Rudder Torque Prediction Method considering Maneuvering Motion in Sea Trial
S. W. Lee (DSME, Korea)
Y. S. Hwang (DSME, Korea)
M. C. Ryu (DSME, Korea)
Abstract: In order to improve the accuracy of the prediction method for steering gear capacities, DSME has performed a comparison between the steering gear torque obtained during sea trial and the predicted one in the design stage. In steering gear test, one of the sea trial items, the pressure values of steering gear cylinders are recorded. And this indicated pressure can be used as indirect means of measuring the steering gear torque. The results of the comparison for 20 ships show that the measured values of steering gear torque are influenced by several factors, such as loading condition, type of vessel and rudder holding time in steering gear test. Usually, type of vessel has been considered by changing the safety factor, but the influences of other factors have not been considered properly in the design stage. Assuming that these factors have influence on the maneuverability, DSME has developed new prediction program considering these influences. Maneuvering simulation program has been used in order to calculate the rudder inflow speed and angle during the steering gear test. The rudder is turned alternatively by maximum angle to either side in steering gear test, and the rudder inflow angle is changed according to the ship motion response. For the prediction of the torque of horn rudders, Molland's modified lifting line theory was applied. The steering gear capacity may be determined more reasonably based on this new prediction method considering the maneuvering motion.
Rudder is an important factor to determine the maneuverability of ship, and steering gear is a device to enable the rudder motion. If steering gear capacity is not enough to move the rudder at some condition, ship will get to be uncontrollable. For selecting the proper steering gear, it is important to estimate the torque acting on rudder. But unfortunately, because of complicated flow at stern and uncertainty of environmental condition, it is hard to predict the accurate torque by model scale experiment or theoretical analysis. So until now, many yards including our company have used simple empirical formula like Jossel-Beaufoy with considering safety factor.
In this research, to validate the standard method of DSME for predicting the capacity of steering gear, steering gear torque predicted by empirical formula are compared with the measured values from sea trials. As steering gear torque is not measured directly in sea trial, oil pressure of steering gear cylinder is converted to torque.
We developed steering gear torque prediction program based on the Molland's modified lift line theory. Molland's method has the advantage that this method is based on the experiments and theoretical analysis of horn type rudder.
During steering gear test, rudder inflow is changed according to maneuvering motion. So we simulated the steering gear test by maneuvering simulation program and predicted the rudder inflow speed and angle.
By considering the change of rudder inflow during the steering gear test, we can conclude that the ship having bad maneuverability needs more large steering gear capacity.
2. ESTIMATION OF STEERING GEAR TORQUE BY THE SEA TRIAL RESULTS & DSME STANDARD METHOD
2.1 ESTIMATION OF STEERING GEAR TORQUE BY SEA TRIAL RESULTS
Steering gear torque in sea trial is calculated from the measured oil pressure of steering gear cylinder. Compared with measuring the torque of rudder stock with strain gauge, this method is not so accurate but simple.
The following assumptions are made to convert the oil pressure to steering gear torque.
- The converted torque from oil pressure includes hydrodynamic torque and mechanical frictional torque
- Oil pressure is proportional to the steering gear torque.
- In the case that the ship speed at steering gear test is not recorded, it is assumed that the speed at sea trial is 90% of that used in the prediction with empirical formula in full load condition and 93% in ballast condition.
- We used ratio of draft at stern and rudder height as draft correction factor. If draft at stern is greater than rudder height, we didn't apply draft correction.
- Rudder inflow speed is same with ship speed.
2.2 Comparison with DSME Standard Prediction Method
DSME have used Jossel-Beaufoy method and safety factor(DSME_FAC) described as a function of ship length.
Safety factor is calculated with the simple formula as follows.
DSME_FAC = 1.4375 for LPP ≤ 200m
DSME_FAC = 1.25x(0.0017xLPP+0.81) for 200m ≤ LPP ≤ 300m
DSME_FAC = l.653 for LPP ≥ 300m
In Fig. 1 , DSME_FAC is compared with the value calculated from dividing the measured torque by predicted one with Jossel-Beaufoy method. DSME_FAC is presented with solid line in Fig.1.
Fig.1 Distribution of Measured Torque
Sea trials of 34 ships including COT, container ship, bulk carrier, LNGC and RORO were used and excepting COT and 2 container ships, all sea trials were performed at ballast condition. And there were many cases that speed at steering gear test and draft were not recorded.
Excepting 5 COTs, all data was within DSME_FAC. And at most cases, sea trial data are within 90% of DSME_FAC. The COTs that exceed the DSME_FAC are all 98K COTs.
Though we can not sure that, as the ship's performance and environmental condition are not considered in detail, it seems that we should consider another factor affecting the rudder torque such as the maneuverability of vessels.
3. EFFECT OF MANEUVERABILITY ON RUDDER TORQUE
3.1 A Development of Numerical Program for Rudder Torque Prediction
Fig. 2 An Example View of Developed Program
Empirical formula of Jossel-Beaufoy is made from regression analyses of experimental data of all movable rudder. The pressure distribution of all movable rudder is known to be different from that of horn rudder which we adopt for commercial vessels. So safety factor has been considered, but the theoretical basis is weak.
Molland's method using lifting line theory can consider the dimensions of horn rudder and rudder inflow angle. But, it is not commented in Molland's paper how to predict the rudder inflow speed and angle.
To apply Molland's method to rudder design more easily, numerical program is developed as windows version. Fig.2 shows the structure of developed program. Rudder inflow speed and angle according to the types of vessel are simulated by maneuvering simulation program in advance and predicted values are included in the prediction program.
This program can predict the influence of rudder holding time in steering gear test to measured steering gear torque as well.
3.2 Rudder Inflow Calculation by Maneuvering Simulation Program
Though rudder inflow speed and angle is considered in Molland's method, generally we have used this method with the assumptions that the rudder inflow angle is 0 and rudder inflow velocity is same with ship speed. But by investigating the sea trials of 2 ships that we measured the steering gear torque at rudder stock with strain gauges, we could see that difference between predicted and measured torque is changed according to the rudder holding time. These results are shown in Table.1. Rudder holding time in here is time to hold the rudder when rudder angle is maximum at port or starboard, before changing the rudder angle to opposite direction.
Table 1 The Measured Torques with Strain Gauge
||13 sec./15 sec.
|Estimated Torque (by J-B Method)
With increase of rudder holding time, measured torque grew larger compared to the predicted value by Jossel-Beaufoy. We think that the change of rudder inflow angle according to rudder holding time is the cause of this.
To consider the influence of rudder holding time, steering gear test is simulated with changing the rudder holding time.
As maneuvering simulation program uses the information about the principal dimensions of hull, rudder and propeller characteristics, this steering torque prediction program is thought to consider the type of vessel.
3.2.1. Rudder Inflow Speed
Fig.3 shows the simulated rudder inflow speed of 158K COT.
Fig. 3 Simulation of Rudder Inflow Speed in Steering Gear Test
When rudder holding time is 10 sec., the change of rudder inflow speed is below 1 knots. As the maximum torque is expected to be measured when the rudder angle has changed from 35 degrees to -35 degrees, we compared the rudder inflow speed at that time with the ship speed and showed the results at Table 2. If the results of LNG Carriers are left aside, the ratios of rudder inflow speed and ship speed is about 1.
Table 2 Ratios of Rudder Inflow Speed to Ship Speed
||Rudder Inflow Vel./Ship Speed
Fig. 4 Rudder Inflow Speed Variation according to Rudder Holding Time
Fig.4 shows the changes of the rudder inflow speed of product carriers according to the rudder holding time. Rudder inflow speed does not change so much according to the rudder holding time. Simulation results of other types of ship are similar with that of product carriers, so we used ship speed as rudder inflow speed for steering gear torque prediction.