Kinetic energy dissipated by the moving rower. Revised September 2009 homepage

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1 Kinetic energy dissipated by the oving rower. Revised Septeber 2009 hoepage Introdction The boat is oving throgh the water and the rower is oving on the seat with respect to the boat. Better: rower and boat are oving with respect to each other. Discssed is the qestion how ch energy is dissipated as a reslt of the repeating acceleration and deceleration of the rower and the boat. To introdce the proble the discssion will be introdced by considering the sitation on the ergoeter. The sbject is also covered by Bill Atkinson. On the Concept 2 ergoeter On the Concept 2 ergoeter the sitation is soewhat sipler as there is no relative otion of the seat with respect to the boat bt otion with respect to the earth only. Sitation 1. The rower is oving to and fro withot plling the chain. The following explanation is valid for oving in both directions. Sliding distance s = 0.6 Velocity profile: trianglar, ax speed reached at 0.3 Max. speed 1 = 1 /s Average speed a = 0.5 /s Tie to go one way T1 = 0.6/0.5 = 1.2s Cycle tie T = 2.T1 = 2.4s Stroke rate SR = 60/2.4 = 25/s Moving ass = 60kg Kinetic energy at top speed E = = = 30 J Kinetic energy loss expressed as ean power P = E/T1 = 30/1.2 = 25W The sae calclation yields for the oveent in both direction so we can say the rower is constantly (bt averaged over the cycle) delivering 25W. Soe frther considerations. Maxi seat speed is reached after T1/2 s. The acceleration of the ass is a=1/(t1/2) = 1/0.6 = 5/3 /s 2 The leg force F = a = 60 5/3 = 100 N. The work done by the leg to reach the top speed is W = F s/2 = = 30 J Of corse E = W. Dring the acceleration of the ass, force and velocity have the sae direction; the work dring this period is positive. Dring the deceleration of the ass, force and velocity have opposite direction, the work done is negative. In a conservative syste (with springs e.g.) the energy is stored by the syste and is not lost. The syste nder consideration is not conservative and the kinetic energy is siply lost. Besides the deceleration of the ass reqires soe effort of the rower, he has to do soe work. This work is neglected here. Siilar sitations: a person descending a staircase or lowering a lifted weight. I did not find a ethod to calclate the work involved in these sitations in the bioechanical literatre bt the proble st have been addressed soewhere. In the following positive work will be considered as delivered by the rower and sed in a sefl anner: to increase the kinetic energy in the syste or to overcoe the external

2 friction. Negative work will be considered as internal dissipation, seless bt not to be delivered by the rower. As fond above: withot plling the chain the rower is prodcing 30J per cycle or an average power of 25W. Sitation 2 This is the coon sitation. When the rower oves away fro the flywheel he plls the chain and when he retrns (recovery) no interaction with the flywheel exists. The recovery eqals Sitation 1. Dring the recovery (sae paraeters as above) the rower prodces 25W and this otpt is not recorded on the onitor. Dring the drive phase the rower aintains a pll on the chain. In the first part of the drive the forces exerted by the rower are sed to accelerate his own body and to pll the chain. His leg force is the s of the chain pll and the force necessary to accelerate his body. In the second phase of the pll his body is decelerated by the chain pll. His leg force is the chain pll ins the force to decelerate his body. This eans that nder noral conditions dring the whole drive the rower s power is positive and all the energy (power) he delivers is recorded on the onitor. The figre below shows the forces on the rower (greyed rectangle) and.a is the inertia force ass ties acceleration (deceleration). F chain.a F chain.a F legs F legs Flegs = Fchain +.a Flegs = Fchain -.a In this sitation the rower prodces 30J dring the recovery or 30/2.4 = 12.5W ore than the onitor indicates. This is a rogh estiate. Usally the ties for the recovery and the drive are different. In the boat Sitation 1. The sitation in the boat is different. First we consider the boat and rower as a syste withot external forces. This is 2 1 U

3 1 = ass of boat and part of the ass of rower fixed to the boat [kg] 2 = oving ass of rower [kg] = speed of 2 with respect to 1 [/s] U = speed of 1 [/s] with respect to earth At the start of the seat otion = 0 and U = Uo, the axi vale of is = 1, and the corresponding speed of 1 is then U = U1 (ini vale). After the seat has stopped again U = Uo, this follows fro the principle of conservation of oent. The kinetic energy in the syste before and after the seat otion (otion of 2) is the sae becase the velocities are the sae. When reaches its axi vale, the kinetic energy in the syste reaches its axi vales. This difference in the aont of kinetic energy has to be delivered by the rower to the syste and is then lost: dissipated in the scles and articlations of the rower as in the case of the ergoeter bt the aont lost energy is different as will be shown. Moent at the start and at the end of the seat otion: Q0 = (1 + 2).U0 Moent at axi vale of : Q1 = 1. U1 + 2.(U1 + 1) Conservation of oent: Q1 = Q0 or 1.U1 + 2.(U1 + 1) = (1 + 2). U0 this yields: Kinetic energy at the start (and at the end) of the seat otion is: Kinetic energy when = 1 is: And expanded:

4 The difference Δ 1 - Eo is after soe (and tedios) algebraic aniplation Reark: In this expression 1 an 2 appear in the sae way. Interchange of 1 and 2 does not inflence the reslt U0 and U1 are absent In this derivation was >0. When <0 the reslt appears to be the sae. For the single scll we take as for the person on the ergoeter for the ass oving with the seat 2 = 60 kg. The ass oving with the boat is the reaining ass of the rower pls the ass of the boat or 1 = 30 kg. When 1 = 1 /s again, the energy loss is now: Expressed as average power this is 20/1.2 = 16.7W Copared with 30J or 25W on the erg. The ass distribtion is that of a noral boat When a roll rigger is considered and we asse 1 = 60 kg and 2 = 30 kg the reslt is the sae. For the type of energy loss as discssed here the roll rigger does not offer any advantage. Sitation 2 As sitation 1, bt rower is plling the oars. For the retrn it does not ake any difference. For the drive it ay be expected that there is a sitation as on the erg when plling the chain. Force and (relative) velocity have the sae direction. The rower is dring the whole drive generating power. Kinetic power is transferred to the oar, no power is dissipated. The next figre is a reslt of the silation odel. (Different paraeters as sed above). It shows the leg force dring the whole cycle. Only in the second part of the retrn force and velocity have an opposite sign bt the force is here very sall. A very sall aont of energy is dissipated. In the sall transition zones the sitation is not qite clear bt that is for this discssion less iportant. Conclsion In rowing in racing shells the energy loss de to oent transfer is sall. This is another conclsion than Atkinson s. For a echanical syste, sipler than rowing it is

5 force [N] shown that energy loss de to oent transfer can reach non-negligible vales. Click here Fleg tie [s] drive first part of retrn second part of retrn Leg force dring drive and retrn retrn

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