34 results about "Internal ballistics" patented technology

The invention provides a liquid-gas phase change ejection inner trajectory modeling method, a liquid-gas phase change ejection simulation method and electronic equipment. A liquid-gas phase change ejection system comprises at least one phase change power unit. The liquid-gas phase change ejection inner trajectory modeling method comprises the step of dividing a liquid-gas phase change ejection inner trajectory into a phase change power unit flow model, a primary chamber energy model and a projectile body motion parameter model. According to the method, the liquid-gas phase change ejection inner ballistic model comprising the multiple phase change power units is constructed, the acting time of the phase change device is prolonged, the preset speed can be achieved when the ejection overload control requirement is high and the overload does not exceed the limit value, and the inner ballistic parameter change process in the carbon dioxide phase change ejection expansion acting process can be accurately calculated.

The application discloses a kind of artillery barrel residual life prediction method, to the interior ballistic parameter obtained in artillery shooting process as foundation, in the process of each ammunition launch, the pressure of the bottom of the shell and the movement speed of the projectile at multiple discrete time points in the movement stage of the barrel are collected in real time, and the integrated feature vector for representing single shot process is constructed in combination with artillery state information, based on integrated feature vector, single wear prediction model based on BP neural network is constructed and trained, after model training is completed, the wear of barrel caused by each shot is predicted using single wear prediction model, and the degradation state of barrel is dynamically updated through wear accumulation mechanism, in combination with the preset barrel wear failure threshold, the wear evolution in the subsequent shooting process of artillery barrel is forwardly predicted, and then the residual available firing number of artillery barrel is obtained, to realize the quantitative evaluation of residual life.

The present invention belongs to the field of power launch experiments, and specifically relates to a gas ejection experimental device. It comprises a pressure chamber, a rear flange, a gas-sealing sleeve, a launch tube, a front head, a sensor fixing base, a barrel ferrule, and a dummy projectile, which are arranged in sequence. The pressure chamber is connected to the rear flange via a flange, the gas-sealing sleeve is placed in the launch barrel in the manner of a piston, and the rear flange and the launch tube, as well as the launch tube and the front head, are connected via threads. The present invention can experimentally measure the ejection internal ballistics by installing different charge gas generators in the pressure chamber. By varying the length of the engine growth tube, the internal ballistic characteristics under different low-pressure chamber initial volumes can be obtained. The front head of the present invention is equipped with a sealing tray recovery device, which can effectively improve the pressure release process after ejection, prevent the rapid escape of high-temperature gas, and enhance the concealment of the launch site.

The invention discloses an energetic propellant based on magnesium-nickel-based metal hydride blending as well as a preparation method and application of the energetic propellant. The preparation method comprises the following steps: step 1, taking metal Mg and Ni elementary substances as raw materials, and preparing magnesium-nickel-based metal alloy powder by adopting a mechanical alloying method; s2, the magnesium-nickel-based metal alloy powder is subjected to hydrotreating, and magnesium-nickel-based metal hydride is obtained; and S3, the magnesium-nickel-based metal hydride is coated with graphene, mechanical ball milling is conducted, the magnesium-nickel-based metal hydride and a monoaromatic propellant are mixed, and the energetic propellant based on magnesium-nickel-based metal hydride mixing is obtained. The characteristic that metal hydride can release hydrogen in a high-temperature environment is utilized, and the release rate of hydrogen energy is regulated and controlled through the size and the proportion, so that the combustion characteristic of propellant powder and the chamber pressure of an inner trajectory during artillery launching are changed, and finally the kinetic energy of a gun muzzle is improved.

The invention relates to a system and a method for measuring ballistic trajectories in a light-gas gun and an artillery, and the system comprises a first microwave source assembly, a first power amplifier, a first circulator, a horn antenna, a second microwave source assembly, a second power amplifier, a second circulator, a linear polarization antenna and a microwave reflection and transmission plate, the directions of microwaves emitted by the horn antenna and the linearly polarized antenna form an angle of 90 degrees, the microwave reflection and transmission plate is arranged on an angular bisector of the angle formed by the horn antenna and the linearly polarized antenna, and the microwave reflection and transmission plate enables short-wavelength microwaves emitted by the horn antenna to be directly transmitted to a target to be measured. And long-wavelength microwaves emitted by the linear polarization antenna can be reflected to a to-be-measured target according to an angle of 45 degrees. According to the system for measuring the ballistic trajectory in the light-gas gun and the artillery, long-wave microwaves are reflected on the front surface of forward gas, short waves are reflected on the surface of a projectile, and therefore long-distance, continuous and simultaneous measurement of the speed of the forward gas and the speed of the projectile is achieved.

The invention discloses a method for analyzing the reliability of a gunpowder igniter in a low-temperature ignition failure mode, which comprises the following steps of: firstly, carrying out characterization analysis on the ignition failure mode of the gunpowder igniter in a low-temperature environment, identifying main uncertain factors influencing the low-temperature ignition reliability by adopting a fault tree method (FTA), and determining the probability distribution characteristic of the main uncertain factors; then, an implicit performance function of the failure mode is established. In order to clarify a deterministic relationship between a performance parameter and a design variable, an inner ballistic simulation model for low-temperature ignition of a gunpowder igniter is constructed based on an inner ballistic theory, and a Kriging agent model is further established by using the simulation model. And finally, sampling and solving the Kriging model through an MCS method (Monte Carlo simulation) to obtain the failure probability and reliability of the low-temperature ignition failure mode of the gunpowder igniter. The reliability of the gunpowder igniter under the low-temperature condition can be accurately evaluated, and a theoretical basis is provided for product improvement design.

The invention discloses a millimeter wave large dynamic adaptive time-frequency modeling method based on deep learning. The method comprises the following steps: firstly, actually measuring baseband Doppler signal data by cleaning an external field radar, fitting an in-chamber projectile motion model, and constructing a simulation echo signal model superposed with noise; secondly, performing down-conversion processing on the echo signal, filtering noise by using an adaptive filter, and extracting a pure baseband Doppler signal; converting the signal into a projectile speed curve, and extracting input / output features to construct a data set containing a training set and a test set; and finally, through deep neural network training and testing, establishing an in-gun ballistic performance prediction model. According to the method, the analysis efficiency and prediction precision of the projectile velocity curve in a complex environment are remarkably improved, and reliable technical support is provided for ballistic performance evaluation in a weapon system.

This invention belongs to the field of commercial aerospace and solid rocket engine performance optimization, and discloses a low-cost dynamic envelope inference method based on neural networks. The method includes: establishing a geometric model characterized by feature parameters for each propellant type; constructing a training sample dataset for each propellant type based on the feature parameters at a first scale, and calculating the burn surface area sequence and free volume sequence of each training sample as labels using the burn surface shift step size; training a first neural network and a second neural network for each propellant type using the training samples; constructing a prediction sample dataset for each propellant type at a second scale, and obtaining the result for each prediction sample using the corresponding first and second neural networks; constructing an engine thrust calculation model by combining zero-dimensional internal ballistic equations and one-dimensional steady isentropic flow theory, and calculating the engine thrust for each prediction sample, thereby obtaining the rocket engine dynamic envelope corresponding to each propellant type.

This invention discloses a one-dimensional internal ballistic calculation method for multi-propellant rocket engines that considers differences in gas properties. The method includes: establishing a physical model of a solid rocket motor; establishing a transient control equation set to calculate the density of the mixed gas, combustion chamber temperature, gas velocity, and combustion chamber pressure at the next time step; obtaining the remaining gas volume of different propellants at the next time step; updating the weighted average of physical property parameters; calculating the burning rate and burning surface area at the next time step; repeating the above operations until the propellant grain is completely burned out, thus completing the one-dimensional internal ballistic calculation. This invention considers the mixing process of gases generated by different propellants during the combustion of a mixed-charge solid rocket engine, resulting in accurate calculation results.

The invention discloses a projectile initial disturbance suppression device for an electromagnetic rail gun. The projectile initial disturbance suppression device comprises an orientator, a muzzle surrounding shell, an arc suppression shell, an insulating spacer and a fastening ring, an insulation bearing space is provided for the shot and the armature at the moment after the shot is out of the chamber through the orientator, under the limiting action of a reducing guide rail and a fastening guide rail in the orientator, the postures of the shot and the armature are restrained, and the angular displacement and the angular speed generated by the shot at the inner ballistic stage are reduced; the arc-extinguishing part and the fastening ring of the arc-extinguishing shell are arranged outside the tapered guide rail and the fastening guide rail in a sleeving mode respectively to provide supporting capacity, the arc-extinguishing part of the arc-extinguishing shell is provided with metal grid pieces and narrow slits, electric arcs generated after the pivot rail is separated can be cut off and led to the outside for combustion, the influence of electric arc combustion and explosion on the moving posture of the projectile is weakened, and the service life of the projectile is prolonged. The fastening ring provides high-strength support for the tail end of the orientator, the reinforcing ribs are used for reinforcing the restraining capacity, the initial disturbance of the projectile is finally controlled within a low range, and the shooting precision of the electromagnetic rail gun is improved.

The present invention proposes a method for calculating the interior ballistic characteristic parameters of a mixed charge under plasma ignition. The method includes determining the discharge parameters of a pulse power supply; establishing a formula for the gunpowder burning rate under plasma enhancement; determining the shape functions of two gunpowders; establishing a projectile motion equation and an electrothermal chemical launch interior ballistic equation; substituting the input electrical energy into the electrothermal chemical launch interior ballistic equation, combining the gunpowder burning rate formula and the shape function to perform a time-advancing solution, and finally using the projectile motion equation and the electrothermal chemical launch interior ballistic equation to obtain the internal pressure and projectile velocity curve during the projectile's discharge process. The present invention solves the problem of existing electrothermal chemical launch interior ballistic models that only consider a single charge structure, and can quickly and effectively calculate the internal pressure and projectile velocity curve during the discharge process of an electrothermal chemical launch projectile with a mixed charge structure.

A ballistic detection system includes a projectile detector; electromagnetic radiation detection equipment; and a ballistics analysis computer configured to obtain image data captured by first and second cameras in accordance with timing specified by the projectile detector, determine points in three-dimensional space, which correspond to image artifacts of a projectile, using intrinsic and extrinsic parameters of the first and second cameras, define a trajectory of the projectile within a target volume using the points in three-dimensional space, and optionally find a point of intersection of the trajectory of the projectile with an object associated with the target volume.

The invention relates to an inner ballistic trajectory design method for a floating series double-chamber balance gun. The inner ballistic trajectory design method comprises the steps of dividing an inner ballistic trajectory process period, establishing a gunpowder combustion model in a main chamber and an auxiliary chamber, establishing a projectile motion model, establishing a balance body motion model, establishing an auxiliary chamber motion model and establishing an inner ballistic trajectory energy conservation model. Based on a novel floating series-connection double-chamber structure for a balance gun, construction of an inner ballistic model is completed, and optimization design is conducted on the chamber structure and charging parameters. The problem that a large-diameter barrel weapon generates high bore pressure under the high initial speed index can be effectively solved. On the premise that the maximum chamber pressure is not increased, secondary acceleration of the projectile is achieved, and the outlet speed and the flight performance of the projectile are remarkably improved. According to the method, an important theoretical reference and a practical technical method are provided for design and development of the high-initial-speed large-caliber balance gun in the future, and the method has wide application prospects and great military value.

The present application provides a kind of gas actuator interior ballistic analytical calculation method considering leakage, steps are as follows: step 1: gas actuator interior ballistic mathematical model establishment: step 2: gas actuator pressure characteristic analytical solution calculation: step 3: gas actuator work characteristic analytical solution calculation.The gas actuator interior ballistic state parameter calculation method provided by the present application can be used for the evaluation and optimization of the overall design stage of gas actuator, and improves the design efficiency.By analytical solution, the influence of gunpowder gas leakage on the output characteristics of gas actuator is corrected, and it is no longer constrained by the mass conservation assumption, thereby improving the accuracy of interior ballistic prediction results.Gas actuator output characteristics are directly calculated by analytical formula, without using numerical method to integrate and solve the entire working process, which significantly reduces the calculation time.

The invention provides an internal and external ballistic parameter optimization method based on an NSGA-III algorithm and multi-factor coupling, and the method is used for optimizing an engine design scheme of an aircraft, and comprises the steps: obtaining an initial population containing a plurality of initial individuals, each initial individual representing a group of design variables of an engine; the initial individual is any one of missile appearance parameters or launching initial state parameters; for each initial individual, performing multi-factor coupling to obtain a plurality of aircraft state parameters corresponding to the initial individual and inner trajectory parameters corresponding to the aircraft state parameters; and performing parameter optimization on the initial individuals in the initial population by using an NSGA-III algorithm according to the plurality of aircraft state parameters and the respective corresponding inner ballistic parameters to obtain a parameter optimization result, thereby optimizing the engine design scheme on the premise of ensuring the optimal outer ballistic.

The application discloses an interior ballistic nonlinear interval uncertainty optimization method based on an affine algorithm, determines Chebyshev polynomial order and uncertainty design variables, wherein the uncertainty design variables are charge mass, powder grain arc thickness, powder grain aperture and charge chamber volume; a mixed charge classical interior ballistic model based on thermodynamics is established, corresponding ballistic parameters are calculated, including projectile initial velocity, maximum projectile bottom pressure, muzzle pressure and maximum negative pressure difference; a Chebyshev polynomial proxy model is constructed; intervals of uncertainty objective functions and uncertainty constraint functions corresponding to the uncertainty design variables are obtained; the uncertainty objective functions and the uncertainty constraint functions are converted into affine forms including central values and deviation ranges; the interior ballistic uncertainty optimization problem is converted into a deterministic optimization problem; and an optimization solver NSGA-II is used for analog search to solve a Pareto optimal solution set. The method is suitable for efficient solution of engineering uncertainty optimization problems.

A ballistic target based on an electromagnetic catapult-assisted three-stage light gas gun includes a first-stage gas propulsion section, an electromagnetic catapult device, an armature, a first-stage piston, a first-stage high-pressure pump pipe, a first- and second-stage connecting mechanism, a second-stage pump pipe, a second-stage piston, a second- and third-stage connecting mechanism, a projectile, a launch tube, an expansion tank, a test chamber, and a measurement and control system. The first-stage gas chamber releases high-pressure gas to drive the armature and the first-stage piston forward and out of the first-stage gas pump pipe. Within the first-stage electromagnetic pump pipe, the armature pushes the first-stage piston to move and compress the light gas under the combined action of the high-pressure gas thrust and electromagnetic force. The high-pressure light gas in the second-stage gas chamber breaks through the second-stage diaphragm, pushing the second-stage piston to compress the light gas in the second-stage pump pipe. The high-temperature and high-pressure light gas in the third-stage gas chamber breaks through the third-stage diaphragm, driving the projectile at high speed out of the launch tube, through the expansion tank, and into the test chamber. The present invention improves the driving capacity of traditional three-stage light gas guns by several times, and has better and more controllable interior ballistic performance. It is also safer, cleaner, and more efficient.

The present application relates to ammunition technical field, especially a kind of full shape blank cartridge for completing disintegration after projectile ejection by launching energy, it is composed of launching charge and projectile, the projectile includes bullet body, wind cap, pressure limiting sheet and counterweight filling;The bullet body is the structure of the cylinder with one end sealed and the other end open, it is equipped with fire hole in sealed end, the fire hole is covered by pressure limiting sheet on the outside of sealed end, and the sealed end is partially assembled in launching charge, the open end of bullet body is buckled with wind cap;The counterweight filling is filled in the inner cavity of bullet body.The present application relies on the structural design of projectile to ensure that it has similar interior ballistic performance with standard product during shooting, and the sensory experience is basically consistent with live ammunition shooting, it can be used for training soldiers to master the basic shooting action of grenade launcher, also can be used for live exercise, fill the blank of grenade on blank cartridge;The projectile does not contain any dangerous sensitive material such as explosive, no explosion danger.

The invention discloses an ejection inner trajectory adjusting method based on a solid cooling agent, in the method, a cooling device loaded with the solid cooling agent is introduced, and the fuel gas temperature is reduced through the cooling device, so that an ejection inner trajectory system can adapt to the low-overload and high-initial-speed requirements of an inner trajectory under the condition of small initial capacity.

The invention belongs to the technical field of solid rocket engine design, and discloses a forward inner trajectory prediction and reverse grain design method based on machine learning. Obtaining an inner ballistic parameter data set based on parameterized calculation software; establishing an inner ballistic parameter forward prediction model; after the inner trajectory parameter forward prediction model is trained, parameter prediction is carried out according to design data; establishing an inner ballistic parameter reverse prediction model; and training an inner ballistic parameter reverse prediction model and performing parameter prediction by using the new inner ballistic parameters. The inner ballistic parameter forward prediction model avoids the problem of low efficiency in the inner ballistic calculation process by using parameterized calculation software, and the inner ballistic parameter reverse prediction model can realize the reverse design of the metal wire embedded grain according to the task requirement of the inner ballistic design.

This invention discloses a discrete pulse timing fitting control method for a complex power source series catapult launch, capable of controlling the mass flow rate of multiple small pulse engines. The method achieves consistency between the fitted mass flow rate curve and the theoretical fitting result, maintaining constant overload and stable operation of the missile during launch. The method includes the following steps: Step 1: Solve for the ideal overload using internal ballistics knowledge based on the required missile parameters. Step 2: Obtain the ideal pressure according to the dynamic equations. Step 3: Substitute the ideal pressure into the control equations to obtain the ideal engine mass flow rate. Step 4: Determine whether the interpolation between the ideal engine mass flow rate and the actual mass flow rate meets the requirements. If yes, return to Step 2; otherwise, proceed to Step 5. Step 5: Open a new release point; calculate the actual mass flow rate, and return to Step 2.

The invention relates to a high-speed closing device suitable for preventing a light-gas gun from following airflow and fragments, and relates to the field of light-gas gun launcher equipment, the high-speed closing device comprises a mounting seat, a baffle, a tension spring, an electromagnet and a reset wrench, the mounting seat is fixedly connected in a cavity between a light-gas gun bullet channel through hole and a separation hole; a separation hole is formed between the ballistic through hole and the separation hole so that a model launched by the light-gas gun can fly into the separation hole from the ballistic through hole, one end of the baffle is hinged to the mounting base so as to cover the separation hole after rotating, one end of the tension spring is fixedly connected with the mounting base, and the other end of the tension spring is fixedly connected with the baffle so that the baffle can be pulled to the separation hole within 30 ms; the electromagnet is fixedly connected to the position, above the baffle, of the mounting base so as to limit the baffle to move towards the separation hole, one end of the reset wrench is hinged to the baffle so as to enable the baffle to rotate away from the separation hole, and the device has the advantage that interference airflow and fragments caused by light-gas gun launching in the ballistic target test can be rapidly restrained.

The present invention discloses a forming core mold and a forming method for a radial annular groove grain of a solid rocket motor, belonging to the technical field of aerospace. The present invention combines a combustible core mold assembly with an ablatable core mold. By using the ablatability of the ablatable core mold, strength support is provided during the propellant loading process, enabling the grain to form a specific structure. After the propellant loading, it is removed by ablation. The combustible core mold assembly, on the one hand, provides protection for the grain during the removal process of the ablatable core mold, and on the other hand, burns rapidly after the engine ignition without affecting the internal ballistic characteristics of the engine. The present invention solves the problem of difficult forming of the radial annular groove grain, and can realize the rapid forming and production of multiple radial annular groove grain structures; the present invention can realize the rapid preparation of complex grain structures such as radial annular grooves, providing a rapid and efficient means for the design and production of complex grain structures. At the same time, compared with the existing disassembled combined core mold, this method can improve the production efficiency.

The application discloses a single-chamber double-thrust solid rocket engine charging structure and process, which comprises a grain, a heat insulation layer and a combustion chamber shell. The inner surface of the combustion chamber shell is subjected to sand blasting treatment and uniformly sprayed with adhesive, and then is bonded with the heat insulation layer. The inner surface of the heat insulation layer is roughened and uniformly sprayed with a lining layer. The grain is integrally solidified on the inner surface of the heat insulation layer by adopting a vacuum wall pasting pouring process. The solid rocket engine combustion chamber charging structure of the application adopts a variable cross-section integrated design, improves the complexity of the traditional series combination type single-chamber double-thrust star hole grain forming process, avoids quality problems such as debonding, slag inclusion, air bubbles and cracks of the combination type star hole grain in the forming process of the transition section, guarantees the charging structure integrity and interior ballistic performance, realizes the minimum initial thrust required for the missile to leave the rack and the characteristic requirement of the front position of the missile mass center, effectively solves the problem of missile flight instability, improves the missile flight reliability, and is successfully applied in a type.

The application discloses a kind of multi-propellant zero-dimensional interior ballistic calculation methods considering the difference of gas properties, which includes establishing the physical model of solid rocket engine, obtaining the initial parameters of physical model;According to the initial parameters of physical model and the conservation relation, the transient control equation is established, and the combustion chamber pressure at the current time is obtained;The gas balance of different propellants producing gas at the next time is calculated;Obtain the physical property parameters of mixed gas at the next time;The burning rate and burning area at the next time are calculated;Repeat the above steps until the burning area is 0, and the zero-dimensional interior ballistic calculation is completed.The application considers the mixing process of different propellants producing gas during the combustion process of mixed charge solid rocket engine, and the calculation result is accurate.

The invention provides a device and method for continuously measuring the inner ballistic velocity of a two-stage light-gas gun, the device comprises a gas chamber, a pump pipe, a piston arranged in the pump pipe, a transmitting pipe located at the front end of the pump pipe, a measuring assembly, bulletproof glass, a data collector and a controller, the measuring assembly comprises a first laser displacement sensor and a second laser displacement sensor, the first laser displacement sensor is installed at the front end of the piston, the second laser displacement sensor is located in front of the transmitting tube, displacement data of the piston and the projectile can be measured in real time, and motion parameters of the piston and the projectile can be accurately obtained. According to the invention, the continuous change process of the inner ballistic parameters in the ultra-high-speed launching process of the secondary light-gas gun can be accurately measured under the closed condition, the time sequence synchronous recording of the inner ballistic parameters of the piston and the projectile is ensured, and the motion state of the piston and the projectile at any moment can be obtained.

This invention discloses a silent mortar shell and its usage method. The shell includes a projectile (1), a tail tube (2), a piston (3), a tail fin (4), and a main charge (5). The piston (3) is provided with a projectile belt (6), a primer (7), and a ignition tube (8). The projectile belt (6) is located outside the piston (3). The front part of the inner cavity of the tail tube (2) is provided with a bevel (9), and the rear part is provided with a tail cone (10). The surface of the bevel (9) gradually narrows from front to back, and the inner surface of the tail cone (10) gradually narrows from front to back. The projectile belt (6) is initially stuck at the bevel (9). The space between the piston (3) and the projectile (1) forms a chamber (11). The main charge (5) is located in the chamber (11). After the primer (7) is fired, it can ignite the main charge (5) through the ignition tube (8). The tail fin (4) is connected to the rear part of the tail tube (2). This invention provides starting pressure through the cooperation of the cartridge belt and the breech bore, ensuring internal ballistic performance and enabling silent, smokeless, and lightless firing.

The present invention provides a liquid-gas phase-change catapult interior ballistics modeling method, simulation method, and electronic equipment. The liquid-gas phase-change catapult system of the present invention includes at least one phase-change power unit. The liquid-gas phase-change catapult interior ballistics modeling method includes dividing the liquid-gas phase-change catapult interior ballistics into a phase-change power unit flow model, an initial volume chamber energy model, and a projectile motion parameter model. The present invention constructs a liquid-gas phase-change catapult interior ballistics model comprising multiple phase-change power units. The phase-change device increases the operating time, which can achieve a predetermined speed without exceeding a limit when catapult overload control requirements are high. The method can also accurately calculate the changes in internal ballistic parameters during the expansion and operating process of a carbon dioxide phase-change catapult.

1. The name of the design product: the target of the sky screen. 2. The use of the design product: for the collection of the muzzle velocity of the gun interior ballistic parameter. 3. The design points of the design product: in shape. 4. The picture or photo that can best show the design points: the perspective view.

This invention belongs to the field of commercial aerospace and solid rocket optimization, and discloses a solid rocket trajectory optimization design method based on internal ballistic parameterization modeling. The method includes: determining the structural and energy characteristic parameters of the solid rocket motor; designing different types of propellant grains and constructing their geometric models; determining the internal ballistic parameterization model of the motor; constructing a dynamic model for joint optimization of the internal and external trajectories of the solid rocket; based on the dynamic model, setting the optimization objective of the joint internal and external trajectory optimization problem and representing it with a performance index function, and setting the constraints of the joint internal and external trajectory optimization problem; discretizing the dynamic model, performance index function, and constraints, converting them into a nonlinear programming problem and solving it to obtain the optimization results corresponding to each type of propellant grain; determining the performance index corresponding to each type of propellant grain based on the optimization results, and using the performance index to determine the propellant grain as the optimal design scheme.