Tank Testing
Tank testing is the traditional method of predicting the performance of vessels. Since it is far too expensive to build full-size ships to test different hull forms, models are built for testing instead. Please visit my Naval Architecture Primer for information on resistance for more understanding on the importance of scaling and other factors.
Model Preparation
The tank used in testing the Mk II Navy 44 STC was the 120 ft tow tank located in USNA's Hydromechanics Laboratory. The towing rig on the 120 ft tank required extensive preparation. The attitude of the model needed to be set in almost any condition of heel, yaw angle, trim, heave, and rudder angle (Figure 1).
Fig. 1 : Degrees of freedom in model testing
The requirements on the rig were:
- Infinitely adjustable in yaw from 0 to 10 degrees. Yaw is the angle at which the bow points when traveling through the water.
- Infinitely adjustable in heel from 0 to 35 degrees (or deck submersion). Heel is the angle at which the boat rolls around the longitudinal axis of the boat.
- Infinitely adjustable in rudder angle from 0 to 10 degrees.
- Infinitely adjustable in initial trim until deck submersion. Trim is an angular measurement of how either the bow or stern is submerged relative to a lateral axis through midships.
- Free to trim.
- Free to heave. Heave is the vertical movement of the entire boat into or out of the water.
Because of the forces and attitudes specific to sailing craft, more instrumentation than just drag was needed. For the Navy 44, the recorded data included:
- Drag parallel to motion of travel
- Lift perpendicular to motion of travel
- Yawing moment
- True speed
- Degrees of change in trim
The model was received from the USNA Model Shop built to the lines supplied by Pedrick Yacht Design. The model was measured and put to a position of 0 degrees heel and trim to find midships and the centerline. A small aluminum plate was mounted to be flat at this baseline upright condition. Lines of centerline and midships were etched into the plate. A bulkhead was installed in the model a few inches forward of midships. Attached to the aft side of the bulkhead were two aluminum plates which could be adjusted so that the model was set in a position of heel. Forward of the aft plate was a cylinder of bearings which housed the heave post and left the model free to trim (Figure 2).
Fig. 2 : Bulkhead and heave post
A pin was attached to the transom on centerline. This connected to a stiff carbon fiber rod which could be extended and was itself connected to the tow rig. The rod allowed the model to be set in a yawed position (Figure 3).
Fig. 3 : Yaw Adjuster
A 4" tiller was attached to the rudderpost. At the end of the rudder was a pin which connected to an electronic caliper. The other end of the caliper was pinned to the hull. The caliper allowed for extremely precise measurements in rudder angle (Figure 4).
Fig. 4 : Rudder Adjuster
Next, three force blocks and two inclinometers were calibrated. Force blocks measured resistance in the direction of travel (drag), lift perpendicular to motion at the heave post (fwd-lift), and lift perpendicular to motion at the aft pin (aft-lift). The directions of these forces are shown in Figure 5. Inclinometers would measure change in trim and heel. The aft-lift block would be used to measure the longitudinal (yawing) moment. All force blocks were calibrated using standard weights up to twice the expected loads. The inclinometers were calibrated using a stand-alone electronic inclinometer on an adjustable surface. Both inclinometers were calibrated to their rated maximum incline.
Fig. 5 : Schematic indicating measured forces
The drag and lift force blocks were both rated to a 25 lb capacity. This was to minimize the effect of cross-moments interfering with the force acquisition. The aft-lift block did not have any interfering moments and was rated at 5 lbs. In the calibration for all force blocks, the maximum linear deviation was 0.116% on the 5 lb aft-lift block. This corresponded to a standard deviation of 0.0037 lbs, which was considered very acceptable.
The heave post was attached to the drag block, mounted underneath the lift block, and finally secured to a square aluminum beam on the carriage. The aft-lift block was mounted to an "L"-shaped beam, which was clamped onto the after end of the carriage. The inclinometers were mounted to the aluminum plate inside the model. The speed of the carriage had been previously calibrated and was measured at the motor's gears.
After the inclinometers were added, the model was weighed and trimming weights were added in order to scale the model geometrically. Placing the model in the water, the weights were moved so that the model had no trim. The position of these weights marked 0-degrees of trim, and a ruler was drawn on the centerline to measure the trimming arm induced by the weights. Figure 6 shows the final model setup:
Fig. 6 : Model ready for testing
All force blocks and inclinometers had wires which ran to two amplifiers mounted on the tow rig (Figure 7). The data then ran from the amplifiers to an analog-digital converter and finally through a USB connection to a PC. Before gage calibrations, the amplifier was set to return values in the linear region of output.
Fig. 7 : Amplifiers mounted on the tow rig
The final stage in testing was to find the position of 0 degrees of yaw. The model was attached to the rig without the rudder and with 0-degrees heel and trim. The model was then run down the tank a minimum of four times where each trial varied by yaw. Model speed was held at a constant 3.2 ft/s. This speed was to ensure typical flow conditions across the appendages, but with minimal wavemaking interference. Plots were constructed of inches of yaw adjustment versus pounds of side force. The position of 0 degrees of yaw was marked at the point of no side force.
Next the rudder was added, and the process of finding 0 degrees of rudder was identical to the above process, except the rudder angle was adjusted vice yaw. Again, the point of no side force marked the position of 0 degrees of rudder. This position of 0-rudder, 0-yaw, 0-trim, and 0-heel was considered the standard upright condition.
The typical standard deviation in calibrating the yaw and rudder angles was 0.019 lbs as measured by both lift blocks. These calibrations were checked every time the model was taken out of the water, which was at least after every day of testing.
Tank Tests
There were three parts of tank testing:
- Unstimulated Upright Conditions
- Stimulated Upright Conditions
- Stimulated Sailing Conditions
The goal of unstimulated testing was to find a baseline for the evaluation of the later-added turbulence stimulators.
Stimulators were added to the model to try to create turbulent flow condition around the model. These stimulators were placed at a position to trip the flow where turbulent flow would begin on the ship. Details of these stimulators are discussed in the "Stimulated Upright Condition" section. Additional stimulators were added after all other testing was completed in order to factor out the added resistance due to the stimulators.
The stimulated upright condition provided results which represent the motoring condition of the vessel. The upright resistance of a vessel is also typically used to judge its overall resistance against other vessels. In the upright condition, heel angle, yaw angle, and rudder angle were all set at zero degrees. The vessel was trimmed to its designated waterline and was left free to trim and heave while at speed due to hydrodynamic forces.
Stimulated sailing conditions allowed for calculations of the vessel at different attitudes. For sailing conditions, the vessel had a set heel angle, yaw angle, rudder angle, and trim angle. The heel, yaw, and rudder angles were set initially from a chosen matrix. Trim angle was set through trim weights which approximate the aerodynamic trimming moment. This trimming moment was determined experimentally through an initial run for each condition and equaled the countering measured hydrodynamic trimming moment. The model was free to heave in the sailing condition.
Upright Unstimulated Tests
The unstimulated testing was conducted at the standard upright condition. The coefficient of total resistance is shown in Figure 8. The generated curve maintained coherency above Rn=400,000 signaling turbulent flow. Below Rn=400,000, there was significant disorder in the resistance curve, showing that the flow condition was moving from laminar through the transition zone.
Fig. 8 : Drag in upright unstimulated flow
Upright Stimulated Tests
After the unstimulated flow testing was completed, sand strips were applied to the hull to act as turbulent stimulators. Sand strips were placed on the hull 1" aft of the stem and on the keel and rudder at 25% of their chords’ girth. A grain size of 0.5mm to 1.0mm was used and at a width of a 0.25". The grain size was chosen to be as large as the laminar boundary layer in order to disrupt the flow sufficiently. This disturbed boundary layer should change from laminar to turbulent flow. The upright stimulated testing was conducted at the standard condition.
Fig. 9 : Drag in upright conditions
The results of both unstimulated and stimulated conditions are shown in Figure 9. The stimulated condition showed a uniform increase in total resistance. The added resistance was from the friction caused by the sand strips and also indicated that the flow condition did not substantially change at Rn > 400,000. The meaning of this was that it was considered safe to assume ship-like turbulent flow above Rn = 400,000. Stimulated tests performed below Rn=400,000 showed that the fluid flow was still in the transition zone on at least some part of the vessel.
Additional sand strips were added to the model to calculate the added friction from the strips. The first set of additional strips doubled the width of the previous strips and was located aft of and adjacent to the previous strips. The second set of strips brought the width up to three times the width of the original strips. The third set of strips was aft of and adjacent to the secondary strips. Testing of the strips populated only the lower Reynolds number conditions since the strips were used only for Prohaska analysis of the data.
Fig. 10 : Drag in the upright conditions with additional sand strips
Again, the additional sand strips show a general increase in resistance Figure 10. The trend in the resistance curve was maintained after Rn = 300,000. Below Rn = 300,000, separation between the second and third sand strip increased. This showed the presence of laminar flow even with the extra turbulence stimulators. Because of this, results below Rn = 300,000 with additional sand strips were questionable.
Stimulated Sailing Tests
The sailing conditions were estimated from attitudes and conditions predicted by the PCSail VPP. This matrix varied by speed, heel angle, yaw angle, and rudder angle.
PCSail was run at true wind speeds of 6, 12, 18, and 24 knots and at 40, 60, 90, 120, and 170 degrees to the wind. The VPP determined the values of boat speed and heel angle for each of these 20 conditions. The values of speed and heel are shown in Figure 11.
Fig. 11 : Sailing tests matrix
The points picked for positions of speed and heel were near to the VPP's prediction. These points were picked so that the true sailing conditions could be interpolated from the matrix once the testing had concluded. Furthermore, the speed of the carriage could be set only approximately at its input dial. Therefore, the desired speed of each test differed slightly from the resulting speed of the carriage.
Each sailing test had a predicted yaw and rudder angle from calculations added to the PCSail VPP. However, as the sailing testing was conducted at first in unstimulated flow, it was found that the aft-lift block was recording negative forces on the model which was opposite of the predicted aerodynamic force. The modifications to the PCSail VPP had estimated the angle of attack on the keel and rudder from their calculated coefficients of lift, while the lifting force due to the canoe body was assumed zero. The PCSail modifications to find rudder angle and keel angle proved to be incorrect. This was due either to the lift caused by the canoe body itself or from unusual flow patterns at the rudder possibly due to laminar separation.
The result of this finding was two-fold. First, the unstimulated testing was adjusted to include only the upright condition. Secondly, the test-matrix was reevaluated so that true sailing conditions could be found.
A test was performed to find how yaw affected the boat's characteristics. From this test of yaw shown in Figure 12, it was determined that for small angles of changes in yaw the lift would change linearly. In the new test matrix, instead of trying to predict the yaw and rudder angles, set angles were chosen. Yaw angles of 0 and 4 degrees and rudder angles of 0, 3, and 6 degrees were used for each sailing condition. Ultimately, for the sailing matrix with 20 variations of speed and heel, there were a total of 120 tests which included rudder and yaw angle.
Fig. 12 : Lift linearity for small changes in yaw
Prohaska Analysis
The total resistance is assumed to be composed of viscous and wavemaking factors. Viscous resistance is composed of frictional resistance multiplied by a form factor. Because of Bernoulli’s principle, an incompressible fluid has to change velocity while moving across a form which is not flat. The increased velocity of the fluid creates increased frictional resistance across the form, and that component is calculated in the viscous resistance term as the form factor, k.[6]
To calculate the form factor, a process similar to the Prohaska method is used. Prohaska suggested that the form factor could be reduced from Eqn(1)
The International Tank Testing Committee in 1978 recommended modifying Prohaska’s method to use Eqn(2) where n is a power of Froude number being: 4 less than or equal to n and 6 greater than or equal to n.
Typically, a plot is constructed where CT / CF are ordinal values and Fn / CF are abscissa values. The form factor is derived as an ordinal-intercept of the best-fit linear regression. Values used for computation should be at as slow a speed as possible without reaching into the scale-effects region.
The unstimulated and stimulated upright tests were analyzed using Prohaska plots to find the form factor of the model.
Fig. 13 : Prohaska plot of unstimulated data
The data which showed linearity without scale effects was used for the Prohaska plots in Figure 13. The best-fit lines produced ordinal-intercepts of 1.009, 1.035, and 1.054 for n values of 4, 5, and 6, respectively. The Fn / CF Prohaska plot produced the best-fit line, so the value of 1+k for the form factor in unstimulated flow was 1.009.
The same method was used for stimulated flow.
Fig. 14 : Prohaska plot of stimulated data
The data was sorted to find good points for the Prohaska plots in Figure 14. The best-fit lines produced ordinal-intercepts of 1.168, 1.181, and 1.209 for n values of 4, 5, and 6, respectively. Again, the Fn / CF Prohaska plot produced the best-fit line, so the value of 1+k for the form factor in stimulated flow was 0.168. The value of 0.168 included both form factor and the effect of one strip of sand. This form factor was used to compute the viscous friction from the model to the coefficient.
Finally, the sand-strip stimulation data was analyzed.
Fig. 15 : Prohaska plot of additional sand-strips data
The data for both extra sand strips were analyzed for n values of 4, 5, and 6 (Figure 15). The Fn / CF Prohaska plot fit the best line through both sets of data. The ordinal-intercept of the two sand strips plot was 1.290 and of the three sand strips plot was 1.356.
The difference in form factors between the additional sand strips gave the added form factor due to the sand strips. The difference between these values was 0.065. Assuming that the testing with only one sand strip indicated the true flow conditions around a full-size vessel, the difference from the sand strips was subtracted from the stimulated form factor. Therefore, the adjusted form factor for the hull was 0.103. The form factor of 0.103 was used to scale up the coefficient data to the ship scale.
An interesting look into flow affects was seen by superimposing the viscous coefficient over the total resistance coefficient for each sand strip condition (Figure 16). The points to notice were at the intersections of each total resistance curve and viscous resistance curve. Most of these interactions occurred around Rn = 375,000. Data acquired at Reynolds numbers lower than 375,000 had significantly lower resistance than at points where Rn > 375,000. The data having lower resistance indicated a large amount of laminar flow, and did not properly model the flow conditions found on the full-size vessel.
Fig. 16 : Total and viscous resistance for all upright data
The exception to the rule of a decreasing coefficient of total resistance with decreasing velocity is below Rn = 250,000. These very-slow test points had entirely laminar flow, and the laminar friction coefficient dominated resistance. Eventually, these slow test points would drive the total resistance coefficient to a limit of infinity at low velocities.
Since the form factor was found, the viscous component of resistance was subtracted from the total resistance to leave wavemaking resistance (Figure 17). Notice that below a Froude number of 0.18 (Rn = 400,000), there was a considerable amount of data which had a negative wavemaking coefficient. The negative wavemaking coefficient indicated that there was a considerable amount of laminar flow across the model at those points.
Fig. 17 : Wavemaking resistance in the upright condition
Froude proposed that ship predictions could be made by scaling only the wavemaking resistance from model tests. The viscous component of resistance for the ship would be calculated using the form factor which was found for the model. Powering required to pull a ship through the water is known as effective horsepower. Power is the product of force over a velocity, therefore, for English units power is Eqn(3) where velocity is expressed in knots, and resistance is in pounds.
From the acquired upright data, both the resistance and effective horsepower were calculated for the full-size Mk II Navy 44 STC (Figure 18).
Fig. 18 : Upright resistance and horsepower
Difficulties in Tank Testing
From the beginning of tank testing, there were two major problems. The first problem consisted in realignment. After the initial alignment, the rig was assumed straight. However, after checking the alignment again after some of the initial unstimulated flow cases, it was found that the square beam was not rigidly attached to the carriage. To solve this, both the square beam and the "L" beam were screwed into the carriage - not just clamped.
Another major difficulty throughout the project was the presence of transient noises in the system (Figure 19). The result of this noise was to multiply the raw forces to many times the actual forces. Many Fourier-transforms were performed on the data to try to identify the source of the errors. The Fourier-transforms could not find a frequency of the noise which was distinguishable from the standard data frequencies.
Ultimately, it was shown from an oscilloscope that the noise had a beat signal. The source of the beat could not be found. However, the data acquisition system was modified to truncate the data near the zero-crossings of the beats. This method adjusted the starting and ending points of the data to find the lowest standard deviation. In between the truncation limits, the data was averaged to find the steady-state force without the influence of noise.
Fig. 19 : Fwd-lift force block raw data for typical sailing test
Another work-around to reduce the error associated with the transient noise was to drastically increase the rate of sampling. Using this method, a greater percentage of the noise averaged itself out as sampling was increased from 25 Hz to 143 Hz. This method required moving to a laptop instead of a PC. This was because the PC's data acquisition was connected by a USB connection which could not handle the high sampling rate. The laptop used a parallel connection for data acquisition which could receive high data rates. On the higher data sampling system, the beat signal was visible in the data (Figure 19).
References
1. Bertin, John J. Engineering Fluid Mechanics. Prentice-Hall. Englewood Cliffs, NJ. 1984.2. Fox, Robert and Alan McDonald. Introduction to Fluid Mechanics. John Wiley & Sons. New York, NY. 1973.
3. Franzini, Joseph B. and E. John Finnemore. Fluid Mechanics with Engineering Applications. 9th Ed. WCB/McGraw-Hill. Boston, MA. 1997.
4. Larsson, Lars and Rolf E. Eliasson. Principles of Yacht Design. 2nd Ed. International Marine. Camden, ME. 2000.
5. Tupper, Eric. Introduction to Naval Architecture. Society of Naval Architects and Marine Engineers. Jersey City, NJ. 2000.
6. Van Manen, J.D. and P. Van Oossanen. "Resistance." Principles of Naval Architecture. Society of Naval Architects and Marine Engineers. Jersey City, NJ. 1988.