      # Power And Kinetic Energy In Rowing Power and kinetic energy

Recently, we had an interesting discussion with Mathijs Hofmijster about power in rowing (full text is here). The point I made is that power measurements and the ŌĆ£Applications of Newton's LawsŌĆØ (analysis of the power transformation into motion and kinetic energy, which Mathijs tried to do) are two different areas and utilise different methods of analysis. The first area targets how the power is PRODUCED; the second ŌĆō how it is USED.

For example: in a car, the definition of the engine power production is very simple: a product of torque on the crankshaft by its rpm. Engine power does not depend on accelerations and movements of the car and could be determined accurately and reliably if two of its components are measured. Similarly, in rowing and cycling there is only one channel of power transfer to the external environment: the oar in rowing, and the crankshaft-chain in cycling. Other cyclic sports (running, swimming, canoeing, skiing, etc.) are not as ŌĆśluckyŌĆÖ- they require more sophisticated methods to calculate power production. Therefore, net rowing power can be determined accurately and reliably with force-velocity or torque-rpm measurements at the oar. No arguments were presented to disprove this statement yet.

Analysis of a rowerŌĆÖs power conversion into motion and kinetic energy of the rowing system starts with choosing the reference frame (RF), followed by the ŌĆ£free bodyŌĆØ, and then its interaction with the environment. If the RF related to the environment is chosen (water surrounding the boat, not the ŌĆ£EarthŌĆØ, i.e. the shore, proposed by our respected opponents), the ŌĆ£free bodyŌĆØ can only be the whole rower-boat-oar system, not the rower themselves. An obvious reason for this is the following: rowers and cyclists do not interact with the environment directly (as runners and swimmers do): they transfer power through a gear mechanism, which converts the power by increasing velocity, but decreasing force. In rowing, only the blade reaction force and the drag force at the hull are external relative to the rowing system. All other forces applied by the rower (handle, stretcher, gate forces) are internal ones and cannot be referred to the environment directly. Therefore, it doesnŌĆÖt really make sense to multiply internal forces by their velocities relative to the external environment, which is what our opponents have done. Here is our model of power transformation into kinetic energy in rowing (Fig.1), excluding any mathematics for simplicity.

1.                The rower is the only source of energy that moves the whole rower-boat system. The rower applies Gross Power at the handle and the stretcher, which should be defined using the rowerŌĆÖs CM as the reference frame. This is a non-inertial RF, but this does not affect power calculations if forces and velocities are measured directly.

2.                From the rower, power is applied to the oar and becomes Net Power transferred to the external environment. As the oar rotates around the pin mounted on the boat, the boat RF should be used. This is also a non-inertial RF, but again the Net Power is determined correctly if the oar torque and angular velocity are measured.

3.                In this transformation between RFs, some power is lost in relative movements between the boat and rower (inertial losses), so Net Power is lower than Gross Power by 5-7% (RBN 2010/05).

4.                At the oar, the Net Power is converted: the blade velocity is nearly doubled compared to the handle velocity, and the force proportionally decreases.

5.                The blade force is applied to the water, which creates an opposite reaction force, moving the whole system forward. In this case, an inertial environment RF based on the water surrounding the boat should be used. Power converted into kinetic energy of the system is the product of the forward component of the blade reaction force by the velocity of the systemŌĆÖs CM.

6.                The velocity of the systemŌĆÖs CM is lower than the blade velocity relative to the boat, so in this way a proportion of the blade power (15-20%, RBN 2012/06) is wasted into blade slippage in the water.

7.                The blade reaction force is transferred back through the oar and shared between the two main components of the system: the rower and the boat. The shares depend on the ratio of the handle/gate/stretcher forces and vary during the drive: a higher stretcher force (when a rower emphasises the leg drive) accelerates the rower, but slows down the boat; higher handle/gate forces (upper body emphasised) accelerates the boat, but negatively affect the rowerŌĆÖs acceleration.

8.                The power that is applied to the rower and boat masses and converted into their kinetic energy is a product of their shares in the blade propulsive force by their velocities relative to the water in the environment RF.

9.                Two components of the system, the rower and the boat, not only receive kinetic energy through the oar, but also exchange it between themselves. During the recovery, the oar supplies no energy, but the rower pulls the stretcher and transfers his kinetic energy to the boat, which accelerates. Energy exchange also happens during the drive: after the catch, the rower actively accelerates his CM using the leg drive, taking kinetic energy from the boat, which receives negative acceleration. As this exchange is provided by the rowerŌĆÖs efforts and has nothing to do with the external environment, it is logical to suppose that the rower RF should be used, or an inertial RF moving with constant velocity equal to the average of the system over the cycle. This makes the analysis quite challenging, because the source of kinetic energy is not always clear. The complexity is multiplied by the number of rowers in a crew.

10.             Finally, all kinetic energy is lost in the water and to air drag resistance. The main part is spent on the water drag at the hull, which is equal to the product of the boat drag factor by the cube of its velocity in the water, so the highest losses occur at the highest boat velocity during the recovery.

The mathematics of this model will be presented in a future Newsletter, confirmed with measured data.

┬®2018 Dr. Valery Kleshnev www.biorow.com