The Art of Dredging

Dredging and shipping

STPM Accuracy

This is an article in a series of three about STPM:

This article describes in detail how to estimate the total accuracy on a STPM-system, horizontal and vertical.

For the purpose of this article, we take an imaginary dredgepipe:

**L1: length upperpipe, from center suction inlet to hinge (cardan)**

**L2: length lowerpipe from hinge to heel draghead **

Accuracy of an STPM-system

The total accuracy of an STPM-system depends on:

- accuracy of signal transmission
- sensor accuracy
- accuracy of motion sensors (M.R.U., gyro)
- accuracy of the positioning system

**Signal transmission**

In order to determine the total error on the calculated position of a draghead, we also take a look at transmission of sensor-signals to the processing unit.

The signals measured by the sensors are send to the dredge computer either via galvanic separators (often as a 4-20mA. signal) or as a bit signal.

If galvanic separators are used an extra tolerance has to be taken into account for a distortion of the signal of appx. 0.1-0.2% (according buidlers' specs).

Experience of elec's on board is that tolerances of 0.1-0.2% are rather optimistic; more so when the transmitted value is in the middle of min. and max. limit of the separator.

The position of the draghead, relatively to ship's reference origin, is determined by angle measurement, horizontally (X, Y) and vertically (Z).

**Vertical position (Z)**

The vertical position of the drag head can be checked / calibrated by attaching a pressure sensor to the heel of the drag head. The depth of the drag head is directly proportional to pressure.

Limitations of thissystem:

- The relation depth – pressure is varying for different salinity, density and temperature of the seawater through the vertical water column. These parameters can have a significant influence on the correct depth calculation on larger depths. Beyond 40 metres waterdepth, this is believed to affect the accuracy of this measurement.
- Important are the correct distances of the pipes (hinge to hinge), and the offsets of pressure sensor to centreline of hull inlet, offsets in dragheads, correct angles of bend pipes in the suction pipe, etc, etc,.. all used by the dredge computer to calculate depth of the draghead.
- The depth sensor at the hull inlet has to be checked manually (with measuringtape). This is a pressure (draught) sensor, which are known to be affected by marine growth on the face of the sensor.

For measuring the vertical angles the system on board most trailer dredgers pendulum-sensors are used, with a typical accuracy of appx. 0.2° (non linearity + resolution). Check builders' specs onboard for exact accuracy values.

With the imaginary dredge configuration in mind; this means a maximal vertical error of Evert=Tan(0.2°)*L1+Tan(0.2)*L2 . In reality; this will be 0.2- 0.5 meter.

If sensors are worn (especially pendulums; which are part mechanical sensors); errors can have much larger values than this. More on that in a later article.

The signal given by the pendulumsmay be send via galvanic separators. Due to these galvanic separators an additional distortion error of 0.1% has to be taken into account (see supra). ** Tolerance** of the **vertical** measurement by pendulum sensors is then: Evert*1.01

The depth sensor at the hull inlet has an accuracy -based on experience- of no more than 10 cm (depends on manufacturer).

This has to be added to** vertical error** on the z value: Evert + 0.1m

**Horizontal position (X, Y)**

To determine the horizontal position of the drag head (referenced to the ship's origin on board), again angle measurement is used.

The calibration of these sensors is done by putting the suction pipe in its saddles. The exact position and angles of the pipe relative to the ship's origin reference are known when the dredgepipe is resting in the saddles.

The position of the drag head can also be checked by using an independent D-GPS signal (preferable with a hyper-accurate RTK signal). Problem here is find the exact location of the centre of gravity on the draghead.

Typical angle-transducers have a maximum deviation of 1‰ on 355°, or 0.355°. (Again, check the specs of your system).

When this is calculated for a fictive deepdredge pipe; the accuracy of the horizontal positioning is

Ehor=Tan(0.355°)*L1+Tan(0.355°)*L2. Errors can amount to 1m for longer dredge pipes.

The signal from the horizontal angle-tramsducer may be send via a galvanic separator. Due to these galvanic separators the additional error of 0.1% has to be taken into account. Total **horizontal tolerance** of the horizontal measurement by angle sensors is Ehor*1.01.

**Motion correction**

Once the position of the draghead is determined in relation to the ship's origin; its position in the geographical grid has to be determined.

Therefore the relation: GPS antenna – ship's origin has to be known. This relation is subjected to movement of the ship: roll, pitch, and Yaw

- Gyro - yaw

The gyro is measuring the “rotation” of the vessel around its centre of gravity. The error on this instrument is depending on the vessel’s speed, the vessel’s latitude and the heading. This so-called speed-latitude error has been discussed before on this website, here ; this table gives the error for several cases.

Take e.g. latitude 55° at 4knt, on a northerly course, as input in this table. This gives an accuracy on the gyro of 0.4°. To calculate the error, the distance between the draghead and the ship's origin reference line (x-axis) has to be known (L3) .

So the **gyro error for sailing at 4 knt is: Egyro=tan(0.4**°)***L3 ; **an error of appx. 20 cm.

- Motion Reference Unit (MRU) - roll & pitch

Roll and pitch can be derived from draught sensors. However, when the ship is sailing; flow and pressure patterns underneath the sensors cause significant errors, which increase with sailing speed.

Therefore, if accuracy is paramount, only dedicated moton sensors (MRU’s) are used for the roll and pitch correction.

Typical dynamic accuracy of an off-the-shelf MRU on roll and pitch is 0.15° RMS and 4% scaling factor. Again, to get an impression what this means for the accuracy of the draghead the distance GPS antenna – node has to be known.

Maximum erros for roll and pitch are calculated in the same manner as for yaw (gyro, see above). For large ships, this may amount to 10 cm roll error, ad 10 cm pitch error.

Since MRU-sensors may be prone to a time delay, these errors may be larger.

- GPS system

Some D-GPS systems have an accuracy of 0.1 meter, others go with 2-3 metres.

All the movements occur at the same time their errors might enlarge or reduce the total error on the positioning. The above has not the intention to give exact figures on the position error of the draghead, but rather to give an indication of scale.

**Deepdredge pipe of "Leiv Eiriksson" **

Marc Van de Velde,

all kudos to Ruben Duyver, operational superintendant "Leiv Eiriksson"

august 2011

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