THE LESSONS OF 200 YEARS That rate of change in velocity, positive and negative, is defined as acceleration8669 or its opposite, deceleration. According to the famous equation, F = ma, force can be defined as the effort it takes to instantaneously change the velocity of an object of a certain mass at a certain rate. In rowing, the mass of the boat is constant, so apply force and the boat accelerates. Apply more, and it accelerates more quickly. So far, so good. The familiar use of the above terms corresponds pretty well with their scientific meanings. Now the defini- tions must get a bit more precise. Work is defined as the transference of energy equal to the force applied to an ob- ject multiplied by the distance the object moves. W = fd. If it takes a certain amount of work to move a heavy box one meter, it takes twice as much work to move it two meters. Analyzing Force Curves When graphing what is familiarly called a “force curve,” with the y-axis force and the x-axis distance, if you break up the area un- der a rowing force curve into a series of nar- row vertical columns under each point on the curve, the area of each column would be the product of its height and its width, the force at that particular brief moment times the small amount of distance traveled during the moment the force is applied. Force times distance, i.e., the work. If one uses calculus, one can mathematically increase the number of columns to infinity, shrink them to infinitesimal width, sum them and get the work expended during the entire stroke. Therefore, the area under the curve represents the work during the pullthrough. Not surprisingly, if you want to move the 8669 In calculus, acceleration is the derivative of velocity. boat, all other things being equal, the more area under the curve, the more work, the better. Power is the amount of work done per unit of time. If you can move that box two meters in ten seconds, it takes the same amount of work but twice as much power to move it the same distance in five seconds. The problem is that while coaches and rowers often use the words “force” and “power” interchangeably, they have very different meanings. Translating this into words that rowers can relate to, work depends on force. The higher you can make all of those infinitesi- mally narrow columns, the more area under the force/distance curve. Power adds in the time factor, and that is relevant. The rower wants to get through the stroke as quickly as possible, imparting as much velocity as possible to the system. Contemporary biomechanist Valery Kleshnev has prepared the chart on the fol- lowing page which illustrates well the dis- tinction between force and power. Kleshnev proposes three highly simpli- fied hypothetical force curves, one front- loaded, a second even and a third back- loaded. The cumulative force applied and the time required to complete the pullthrough is presumed to be identical in all three cases, so the work is the same.8670 Kleshnev: “This is just a very simple model. We are talking about a body some- where in space, no gravity. You just apply force, and body accelerates.”8671 8670 The total velocity imparted to the boat is also assumed to be equal, presupposing that all three curves would be equally effective in translating force into boat moving. In the real world, this is most definitely not the vcase. Not all force ap- plication strategies yield the same results. 8671 Kleshnev, personal conversation, 2011 2439
