Energy efficiency of the rowing oar from catch to square-off

The mechanical efficiency of a rowing oar during the drive phrase may be defined as that proportion of the energy put into the oar by the rower which is "usefully" dissipated in overcoming hull and aerodynamic drag as the boat is propelled forwards. Ignoring friction in the oar gate/pivot, the remaining energy is "uselessly" dissipated by the blade as it shifts and churns water. As an example of energy analysis of propulsion systems, the energy efficiency for a slipping and a non-slipping car wheel is derived. The same method applied to the oar, shows that the efficiency of the oar is inextricably related to the direction of the water reaction force on the blade. If, as is usually assumed, the force is normal to the oar-shaft direction, the efficiency of the oar can be expressed as V sin(A)/(omega l), where V is the hull speed through the water, omega is the rotational speed of the oar, l is the distance from the gate to the centre of force on the blade, and A is the angle of the oar-shaft to the boat forward direction. We consider the efficiency of the oar from catch to square-off, using data gathered from an elite eight rowing at the Australian Institute of Sport. We show that, except for a degree or two of oar-sweep at the catch, when the force is negligible, the efficiency is greatest towards square-off, where a greater portion of the blade force is directed forward, which agrees with the results of Affeld et al. (Int. J. Sports Medicine, 14:S39-S41, 1993). Correlations of force profile shape with average efficiency show that a later application of the maximum force, nearer square-off, is generally more efficient than an earlier application. However, since the oar efficiency increases with boat speed, less efficient oars, for which the maximum force is applied near the catch, cause a greater increase of the boat speed early in the stroke, and this tends to enhance the efficiency of all the oars later in the stroke

Searching for DSMC collision partners using pseudo-subcells

LeBeau et al.[ A.I.A.A. paper 2003-1031, 2003] introduced the “virtual subcell” (VSC) method of finding a collision partner for a given particle in a cell. In the VSC method all potential collision partners in the cell are examined to find the nearest neighbor. To limit the CPU time required for large numbers of particles in the cell the search can be restricted to a subset of all particles in the cell; the nearest particle from that restricted search is used. For 3D hexahedral cells, of various aspect ratios, the expected nearest neighbor distance is found to be given (within few percent) by dn = 0.746L/N^0.383. where N is the number of particles in the cell and L is the cube root of the cell volume. Here I test a modification of the VSC method, the “pseudo-subcell” (PSC) method, whereby the search for a collision partner is truncated whenever a “near enough'” particle is found. The “near enough'” distance, or diameter of the pseudo-subcell, is delta = Fdn. For a factor F = 1.1 there is good chance that a “near enough” particle is, in fact, the nearest neighbor. The mean collision separation (MCS) is then found to be less than 1.04dn. Gallis et al. [AIP Conference Proceedings, v1084, pp299-304, 2009.] report that VSC is computationally efficient for N less than 30, so here the VSC search is restricted to 29 remaining particles. The PSC search is restricted to 33 remaining particles, to yield the same MCS as VSC for large N. The limiting (smallest) value of delta for PSC corresponds to that for N = 30. For large N both methods give a MCS value similar to that which would be expected using 35 standard subcells. PSC uses between 12% and 20% less CPU than VSC. PSC can be tailored to give a range of accuracy and CPU saving compared to VSC. There seems to be no need for a standard subcell method; the PSC search routine can be used in all cases merely by limiting delta and the search length

A Particle-Only Hybrid Method for Near-Continuum Flows

EPSM is a particle simulation method for the simulation of the Euler equations. EPSM is used here as part of a hybrid EPSM/DSMC method for the simulation of near continuum flows. It is used where the flow gradients are not large and the flow is expected to be in an equilibrium state. The gradient of local mean free path has been used to detect those regions where EPSM can be invoked. Results are presented for the unsteady flow of a gas in a shock tube with Knudsen numbers in the initial state of 0.01 and 0.002 either side of the diaphragm (based on the length of the initial low-pressure region). The results for the hybrid method are very close to those for pure DSMC. The execution speed of the hybrid code is 1.75 times that of standard DSMC

Introduction to Direct Simulation Methods for Rarefied Flow

Course notes for a postgraduate seminar series delivered to Professor K. P. J. Reddy's High Enthalpy Aerodynamics Group at the Indian Institute of Science, Bangalore, India, in May and June 2004. A step-by-step approach is taken to simulation of gas flows using Bird's Direct Simulation Monte Carlo method, starting with collisionless flow and progressing to two simple collision models: the Maxwell molecule and the Hard Sphere molecule. These molecules display a viscosity relationship mu~T and mu~sqrt{T} respectively. A new approach to simulating a more realistic viscosity mu = mu{T} (collision rate DSMC or nu-DSMC) is explained. Example FORTRAN codes for the simulation of the unsteady flow in a shock tube, using the various collision models, may be downloaded from Web links within the PDF file

A Note on Relativity Before Einstein

A [1983] review, 'Relativity before Einstein' made no mention of the work of Joseph Larmor, whose early derivation of the Lorentz transformation seems to be less well known than those of Lorentz and Poincare. In 1897, Larmor, starting from a first-order transformation similar to Lorentz's first order version, presented the correct form of what is now known as the Lorentz transformation. In his presentation of the theory in 1900 Larmor saw the time dilation effect as a consequence of Maxwell's electromagnetic theory. It was Lorentz who, in 1895, introduced the notion of the relativity of simultaneity (local time), without the time dilation effect. Poincare in 1900 discussed how Lorentz's local time would arise from the procedure of synchronizing moving clocks by exchanging light signals assumed to travel at the same speed in either direction. Lorentz presented the correct version of the transformation in 1899, and discussed the variation of mass with velocity arising from it. In 1902 Lorentz was aware of Larmor's 1897 work but apparently missed its significance. Nevertheless, the credit for the first presentation of the Lorentz transformation including the crucial time dilation belongs to Larmor

The direction of the water force on a rowing blade and its effect on efficiency

Previous estimates of the efficiency of rowing have assumed (in the absence of any better data) that the water reaction force on the rowing blade, the `blade force', acts in a direction normal to the blade chord-line (oar shaft direction). In 1967 Wellicome suggested that there may be a component of the blade force parallel to the chord-line, pointing outwards, which would make the oar more efficient in the early part of the stroke [Rowing: A Scientific Approach, A Symposium, (Williams, Scott, eds.), Kaye and Ward Ltd, London, 1967]. The recent steady-flow 1/4-scale model tests of Caplan and Gardner [J. Sports Sciences, v25:643-650, 2007] detected a small such parallel force on the asymmetrical Macon and Big Blade shapes. It is possible that this component of force is actually zero within the experimental error, but if the direction of the blade force is tilted away from normal by the amount shown in the model tests, the efficiency of rowing propulsion may be one or two percent greater than previously estimated. However, those previous estimates of efficiency ignored the effect of oar bending which could reduce the efficiency of rowing by as much as 5%. There are reasons to suspect that the scale model results cannot be used to predict the magnitude or the direction of the force on a full-size oar during rowing: the flow is unsteady, and a crucial non-dimensional parameter, the Froude number, is significantly different in the two cases. It might be possible to detect a forward component of the blade force during rowing by measuring the tension strain such a force would produce in the oar-shaft outboard of the gate/pivot

Scaling Parameters In Rarefied Flow: Breakdown Of The Navier-Stokes Equations

This is an updated version of notes from a seminar delivered in 2004. Although the text has been revised this update is still in note form. References missing from the original have been added, as well as appendices giving the data taken from two undergraduate theses undertaken at the University of Queensland. In high altitude flight the average spacing between the molecules of the flow gas is not negligible compared to a typical dimension of the flow field. In this case, the gas does not behave like a continuum and its discrete particle nature must be considered. The continuum assumption "breaks down" and the Navier-Stokes equations can, in theory, no longer be shown to be valid, particularly for high speed flight. The fundamental equation describing the flow at the particle level is the Boltzmann quation, from which the Euler equations, the Navier-Stokes equations and more accurate Burnett equations may be derived under various assumptions. Various scaling parameters have been suggested to identify the regimes in which these different equations are valid, ranging from the Knudsen number, Tsein's (1946) parameter, Cheng's (1961) rarefaction parameter, Bird's (1970) breakdown parameter, and a form of the viscous interaction parameter derived from shock-boundary layer theory. All these depend primarily on the non-dimensional group (Ut_c/L), which must be small for the Navier-Stokes equations to remain valid. U is flow speed, L is a flow length, t_c is a collision time. We show how all these parameters may be derived from the Boltzmann equation and interpreted as the ratio of typical shear stress to pressure in the flow. Cheng's parameter accounts for collision rate in some characteristic region of the flow. It appears to be the best correlation parameter for high-speed blunt body flow. For slender body flow the viscous interaction parameter based on a reference boundary layer temperature, a "modified Tsein parameter" similar to Cheng's parameter, appears to be best. Comparison of Navier-Stokes calculations and direct simulation solutions of the Boltzmann equation show that the Navier-Stokes equations may be adequate for almost rarefied flow (at least for hypersonic flow round a cyclinder)

Vibrational degrees of freedom in the Total Collision Energy DSMC chemistry model

The Total Collision Energy (TCE) model is used to simulate chemical reactions in the Direct Simulation Monte Carlo method. Colliding particle pairs with total collision energy (translational plus internal energy) greater than an activation energy are accepted for reaction with a probability which depends on the amount of the collision energy in excess of the activation energy. Constants in the probability function are adjusted to match experimentally determined rates in an Arrhenius form under thermal equilibrium conditions. The model thus attempts to extrapolate equilibrium reaction rates to non-equilibrium conditions by using microscopic based information from colliding particle pairs. However, the number of active “degrees of freedom” (DOF) in the vibrational energy mode contributing to the total collision energy must be specified for each collision pair; various methods have been proposed for this. It is shown that the different calculation methods can alter the equilibrium reaction rate returned by the TCE model, and can have significant effects throughout non-equilibrium flow-fields. If we assume, as is usual, that all of the internal energy is available for the reaction, we consider that the most consistent and physically intuitive approach is to determine the number of active DOF from the local macroscopic temperatures in the cell

Modified GHS collision model compared with VHS

At low temperatures, where the attractive intermolecular forces are important, the GHS collision model produces a more realistic variation of viscosity with temperature than the standard Variable Hard Sphere (VHS) collision model. A slight modification of the GHS model,[Macrossan and Lilley, J. Thermophysics Heat Trans, 17, 289-291, 2003], makes it no more than 5-15% more computationally expensive than the VHS model. We calculate the supersonic flow of Argon, with a freestream temperature of 100 K, and stagnation temperature of 1300K, around a flat plate normal to the freestream (see Fig. 1). flow. The temperature in the wake region is approximately 500 K, so the viscosity of the two models differs in the wake region. This leads to small differences in the temperature field and the size of the re-circulation region for the GHS, compared with the VHS collision model

Computational study of the Froude number effects on the flow around a rowing blade

We consider some scale model experiments in which the forces on rowing blades were measured [Caplan and Gardner, J. Sport Sciences, 25(6), 653-650, 2007]. The experiments were conducted in a flume at a single flow velocity which corresponded to a Froude number, based on the depth dimension of the blade, very close to the critical value of unity. For real rowing, the blade moves at speeds corresponding to Froude numbers in the range of approximately 0.3 to 3.5. We use a computational fluid dynamics (CFD) analysis to investigate the Froude and Reynolds number effects on the forces on a flat plate `blade', as well as the effects of the flume size relative to the model size in the experiments. We consider only one orientation of the plate to the flow velocity and we consider only idealized steady flow. We find that the flume in the experiments was probably too shallow, so that the measured force coefficients could be 6\% higher than for rowing in deep water. Using a series of calculations for fluids with different densities, we show that the force coefficient is independent of the Reynolds number for the range of Reynolds numbers characteristic of real rowing, but is a strong function of the Froude number. There is a sudden decrease of some 30\% in the force coefficient as the Froude number changes from sub-critical (less than 1) to super-critical (greater than 1). For Froude numbers greater than 2 the force coefficient increases steadily with Froude number