Description of Recent Talaria IV Developments
Several technologies are necessary to develop a submerged foil computer controlled hydrofoil, e.g. the control law mathematics, software, digital and analogue electronics, hydraulics, structural, mechanical and hydrodynamic design. A background in most of these can be obtained though academic study, however I have found that little seems to be available to aid in the choice of specific components for such a system. In this note I would like to describe a set of component choices, enablers, and construction details not found in engineering texts that that have produced a functioning system for the height control of Talaria IV.
Talaria IV is a canard configured submerged foil hydrofoil with its steering and flying height controlled by to bow strut and foil. From its first flight in 1992 to 2008 it utilized for height control, a mechanical surface follower. A surface skimming plate was projected forward from the bow strut 3 feet using a four bar linkage. It was attached to the bow foil, changing its angle of attack as a function of the boat’s height above the water surface. The mechanism’s feedback was set at .1 radian foil angle per foot of height variation. Via the four bar linkage the angle of the skimmer plate was set to pierce the upper portion of a steep wave rather than ride over it causing the boat to fly through a steep wave rather than attempting to lift itself over. This feature was intended to increase the likelihood that the bow foil would not fly out the far side of a wave, ventilate, and subsequently fall into the next wave. This mechanism performed very well. It was however technologically inconsistent with the boat’s analog computer based roll control system and detracting from the boat’s image. Thus a computer controlled height control system has been installed.
The new or replaced components are the bow strut, digital computer, its software in C++, the control law, ultrasonic height sensors, vertical accelerometer, foil position sensor, RPM sensor, bow foil actuator, servo valve/manifold and electronic interface to the computer.
Several years ago Tom Speer introduced me to XFOIL, a DOS computational fluid dynamics program, downloadable from the NET. With it a new bow strut was designed.
The leading 9” of its 13” cord is cast of 535 aluminum. The trailing edge, housing the bow foil actuator and linkage, is of fiberglass. The casting pattern included a 1.3% allowance for shrinkage. The resulting casting was within a 10 thousands of the design dimensions.
Hydraulics and foil position sensor
An additional Moog 62 series servo value was added to the hydraulic manifold to control the angle of attack of the bow foil. It is controlled by the computer’s DAC output, using a LT1010 amp. The bow foil is actuated by a 1” ID, 2” throw cylinder milled from 1.25” x 1.5” aluminum and anodized. Inserted into the cylinder is a 2.5” variable impedance position transducer spool. It is wrapped with about 10,000 turns of .008 diameter wire set in epoxy on a plastic spool such that it yields an approximately linear response. It is further linearized within the computer with a polynomial fit. The transducer is driven by a 1500hz +/- 15 volt square wave, via a LM324 amp, rectified and smoothed for input to the computer’s ADC.
Computer and electronic interface
For the digital computer a SBC0489 from Micro/sys was chosen. It has a 133Mhz 486DX class processor, 64M of DRAM, 8 channels of ADC, 1 MB flash memory, 4 channels of DAC, 4 counter /timer channels, a RS232 interface, VGA screen driver and a floppy disk port. It uses 5 volt power, has no fan, and comes with C++ software examples. An additional 8 ADC channels were added using a PC104 compatible TS9700 from Technologic Systems. While executing the flight control software and displaying the control system’s parameters on a 10 inch flat LCD screen, it updates at 70 Hz. The SBC0489 and MEM sensors are powered by a Wall 25 watt, 5 volt DC/DC converter. The servo valves are powered by a a Wall +/-5 volt DC/DC converter. The flap position sensors by a Wall +/-15 volt DC/DC converter. The signal conditioning is done with LM324 amps. The screen is a Anrecson 1000 nit 10.4” sunlight readable LCD.
The red square is the TS9700 below it is the SBC0489. In front is the interface circuitry and behind under the SBC0489 are the power supplies.
The 1500 lines of source code are in C++. About half are for the display, the rest, the control algorithm and interfacing subroutines. A Borland C++ 5.02 compiler generates the executable code. The executable code is transferred to the SBC0489 flash memory through its floppy drive.
The picture of the screen below is taken with the boat in its cradle. The speed is zero and the control surfaces are near their extreme positions. Zero height is measured from the keel. Flying height is about 12 inches.
The control law is derived using the Linear Quadratic Regulator algorithm coded in Visual Basic. A similar set of code yields the Kalman gains. Many of the resulting control system parameters vary significantly with speed.
Talaria’s maximum banking angle is about 30 degrees. Thus a fixed ultrasonic transducer, measuring height, must return a measurement when directed up 30 degrees off axis. In addition, the wave surface angle can further increases the off axis return requirement. There a many ultrasonic transducers available, however, they are nearly all designed to produce a narrow beam. The Matbotix XL-MaxSonar-WR1, encased in PVC, has a narrow eight degree beam, however by removing its cone to within .15 inch of the transducer face the beam width is widened. It samples at 10 Hz. This slow sampling rate is due to its filtering algorithm which takes half of its update cycle. Because half of its cycle is spent in internal processing two WR1 sensors can be alternatively triggered without mutual interference. Together they sample at 20 Hz. They are mounted splayed to improve the signal return probability when banked. They can be seen in their housing near the gunwale in the bow strut picture.
The accelerometer is an ADXL203, mounted inside the boat’s bow. It uses 5V power and produces a voltage signal.
Because some of the control parameters vary with speed, the RPM input, via a frequency to voltage converter, is used to provide a speed input to the control algorithm. The speed input is also used to adjust the aft foil flaps to maintain the aft foil’s flying height over its speed range and will, as an emergency feature, rapidly set the boat down given a fast reduction in RPM.
The replaced mechanical height control mechanism did not have a damper, consequently, when traveling over wavelets, it tended to bounce. The bouncing induced a low frequency vertical vibration at the boat’s bow. With the electronic system the ride is smooth. Also because the height control parameters are speed variable a constant height is maintained across its flying speed range. There is a 7 minute video of Talaria IV produced by Ray Vellinga flying with its new system on YouTube entitled “Hydrofoil Dreamin”.
A design objective is a takeoff speed less than the boat’s the hump speed, and secondarily, to maximize top speed. The design options for the bow foil are: foil area, aspect ratio, thickness, and section. The material is unidirectional carbon fiber with a fiberglass core.
The bow foil is very lightly loaded at the beginning of a takeoff run. As the stern lifts it becomes fully loaded. Consequently the lift - area requirement of the bow foil occurs at a higher speed than that of the stern foil. Thus it can be more heavily loaded. In addition, for pitch stability, the derivative of lift versus angle of attack should be lower for the bow foil than the stern. For a take off speed below hump speed the loading of the aft foil is 577#/ft2 . The bow foil’s loading is 619#/ft2 .
The bow foil is articulated in angle of attack. It is pivoted on a shaft just forward of its center of loading. The size of the shaft and thus its bearing block are dictated by 1700# loading on the bow foil. The bearing block’s thickness is 1.25”, constraining thickness of the bow foil.
Within the constraints of loading, thickness, and material stiffness, the section was designed with XFOIL, ncrit =3.
The formula y(x)= t xa (1-xb) was used to generate the symmetric sections.
Where y(x) = +/- thickness, x = cord (0-1), t = thickness parameter (.1045), a (.52) and b (2.1) are shape parameters. Camber was generated using the same formula, (.0245), (.54), (2.4).
With a minimum drag at maximum speed section the center thickness determined the center cord, 11.75”. With that and stiffness the span and aspect ratio were largely determined.
The aft foil performs two functions, roll authority and lift. The design objective to keep the foils within the beam of the boat limits roll authority. To maximize roll authority the full span flaps are 1/3 of cord. With the span at the boat’s beam, 8’, and the takeoff speed below hump speed the foils area is determined. Its loading is 577#/ft2, cord 9”, total span 95”.
The aft foil has hinged flaps with 3 hinge bearings, each end and near the center. The flaps are actuated from the center pod by hydraulic cylinders with a 2” throw actuating a 2.6875” bell crank. The torque is thus transmitted through the flaps from the center to the outboard end. Carbon fiber inboard flaps were found not to have the necessary torsional stiffness. Welded 316 stainless steel inboard flaps were constructed. The outboard flaps are of carbon fiber.
A design requirement is that flap - foil interface not significantly diverge. Thus the bending of the foil versus the flaps must be minimized. This imposes a stiffness requirement on the aft foil. Below, the purple line shows the absolute divergence of the foil and flap with a plus one G load. The maximum divergence is .0373”. Also, the center hinge is located at 25.55” of the 45.4” span to minimize the divergence.
As with the bow foil, the design objective is takeoff below hump speed and then the maximization of top speed. To maintain pitch attitude over the speed range the flaps are biased as a function of speed. Relative to 36 knots, the flap bias at takeoff is 3.3degrees down.
Give the loading, flap setting, span, and takeoff speed the cord can be determined. Section thickness, with a small impact on drag, and carbon fiber skin thickness (cost) are traded to make the foil thickness choice. Its thickness is .95” and cord 9”. Using the same section generating formula as the bow foil its symmetric section parameters are: .0990, .53, 2.1. Camber parameters are: .026, .48, 2.0.
The foil has 10 degrees anhedral. This is primarily to lower the foil tips to reduce the likelihood that they will broach during a banked turn in waves. It also increases roll authority slightly.
The dominant structural requirement for Talaria's struts and foils of is longitudinal stiffness and sometimes strength. The loads and dimensions are such that the unidirectional carbon fiber must be thick, generally more than .25”. Unidirectional carbon fiber is very dense and does not infuse well without a flow medium. An imbedded flow medium, of course, reduces the fiber content of the layup. I found via experiment that I could not reliably infuse unidirectional carbon thicker than .125”.
The layup procedure I adopted was to set up the mold for infusion, hand layup the carbon fiber with resin, lay in the woven fiberglass core dry, seal the mold, establish the vacuum and let the excess resin infuse from the carbon into the core. Then infuse the remaining dry core.
It worked best to layup each side of the strut or foil separately and glue them together after the initial cure.
Aft Hydraulic Cylinders
The aft hydraulic flap cylinders have an ID of .94”, rod of 3/8”, and a throw of 2”. They include an embedded position sensor. The sensor is a coil of 6000 wraps embedded in epoxy around an Acetal spool. A 1600 Hz square wave, at +/- 15 volts, drives the coil. The circuit terminates with a 500 ohm resistor to ground. The square wave is attenuated by a steel rod attached to the cylinder’s piston rod. As the piston is retracted the attenuation increases. The attenuated wave is rectified, smoothed, and read by the flight computer’s analog digital converter. The piston slides in a stainless steel (SS) sleeve pressed onto a 316 SS cylinder end block. The block holds an 1/8” pipe flare fitting, a bronze bushing, and the rod seal. The piston is of Acetal. The SS sleeve overlaps the end O-ring of the spool. This seals the hydraulic oil from the coil. At the other end of the coil is an O-ring that seals the coil from the outside – water. The body of the cylinder is carbon fiber epoxy rather than a metal. The coil’s transmission is attenuated by metal, thus its output variation is would be decreased by using a metallic cylinder body.
Bow Hydraulic Cylinder
The bow foil actuation cylinder has an ID of 1”, rod of ½”, and throw of 2”. It is machined from an aluminum block and anodized. Its design is similar to the aft cylinder but does not include the coil spool.