[ 0060 ] fig1 shows a wheel rim 10 equipped with an annular safety insert 13 resting on the bearing 11 of the rim 10 . the particular geometry of that wheel rim 10 is described in french patent application no . 2 , 713 , 558 . it represents two bead seats of different diameters and is particularly adapted for easy placement of that safety insert 13 . this assembly makes running possible in spite of a considerable pressure drop in the tire 12 . in the case of such running , the interior of the deformed tire rubs on the outer surface of the insert , producing heat which limits the radius of action available ; it is therefore important for the driver to be informed as soon as a tire bears on its insert 13 . for that purpose , a safety insert containing means for generating harmonic vibrating warning signals of the turn of the wheel ( that is , of the rotation frequency of the tire ) is advantageously used as insert . the insert shown on fig2 a and b is made of soft elastomeric material . it contains a generally ring - shaped base 14 , reinforced by a ply ( not represented ) longitudinally oriented roughly at 0 °, a generally ring - shaped crown 15 with axial bars 19 on its radially outer wall ( fig2 b ) and arched walls 16 . between walls 16 there are recesses 17 which can axially cross the insert 13 completely or partly . the base can contain an abutment 18 to be placed on the outer side next to the tire bead . the axial orientation bars 19 have sides 191 whose inclination from normal to the tread in the longitudinal direction varies as a function of azimuth , as represented on fig3 . that inclination follows a roughly sinusoidal course submultiple of order 2 of the turn of the insert . on running flat on the insert , the bars supporting the tire will be crushed with a slight longitudinal displacement of amplitude and direction variable with the inclination of those bars . that displacement will be transmitted to the tire by adherence between the insert and the inner surface of the tire and results in the appearance of instantaneous rotation speed fluctuations of the mounted assembly and , therefore , of the wheel . those fluctuations will , in the present case , preferably be centered on harmonic 2 of the spectrum of wheel rotation speeds . such an insert therefore comprises an example of means for generating rotation speed variations of the wheel it equips on running flat . a similar result can be obtained by varying the radial stiffness of the insert as a function of the azimuth or its radius . [ 0065 ] fig4 represents a diagram of an insert 20 having a variation of outer radius among three values r1 , r2 and r3 such that r1 & gt ; r2 & gt ; r3 with a progressive variation of that radius between maxima and minima . the two zones of outer radii r1 are at 180 ° from one another and so are the two zones of radii r2 ; the four minima of radii r3 are each between two maxima r1 and r2 . this result , on running flat , in a variation of that radus as a function of α with two fundamental harmonics , the first of frequency 2 , due to the first two maxima of radus r1 and the second of frequency 4 due to the presence of the four maxima of radius r1 and r2 and of the four minima of radius r3 . in that example , the r1 - r3 difference is equal to 5 mm and the r2 − r1 difference is equal to 3 mm . [ 0066 ] fig5 represents a diagram of an insert 30 which has a variation of radial stiffness among three values k1 , k2 and k3 , such that k1 & gt ; k2 & gt ; k3 , with a progressive variation of that stiffness between the maxima and the minima . as previously , the two zones of stiffness k1 are at 180 ° from one another and so are the two zones of stiffness k2 ; the four minima of stiffness k3 are each between two maxima k1 and k2 . this results , on running flat , in a variation of that stiffness as a function of a with two fundamental harmonics , the first of frequency 2 , due to the first two maxima of stiffness k1 and the second of frequency 4 due to the presence of the four maxima of stiffness k1 and k2 and of the four minima of stiffness k3 . [ 0067 ] fig6 represents a diagram of an insert 40 presenting a combination of a variation of outer radius and a variation of radial thickness . each characteristic presents two maxima ( r1 , k2 respectively ) and two minima ( r2 , k1 respectively ), shifted angularly by 90 ° from one another . the radial thickness maxima are sufficiently localized to produce on the insert 40 assembly a crushed radius variation on bearing with four maxima . consequently , that insert also produces an harmonic excitation concentrated on harmonics 2 and 4 , but presents the advantage of having a weighting variable as a function of speed . the applicant observed , in fact , that the radial variations of stiffness were more perceptible at low speed and that the outer radius variations were more perceptible at high speed . [ 0069 ] fig7 represents a vehicle equipped with a system of detection of a run - flat condition according to the invention . the vehicle contains four wheels 1 a , 1 b , 1 c and 1 d equipped with tires . each mounted assembly ( tire and wheel ) contains means for generating vibrating warning signals on running - flat of the tire , for example , one of the safety inserts presented in fig2 to 6 . close to each tire there is a sensor of angular displacement 2 a , 2 b , 2 c and 2 d of the wheel concerned . each sensor is coupled to a notched disk 21 a , 21 b , 21 c and 21 d respectively , as well known . the notched disks 21 a , 21 b , 21 c and 21 d are made of magnetic disks attached coaxially with the corresponding wheels . the sensors 2 a , 2 b , 2 c and 2 d are placed close to the notched disks 21 a , 21 b , 21 c and 21 d at such distance that rotation of the notched disk near the sensor creates a signal variable with the angular displacement of the notched disk . the average frequency of that signal gives the angular rotation speed of the wheel . the variable signal of each sensor 21 , 2 b , 2 c and 2 d is entered in a central unit 3 . the central unit 3 comprises a signal analyzer which analyzes those signals . the result of the analysis is transmitted to a display 4 in order to inform the driver of the vehicle when a roll - flat condition of a tire is detected . when the vehicle is equipped with a wheel antilock device , the aforesaid sensors 2 and the central unit 3 can be those of the antilock device . under these conditions , all of the stages of the method according to the invention can be ensured by specific software incorporated in the computer of the antilock device . it is advisable to provide a suitable display 4 . [ 0071 ] fig8 represents a general diagram of the method of detection according to the invention . from the measurements f ( α , t ) of the sensors 2 a , 2 b , 2 c and 2 d , the central unit 3 performs the following operations for each wheel : performing an harmonic analysis of dα ( t )/ dt by known means , for example , with a fourier transform , in order to obtain dα ( v )/ dv ( see fig9 ); determining the angular rotation speed of the wheel v 0 , corresponding to the frequency of harmonic 1 ; determining the energy e sol of the spectrum of speeds dα ( v )/ αv in a frequency band not including an harmonic of the turn of the wheel , for example , between harmonics 5 and 6 ; determining the energies of the spectrum of speeds dα ( v )/ αv in two narrow bands of width in the order of 2 to 10 hz centered on harmonics 2 to 4 , namely , energies e v2 and e v4 , and adding them in order to obtain σe v1 ; comparing v 0 to a threshold a , and if v 0 is lower than a , resuming the cycle of measurements ; if v 0 is higher than a , comparing σe sol to a threshold b , and if e sol is higher than b , resuming the cycle of measurements ; if e sol is lower than b , comparing σe vi to a threshold c ; and if σe v1 is higher than c , setting off an alarm , unless resuming the cycle . for each harmonic analyzed , a suitably programmed microprocessor calculates the energy of the harmonic by the integral of the peak emerging from the background noise , the background noise being determined from a frequency band encompassing the narrow band analyzed . value σe vi is a function of the speed of the vehicle and of the energy level of the spectrum of speeds linked to the unevenness of the road . several values of threshold c can thus advantageously be used as a function of speed of the vehicle and of the value of e sol . the first test using v 0 entails not setting off any alarm when the rotation speed of the wheel and , therefore , the speed of the vehicle is less than a given threshold , in the order of 20 to 30 km / h . the second test also entails neutralizing the alarms when the energy e sol is higher than threshold b , that is , when the unevenness of the road is very great and thus likely to disturb the measurements markedly . those two tests make it possible to limit the number of false alarms very appreciably . as it is always possible for one or more peaks to be disturbed by other sources , for example , by engine vibrations , it is useful to complete that overall energy analysis by verifying that at least two of the harmonics analyzed have had a significant energy evolution . that additional step appreciably improves the reliability of detection . [ 0087 ] fig9 represents an example of a spectrum of speeds of the wheels on running at normal inflation pressure ( white curve ) and in run - flat condition bearing on a safety insert ( black curve ). the vehicle is a peugeot 405 , running at 70 km / h on a standard course . the tire 12 , considered in run - flat condition , is supported on the radially outer wall of a standard safety insert not containing means generating warning signals arranged around the rim of the wheel . such an insert is described in patent application ep 0 796 747 . the white curve ( running at normal inflation pressure ) presents a notable maximum centered on harmonic 1 . that explains why it is preferable to exclude that harmonic in analysis of the spectrum of wheel vibrations . the black curve ( running flat ) presents substantially higher energy levels for each harmonic starting from harmonic 2 . that well illustrates the effectiveness of analysis of harmonic 2 and 4 in order to detect a run - flat condition of the tire . the method of detection according to the invention is already effective when the tire is supported on a safety insert not generating vibrating warning signals . but that method is particularly well suited for detecting a support on inserts containing such warning means and , notably , means generating harmonic signals of the turn of the wheel . the invention also concerns a tire 50 ( fig1 ) equipped with means 60 generating vibrating warning signals on running at camber higher than a given threshold . that tire 50 contains a crown 51 , a sidewall 52 and a bead 53 . the sidewall 52 and the bead 53 are equipped with inserts 54 , 55 , 56 enabling that tire to support its load on running at zero inflation pressure . the insert 54 contains a reinforcement 60 in the bead and sidewall , the radial height of which varies according to an harmonic function of the azimuth , as shown on fig1 . that reinforcement 60 will result , on running at a tire deflection higher than a given threshold , in a variation of radius under load of the tire and in the appearance of a multiple harmonic signal of the turn of the wheel detectable by the system and method previously described . the reinforcement 60 can be placed on both sides of the tire or on only one side . in the latter case , it is preferable for it to be the inner side in order not to degrade the behavior of the tire on turning . that also has the advantage of not setting off an untimely alarm on turns taken at high speed . [ 0094 ] fig1 and 13 represent a wheel 70 having a disk 71 and a rim 72 equipped with means for generating vibrating warning signals on running flat . the rim 72 contains an interior flange 73 . the radial height of that interior flange 73 varies as a function of its azimuth according to a law presented on fig1 . the variation involves less than half the circumference . the variation of radial height of the rim flange can also be obtained by fastening a complementary part . consequently , when the wheel 70 is equipped with an ordinary tire under a load or with an inflation pressure such that the deflection taken by the tire is higher than in normal conditions of use , the radial variation of height of the interior flange will result in the appearance of vibrating warning signals . those signals can be detected by the system or method previously described . on running under normal load and inflation pressure conditions of the tire and , therefore , of tire deflection , modification of the rim flange of fig1 and 13 only results in a minimal modification of the bearing conditions of the bead on the interior flange . as previously , it is important to arrange that variation of radial height of the flange on the interior flange in order not to disturb performance of the tire on a turn and to favor detection on running in a straight line .