# Weighing a boat without lifiting

Two of the articles on stability in a recent issue ("First perfomance test," and "Fighting capsize," Issue No. 61) raised the question of estimating the weight of a vessel. Presented here is a dockside technique of weight estimation that requires only simple tools.

The procedure involves moving the vessel a short distance by applying a constant force and measuring the elapsed time. The formula to estimate the weight is: ) ÷ s

W is the weight in lbs, F is the applied force in lbs, s is the distance traveled from rest in feet, and t is the elapsed time in seconds.

For example, if a constant horizontal force of 21.25 lbs applied to a vessel initially at rest moves it a total of 8.25 inches (0.6875 feet) in 6.4 seconds then we have:) ÷ 0.6875

A first guess says that the vessel weighs about 20,400 lbs.

This formula ignores the drag of the vessel through the water and friction in the pulley. However, if the speed is kept low, the effect of drag is small. Clearly, this experiment should be done when there is no wind or current. A horizontal force can be applied using an appropriate weight, light line, and a good block with ball bearings. The distance can be measured accurately by placing the weight a known distance above the dock. Time is harder to measure, and the formula is very sensitive to errors in time, but on trials with two people working together, we felt that we got the time to within 0.4 seconds.

In our trials, we used a bucket of water for the weight and pulled the boat back to raise the bucket about a foot. The boat was then secured and we waited until all the transient motions in the system had died out before releasing the boat. We found our results to be very inaccurate unless we were careful to be sure that the boat moved in a straight line.

We guessed that drag and friction absorbed 4% of the work done by the bucket of water. Thus, for a final estimate we reduced the 20,400 weight estimate by about 4% to 19,600.

How accurate are these results? An analysis of the basic equation reveals that a 1% uncertainty in either applied force or distance traveled gives a 1% uncertainty in estimated weight and a 1% uncertainty in time doubles to give a 2% uncertainty in estimated weight. We used a beam balance to weigh the bucket and water so the uncertainty in the 21.25 lbs is less than 1%. The measured 8.25 inches is probably within 1/8 of an inch or about 1.5%. The 0.4 second uncertainty in the 6.4 seconds of elapsed time is 6.25% which doubles to 12.5%. Assuming these errors to be independent, we add 1% + 1.5% + 12.5% to obtain a maximum 15% uncertainty in the estimated weight of the boat.

For this boat the manufacturer claims an empty dockside weight of 16,000 lbs. The owner lives aboard, and this boat certainly was not empty at the time of the experiment.

Bob Gillespie is a retired professional engineer, and Tom McCullough is a mathematics professor at California State University at Long Beach.