EP0329524A1 - Device to compute the integration step of a shell trajectory - Google Patents

Abstract

This method of calculation consists in a preliminary stage: &cirf& in calculating, for different firing configurations, a reference trajectory (Tref) with a given relatively small integration step called the reference step (H), &cirf& at various points (P) of the different reference trajectories obtained in this way, in successively trying different values of the integration step (1, 2, 3) which increase from the reference step until the deviation from the reference trajectory is greater than a predetermined limit ( epsilon P) called the tolerable position error per integration step. In this case, the integration step adopted, called the limiting integration step, is that corresponding to the last trial carried out, &cirf& in modelling the limiting integration step from the data obtained in this way in terms of the various parameters defining the points on the trajectories and the firing configurations, - at the time when the integration step is to be calculated, in calculating the limiting integration step, using the model established in the above preliminary stage, in terms of the parameters existing at the point on the trajectory where this calculation is to be carried out and in terms of the firing configuration in question. <IMAGE>

Description

The present invention relates to a method and a device for calculating the integration pitch of shell trajectories.

In the field of ballistics, we know how to calculate the firing elements (rise, azimuth, event) to apply to a gun, relative to a given firing configuration (target-gun position, geographic and meteorological data, characteristics of the shell ) so that the shell thus fired reaches the target.

For this, several trajectory integration calculations are carried out, with successive corrections from firing conditions chosen initially, until the shell drop point is located within defined limits with respect to the target.

|, où k désigne une constante, et

et

les vecteurs vitesse et accélération de l'obus.The integration method itself classically consists of an arbitrary integration algorithm (predictor-corrector, Runge-Kutta, Taylor ...) with a variable integration step according to the point considered of the trajectory, given by h = k . |

|, where k denotes a constant, and

and

the velocity and acceleration vectors of the shell.

This method, although precise, has the disadvantage of lacking speed since the integration step thus calculated is not really optimized as a function of the point considered in the trajectory, in the sense that it would sometimes be sufficient to use a no higher value integration without affecting the calculation accuracy.

The subject of the present invention is a method for calculating such an optimized integration step, that is to say the maximum integration step compatible with the required precision, making it possible to save on the integration time of the trajectories. without losing on the precision of the integration calculation.

The method for calculating the integration pitch of shell trajectories according to the invention essentially consists of:
- in a preliminary stage:
. to calculate, for different firing configurations, a so-called reference trajectory, with a given integration step, relatively small, said reference step,
. to successively try, at different points of the different reference paths thus obtained, different values of the integration step, increasing from the reference step until the difference with the reference path is greater than a predetermined limit, said tolerable position error by integration step, in which case the integration step adopted, called limit integration step, is that corresponding to the last test carried out,
. to model the limit integration step from the data thus obtained, as a function of different parameters defining the points of the trajectories and the firing configurations,
- when the calculation of the integration step is to be performed, to calculate the limit integration step using the model thus established beforehand, as a function of the parameters existing at the point of the trajectory where this calculation is to be performed, and the firing configuration considered.

• - La figure 1 est un diagramme destiné à illustrer le procédé de recherche du pas d'intégration limite ;
• - les figures 2a et 2b sont des diagrammes illustrant la modé- lisation du pas d'intégration limite ;
• - la figure 3 est un organigramme qui recense les opérations à effectuer dans les moyens de calcul associés à la batterie de tir, en vue de calculer le pas d'intégration limite.

Other objects and characteristics of the present invention will appear more clearly on reading the following description of an exemplary embodiment, made in relation to the attached drawings in which:

• - Figure 1 is a diagram intended to illustrate the process for finding the limit integration step;
• FIGS. 2a and 2b are diagrams illustrating the modeling of the limit integration step;
• - Figure 3 is a flowchart which lists the operations to be performed in the calculation means associated with the firing battery, in order to calculate the limit integration step.

Firstly, in relation to FIG. 1, the principle of the method which optimizes the integration step is exposed.

Or an arbitrary integration algorithm (predictor-corrector, Runge-Kutta, Taylor ...) intended to estimate the trajectory. At each step, the kinematic state (i + 1) is constructed from:
- kinematic state (i) (position, aerodynamic speed, rotation speed, vector obliquity);
- local weather data (temperature, pressure, wind speed);
- geographic data (latitude of the shooting location);
- characteristic data of the shell (mass m ...).

The set of these variables constitutes a point P of the trajectory.

At any point P, we can associate a maximum integration step, called time limit, noted h _limit , and which is determined as follows.

From P, we generate:
- a reference trajectory T _ref with a weak step H (H = 0.05 seconds for example);
- Several trajectories with a step that is made to grow as long as the difference E with T _ref remains less than a value ε _p called tolerable position error per step, the determination of which will be specified later. In FIG. 1, three trajectories have thus been shown by way of example:
trajectory 1 (test of h = 2H): E <ε _p
trajectory 2 (test of h = 3H): E <ε _p
trajectory 3 (test of h = 4H): E> ε _p

We thus obtain in this case, for the point P considered: h _limit = 3H.

By repeating this calculation for various points P, we thus constitute a database made up of couples ( _limit h, X), the term X covering the variables to be considered at each point P, namely: kinematic state at this point, geographic and meteorological data at this point, characteristics of the shell.

This calculation is then repeated for different firing configurations T, each of which is characterized by the following parameters: firing conditions applied to the cannon, geographic and meteorological data, characteristics of the shell (mass, ejection speed).

One thus constitutes a database (T, X, ε _p , h _lim ) h _lim being calculated as indicated previously.

This method is relatively costly in calculation time, but it does not have to be implemented in the field, in the calculation means associated with the firing battery; it will advantageously be implemented beforehand, with more efficient calculation means than those associated with the firing battery, the performance of which is obviously limited for reasons of bulk. Since this database cannot be exhaustive, it is necessary, if we want to effectively reduce the time taken to calculate trajectories in the field, using the calculation means associated with the firing battery, to determine a means quick calculation of the h _lim value corresponding to any point P, from this database and according to the parameters existing at the point considered and the firing configuration considered.

For this, once the database is constituted, we proceed to a modeling of h _lim , knowing that the sought-after model must best satisfy the constraints of precision, calculation time, and memory space in the calculation means associated with the firing battery.

To do this, we first search for so-called explanatory variables, that is, variables according to which the variable to be modeled h _{lim is} expressed according to a certain function.

This geometrically amounts to carrying out a projection of the set of points representing h _lim in the space of the different variables "x" of the set (T, X, ε _p ), on each plans (h _lim , x), then to select those of these variables "x" having the strongest explanatory power.

To take account of the desired speed objectives, h _lim is expressed linearly, by domain, of the explanatory variables. After implementing this method, we are thus led to note that in a "high Mach" area, that is for the values of M greater than a certain value M _o , h _{lim is} expressed linearly, by domain, as a function of M⁻², ε _p , P _r , m, T _e and U _o , an expression of the form:
h _lim = a ⁱ _o + a ⁱ ₁ M⁻² + a ⁱ ₂ ε _p + a ⁱ ₃ P _r + a ⁱ ₄ m + a ⁱ ₅ T _e + a ⁱ ₆ U _o
where M denotes the Mach number (ratio of the speed of the shell to the speed of sound), P _r the local pressure, m the mass of the shell, T _e the temperature and U _o the speed of ejection of the shell.

Within the "high Mach" zone (M> M _o ) we are still led to distinguish four zones delimited by values M₁, M₂ and M₃ of M⁻²; each of these zones corresponds respectively to a set of coefficients a ⁱ ₁, a ⁱ ₂, a ⁱ ₃, a ⁱ ₄, a ⁱ ₅ and a ⁱ ₆ (1 ≦ i ≦ 4)
used in the expression of the above model.

In a "weak Mach" zone, ie for the values of M less than M _o , h _{lim is} expressed linearly, by domain, as a function of p, ε _p , M, T _e and W _X where W _X denotes the component wind in the horizontal direction, and p the slope of the trajectory is an expression of the form
h _lim = b ⁱ _o + b ⁱ ₁ p + b ⁱ ₂ ε _p + b ⁱ ₃M + b ⁱ ₄ T _e + b ⁱ ₅ W _X

Within the "weak Mach" zone (M <M _o ), we are also led to distinguish four zones delimited by three values p₁, p₂ and p₃ from the slope p of the trajectory, and for each of the zones thus obtained, we are also led to distinguish two cases, depending on whether M⁻² is greater or less than a value M₄.

Each of the eight zones thus defined corresponds to a set of coefficients b ⁱ ₁, b ⁱ ₂, b ⁱ ₃, b ⁱ ₄, b ⁱ ₅ (1 ≦ i ≦ 8) used in the expression of the above model. These different cases will appear in FIG. 3 which will be described later.

In Figure 2b we graphically represented the model allowing to approximate h _lim in a limited space for more clarity with the two explanatory variables ε _p and M⁻² and in this space we considered only the case M> M _o (area "High Mach"). This model is constituted by a succession of planes which each project, as represented on figure 2a, in each of the planes (h _lim , ε _p ) and (h _lim , M⁻²) according to the line segments resulting from the modeling linear.

In the case of a space not limited to two explanatory variables, the concept of plane would be replaced by that of hyperplane.

The models being thus determined, the calculation of the optimized step of integration of the trajectories, carried out in the field by the calculation means associated with the firing battery is done as shown in the flowchart of FIG. 3.

It will be noted that the number of operations added by the calculation of the model is negligible compared to the total number of operations required by an integration phase (which requires two calculations of the derivative of the state vector).

The positioning test and model calculation operations correspond to those described above and will therefore not be described again.

The values of the parameters which it is necessary to know at the point considered are the values of the parameters M, U _X , U _Y , U _Z , A _o , T _e , P _r , U _o , W _X , m. The parameters U _X , U _Y , U _Z designate the components of the absolute speed of the shell at the point considered; A _o indicates the rise of the barrel.

The values of the parameters U _X , U _Y , U _Z are necessary for the calculation of the number of Mach M (and M⁻²) and of the slope p.

The value of the increase A _o is necessary for the calculation of the tolerable position error by step ε _p at the point considered.

The calculation of ε _p is in fact also carried out using a pre-established model, and when establishing this model, we note that this variable ε _p can be modeled as a function of A _o , according to three straight line segments of shape :
ε _p = c ⁱ _o + c ⁱ ₁ A _o
each of the three line segments being defined by a set of coefficients c ⁱ _o , c ⁱ ₁ (i = 1.3) A _o taking its values on three domains [A₁, A₂] [A₂, A₃] and [A₃, A₄ ]. This modeling of ε _p is obtained from a database (ε _p , T) which can itself be obtained in the following way. For a given firing configuration T and for each point P, we try different values of ε _p by applying each time the "limit time" method as described above in relation to FIG. 1, and this successively for all points of the trajectory portion connecting point P considered to the point of fall of the shell. We then retain the maximum value compatible with the precision requested at the point of fall of the shell, and we repeat this method for different firing configurations.

The method according to the invention makes it possible to significantly reduce the calculation times and to dispense with operators specialized in the calculation means associated with the firing battery; the architecture of these is simplified and their energy consumption reduced, which is fundamental for problems of portability and autonomy.

By way of example for a medium distance shooting (15 to 20 km) while a traditional trajectory calculation requires around sixty integration steps, the method according to the invention makes it possible to reduce this number to around twenty.

Claims (5)

1. Device for calculating the trajectory of shells with a view to controlling a cannon, characterized in that it comprises, for the calculation of the integration pitch of said trajectory:
. means for calculating, for different firing configurations, a so-called reference trajectory, with a given integration step, relatively small, said reference step,
. means for calculating, at different points of the different reference trajectories thus obtained, the difference between the reference trajectory and different trajectories obtained by increasing the integration step, from the reference step, until this difference is greater than a predetermined limit, called tolerable position error by integration step, in which case the integration step adopted, called limit integration step, is that corresponding to the last trajectory obtained,
. means for carrying out a modeling of the limit integration step from the data thus obtained, as a function of different parameters defining the points of the trajectories and the firing configurations. 2. Device according to claim 1, characterized in that it comprises means for calculating the limit integration step using the model thus established, according to the parameters existing at the point of the trajectory where this calculation is to be performed , and the firing configuration considered. 3. Device according to claim 1, characterized in that it further comprises:
means for calculating the limit integration step for different values of the position error, and this for the entire portion of the trajectory connecting the point considered to the point of fall of the shell;
means for determining, among these different values of the position error, the maximum value compatible with the precision tolerated at the point of fall of the shell,
means for modeling this maximum value, known as a tolerable position error by integration step, from the data thus obtained. 4. Device according to claim 2, characterized in that it comprises, for calculating the limit integration step:
- means for calculating, at the point where this calculation of the trajectory is to be carried out, the Mach number M of the shell, the value M⁻², and the slope p of the trajectory,
means for positioning these three values with respect to particular values determined by modeling, respectively M _o , M ₁ , M ₂ , M ₃ , M ₄ , p₁, p₂, p₃, such as:
h _lim = a ⁱ _o + a ⁱ ₁ M⁻² + a ⁱ ₂ε _p + a ⁱ ₃ P _r + a ⁱ ₄ m + a ⁱ ₅ T _e + a ⁱ ₆ U _o
for high values of the Mach number of the shell, that is M> M _o, and:
h _lim = b ⁱ _o + b ⁱ ₁ p + b ⁱ ₂ ε _p + b ⁱ ₃ M
+ b ⁱ ₄ T _e + b ⁱ ₅ W _X
for low values of the Mach number of the shell, that is M <M _o,
the terms a ⁱ and b ⁱ designating a set of coefficients, of different values according to the position of M⁻² with respect to the values M₁, M₂, M₃ in the case M> M _o , or according to the position of the slope p of the trajectory at the point considered and of the Mach number M of the shell, compared, respectively, to the values p₁, p₂, p₃ and M₄ in the case M <M _o ,
ε _p denoting the tolerable position error by integration step, T _e the temperature at the point considered of the trajectory, P _r the local pressure, m the mass of the shell, U _o the speed of ejection of the shell, and W _X the component of the wind in the horizontal direction at the point considered of the trajectory;
means for calculating, by means of the h _lim model selected at the end of these positioning tests, the value of the integration step limit at the point considered. 5. Device according to claims 2 and 3, characterized in that it further comprises means for calculating the position error ε _p tolerable at the point considered, according to the model:
ε _p = c ⁱ _o + c ⁱ ₁ A _o
the terms c _i designating a set of coefficients of different values according to the position of A _o (A _o designating the rise of the canon) with respect to particular values A _i determined by modeling the tolerable position error by integration step .

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