THE METEOROLOGICAL ROCKET SYSTEM FOR ATMOSPHERIC RESEARCH

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1 THE METEOROLOGICAL ROCKET SYSTEM FOR ATMOSPHERIC RESEARCH Komissarenko Alexander I. (1) Kuznetsov Vladimir M. (1) Filippov Valerii V. (1) Ryndina Elena C. (1) (1) State Unitary Enterprise KBP Instrument Design Bureau (Tula) ABCTRACT In article questions of designing of designing and definition of dispersion of nasal parts of meteorological rockets in a falling point are considered. 1. INTRODUCTION The Meteorological rocket system (further as rocket system) is designed for analysis of atmospheric components: a temperature density pressure direction and velocity of wind charged particles and ozone as well as D-particles of the ionosphere. Figure 1 shows a functional diagram of the rocket system. Maximum velocity m/s up to 2000 Altitude km: - end of active phase motor lift apogee 100 Range of fall km: - motor - head Time s: - to reach apogee - total flight Caliber mm: - head - booster Maximum launching overload g 220 Motor characteristics Weight of loaded motor kg 37.8 Powder charge kg 32 Operating time s 2 Figure 3 shows sustainer stage of the Mera rocket launcher 2 Mera meteorological rocket 3 - motor unit 4 - head 5 instrument unit with GLONAS navigation system 6 parachute 7 ground telemetry station. Figure1 Functional diagram of rocket system 2. METEOROLOGICAL ROCKETS General view of the Mera meteorological rocket is shown in Fig. 2 head propulsion 1 fairing 2 timer 3 body 4 payload ejector 5 container 6 parachute system 7 payload with GLONAS navigation system 8 wing. Fugure 3 The cruising stage of the Mera rocket. Instrument section diagram including a telemetering unit is given in Figure 4. Instrument section Figure 2 Mera rocket Table 1 Specifications of Mera rocket. Description Launching weight kg: - rocket - head - payload - containerized rocket (on launcher) Value Figure 4 Instrument section diagram The telemetering section is integrated with the navigation system in this diagram. It is possible to develop a series of meteorological rockets with various specifications which may be used for research of atmospheric characteristics and that are shown in Figure 5. Proc. 20th ESA Symposium on European Rocket and Balloon Programmes and Related Research Hyère France May 2011 (ESA SP-700 October 2011)

2 Table 2 Figure 5 Meteorological rockets for research of atmospheric characteristics Description Weight kg Swinging angles º: - in azimuth - elevation Time of launcher readiness min: - from travelling configuration to operating position - from operating position to travelling configuration Dimensions mm Travelling configuration: -length -width -height Operating position -length -width -height Value Minus Functional diagram of the trajectory stabilization unit is given in Figure 6. Figure 6 Functional diagram of the trajectory stabilization unit The trajectory stabilization unit makes it possible to reduce scattering of the cruising stage drop point up to 03o. 2. Figure 9 Shows travelling configuration of the launcher on march In the process of development of the meteorological rocket main task is to determine dispersion of points of head part falling. 3. LAUNCHER The launcher of the Mira rocket is shown in fig. 7. Figure 9 shows travelling configuration of the launcher on march. transport-launching container with rocket Mera launcher Figure 7 The meteorological rocket at the launching position. Functional diagram of launcher with the guidance instrument section is given in Figure 8. 1 launcher 2 guidance unit 3 navigation unit 4 azimuth sensor 5 elevation sensor 6 elevation laying drive 7 azimuth laying drive Figure 8 Functional diagram of launcher with the guidance instrument section DISPERSION OF THE METEOROGICAL ROCKETS Main source of dispersion is an angular deviation which emerges at the beginning of an active part of flight from the following main factors: - initial angular velocity - initial exit angle -thrust eccentricity - longitudinal and traversal components of wind velocity. Initial part of active flight angular deviation increases presents crucial section of the rocket flight trajectory. Crucial part extends up to the point for the first time after the rocket take-off the angle of attack turns to zero. Angular deviation increases prior to the crucial part of the trajectory. Thereafter it remains relative stability. To analyze the rocket dispersion at the end of active part of the flight we take the following: -consistency of acceleration along the entire active section of the trajectory - mean value of moment of inertia - midposition of center of gravity - value of coefficient of aerodynamic force included into formula which is used for estimation of transversal stability coefficient mz! as well as midposition of the rocket pressure are taken as being equal to its value at subsonic velocities.

3 - coefficient of dynamic stability is taken as a summarized characteristic of dispersion К estimated by the following analytical dependence: (1) m z α - coefficient of longitudinal stability ρ air density S frontal area of sustainer L characteristic length of a rocket J zz equatorial moment of inertia Angular deviation of rocket under initial disturbance of angular velocity The system of equations in this case under the same assumptions as in the introductions can be written in the following way: rocket pitch angle V rocket absolute velocity α angle of attack a rocket acceleration θ angle of velocity vector. This system of equations should be solved under the following initial conditions: Re-arrangement of the system (2) results in the following: U=αV x - rocket path. This system of equations should be solved under the following initial conditions: (2) (3) Let s input new integration variable: Having done integration part by part and putting functions of Bessel and Fresnel integrals we ll have: Fresnel integrals in dependence (5) are: Bessel functions are: 3.2. Angular deviation of rocket under initial disturbance by angle In compliance with above-stated data we have the following: U=αV To determine arbitrary constants С 1 and С 2 in this case we have the following initial conditions: These initial conditions reduce to two equations for С 1 andс 2. (5) The solution of a linearly uniform differential equation (3) can be written in the following way: To determine arbitrary constants С 1 and С 2 we use initial conditions: Solution of these equations results in the following expressions for С 1 and С 2 : So the expression for U can be written as follows: We ll find a formula for θ So the expression for U can be written in the following way: Substitution of (4) in (3results in: Having done integration part by part and putting functions of Bessel and Fresnel integrals we ll have:

4 Then angular deviation θ take on the following form: (11) 3.3. Angular acceleration of rocket under gravity In this case main equation may be written in the following way: It should be remarked that an integral in the form (11) can be expressed through functions of Bessel and Fresnel integrals by substitution ξ=kx then: g- acceleration of gravity. The expression for the derivative of vector velocity angle θ will be as follows: Further the solution is performed in the same way as in the previous section there for we ll write the solution finally at once: In this expression we have: 3.5. Angular deviation of rocket under eccentricity of reactive force at arbitrary rule of rolling The System of equations for a single channel under slow rolling and same as above-stated assumptions can be written as follows: (13) To simplify writings let s introduce additional designations: (9) The calculation of the equation system at the first phase: (x 0 x x 1 ) x 1 corresponds to a distance passed by the rocket by the moment when sin γ(x) for the first time turns to zero. Due to arbitrary character of initial roll angle we assume that at x=x 0 γ(x 0 )=0.785 (i.e. at initial phase of eccentricity of 45 0 and further on γ(x) increases. For the first phase under assumption of sin γ (x)= const the system of equqtions is: Then (14) 3.4. Angular deviation of rocket under cross wind The reduce to x and U=αV results in the equation for U : We estimate it under initial conditions: (10) F reactive force ε linear eccentricity. Using the calculation pattern in the same way as previously we may have final expression for tilt angle of velocity vector versus dimensionless path passed by the rocket:

5 m averaged weight of the rocket at active phase of flight. Using (15) и (13) we ll have: (16) In the same way it is possible to demonstrate the following: So we have: Ф 2 (ξ 1 ) Ф 3 (ξ 1 ) А 2 (ξ 0 )- in the same way as it was stated previously but with index 1. In these expressions K 1 (γ) is average integral value of sin γ(x) at initial phase. The calculation at the second phase (x 1 x x 2 )x 2 corresponds to the path passed by the rocket by the moment when turns to zero for the second time. In this case the calculation of equation (13) can be expressed as follows: The value of angle θ at the end of the second phase can be estimated from the relation: Sign «-» before the third term will result from sin γ(x) <0 at the second phase. K 2 (γ) is average integral value of sin γ(x). We ll find the expression as required for estimation the increment of angle θ at the second phase. Calculation of the equation system at the third phase (x 2 x x 3 ). x 1 presents the distance passed by the rocket by the moment of third turning of sin γ(x).to zero. The expression for the third phase can be written in the same way as for the second phase: Δθ 32 Due to reasons stated above it can be written in the following way: The integral is same as the Let us find the expression for Δ θ 31 integral calculated for the first phase but limits of integration. Therefore:

6 - sensitivity of angle of velocity vector to eccentricity ( ) - sensitivity of angle of velocity vector to initial angular component (5) - sensitivity of angle of velocity vector to cross The value of angle θ at the end of third phase can be estimated by the formula: The formulas for θ calculation at the end of the fourth fifth etc. can be written in the same way. For example for the fourth phase we ll have the following: For the fifth phase: wind σ - RMS value of pitch and yaw angle σ ε - RMS value of thrust eccentricity σ w RMS value of longitudinal component of wind velocity Formula (30) presents analytical dependences for vertical angle of velocity vector θ same as the dependence for horizontal angle of velocity vector φ. Knowing ballistic wind in the layers of the flight trajectory W σ it is possible to calculate dispersion of head parts of the meteorological rockets: (31) х horizontal projection of slant range in the point of fall. W бz W бx component of ballistic wind σ z σ x - RMS value of linear deviations in plane ОХZ. 4. RESULTS OF CALCULATIONS Figure 10 presents the results of estimations based on analytical dependences considered in the previous sections and calculations of the complete system of differential equations that describe movement of rockets of the offered series (fig. 5). It is reasonable to bear in mind that at the end of the last phase sin γ(x) may not turn to zero. It should be taken into consideration during calculation K i (γ). The value of coefficients K i (γ) for the first phase K i (γ)=0725. For all further but last K i (γ)=0637. For the last phase value of K i (γ) should be calculated individually for each case Generalizing characteristics of the rocket dispersion at the point of the head part fall. General dispersion by the end of the motor operation is calculated through the following dependence: Figure 10 Flight trajectories of a series of meteorological rockets at a launching angle of Dispersion of the head part (φ = 3 4º). Dispersion of the head part trajectory stabilization unit (φ 1 = 03º). - sensitivity of angle of velocity vector to initial angle (6)