The kayak shown in the pictures is a 13’8” tandem unit that has a maximum width of approximately 30 inches. The non-adjustable rear seat was removed, leaving a large open cockpit suitable for mounting the battery and motor controls. A small panel or dashboard was installed in the front of the cockpit containing voltmeters and a 12 volt accessory jack. A pulse width modulation (PWM) unit, powering the motor, is located on the underside of the dashboard.

The Navigator trolling motor was originally manufactured to be attached to the anti-ventilation plate of an outboard motor. A mounting framework was constructed from steel tubing to serve both as a motor mount and a base for the solar panel. The speed and forward/reverse control for the motor is hand operated and connected to the rest of the motor electronics through a plug-in cable. Steering is accomplished by the rudder pedals and cables being attached directly to the pivoting motor shaft making the kayak extremely responsive and maneuverable.

The solar panel, which measures 28 inches by 60 inches, is attached to the tubing framework directly behind the operator’s seat. The original charge controller was replaced with a new design, which was installed beside the PWM unit so the operator can clearly see the LEDs that indicate charging and a full charge in the battery.  A flotation bag, or other gear, may be placed in the remaining space beneath the solar panel. A deep cycle AGM battery is located as far forward as possible to keep the kayak in trim.

After the boat was constructed, a series of tests and measurements were run, both in a lake and the Saint John’s University swimming pool, to learn more about the boat’s performance. Additional measurements were made outside in direct sunlight to determine the capabilities solar panel. Three physics majors from Saint John’s assisted with the measurements.

Measurements for the Solar Kayak

The motor required 2 amps just to get the prop spinning. After about 3 amps, the speed increased proportionately with the current, reaching a top speed of slightly more than 4 mph while drawing 18 amps.  A solar powered boat doesn’t have any energy to waste, so understanding its performance is important. A performance profile for the solar kayak was established by measuring current (amperes) drawn at various speeds then plotting a graph of “speed per current unit squared” versus “speed”. As was stated, at currents less than 2 amps, the motor did not have enough torque to spin the prop in water. At higher currents, the performance peaked then gradually dropped off in an inverse square manner. Signs of a hull speed limitation did not appear at the speeds tested.

Since speed is the rate of distance traveled and power is the rate of energy conversion, a mph/watt calculation ( proportional to speed per current squared) would be similar to a distance traveled per energy unit calculation. The performance curve illustrates how distance traveled per energy unit varies with speed and supports the notion that drag (and thrust) increases with the square of the speed. When the speed doubles from 1.5 mph to 3.0 mph, the distance traveled per energy unit drops to about ¼ of the first value. Since the work done (energy converted) by the motor, when moving the boat, can be equated to the product of thrust and distance, the thrust required to overcome drag must have increased by a factor of approximately 4.


The highest performance (peak on the curve) operating speed for the boat is probably about 1.5 mph. This speed is not necessarily a practical speed for general use. To determine what is practical, it is necessary to look at the balance between current input from the solar panel and compare it to the current drawn at various speeds. In full sunlight, using only the primary panel, a speed of about 1.7 mph. would represent self-sufficiency for the boat, but a higher speed combined with periods of rest, while the battery recharges, might be more practical. For example, the operator may wish to travel at a more respectable speed of 3.0 mph. while occasionally taking a break. In this case, a 25% duty cycle would be needed. If the boat were used for fishing, a 25% duty cycle would be reasonable, considering how fishing is usually done. River travel, with the current, would also be practical.

Solar Panel and Charge Controller

The 100 watt solar panel is well matched to 12-volt lead-acid storage batteries. It delivers peak power (closer to 70 watts, the day tested, than the rated 100 watts) at approximately 14 volts, which is typically close to the charging voltage for both wet and gel batteries. The charge controller furnished with the panel, however, did not perform well. The controller contains a power transistor with a very small unventilated heat sink that quickly overheats when the panel nears its maximum output. A thermal cut out switch cycled on and off, giving the charging circuit a duty cycle no better than 50% at a 5 amp charge rate. In addition, the factory selected on-off voltages tended to drift with temperature changes, the cut off voltage was too high for some 12 volt gel batteries and the voltage drop across the controller circuit was larger than necessary. The heat sink was replaced with a larger one, but the other problems could not be easily corrected.

A new charge controller was designed that made full use of the panel’s output. The controller installed in the kayak maintains the battery by reducing the charge rate to a trickle as the battery reaches a fully charged state. The controller drops less than 0.5 volts when the charging current is 5 amps.

Propeller Considerations

There is also a concern about matching the motor propeller to the boat in order to maximize performance. The boat speed produced by the motor depends on the rpm rate of the motor and the pitch of the prop. The pitch indicates how far forward the motor will move during one revolution of the prop. In reality, the motor only moves some percentage of that distance due to prop “slip”. For example, a prop slip of 15% means the motor will move forward only 85% of the predicted distance. Some slip occurs whenever the prop is producing thrust. If the boat is being towed and the prop is freewheeling, the slip is 0%. If the boat is tied in place as the motor runs, the slip is 100%. Increased drag that occurs at higher speeds can increase prop slip. If this becomes too large a factor, it may be necessary to reduce the pitch of the prop to reduce the maximum speed. To maintain the same thrust, the prop diameter can be increased to compensate for less pitch. Increased drag also increases the load on the motor, which, if excessive, can cause it to draw more current just to maintain the same rpm rate. It is similar to pushing too hard on an electric drill while trying to increase the rpms. The drill may stay at the same speed or even slow down while drawing more current. The loading effect exists whether the excessive drag is caused by increased speed or by increased weight of the boat and its contents.

Prop diameter and pitch are important factors to consider. Motor manufacturers often offer propellers with varying diameter and pitch to match the design of the boat. Since most trolling motors are designed to run at a maximum speed of approximately 5 mph, the factory prop is probably a good match for a boat that has a hull speed of at least 5 mph. No props other than the factory prop were used during the measurements since no signs of excessive drag were observed.

One way of reducing prop slip, without changing the prop, is to channel the water flowing through the prop more directly toward the rear. A Kort Nozzle produces this effect by surrounding the prop with a cylinder that is slightly tapered toward the rear. Kort Nozzles are generally used for heavily loaded boats like tugs and ferries, but might be somewhat helpful for this light boat.


Efficiency

You may have noticed that no mention has been made of efficiency. The reason is that the term can be very misleading unless clearly defined. In the study of physics, the definition is very precise. It is the ratio of energy output for a given process or device to the energy input. It can also be defined in terms of energy transfer rate as power output to power input. In general usage, however, efficiency can be any measurable output divided by any measurable input. The number of paper clips manufactured per dollar spent represents efficiency also. The performance indicator used here (distance moved per energy unit) may seem like a measure of efficiency and it decreases dramatically with increasing speed. But, if we stick to the physics, backed by our measurements, the efficiency of this boat remains fairly constant over the range of speeds tested. How can this be?

For the moving boat, the input power to the motor is the product of voltage and current and the output power can be found from the product of thrust and speed. Since thrust needed to overcome drag increases with the square of speed, the input power must increase to compensate for the increases in output power. Even if the efficiency remains constant, the distanced traveled per energy unit will drop. The same logic can be applied to gas guzzling boats. They are not necessarily inefficient. They just weigh too much and go too fast.

What is Hull Speed?

Boats with hulls that are not designed to plane such as sailboats, canoes and kayaks, are often described as having a “hull speed”. The hull speed may be viewed as a maximum achievable speed, not because it is impossible to go faster, but because it would take an inordinate amount of power to reach higher speeds. The hull speed limitation is due to several factors. One is drag or friction between the moving hull and the water. At slow speeds in still air, friction of the water is a major factor. As the speed increases, additional energy is dissipated by the generation of waves (boat wake). The amount of energy used to generate wake increases rapidly with increasing speed. As long as wind and the presence of other waves are ignored, the production of boat wake may be considered the dominant factor when hull speed is being approached. Hull speed has been studied and modeled extensively. An empirical formula that is often used to calculate hull speed for small boats is:

Hull Speed = C*(Waterline Length)^0.5

If the length is expressed in feet, the hull speed will be in knots. C is a constant for any given boat that depends on the nature of the hull. Generally C is in the range from 1.2 to 4.0.   Narrow, sleek hulls would have the highest value for C. A value commonly used for sailboats is 1.34. Assuming that C = 1.34, twenty feet of waterline will produce a hull speed of approximately 6 knots.

If one wishes to visualize how hull speed is established, it is helpful to consider the appearance of the boat wake. A wave crest is formed at the bow of the boat and another crest further back along the sides of the boat. As the boat speeds up, the second crest slips back near the stern. It may form right at the stern or slightly behind. This creates a wave trough in which the boat is essentially trapped. A planing boat has enough power to climb out of the trough. The amount of power needed to reach the hull speed will depend on the weight of the boat and contents.

Energy expended attempting to exceed the hull speed, in a non-planing situation, is definitely energy wasted. Even at speeds less than the hull speed, the energy requirement will become greater as the speed approaches the hull speed. A rule of thumb often used at speeds less than the hull speed is, “the thrust needed to move the boat will increase with the square of the speed”. A “sweet speed” can usually be found that represents an acceptable balance between speed and fuel economy.