Patent Application
20180188134
The present invention relates to a method and system for determining the aerodynamic resistance of a moving object and/or person. More particularly, the invention relates to a method and system for determining the aerodynamic resistance of a cyclist. It will also allow him to improve his performance by adapting his position on the bicycle to minimize said aerodynamic resistance.
It is well known that aerodynamic resistance is made up of two forces, namely drag and lift. In cycling, for example, in light of the movement speeds, the lift is considered negligible, such that the aerodynamic resistance is therefore likened to the drag.
In a manner known in itself, the drag is given by the following equation:
R
A=0.5pApCdVf2
where Ap designates the projected frontal area of the cyclist and his bicycle, Cd is the drag coefficient, ρ is the density of the air and Vf is the flow speed of the fluid on the cyclist's body.
In the context of an aerodynamic study, the quantity that one seeks to minimize is the actual frontal area given by the following equation:
In order to determine the actual frontal area, it is necessary to know the drag RA. It will be noted that the actual frontal area is not a constant, but evolves slightly with the movement speed.
In order to evaluate the actual frontal area of a cyclist, several methods are well known, these various methods being described in the publication by Vincent Chabroux “Approche aérodynamique et biomécanique de l'amélioration des performances de cyclistes en course contre la montre” [Aerodynamic and biomechanical approach to improving cyclists' performance when trying to beat the clock] PhD thesis, Universite de la Mediterranee, 2010 and in the publication by F. Grappe. “Cyclisme et optimisation de la performance: sciences et methodologie de l'entraînement” [Cycling and performance optimization: training science and methodology]. Sciences et pratiques du sport, De Boeck, 2005.
For the most part, these methods can be classified in four groups: mechanical power analysis, towing-based measurement, the deceleration method and wind tunnel measurement.
The analysis of the mechanical power consists of measuring the power delivered by the cyclist owing to a wattmeter at different speeds, then evaluating the drag using a linear regression from said delivered power measurements. This method is relatively precise, but requires several tests under real conditions.
The towing-based measurement consists of measuring the traction forces by towing a cyclist on his bicycle with a car moving at a constant speed. This method is fairly restrictive and lacks precision due to turbulence caused by the towing vehicle.
The deceleration method consists of measuring the deceleration of the cyclist at different speeds. Thus, by using Newton's laws, the drag is calculated. This method is very cumbersome to set up and requires the cyclist to be immobile.
Wind tunnel measurements consist of generating a stream of air over the cyclist/bicycle unit and quantifying the reaction forces on the ground using a force platform. This method, although the most precise, is also the most expensive.
It will be noted that in aerodynamics, it is well known to determine aerodynamic and/or mechanical characteristics, such as the deformation of an object or the drag of an object, for example, using wind tunnel tests. This is in particular the case for documents U.S. Pat. No. 7,997,130 and US 2007/095135.
Document U.S. Pat. No. 7,997,130 describes a system and method for measuring the deformation of an object, such as a fighter aircraft, for example, positioned in the tunnel of a wind tunnel. The object is positioned in the tunnel of a wind tunnel and a system for acquiring a cloud of dots representing at least one surface of the object is recorded. The object is moved in the stream of the tunnel of the wind tunnel and clouds of dots of the surface of the object are also acquired during said movement in order to determine, using a computer system receiving the data relative to the clouds of dots, at least the position of the object, its orientation and the deformation of the surface of the object.
Document US 2007/095135 describes a method for determining the drag of an aircraft comprising providing a model of the aircraft, which is positioned in a tunnel of a wind tunnel in a determined initial orientation, and a plurality of orientation and incline sensors mounted on said model. The model is next moved in the tunnel of the wind tunnel from its initial orientation toward a second orientation in order to determine the drag of the aircraft in the various possible orientations of the latter.
However, aside from the fact that these methods are particularly expensive in light of the need to use a wind tunnel, they are not suitable for determining the aerodynamic resistance of a cyclist in particular.
Recently, a new method for measuring aerodynamic resistance was proposed. This method is in particular described in the publications byT. Defraeye, B. Blocken, E. Koninckx, P. Hespel, and J. Carmeliet. “Aerodynamic study of different cyclist positions: CFD analysis and full-scale wind-tunnel tests.” J Biomech, 43(7):1262-1268, May 2010 and Peter Nicholas Doval. “Aerodynamic Analysis and Drag Coefficient Evaluation of Time-Trial Bicycle Riders.” PhD thesis, University of Wisconsin-Milwaukee, 2012.
This method consists of coupling a 3D model of the cyclist and his bicycle obtained using a scanner with a fluid dynamic digital calculation code. This method makes it possible to obtain aerodynamic drags in accordance with those measured in a wind tunnel. It has the advantage of being done at a lower cost and without needing to use real conditions. However, its main drawback is that it uses a static model that is not representative of a cyclist in the process of pedaling.
One of the aims of the invention is therefore to resolve these drawbacks by providing a method and a system for determining the aerodynamic resistance of a moving object or person having a simple and inexpensive design, allowing contactless measurement of the aerodynamic resistance of an object or a person, such as a moving cyclist, without said object or person moving relative to the ground. A moving person is a person who on the one hand is in motion relative to a fluid, such as the air, and on the other hand, in motion himself, for example a pedaling movement in the case of a cyclist.
To that end and according to the invention, proposed is a method for determining the aerodynamic resistance of an object or a person having its own movement, remarkable in that it includes at least the following steps:
Preferably, said step for acquiring clouds of dots consists of at least the following steps:
Furthermore, the step for determining 3D models as a function of time from dots of the clouds of dots acquired at each moment between the moments tinit and tfin consists of at least the following steps:
Said step for preprocessing of the data relative to the recorded sets of dots consists of at least one step for filtering abnormal dots and/or filtering noise and/or spatiotemporal smoothing.
Furthermore, the step for simulating the movement of the solids described by the clouds of dots corresponding to the object with a person in a fluid, for each moment between the moments tinit and tfin consists of at least the following steps:
Said average of the aerodynamic resistance forces is determined by calculating the quadruple integral of the product of the density P(C,Vx,Vy,Vz) and the aerodynamic resistance forces exerted on the object or the person F(D(C,Vx,Vy,Vz)).
Advantageously, the average of the aerodynamic resistance forces can be calculated considering that:
Another object of the invention relates to a system for determining the aerodynamic resistance of an object or a person having its own movement, remarkable in that it includes at least:
Preferably, said means for acquiring clouds of dots comprise at least:
Said means for determining 3D models as a function of time from dots of the clouds of dots acquired at each moment between the moments tinit and tfin comprise at least:
Furthermore, the means for preprocessing of the data relative to the recorded sets of dots consist at least of a filter for abnormal dots and/or a filter for noise and/or spatiotemporal smoothing means.
Said means for simulating the movement of the solids formed by the clouds of dots corresponding to the object with a person in a fluid, for each moment between the moments tinit and tfin comprise at least:
Said average of the aerodynamic resistance forces is determined by calculating the quadruple integral of the product of the density P(C,Vx,Vy,Vz) and the aerodynamic resistance forces exerted on the object or the person F(D(C,Vx,Vy,Vz)).
The function F is obtained by digital simulation. This digital simulation consists of simulating a flow of air around the moving object, the direction of which is defined by the parameter D. This simulation thus allows a virtual measurement of the aerodynamic resistance forces exerted on the moving object. Said digital simulation is based on the Navier-Stokes equations. For better results, said simulation may use the Reynolds-Averaged Navier-Stokes (RANS) equations, and more specifically the SST (Shear-Stress Transport) model, described in Menter, F. R. (August 1994), “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications”, AIAA Journal 32 (8): 1598-1605.
Furthermore, the average of the aerodynamic resistance forces can be calculated considering that:
Other advantages and features will better emerge from the following description of several alternative embodiments, provided as non-limiting examples, of the method for determining the aerodynamic resistance of a moving object or person according to the invention, from the appended drawings, in which:
Below, we will describe a method and a system for determining the aerodynamic resistance of a cyclist pedaling on a bicycle, said cyclist having a specific movement, i.e., his pedaling movement. However, the method and system may of course be adapted to any object or person having its own movement without going beyond the scope of the invention.
In reference to
Furthermore, the invention also includes a system making it possible to measure, over time, 3D clouds of dots corresponding to the position of dots on the surface of the moving solid, a system making it possible to obtain a correct 3D+t model of the moving solid of interest and a system making it possible to simulate the displacement of the moving solid in a fluid and to measure the forces exerted on this solid.
Said system making it possible to measure, over time, 3D clouds of dots corresponding to the position of dots on the surface of the moving solid is made up of a set of traditional contactless 3D sensors such as time-of-flight cameras, stereoscopic cameras, pattern projection cameras, or the like, placed wisely so as to obtain a set of 3D points completely describing the solid, in the case at hand the cyclist, studied at a time t. This system is capable of acquiring 3D clouds of dots at a pace compatible with the dynamics of the studied movement. One thus obtains a set of 3D clouds of dots representing the solid at different times t.
In reference to
Said system making it possible to obtain an accurate 3D+t model of the moving solid makes it possible to process all of the 3D clouds of dots in order to obtain a 3D+t model of the moving solid. To that end, a set of preprocessing operations is applied to these clouds of dots: filtering for abnormal dots, filtering for noise, spatiotemporal smoothing, etc. Lastly, a meshing operation is applied in order to obtain a 3D+t model usable by the fluid mechanics simulation system.
The system making it possible to simulate the displacement of the moving solid in a fluid and to measure the forces exerted on the cyclist implements traditional digital fluid mechanics methods in order to simulate the displacement of the studied solid in a fluid (air in the case of the cyclist). This simulation is in particular configured by the direction and displacement speed of the fluid relative to the solid, represented by the vector D. It makes it possible in fine to calculate the average F(D) of the aerodynamic resistance forces exerted on the solid throughout the entire movement sequence recorded by the sensors.
Inasmuch as one seeks to study the aerodynamics under real conditions (for example those of outdoor cycling practice), it is important to account for the fact that the relative speed of the solid with respect to the fluid may change over time. To that end, the method according to the invention proposes to model the different variables of the movement by probability laws making it possible to describe a given environment (for example, a particular cycling journey).
To that end, the space is provided with an orthonormal base (i;j;k) such that the studied solid is displaced along the axis defined by i and the ground is parallel to the plane defined by i and j, for example.
The vector D, relative displacement of the solid in the fluid, can then be broken down as follows:
{right arrow over (D)}={right arrow over (V)}−{right arrow over (C)}
where V designates the characteristic vector of the wind and C designates the characteristic vector of the movement of the cyclist.
It is next possible to describe:
{right arrow over (D)}=V
x
{right arrow over (i)}+V
y
{right arrow over (j)}+V
z
{right arrow over (k)}−C{right arrow over (i)}
{right arrow over (D)}=(Vx−C){right arrow over (i)}+Vy{right arrow over (j)}+Vz{right arrow over (k)}
It is therefore possible to write D as a function of C, Vx, Vy and Vz, where C designates the speed of the solid, Vx designates the speed of the wind along the axis i, Vy designates the speed of the wind along the axis j, and Vz designates the speed of the wind along the axis k.
The variables C, Vx, Vy and Vz are next considered to be non-independent random variables whereof the joint probability law is given by the density P(C; Vx; Vy; Vz), this probability law enabling a statistical description of the specific studied environment.
Considering on the one hand that the kinetics of the studied movement are very fast relative to the changes in conditions (i.e., an evolution of the variables C, Vx, Vy and Vz) and on the other hand that the movement sequence is not influenced by the variables C, Vx, Vy and Vz, it is then possible to calculate an average Fm of the aerodynamic resistance forces F exerted on the solid in the studied environment as follows:
F
m
=∫∫∫∫P(C,Vx,Vy,Vz)F(C,Vx,Vy,Vz))dCdVxdVydVz
F is obtained by digital simulation. This digital simulation consists of simulating a flow of air around the moving object, the direction of which is defined by the parameter D. This simulation thus allows a virtual measurement of the aerodynamic resistance forces exerted on the moving object. Said digital simulation is based on the Navier-Stokes equations. For better results, said simulation may use the Reynolds-Averaged Navier-Stokes (RANS) equations, and more specifically the SST (Shear-Stress Transport) model, described in Menter, F. R. (August 1994), “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications”, AIAA Journal 32 (8): 1598-1605.
It is clear that the virtual measurement of the aerodynamic resistance forces may be done using any other method well known by those skilled in the art, in particular from a direct calculation as a function of the measurements making it possible to determine the 3D model of the moving object, without going beyond the scope of the invention.
The model is simulated by using a digital method (finite elements method, finite volumes method, finite differences method, spectral method, etc.) carried out on a computer.
In order to make the model previously described more easily usable by a computer, the latter is advantageously discretized and simplified.
In the specific case of studying the aerodynamics of a cyclist, the following simplifications can be made:
It may be considered that the wind is parallel to the route, i.e.:
V
z=0
Vx and Vy may be expressed as a function of the strength V of the wind and the angle of the wind relative to the axis defined by i:
V
x
=V cos α
V
y
=V sin α
It may be considered that the strength V of the wind does not depend on its direction a and vice versa
It may be considered that the speed C of the cyclist does not depend on the strength V of the wind or its direction a.
Thus, by using the three previous simplifications, the joint probability law can be rewritten in the following simplified form:
P(C,Vx,Vy,Vz)=PC(C)PV(V)Pα(α)
The independence of the random variables makes it possible to express the joint law as the product of the marginal laws associated with each of them. These laws can be defined much more simply than the joint law. For example, PV is traditionally defined as the probability density associated with a Weibull law; Pα is defined as the probability density associated with a uniform law; and PC has a profile specifically depending on the type of studied cyclist event (sprint, stage race, etc.).
It is therefore possible to rewrite the function F, corresponding to the aerodynamic resistance forces exerted on the solid in the studied environment, in the following form:
F({right arrow over (D)})=F({right arrow over (D)}(C,Vx,Vy,Vz))
And in light of the simplifications, we can write:
F({right arrow over (D)}(C,Vx,Vy,Vz))=F({right arrow over (D)}(C,V cos α,V sin α,0))=F(C,V,α)
In order to limit the number of simulations and discretize the model, it may be considered that the cyclist and his movement are symmetrical relative to the axis defined by i. One then has:
F({right arrow over (D)}(C,V,α))=F({right arrow over (D)}(C,V,−α))
Thus, one may settle for varying a from 0 to it during simulations.
Furthermore, one may also consider that the movement of the cyclist is periodic (with a time period of one pedal revolution). One may therefore settle for recording a movement sequence with a duration equal to this period.
To discretize the model, one first chooses Cmax and Vmax on the one hand and SC, SV and Sα on the other hand such that SC divides Cmax, SV divides Vmax and Sα=2π/k with k an integer.
One then has:
It is then possible to approximate Fm as follows:
In this way, the model only requires n=nCnVnα simulations.
Lastly, the examples given above are of course only specific illustrations that are in no case limiting regarding the fields of application of the invention.
| Number | Date | Country | Kind |
|---|---|---|---|
| 1556815 | Jul 2015 | FR | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/EP2016/066531 | 7/12/2016 | WO | 00 |
