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### OPERATION

QUICK FACTS

• Travelling speed in water is 200 mm/s (1 meter in 5 seconds)
• The total weight of the boat is 295g and both vessel & floaters displace 63,000 mm3 of water when submersed to full capacity.
• Propeller rotates at 6,800 RPM
• Project is ready to accommodate Radio Controlled circuits for operation at the distance

HOW IT WORKS

NOTE: operate SLOOP only in swimming pools or bodies of water from which the boat can be easily retrieved.

S-LOOP is a boat formed by a hydrodynamic vessel and accompanying side floaters that is powered forward by the action of a 4 blade propeller. The motor of the propeller is spun at 6,800 RPM at a supplied voltage of 4.5v coming from the series combination of 3xAA batteries. A lifting force acts on each spinning blade as a result, thus pushing the propeller and attached vessel forward.

The direction of the boat is controlled also by lift acting on two airfoils (rudders) located at the rear of the hull. Through a gear reduction, a motor rotates the rudders’ axes changing the angle of attack with respect to the mainstream of air that exits the propeller. The action of the motor is set by means of a mechanical switch that is operated manually and then locked into position to prevent further rudder rotation. S-LOOP will only go in circles, however in further projects at LAYKANICS, we’ll replace this switch by a Radio Controlled unit to able to control S-LOOP at the distance and expand it’s functionality.

The operation of S-LOOP as a whole is achieved through 4 modules, each with functions that are explained below:

FLOTATION MODULE:This is comprised of the main hull (11-SLOOP) and side floaters used from project STRDR (04-STRIDR). The side floaters connect to the hull through a fixture & arm (14,13 – SLOOP) that can be retracted (for storage) or set at different heights to minimize drag. The floaters can be snapped on to the arms at any axial position for proper balancing when into the water (S-LOOP will always trim by sinking the back of the hull).

POWER MODULE:it powers the propeller and the motor rotating the rudders. It’s made out of the battery holder (12-SLOOP), switch stator (10-SLOOP), lock (09-SLOOP) and multiple wires and contacts. The diagram explains how the batteries are connected in series to provide a voltage of 4.5v to the motor of the propeller and 1.5v to the motor acting on the rudders. The clock and anti-clockwise rotation of the rudder motor is achieved by switching polarity at the motor terminals through a clever arrangement: one terminal of the motor is permanently connected to a contact that is common to the positive (+) of battery2 and the negative (-) of battery3. Then the other terminal of the motor is taken to a switch that connects it to either the negative (-) of battery2 (rotation is in one direction) or to the positive(+) of battery3 (polarity is inversed and rotation is in the opposite direction).

STEERING MODULE:is used to give direction to the hull. The rudders have a symmetric airfoil profile around which the air coming out of the propeller circulates. As you’ll see in the LEARN section, when the airfoils are NOT aligned to the flow out of the propeller, a force is generated at their “suction” surface pushing the back of the hull and forcing it to rotate about its own axis. The larger the angle of attack, the larger the force and hence the more pronounced the rotation of the hull and the tighter the loop followed by SLOOP.

The steering module employs a motor housing (04-SLOOP), a securing ring (06-SLOOP) and a speed reducer (15-SLOOP) as printed parts. Motor K1-M1 is meshed to the rudder axes through gears K1-G10 and K1-G60 to reduce the speed of rotation and increase the torque output so that the rudders don’t rotate back at the action of the flow. When setting the position of the rudders, the angle of attack can be measured by marking the gear and comparing it to the graduated scale in the hull. This will allow you to set different loop diameters. The speed reducer at the top has a screw that presses right onto the shaft end of the motor. When screwed in, the load on the rotor is increased and the rotation of the axis made slower. This helps to slow down the response of the rudders as a speedy rotation might be difficult to control.

THRUST MODULE: produces the thrust force required to move the boat forward. The motor spins at a very high speed, creating a lift force on each of the four propeller blades. The blades push both hub and motor forward and with them the whole boat. To achieve a high speed, the motor most be supplied with 4.5v. Because fast speeds can produce an injury, a casing (03-SLOOP) and a mesh (08-SLOOP) enclose the propeller. NEVER run your fingers across while the motor spins!! Also notice that a small weight difference in any of the blades can produce an imbalance which at high speed will result in high vibration. The structure of the casing is made therefore springy to isolate such vibration from the rest of the hull. The strut in “A”-frame shape fixes the module on to the boat. The small lugs on the side are used to secure the wires that feed the motor of the steering module. The axial location of the casing with respect to the strut, can be adjusted by pulling back or forward. This will help balancing the hull and adjust the intensity of the flow over the rudders (slow or fast control). The “T” slot at the bottom of the casing fits the nut for the securing screw that fixes the casing to the strut.

### LEARN

Both the thrust generated by the propeller and the turning action of SLOOP are possible thanks to LIFT. This force is the same force that acts over airplane wings and keeps them flying. It’s a consequence of a pressure difference between the “pressure” and the “suction” surfaces of an airfoil or any object in a flow stream that can produce a curvature in the flow streamlines.

Often, LIFT is wrongly explained by the theory that particles over the curved surface (suction) of an airfoil must travel faster than those on the flat surface (pressure) because it is assumed they flow through it in the same period of time. This explanation is misguiding. In reality, LIFT is generated due to streamline curvature! In this picture, a stream of air is forced to go through a half cylindrical body. The particles of air will travel in the trajectories described by the streamlines. The streamlines closest to the suction surface have a curved path whereas those far away carry a straight one. This means that the particles of air around the suction surface are negotiating a curve or have entered circular motion. Any object -solid or fluid- undergoing circular motion, needs of a centripetal force acting radially and towards the center of rotation (ie you wouldn’t be able to spin a rock attached to a rod without the tension force that the rod exerts on the rock towards the center of rotation, in this case your hand). In the case of a fluid, this force comes from the pressure that the outer layers exert on the inner ones. So the pressure on streamlines far from the curved surface, must be higher than those close to it. The pressure on the streamlines well above the cylinder is atmospheric, which means that the pressure at the curved surface must be lower (or sub atmospheric). At the bottom of the body however, the particles in contact with the surface have not undergone circular motion. In the absence of streamline curvature, the pressure is also atmospheric and larger than those at the suction surface. With higher pressure acting at the bottom than at the top, the net result is a LIFT force.

AIRFOILS

The most efficient profiles to generate lift are airfoils. A commonly used system for airfoil classification is the NACA system. Although the system has variants, the basic 4-digit numbering is explained below:

1st Digit: Denotes the maximum camber as expressed in hundredths of chord length
2nd Digit: Indicates the location from the leading edge at which the maximum camber occurs (tenths of chord)
3rd and 4th Digits: Give the maximum thickness of the airfoil in hundredths of chord length

The propeller of SLOOP uses a NACA 23021 profile.

The actual amount of LIFT on bodies with airfoil profiles depends on the density of air, free stream velocity, and surface area so it is more common to refer to airfoils in normalized terms or coefficients. The coefficient of LIFT is defined as:

$CL(\alpha) = \tfrac{L}{\dfrac{1}{2} \rho V^{2} S}$
CL = coefficient of Lift [ ], L = LIFT [N], ρ = density of air [kg/m3], V = free stream velocity [m/s], S = Span Area (typically chord x span) [m2]

In addition, the amount of LIFT is dependent upon the angle of attack of an airfoil in relation to the flow stream. The angle of attack can be increased to obtain more LIFT, but only in small quantities because at very aggressive angles the streamlines will no longer follow the aerodynamic contour of the airfoil (a situation known as aerodynamic stall). It is common to plot the coefficient of LIFT of an airfoil against different angles of attack. For the airfoil used in the propeller, the lift coefficient plot is shown here (See REF [1])

We chose to operate SLOOP propeller with an angle of attack of 4 degrees, having an expected lift coefficient of 0.7871.

INCIDENCE IN PROPELLERS

You may have noticed that the blades of a propeller are twisted. This is because the tangential velocity of the propeller increases with radial location. In project DRY3R we introduced the concept of velocity triangles and incidence. For SLOOP, the motor design speed is 5,500 RPM and at a tip radius of 42.5mm the tangential velocity is 24.5 m/s. This is really fast and that is the reason why the profile at the tip of the blade is almost tangential when compared to the bottom (which is almost axial). The velocity triangles for a location at the hub and at the tip are shown for you to compare.

REFERENCE
[1] http://airfoiltools.com/

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