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Kayak and Canoe Design Bulletin Board
Kinetic Energy is Still a Moot Point
Posted By: Mike Scarborough In Response To: Re: Kinetic Energy is a Moot Point (Nolan)
Date: Friday, 27 August 1999, at 11:25 a.m.
Lets take a look at two boats. (Because the problem we are trying to solve is the effect of boat weight on paddling effort). Boat A weighs 50 pounds and has a 150 pound paddler for a total weight of 200 pounds. Boat B weighs 100 pounds and has a 150 pound paddler for a total weight of 250 pounds. Both paddlers generate 5 pounds of force as they paddle.
As our two paddlers set off on their trip they accelerate at the rate of A=F/M. Boat A accelerates at a rate of 5/200=.025. Boat B accelerates at a rate of 5/250=.020. Because Boat B accelerates more slowly it takes boat B longer to reach their cruising speed of 3 mph. Once both boats reach 3 mph they both require the same 5 pounds of force to maintain that speed. (Disregarding the difference in drag due to the greater displacment of Boat B). The 5 pounds of force that the paddlers supply is equal to, and in the opposite direction, the 5 pound of force that is generated in the form of drag. The difference is that Boat A is slightly ahead of Boat B because it accelerated to 3 mph slightly faster. The kinetic energy of the two boats is not, however, equal. For Boat A KE=.5*200*3^2=900. For Boat B KE=.5*250*3^2=1125.
Our two paddlers paddle for 3 hours and cover 9 miles. Each paddler maintains the same power output over those three hours, applying 5 pound of force to propel their boat. This 5 pounds of force is used to overcome drag. It doesn't accelerate the boat. It doesn't change the kinetic energy of the boat.
At the end of the trip, with the beach in sight, both paddlers stop paddling at the same time and let their boats drift to shore. Boat B is slightly behind Boat A when they stop paddling, as it has been for the entire trip. Boat A deccelerates due to drag at the rate A=F/M or 5/200=.025. Boat B deccelerates at the rate 5/250=.020. Now Boat B catches up as it dissipates it's greater kinetic energy and both boats come to a stop with their bows touching shore at the same time!
Kinetic energy doesn't play a part in determining the effect of paddling a heavier or lighter boat. The important effect is the increase in displacement, wetted area, and drag (Which we have deliberately ignored until now in order to analyse the kinetic energy aspect of this problem) and I have to leave it to the marine architects among us to quantify that.
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