Boat Resistance Measurements

John Kohnen and I measured the force required to pull my Birdwatcher II, "Wave Watcher," at various speed. Here are the results and some thoughts on the utility of this data. - Bob Larkin

THE QUICK SUMMARY - This story gets a bit technical, so here is a short version. John used his Redwing 18 to pull the Birdwatcher II sailboat hull through the water at varying speeds from 2 to 5.5 kts. We measured the force required to move the Birdwatcher, representing the resistance of the boat to movement.

The resulting curve tended to follow the expected function of resistance being proportional to the speed of the boat squared. A typical point along this line is 22 pounds of resistance at 4-kt speed. This curve can be used to make estimates, such as the speed that electric drives might provide, or the force being provided by a sail combination.

Measurements were also made with the outboard motor down and the centerboard raised. This allows the fraction of the total resistance associated with these components to be determined.

THE FULL STORY - John and I arrived at Fern Ridge, Monday July 22, 2013, to find a pretty good breeze coming out of the Northeast. Boat resistance measurements are affected by the wind, and being new to this measurement, we wanted to measure in reasonably still air. We both had Tuesday available, so when John volunteered to get up at 5 AM to find still air, we had a plan. I was going to spend the night at the lake anyway.

The experiment - At 6 AM on Tuesday, Fern Ridge was glassy. The breeze was building up some by 8AM, but this gave us the window we needed. John put his Redwing 18, "Lazy Jack," into the lake and we connected a 100-ft 1/4-inch polypropylene line from his boat back to the bow eye on the Birdwatcher-II. At the towing end, a 50-lb fish scale was put into the line. John could read both the scales and his GPS from the helm of his boat.

We went out into the lake, and John would set various speeds on the outboard. He would record the speed and the reading on the fish scale. All I had to do was to steer my boat to follow directly behind John. We ended up getting measurements between 2 and 5.5-kts. The hull speed for the Birdwatcher is around 6-kts. The paths of the boats were straight lines to minimize resistance due to lateral movement. In all cases, the boat speed was left at a constant value long enough for transient forces to die out. This could be determined by the speed reaching its highest non-varying value.

The polypropylene line was light enough to easily keep it out of the water. In addition, when we would stop, it floated, keeping it away from the outboard propeller. Polypropylene has low stretch, minimizing springy line issues.

The first, and largest set of measurements was done with the Birdwatcher motor out of the water, but with the center board fully down. Following this, we made a few measurements with the motor down, and with the center board up. The utility of these added measurements will be explained later.

Looking at the data - The plot just above shows the towing force, on the vertical axis, for various GPS speeds, on the horizontal axis. The only thing causing the towing force is the resistance of Wave Watcher. So we label the axis as boat resistance. The fish scales limit the measurements to 50-lb.

The blue data points, for the center board (CB) down and the motor up, are the base case and were taken multiple times. Roughly, the towing force ranged from around 6-lb at just over 2-kt to 50 lb at 5.5-kt. It goes up a lot! Ignoring the red and green points for now, the pencil line was drawn to center the blue points at speed below about 5-kts. In addition, both the horizontal and vertical axes have the same unequal spacing of the grid lines. The spacing used here is called log-log and is chosen to cause data points to appear on straight lines for the case of functions of the form "force equals a constant number times speed raised to some power."

So, what does that mean? The physics of boat resistance has been shown to be caused by friction, when the boat is moving well below hull speed. This is mostly friction in the water, but also can be friction in the air. We are using the term "friction" in a general sense to include the effects of turbulence along the surface along with the rubbing against the boat surface. We exclude the force required to lift the boat up the bow wave, an effect that that appears at higher speeds. Friction forces will follow the special cases of straight lines on our log-log plot. This corresponds to the force being equal to a constant number times the speed raised to the power of about two, i.e., the speed squared. This squared relationship for friction forces is extremely important in everything from vehicle design to weather forecasting. But for our purposes, it allows us to easily analyze the boat speed with a minimum of data.

Now we need to find the slope of a line for a squared function. If we draw a straight line from point (speed=1, resistance=1) to the point (speed=10, resistance=100), all points along that line will follow a squared relationship. In addition, every line that follows any other squared relationship will be parallel to the line we just drew, but shifted up or down. So, if we assume our resistance curve is dominated by friction, as it should be for low speeds, we need only determine the constant number. For this, we can extend the straight line to cover the the speed of 1-kt. At that speed, one squared is still one, and so the force value will be the constant. This is shown on the graph, where for the blue-point curve, the constant is 1.4. The units of this constant are pounds per knot-squared.

Now is a good time to review the data plot and lines to see if we are being open-minded and objective. The reason being that we have constrained the problem by using a straight line on the log-log plot, and also forced this to have a slope of 2. Looking at the blue data points at speeds of 5-kt or less, it seem as though they scatter quite evenly about the center line. There is some noise in the data which is not surprising considering the nature of pulling a boat around the lake. This tracking of the line contrasts with the three blue data points at speeds above 5-kts, or maybe even the 5-kt point, where the resistance seems to be moving above the speed-squared line. Thus, the assumptions of the equation form of the line seem to be supported by the experimental data, for speeds below about 5-kts.

At this point, we have measured the resistance of the hull at slow speeds to be described by "1.4 times the boat speed squared." At speeds above 5-kt or so, it appears the data points are moving higher than this curve. This is expected, as the bow wave effect is becoming significant. To really see this effect would require an all around bigger setup than we were using. More pulling horsepower along with bigger rope and scales would be needed. We will leave this for another experiment.

Looking at the slow speed end for a moment, the people that study fluid flow have found special cases to occur at very slow speeds. These are associated non-turbulent flow around surfaces. I suggest we ignore these issues, since the operation of boats at very slow speeds, i.e., without "way," are just not important. The measurements here start at 2-kts and go up, probably not including the slow cases.

Other Boat Configurations - At first, we kept the configuration of the towed boat (the Birdwatcher) as constant as possible. This gives us a base curve to compare against. Next we changed configuration elements one at a tme while continuing at moderate speeds. We first lowered the 2-HP Honda motor into the water, in its normal position. The motor was not running, but at around 2-kts it started to turn with an obvious noise (as happens when sailing with the motor down). The graph shows two red data points taken with the motor down. Also, a pencil line, with a slope of two, was placed through these points. This is, merely saying that we assume the slope is still some friction curve. Extending the curve down to 1-kt shows the constant to now be 1.95 lbs per knot-squared. This tells us that the boat resistance increases by 100 x (1.95-1.40)/1.40 = 39% when the motor is being dragged along. To me, this is surprisingly high. But, it shows why these measurements can be very useful.

Next, the motor was raised out of the water as in the base case, and then the centerboard was raised. The green markers show these two resistance measurements. The resulting constant drops some to 1.25 lb/kt-sq, a drop of about 11% from the blue data line. The most obvious change is the decrease in wetted surface for the boat, so we can explore that here. The wetted surface for the boat is roughly 80 square feet, with the board down. By itself, the board has a wetted area of about 12 square feet. The decrease in wetted area from raising the board is 15%, in rough agreement with the measured 11% change in resistance.

Thoughts - This has been rewarding as an experiment. This sort of activity is useful for organizing thoughts and for seeing what study and further experiments are needed. But, this is the report of an experiment, rather than of a study. I encourage others to conduct their own experiments and to post the results. From this collective study we can all gain knowledge. From knowledge comes not just satisfaction, but also better boat construction and operation! Special thanks to John for sacrificing his sleep and running "Lazy Jack" so skillfully (at such an early hour!)

References - The study of resistance to movement in fluids has gone on for many years. A couple of Web places to get more information are:

The Wikipedia article on Drag Forces has information on the physics of objects moving through fluids.

John Winters has extensively studied canoe and kayak hulls. information is available at his web site on frictional resistance, along with residual resistance. Examples of the Winters modelling appear most months in the Sea Kayaker magazine reviews of kayaks.

This page was last updated 30 July 2013 & boat name correction 10-2017. Copyright 2013, 2017, Bob Larkin.

Please email comments or corrections to boblark 'the at sign' proaxis dot com