WO2012010158A1

WO2012010158A1 - Method and arrangement for reducing the water friction on water vehicles

Info

Publication number: WO2012010158A1
Application number: PCT/DE2011/001470
Authority: WO
Inventors: Klaus Lindemann
Original assignee: Klaus Lindemann
Priority date: 2010-07-21
Filing date: 2011-07-18
Publication date: 2012-01-26
Also published as: CN102958794A; PL402521A1; DE102010044866A1

Abstract

The invention relates to a method and arrangement for reducing the driving resistance of floating water vehicles having flat underbodies by using a gas layer located under said flat underbodies. Said water vehicles are used in inland water transportation and sea transportation. The aim is to achieve the most uniform possible distribution of the gas layer or air layer under the underbody of the water vehicle, to minimize gas losses, and to smooth the water flow under the gas layer for the purpose of reducing resistance. The proposed solution is to perform at least one first water level measurement L1, L2, or L4 in the front region and at least one second water level measurement L3 in the rear region in at least one chamber (5). The obtained measurement signals are automatically compared and, depending on the determined comparison result, a) the liquid filling level in at least one trimming tank (12) is controlled in such a way that at least the inclination of the water vehicle about the pitch axis is controlled and/or b) at least one underwater wing (15) fastened to the water vehicle or parts of said underwater wing are automatically positioned in such a way that the inclination of the water vehicle at least about the pitch axis is controlled.

Description

Method and arrangement for reducing water friction on vessels

The invention relates to a method for reducing the driving resistance of floating vessels of inland and marine navigation with shallow subsoil by using an underlying gas layer to reduce friction and a suitable arrangement for carrying out the method.

Bistang the driving resistance is reduced in practice only by better shaping of the vessels. The introduction of gas, preferably air, between subsoil and water is already known.

In DE 10 2004 024 343 A1, a method is described in which air is injected at the bow just below the water surface and flows with the flow of water under the ship. However, it is so large amounts of air needed that the blowing already consumes about 40 kW of power according to the described practical test. Added to this is the energy output for pushing down the air volumes under the ship's bottom, which originate from the wake flow and ultimately have to be generated by the propeller.

Known is a device (DE 199 33 942 A1), which should hold air under the subfloor 1 of ships. If no further action is taken, however, significant air losses are to be expected here that would have to be constantly replaced.

The arrangement of microcompartments, as described in US Pat. No. 5,054,412 A and GB 1,300,132 A, leads, according to information in DE 693 09 655 T2, to problems with air retention. The invention has for its object to provide a method for reducing the driving resistance of floating watercraft, with which it is possible to distribute the gas or air layer below the underbody of the watercraft as evenly as possible to minimize gas losses and water flow below the gas layer in order to smooth resistance.

Furthermore, a suitable arrangement for carrying out the method is to be created.

According to the invention the object is achieved by the features specified in claim 1. Advantageous developments of the procedure are given in claims 2 to 10. An arrangement for carrying out the method is subject matter of claim 11. Preferred embodiments of the arrangement are specified in claims 12 to 18.

Along the longitudinal sides of the vessel and centrally in the longitudinal direction of the underside of the hull downstanding walls or bulges are attached, are formed by the at least two chambers in the gas to form a Gas layer between the bottom of the vessel and underlying water is introduced. The space for the gas layer can be circumscribed as a preferred variant.

In a chamber at least a first water level measurement in the front and at least a second water level measurement are made in the rear area.

The received measurement signals are automatically compared.

Depending on the determined comparison result of Ffüssigkeitsfüllstand is controlled in at least one trim container so that at least the inclination of the vessel is controlled about the pitch axis. In addition or alternatively, depending on the comparison of the measurement results, at least one underwater wing fastened to the vessel can be automatically set so that the inclination of the vessel about the pitch axis is regulated. If necessary, only parts of the underwater wing can be adjusted. The two measures can be used individually or in combination. The adjustment of underwater wings is preferably used, in particular to solve the regulation of pitch tilt for ships on the sea with significant swell, where the regulation with the help of trim tanks alone is too slow. In the case of inland vessels, if the oscillation around the pitch axis is too great, this solution is also possible.

Generally, in this patent application, tilting means the angle or spatial position of the vessel relative to the water surface in the chambers below the gas layer below the vessel.

In order to achieve the objectives, little driving resistance with little gas loss, the water level below the vessel should be set at all points largely uniformly to a certain extent above the lower limit of the overall construction. The water level can be controlled individually according to claim 3 via the control of the gas supply for each chamber. To realize the above-mentioned largely uniform adjustment of the water level, the regulation of the inclination about the longitudinal axis (hereinafter called lateral inclination) is necessary. This can be done according to claim 4: From two level measurements <L1, L2) in a chamber on about the same longitudinal coordinate, the lateral inclination is determined and consequently a) by automatic control (by means of pumps) of the level of trim containers and / or b) by autom. Adjustment of underwater wings attached to the vessel regulates the lateral inclination. The underwater wings are preferably used in marine vessels. Since the regulation of the lateral inclination with respect to the angle of inclination must work much less precisely than that of the pitch, it is also possible to use the measurement results for the control of the trim container and / or the underwater wing for the Regulation of the sides must work, it is also possible the measurement results that are relevant for the control of the trim tank and / or the underwater wing for the regulation of lateral tilt, not directly from the level measurements, but indirectly with the advantage of an automatic solder to win.

At least the pitch angle of vessels should always be regulated automatically in normal operation directly by measuring the water levels. A lot would not be suitable because of the often changing influences (on river direction of travel and gradient, on sea swell of the sea and large accuracy requirements).

By means of the features mentioned in claims 5, 6, 7 a uniform distribution of the gas below the subfloor should be solved for the case when the regulation of the inclination does not work sufficiently. This is the case when the sea is too rough. The counter-hitting the water against the subfloor or the plates with holes can not be prevented so that, however, formed in a very short time thereafter again a gas layer to reduce friction. Also possible is the retrofitting of a ship with plates with holes. According to claim 7, an alternative embodiment for the most economical consumption of gas or air is proposed, which is mainly intended for ships with a larger draft.

The claims 8, 9,10 relate only to watercraft whose gas layer is bounded all around sideways, that is, the chambers are limited in the direction of travel front and rear transverse to the direction of bulges to keep the gas losses as low as possible and a relatively thick gas layer enable.

The proposed in claim 8 embodiment with a spoiler edge 3 is intended to smooth the water surface in the chambers and keep as horizontal as possible.

The measures according to claim 9 are intended to limit the gas loss, if the water surface below the watercraft is too restless.

The mentioned in claim 10 conductivity measurement for gas or water allows a water level measurement in the chambers with relatively little cost and good robustness during operation.

Since the electrodes are in rapid contact with air and water and the insulation between the electrodes can be constantly wet, it is necessary to program from which current / voltage ratio and timing a switching pulse should occur.

The electrodes should be arranged so that they are as protected as possible from mechanical damage. The invention will be explained below with reference to exemplary embodiments. In the accompanying drawing show:

1 shows a longitudinal section through a watercraft according to the invention (here as an example a pram),

2 shows a cross section along the line A-A in Fig. 1,

3 partial cross section A-A through the pram with another embodiment of the side wall 7,

4, the bottom view of the Prahms of FIG. 1, in a reduced scale,

5 shows a second embodiment (a sea ship) as a bottom view,

6 is a longitudinal section along the center in Fig. 5,

7 is a section along the line B-B in Fig. 6,

Fig. 8 is a section along the line C-C in Fig. 7 and

9 is a partial longitudinal section of the rear chamber. 5

In the figures 1 to 4 (Embodiment 1) a prawn is shown, which is preferably used in inland navigation. By the arrow marked F in Fig. 1, the power of the pusher ship is to be indicated.

In the following example, the programming of a complete inclination and water level control using the switching points for a barge of inland shipping is to be shown (see Fig. 1 to 4).

The side walls 7 protrude from the bottom 1 of the pram 90 mm down. The target water level 4 is measured from the lower limit of the side walls 7 and is 40 mm. The spoiler edge 3 in the bow area is 30 mm, the Querwulst 8 in the rear area protrudes to 20 mm above the lower limit of the side walls 7. The chambers 5 are on the example watercraft type Elbprahm together about 8.1 m wide and 55 m long with 65 m total length of the watercraft.

The water level measurements L1 to L4 can work with electrical conductivity measurement, sound or float and be attached to the downstanding side walls 7. They continuously supply electrical signals, which are processed centrally. Because of troubled water surface 4 below the watercraft, an average value is automatically formed from the signals of the last 10 seconds, for example, so that unnecessary switching operations are avoided.

For a description of the operation (switching rules):

- Regulation of the pitch inclination of the pram:

If the water levels L1> (L3 + 5 mm), then the pumps P1 and P2 are turned on. If the water levels L1 <(L3 - 5 mm), then the pump P3 is turned on.

If the water levels L1 = L3, then a shutdown of the power supply for the pumps takes place from the side of the pitch control,

The pumps P1 and P2 are each supplied in parallel by the regulation of the pitch and the regulation of the lateral inclination with electricity, so that, for example, the pump P2 despite the above shutdown can continue to promote until the control of the lateral inclination of the barge has completed its task ,

- Regulation of side tilt of the pram:

If the water levels L1> (L2 + 5 mm), then the pump P1 is turned on.

If the water levels L1 <(L2 - 5 mm), then the pump P2 is turned on.

If the water levels L1 = L2, then the shutdown of the power supply for the pumps takes place from the side tilt control.

- Regulation of the water levels of the chambers 5:

If the water level L2> (L2 should + 5 mm), then the fan 9 is turned on and the associated valve 10 is opened.

If the water level L4> (L4soll + 5 mm), then the fan 9 is turned on and the associated valve 10 is opened.

When the water levels L2 or L4 are equal to or lower than their target values, the associated valve 10 is closed, and when L2 and L4 are equal to or smaller than their target values, the blower 9 is turned off.

Function of the equipment for the regulations:

The blower (centrifugal blower) 9 pushes about 40 l / s through two parallel check valves 11 and magnet-operated valves 10 DN 40 into the respective chambers 5. At 1.5 m immersion depth of the blast and 70% efficiency is the electric power for the blower 9 about 1 kW. The inflation of the half full chambers 5 would then take about 280 s.

As well as the fan 9 are also equipment for the tilt control in the bow of the Prahms. On each side is a trim tank 12 with about 4 m ³ volume, respiratory line 13 and pump P1 or P2 (centrifugal pump). Pumps P1 and P2 deliver about 4 to 5 l / s each, require about 200 W of electrical power each and can also be traversed backwards. The pump P3 is also a centrifugal pump, but with a flatter characteristic and 4 to 8 l / s capacity at about 250 W electrical power. All pumps should do without sliding seals.

The entire pipe system with a nominal nominal diameter of 50 mm should be as maintenance-free as possible. Therefore, except for manual shut-off valve 1 (DN 65 to 80) in front of pump P3, only one automatic air valve E with liquid barrier in the pipe system is available. The valve E ensures that the water flow breaks off quickly as soon as a pump is switched off.

If a closed one is desired instead of the described open, circulating water tilt control system, two additional trim tanks of the same size must be installed in the back of the barge. In total, then four pumps and in addition about 55 m pipe with gradient necessary, which can cause greater difficulties especially when retrofitting a Prahms.

Problems with loading the barge:

The discharge and loading takes place in the example without air layer 2 below the prawn. As a result, it is relatively stable in the water despite massive disruptions. The deflation of the air layer 2 can be done by two small, not shown in the drawings valves, or if the draining does not have to go fast, by an intended leak of Rückschiagklappen 11. In Prahm an exact Lot to be installed, the display image comes, for example by means of a video camera on a screen to the loadmaster. At the end of the loading, it should reduce the inclination of the barge around the pitch axis to less than 1: 1000 and around the longitudinal axis less than 1: 250. This can then be compensated by the 2 x 4000 I capacity of the trim container 2 in the example.

The further reduction of the inclination can be effected by remote control of the pumps P1, P2, P3, taking into account the solder or by starting the complete control described in the aforementioned section "Schaltregeln." This automatic control of the Ntckneigung can be more harmonic, if, for example programmed a timing for 10 minutes from the start of the program, which regularly interrupts the air flow for both chambers 5 and thus significantly reduces the average air flow.The tilt control would have reached its target range in less than 10 minutes.

The following embodiment 2 refers to a fast in-line container inboard vessel equipped with underwater wings. When the ship makes such pitch oscillations that too much air escapes from the gas layer 2, an underwater wing 15 is to be mounted behind the propulsion propeller and rudder, similar to that shown in Figs. 5 and 6 for a marine vessel. The angle of attack of the underwater wing 15 is automatically adjusted so that it counteracts the slow pitch tilt oscillations which are detected with the aid of the water level measurements L.

The wing 15 extends 1, 5 m horizontally, is stored at the ends and in the middle, an average of 30 mm thick and 250 mm wide and is to generate at 8 m / s flow velocity up to 6 kN up and down.

If the water surface 4 in the chambers 5 is so restless, for example due to turbulence, that too much air should escape under the rear transverse bead 8, the water flow is calmed by deflecting the water particles 23 about a flow profile 20 in the horizontal direction (see FIG. 9). The airfoil 20 is 20 mm thick, 150 mm wide and extends over the entire width of the rear region of the chambers 5. To avoid damage due to collision with hard water bottom, the airfoil 20 should be pivotally mounted on the subfloor 1. If necessary, it should be pressed down by spring force against a firm stop.

Assessment of benefits / expenses and application variants (inland navigation)

In the present example of the cream (embodiment 1), the cost of materials for a subsequent equipment of an existing Prahms is estimated to be up to 3 t at about 170 1 Prahmleermasse. The proportion of the area surrounded by water, which is no longer supplied with water after being equipped with the air layer system, is about 69% at an average immersion depth of 1.3 m.

Even when retrofitting, for example, a container ship with more than 1000 1 total mass, the cost of materials is estimated at 6 t relatively low.

For newbuilds of the same size and driving speed, a small additional expenditure for the hull compared to the installation of only about half as strong engine compared to the current type of ship without air layer. 2

Therefore, the construction of such a ship would hardly be more expensive than that of a conventional equal transport performance.

Generally brings the gas or air layer 2 in addition to the strong reduction in water friction on the underbody 1 and less pressure difference bow / stern, thus less wave formation and characteristic impedance. Since the water seeks the path of least resistance, the flow velocity at the fuselage sidewalls should be ken, when she gets under the hull. The propeller must, to push less, the water jet also give less speed.

It is only the vehicles with the system to be retrofitted or rebuilt, which are used for many hours on long distances. Also normal cargo motor ships or fast ships for the trailer traffic (for example on Danube, width 22.8 m, draft to 1, 5 m, 114 m long, travel speed 20 km / h, 1800 kW) as well as fast flat passenger ships are suitable. For the above Danube ship, the energy savings could be up to 50%.

Below are to be explained in a further embodiment 3, with reference to Figures 5, 6, 7 and 8, advantageous embodiments for a marine vessel. A marine ship that has been in operation for a long time is to be retrofitted. The requirements are much higher because of the sea waves than in inland navigation, however, the potential energy savings is also greater because of the greater cruising speed and driving power. As an example, a Baltic ferry type 321 Mukran built until 1990, dimensions: length 190 m, width 26 m, draft 6.8 m, engine power 10600 kW, driving speed 31, 5 km / h (from youth + technology 10/1986). Retrofit parts: The side walls 7 protrude 1 m from the bottom 1 of the ship down. The chambers 5 are 120 m long and allow about 42% of the area around the water to be separated from the water.

The pitch angle is regulated by means of trim tanks 12 in the stern of the ship as an open system with pump. The lateral inclination is controlled by means of two trim tanks 12 connected by pipes and two pumps. The volume of the trim tanks 12 is at least so large that normal inaccuracies in the loading of the ship can be compensated. The normal nominal value of the water level 4 should be at 0.5 m, with calm sea less, with restless more. The gas is supplied through the later to be described plates 16 with holes, as well as the water level measurements. The bulges 8 front with spoiler lip 3 and rear without cross according to the shape of the ship, the water flow in part at an acute angle. They protrude down to about 0.4 m above the lower limit of the side walls 7 down. Despite constructive differences, the inclination control works analogously as described above for the Prahm in the above section "switching rules" described.

In significant waves, the regulation of lateral tilt is supported by the automatic rapid adjustment of the angle of attack of each laterally extendable from the hull underwater wings 15 and the regulation of pitch tilt by underwater wing 15 at the stern of the ship. The lateral underwater wings 5 are on average 200 mm thick, 6 m long and are supposed to generate about 300 kN vertical force. According to estimation, you need 43 kW drive power at zero angle of attack. This is likely to rise briefly at 300 kN vertical force to about 400 kW. For the control process, the measured values of the water level 4, as already described above, are averaged over the time axis. The rules of pitch and roll can work separately. They work with the goal deviation zero, the angle of attack of the underwater wing 15 should counteract especially the pitch and roll side movements of the hull.

In case of stronger swell, it is to be expected that the water in the chambers 5 strikes against the ship's bottom 1 from below and rubs. To avoid this to a large extent, 1 plates 16 are provided with holes in the sense of claim 5 below the subfloor. In the example case, the flat subfloor 1 of the ship (see FIGS. 5 to 8) is thermally glued at least within the chambers 5 with cassettes that are open at the top. These then each form gas chambers of 2 m in length, 1 m in width, 0.05 m in height and also extending mainly transversely to the direction Gasverteilkanäle 17 (see Fig. 7 and 8). To stabilize the cassettes or plates 16 are also provided with support elements 18, which are also glued to the subfloor 1.

Because of the small pressure difference between Gasverteilkanal 7 and environment of only about 10 kPa and low tightness requirements, the valve 19 can be realized in the form of a space and cost-saving grid slide with hydraulic or pneumatic drive. For repairs, the thermal bond can be solved again.

The measurements of the water level 4, which are necessary for the control of the valves 19, should work on the principle of sound reflection or conductivity. The measured values do not need to be averaged over the period of time for further use according to claim 7, but can be used directly for the control of the valves 19 directly. When using two differently sized grid slides 19 per cassette, a 3 - stage gas flow graduation is possible, if required, even if pneumatic actuators are used (only open).

The gas is forced down through the 2 mm thick stainless steel plates 16 through 2 mm diameter holes spaced 20 mm apart at about 5 kPa pressure difference. If, in the example, 2.4 m / s of air from a fan is required by the outside air, a blower drive power of about 274 kW is required here. To save power, especially for ships with a greater draft, in certain areas of the ship's underbody 1 (especially behind and laterally behind) in the cassettes can also be an additional Luftsammeikanal. Its armature opens for air return if the water level 4 is a maximum mum value falls below. This means that a part of the 2.4 nfVs air flows in a circle with the help of about 10 kPa fan differential pressure. It will be redistributed under the ship. In principle, the use of engine exhaust gases instead of air is possible. However, the problem of soot and water separation must be taken into account. For example, military speedboats appear as retrofit and new construction variant as favorable application areas for the variant engine exhaust.

As further applications, for the proposed solution, in addition to ferries on side seas for vehicles and passengers and fast container ships are interesting.

Claims

claims

1. A method for reducing the driving resistance of floating watercraft with attached to the underbody (1) along the direction of travel downstanding walls (7) or bulges formed by the at least two downwardly open chambers (5), preferably in the direction of travel forward and behind are bounded by bulges, wherein in the chambers (5) gas for forming a gas layer (2) between the bottom (1) of the vessel and underlying water is introduced, characterized in that in at least one chamber (5) at least a first water level measurement (L1, L2 or L4) in the front and at least a second water level measurement (L3) is carried out in the rear, the received measurement signals are compared automatically and depending on the determined comparison result

a) the liquid level in at least one trim tank (12) is controlled so that at least the inclination of the watercraft is controlled about the pitch axis, and / or

b) at least one underwater wing (15) attached to the vessel or parts thereof are automatically placed so that the inclination of the vessel is controlled at least about the pitch axis.

2. The method according to claim 1, characterized in that the regulation of the inclination of the vessel about the pitch axis takes place so that the gas layer (2) between the bottom (1) of the vessel and the underlying water is evenly distributed.

3. The method according to any one of claims 1 or 2, characterized in that in each of the chambers (5) a water level measurement (L1, L2, L3 or L4) is made, the measurement signal is automatically used to the water level in each chamber individually regulate by gas via a valve (10) is introduced into the corresponding chamber (5).

4. The method according to any one of claims 1 to 3, characterized in that in at least one chamber (5) at least two water level measurements (L1, L2) are made, from the automatic comparison of the measurement signals of the two water level measurements (L1, L2) the inclination of the vessel is detected around the longitudinal axis and as a result a) the levels of at least two trim containers (12) are controlled so that the inclination of the vessel is automatically controlled about the longitudinal axis and / or

b) at least one underwater wing (15) attached to the vessel or parts thereof are automatically placed so as to control the inclination of the vessel about the longitudinal axis.

5. The method according to any one of claims 1 to 4, characterized in that under the underbody (1) at least one horizontal plate (16) is arranged with holes through which gas to form a gas layer down, in the direction of water, is passed.

6. The method according to any one of claims 1 to 4, characterized in that the subfloor (1) is provided with holes through which gas to form a gas layer (2) down, in the direction of water, is passed.

7. The method according to claim 5 or 6, characterized in that the space above the plate (16) or the subfloor (1) is divided into separate departments, in which in the application in each case at least one valve (19) gas is supplied, wherein for each department at least one water level measurement is made, the measuring signals for the automatic control of the valve (19) are decisive, with the aim of the below the subfloor (1) or the plates (16) flowing water as constantly and comprehensively at a distance from the Keep plates (16) or the underbody (1).

8. The method according to any one of claims 1 to 7, characterized in that the gas layer (2) is bounded all around sideways, wherein the front in the direction of travel boundary of the chambers (5) equipped transversely to the water flow at least with a trailing edge (3) for the water flow is to smooth the water flow.

9. The method and arrangement according to one of claims 1 to 8, characterized in that in the chambers (5) transversely to the direction of travel at least one airfoil (20) is arranged so that the vertical water movements of the running water flow below the subfloor (1) are reduced ,

10. The method according to any one of claims 1 to 10, characterized in that in the chambers (5), the measurement of the water level (4) by measuring the electrical conductivity of the medium between at least two electrodes.

11. Arrangement for carrying out the method according to one of the preceding claims, characterized in that arranged on the underbody of the vessel at least along the longitudinal sides of downstanding walls (7) or bulges, wherein the bounded space is divided into at least two chambers (5), into which gas can be introduced between the underbody (1) and the water underneath to form a gas layer (2), and in at least one chamber (5) at least in the front region a first means (L1, L2 or L4) for measuring the water level and in the rear At least a second means for measuring the water level (L3) is arranged, which are connected to a unit for automatically comparing the measurement signals, a control and regulating unit and at least one actuator for changing the liquid level in at least one trim container (2) at least for controlling the inclination of the vessel about the pitch axis and / or at least on the vessel an underwater wing (15) is arranged, wherein at least one actuator of the underwater wing (5) for controlling the inclination of the vessel about the pitch axis via the control and regulation unit is connected to the unit for automatic comparison of the measurement signals.

12. The arrangement according to claim 11, characterized in that in each of the chambers (5), a means (L1, L2, L3 or L4) is arranged for measuring the water level, via which the water level in each chamber (5) is individually controlled by means of a fitting (10) via the gas in the corresponding chamber (5) can be introduced.

13. Arrangement according to one of claims 11 or 12, characterized in that in at least one chamber (5) at least two means (L1, L2) are arranged for water level measurements, which are connected to a unit for automatic comparison of the obtained measurement signals of the water level measurements, and a control and regulating unit, which is connected via at least one actuator with at least two trim containers (12) over the levels of the inclination of the watercraft about the longitudinal axis is automatically controlled.

14. Arrangement according to one of claims 11 to 13, characterized in that under the underbody (1) of the vessel at least one horizontal plate (16) is arranged with holes through which gas for forming a gas layer (2) can be fed.

15. Arrangement according to one of claims 1 1 to 13, characterized in that the underbody (1) of the watercraft is provided with holes through which gas for forming a gas layer (2) can be introduced.

16. Arrangement according to one of claims 14 or 15, characterized in that the space above the plate (16) or the subfloor (1) is divided into separate departments, in which in the application in each case at least one valve (19) gas can be fed , wherein each department is associated with at least one means for measuring the water level, which is connected to a control unit for automatic control of the gas fitting (19).

17. Arrangement according to one of claims 11 to 16, characterized in that the gas layer (2) receiving space on the underbody (1) of the vessel is bounded by walls and / or bulges all around sideways, wherein the front in the direction of travel boundary of the chambers (5 ) is equipped transversely to the water flow at least with a tear-off edge (3) for the water flow.

18. Arrangement according to one of claims 11 to 17, characterized in that in the chambers (5) transversely to the direction of travel at least one flow profile (20) for reducing the vertical water movements of the driving water flow below the subfloor (1) is arranged.