a random effect Probit model estimated using Gaussian quadrature techniques. The corresponding estimates are reported in Table

  managed by the same company in a country A and in a country B , respectively, with (.) as the univariate distribution function. After denoting the mean probabilities in each country from a Probit model as

Figure 1 .FigureFigureFigure

 1 Figure 1. Number of vessels managed and owned by the top-five managers and technical managers, 2009A. By managers 232

Table 1 . Ownership structure by vessel characteristics 2009 (45,456 vessels)

 1

	Variables		Distribution	Owner	manager
			(in %)	(in %)
	Age	0-4	27.2		56.9
		5-9	12.3		60.7
		10-14	11.9		59.4
		15-19	9.3		56.5
		20-24	9.3		55.3
		25-29	12.7		52.5
		30-34	9.2		50.2
		35 and more	8.2		39.1
	Size (gt)	1,000-4,999	38.7		47.0
		5,000-9,999	14.5		55.3
		10,000-24,999	18.3		59.5
		25,000-49,999	17.1		60.8
		50,000 and more	11.4		64.4
	Type	Bulker / combination	18.2		54.3
		Container	11.3		57.6
		Dry cargo	24.3		47.9
		Offshore	9.1		64.6
		Pass./Ferry	5.0		46.2
		Reefer	3.8		40.5
		Roro	4.4		61.5
		Tanker	23.9		60.1
	All		100.0		54.8
	Source: Author's calculation based on Lloyd's Register Fairplay -World Shipping Encyclopaedia (June 2009)

Table 2 . Probability of having a vessel with the same owner and manager, 2009

 2 Author's calculation based on Lloyd's Register Fairplay -World Shipping Encyclopaedia (June 2009) Note: Estimates from random effect Probit models. Significance levels are 1% ( *** ), 5% ( ** ) and 10% ( * ).

	Variables

Table 3 . Probability of outsourcing the management of a vessel by vessel type, 2009

 3

	Variables		(1) Container	(2) Dry cargo and bulker	(3) Tanker
			coef.	t-value	coef.	t-value	coef.	t-value
	Constant		0.247	1.20	-0.408***	-3.56	0.105	1.03
	Age	0-4	Ref		Ref		Ref
		5-9	0.064	0.68	0.187***	3.10	0.040	0.62
		10-14	0.094	0.72	0.253***	3.60	0.045	0.58
		15-19	0.023	0.16	0.218***	2.79	0.038	0.41
		20-24	0.299*	1.80	0.242***	3.15	-0.095	-1.07
		25-29	0.159	0.98	0.210***	2.87	-0.112	-1.27
		30-34	0.259	1.03	0.133*	1.69	-0.135	-1.21
		35 and more	-0.555**	-2.20	-0.064	-0.70	-0.526***	-4.57
	Size (gt)	Quintile 1	Ref		Ref		Ref
		Quintile 2	0.193*	1.74	0.146**	2.35	0.056	0.81
		Quintile 3	0.196	1.31	0.190**	2.18	0.231***	2.86
		Quintile 4	0.235	1.41	0.150	1.24	0.176	1.64
		Quintile 5	0.153	0.76	0.180	1.31	0.322***	2.75
	Owner's country Japan	0.369	1.23	0.352**	2.29	0.058	0.45
		Germany	0.005

Table 4 . Decomposition of differences in outsourcing rates, 2009

 4 Author's calculation from Lloyd's Register Fairplay -World Shipping Encyclopaedia (June 2009) Note:

	Country		Japan	Germany	China	Greece	US	Norway
	Japan	Total difference	-	0.130	-0.190	0.379	-0.026	-0.013
		Dif. in characteristics	-	0.070	-0.165	0.028	0.117	0.030
		Dif. in returns	-	0.060	-0.025	0.351	-0.143	-0.043
	Germany Total difference		-	-0.320	0.249	-0.156	-0.143
		Dif. in characteristics		-	-0.070	0.004	0.127	0.135
		Dif. in returns		-	-0.250	0.245	-0.283	-0.278
	China	Total difference			-	0.569	0.164	0.177
		Dif. in characteristics			-	0.089	0.153	0.076
		Dif. in returns			-	0.480	0.011	0.101
	Greece Total difference				-	-0.405	-0.392
		Dif. in characteristics				-	0.091	0.003
		Dif. in returns				-	-0.496	-0.395
	USA	Total difference					-	0.013
		Dif. in characteristics					-	-0.015
		Dif. in returns					-	0.028
	Norway Total difference						-
		Dif. in characteristics						-
		Dif. in returns						-
	Source:

For example, an owner with four vessels contributes four observations to the vessel sample but only one to the owner sample.

Detailed results are available upon request from authors.

This is because of the importance of German KG partnership systems, which provide tax exemptions for investments in containerships. German vessels are, therefore, relatively younger as a result of the surge in investment for these vessels in recent years[START_REF] Cariou | Liner shipping strategies: An overview[END_REF].