Method for determining the aerodynamic moment of resistance of a wheel

Abstract

A method for determining the aerodynamic moment of resistance M.sub.aero-EM of a wheel by calculating the variation with respect to time, of the product of the rotational speed of at least one wheel set in rotation about an axis and of the inertia of the said wheel about the said axis, the wheel being equipped with a device for picking off and recording the numerical values of its rotational speed. The wheel is protected by a removable cap and in is subjected to a flow of air.

Claims

1. A method for determining the aerodynamic moment of resistance, M.sub.aero-EM of a wheel that is equipped with a device for picking off and recording the numerical values of its rotational speed and that is protected by a removable cap, comprising: setting the wheel in contact with a rolling road initially at a time t.sub.0; taking the wheel out of contact with the road at a time t.sub.1 subsequent to t.sub.0, while at the same time continuing to subject the wheel to a flow of air recording numerical values of the rotational speed of the wheel set in rotation about an axis; calculating the variation, with respect to time, of the product of the rotational speed of the wheel set in rotation about an axis, and of the inertia of the wheel about the axis, inputting the measurements of the rotational speed (t) of the wheel, picked up as a function of time, into the following mathematical formula:
I.sub.EM(d(t)/dt)=M.sub.aero-EM(t)+M.sub.f(t)(I) where I.sub.EM represents the value of the moment of inertia of the wheel about the axis of rotation, (t) represents the instantaneous rotational speed of the wheel, M.sub.f(t) represents the value of the moment of friction of the hub of the wheel, and M.sub.aero-EM(t) represents the instantaneous aerodynamic moment of the wheel.

2. The method according to claim 1, wherein the flow of air has a main direction substantially parallel to that of the wheel.

3. The method according to claim 1, wherein the flow of air has a main direction at an angle of between 40 and +40 with respect to that of the wheel.

4. The method according to claim 1, wherein the axis of the wheel remains fixed relative to the ground.

5. The method according to claim 1, wherein the flow of air has a speed identical to that of the rotational-drive means.

6. The method according to claim 1, wherein the flow of air has a speed different from that of the rotational-drive means.

7. The method according to claim 1, wherein the wheel comprises at least one means of holding the wheel suspension.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) The invention will now be described with the aid of the examples and figures which follow, which are not in any way limiting and in which:

(2) FIG. 1 depicts the variation of the product [I.sub.EM (t)] as a function of time, according to an embodiment of the invention, for two different wheels, one comprising a tire with a smooth sidewall and the other tire with a sidewall covered with rough elements,

(3) FIG. 2 depicts the variation in the instantaneous aerodynamic moment of resistance M.sub.aero-EM(t) as a function of the ratio established between the speed of the flow of air and the speed of the wheel, according to an embodiment of the method of the invention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

(4) In order to implement this method, a wheel is placed on a rolling road in an aerodynamic wind tunnel. The wheel is kept in contact with the rolling road. The wheel is connected to a means of taking it out of contact with the rolling road. A means for holding the wheel in each of its positions allows it to be stabilized while measurements are being taken.

(5) The wheel is equipped with a device intended to pick off and record the numerical values of its rotational speed (t).

(6) Having run the wheel on a rolling road for a given length of time, the wheel is taken away from the rolling road so that it breaks contact with the rolling road. The wheel therefore moves freely, subjected simply to the flow of air from the wind generator. The rotational speed of the wheel is recorded throughout the operation.

(7) According to an alternative form of embodiment of the method according to the invention, the wheel may be mounted on a vehicle which will then be fixed to the ground using pylons. A means of raising the vehicle allows the vehicle to be taken away from the rolling road, thus allowing the wheel to continue to rotate under the sole influence of the wind generator. Fixing the vehicle to the ground makes it possible firstly to dictate the attitude of the vehicle and, secondly, to stabilize it as it is raised. The wheels mounted on the vehicle are initially placed in contact with a rolling road intended to bring the wheel up to a desired rotational speed V.sub.0. The wind generator subjects the vehicle to a flow of air of the same speed V.sub.0.

(8) Applying mathematical formula (I) below makes it possible to obtain the value of the aerodynamic moment of resistance M.sub.aero-EM(t) of the wheel as a function of time using the following mathematical formula (I):
I.sub.EM(d(t)/dt)=M.sub.aero-EM(t)+M.sub.f(t)(I)

(9) I.sub.EM, which represents the value of the moment of inertia of the wheel, can be measured for example using a torsion pendulum.

(10) M.sub.f(t), which represents the value of the moment of friction of the hub of the wheel, can be calculated, for example, from the technical data supplied by the bearing manufacturer.

(11) The value (d()/dt) for t=t.sub.0 (namely when the wheel leaves the rolling road) is obtained from the recording of the rotational speed as a function of time.

(12) FIG. 1 shows the results comparing the variation in aerodynamic moments of resistance of a tire with a smooth side wall and of a tire with sidewalls covered with rough elements both mounted on an identical rim. These two tires are mounted on the front right side of a passenger car. The speed V.sub.0 of the wheels driven by the rolling road is equal to 120 km/h. The wind tunnel generates a flow of air at a speed of 120 km/h.

(13) In this FIG. 1, the curve 1 corresponds to the tire with the smooth sidewall and the curve 2 to the tire with the sidewalls covered with rough elements. The two wheels are made up of identical rims. FIG. 1 shows that the rotational speed of each tire mounted on rim does not change in the same way. The rough elements are defined as being elements made of a rubber of substantially cylindrical shape, of a height equal to around 4 mm and of a diameter equal to around 4 mm. In this instance, 250 elements are arranged uniformly on each of the two sidewalls.

(14) Specifically, the tire with the rough sidewalls induces a more rapid deceleration than the tire with the smooth sidewall, because of the higher parietal stresses on the tire with the rough sidewalls.

(15) At the instant t=t.sub.0, the difference in behaviour of each type of tire exhibits a difference in ventilation torque of around 1 N.Math.m. This measurement can be considered to be repeatable because it has a standard deviation of 0.01 N.Math.m.

(16) This difference in value of the aerodynamic moment of resistance is equivalent in a passenger car equipped with four wheels to a difference in aerodynamic drag representing approximately 3% of the overall drag of the vehicle.

(17) This difference in value of the aerodynamic moment of resistance leads, for a passenger car equipped with four wheels, to a difference in fuel consumption which is equivalent to a difference in aerodynamic drag representing approximately 3% of the overall aerodynamic friction drag of the vehicle.

(18) FIG. 2 corresponds to a situation in which the direction of the main flow of air is aligned with that of the wheel but in which the speed of the flow of air is different from that of the wheel. In other words, the speed V.sub.0 of the wind generator is the same and still equal to 120 km/h, and the speed of the wheel V.sub.wheel is variable, and varies progressively from 120 km/h to 0 km/h.

(19) FIG. 2 corresponds to the actual situation in which the wheel, protected by a cap, is experiencing a headwind because V.sub.0>V.sub.wheel.

(20) The aerodynamic moment of resistance M.sub.aero-EM is measured for various wheel speed values. Each value of M.sub.aero-EM is then plotted as a function of the ratio [(V.sub.0V.sub.wheel)/V.sub.0] which is equal to zero when V.sub.wheel=V.sub.0=120 km/h, and which is equal to one when V.sub.wheel=0 and V.sub.0=120 km/h. That then yields the curve 1 depicted in FIG. 2.

(21) As the curve 1 of FIG. 2 shows, it may be said that the aerodynamic moment of resistance experienced by a vehicle driving at 60 km/h, and experiencing a headwind also having a speed of 60 km/h, is lower (approximately 1 N.Math.m in absolute terms, for [(V.sub.0V.sub.wheel)/V.sub.0]=0.5) than the aerodynamic moment of resistance experienced by the same vehicle driving at 120 km/h in the absence of external wind (3 N.Math.m approximately in absolute terms, for [(V.sub.0V.sub.wheel)/V.sub.0]=0) despite the fact that the relative wind is the same in both instances, namely 120 km/h.