2014 Vol. 40, No. 4

Display Method:
Influencing depth under aircraft loads of runway
Zhang Xianmin, Xue Huaxin, Dong Qian, Sun Zhichao
2014, 40(4): 427-432. doi: 10.13700/j.bh.1001-5965.2013.0300
Abstract:
In view of the current situation that the relationship among the influencing depth, the pavement structural parameters, the configuration of landing gear and take-off ground speed was not taken into consideration by the present rigid pavement, a finite element model of 45 m×15 m×10 m was built by means of the ANSYS software. The influencing depth of B737-800 under dynamic loads in some conditions with different parameters, including the thickness and modulus of surface and base and soil matrix layers, was calculated. Compared with other 4 aircraft types, the results were used to analyze the influence of the configuration of landing gear. At the same time, the dynamic curve related to the influencing depth during the period of B737-800's take-off was obtained. The results show that the influencing depth decreases linearly with the increase of thickness and modulus of surface and base layers, whereas increases quadratically with the increase of modulus of soil matrix which is most sensitive to the influencing depth. Besides, the configuration of landing gear makes a great contribution to the influencing depth. During the take-off period, the influencing depth changes non-linearly with a slight increase at the beginning and then a sharp decrease. The study provides the theoretical basis and reference to the selection of the structural parameters of pavement and maintenance of pavement in airports.
Influence of frequency mixing on vibration test of fiber optic gyroscope
Song Ningfang, Zhao Yafei, Pan Xiong, Zhang Chunsheng
2014, 40(4): 433-438. doi: 10.13700/j.bh.1001-5965.2013.0335
Abstract:
Frequency mixing happening in vibration test on fiber optic gyroscope (FOG) can cause signal distortion of the output of FOG, which will influence the test result. In order to verify the consequence of frequency mixing and restrain it, a closed-loop data acquisition system which was used to get the original output of FOG (namely closed-loop data) was designed and realized (the speed could reach 1 MHz×16 bit). The character of closed-loop data in vibration test was analyzed and the fact that the vibration error could not be wiped out by filter was known, which would cause frequency mixing if the sampling frequency was not proper. The frequency mixing was verified through simulation by matlab and vibration test on FOG. The restraining method of frequency mixing was given. Experiments show that for the FOG whose data acquisition process was designed as what was referred, the design improved could avoid frequency mixing very well.
Numerical simulation analysis of steady-state properties of gas face and cylinder film seal
Ma Gang, Sun Xiaojun, Luo Xianhai, He Jun
2014, 40(4): 439-443. doi: 10.13700/j.bh.1001-5965.2013.0322
Abstract:
Aimed at the special condition of fluidic dynamic seals of high speed fluid machineries such as the aero-engine, a new type of sealing form, gas face and cylinder film seal was proposed. According to the structure characteristics of the gas film seal, the mathematical analysis model of the gas face and cylinder film seal was built. Then the model of gas film's three-dimensional flow field was numerically calculated by Fluent in the form of turbulent flow. The influence of sealing geometry structure parameters on the stability performances of the seal such as face opening force Fd, cylindrical opening force Fc, leakage Q, and friction torque M was studied. The geometry structure parameters include gas face film thickness, face groove depth ratio, cylindrical film thickness, cylindrical eccentricity, cylindrical groove depth ratio, and cylindrical groove width ratio.
Influence of laser shock peening times on microstructure and hardness of TA15 titanium alloy
Zhu Ying, Fan Bowen, Guo Wei, Kang Hui
2014, 40(4): 444-448. doi: 10.13700/j.bh.1001-5965.2013.0305
Abstract:
Q-switched Nd glass laser with 20 J energy was used to shock TA15 titanium alloy in different times. Results show that laser shock peening (LSP) can produce micro plastic deformation, form dense micro pits and refine the grain size. When the number of impact times increases, the depth of the micro pits increases, but after the impact times is more than twice, the depth of the pits will stop increasing, so the highest impact times is twice in this experiment. Under the impact times of twice, the dislocation density is increasing with the increase of impact times. In the process, the dislocation will pile up, snarl, and proliferate. The hardness of the material increases because of the variation of microstructure above. The surface hardness and the depth of affected layers increase due to the increase of the shock times.
Decoupling PI controller design for aeroengine
Gao Yahui, Zang Jun, Yao Hua, HUANG Jinquan
2014, 40(4): 449-454. doi: 10.13700/j.bh.1001-5965.2013.0312
Abstract:
In discrete-time domain, the optimal PI controller design problem for aeroengine was researched. Firstly, a general coupling PI controller design method was presented. The key ideas were to construct Lyapunov function to guarantee the closed-loop stability, and the performance was optimized under the given evaluation index. The controller design results can be cast as a convex optimization problem involving a set of linear matrix inequalities (LMIs), which can be solved efficiently with commercially available software. Then, considering engineering application status in China, to suit for the large thrust turbo fan aeroengine model characteristics and meet the control requirements, a decoupling PI controller design method was developed based on the general method, by constructing special PI controller and matrix variables. The influence of performance evaluation index matrix selection to controller design results was discussed, and the suggested structure of performance evaluation index matrix was presented. Finally, an example was presented to verify the proposed theoretical results.
Loop parameters on dynamic characteristics of digital closed-loop accelerometer
Zhang Xi, Zhang Shengyan, Li Lijing, Wang Hongbo
2014, 40(4): 455-460. doi: 10.13700/j.bh.1001-5965.2013.0301
Abstract:
The bandwidth of the digital closed-loop quartz-flex accelerometer was only 10 Hz under the integral controller. The servo loop parameters were adjusted to improve the system dynamic performance, and a proportional integral controller was designed to ensure that the system was no difference. The system mathematical model was established. With the method of implicit function, the influences of the loop parameters (including sampling coefficient, proportional coefficient and integral coefficient) on the closed-loop bandwidth, stability and static accuracy were analyzed. To build the system prototype, experimental results of the bandwidth and zero bias stability show that the system bandwidth is positively correlated with the loop parameters, among which proportional coefficient is the most significant factor on the dynamic characteristics of the system. Test results are in consistence with the theoretical analysis, which provides the theoretical basis and experimental instruction for dynamic characteristics adjustment of the digital closed-loop accelerometer.
General forward kinematic algorism for three-chain parallel manipulator
Zhou Wanyong, Chen Wuyi, Liu Huadong
2014, 40(4): 461-466. doi: 10.13700/j.bh.1001-5965.2013.0337
Abstract:
To solve the problem that actual geometric parameters are not equal to nominal ones in parallel manipulator, a general forward kinematic algorism, containing all of the geometric parameters, was proposed. The general 3RPS parallel manipulator, with compound spherical joints, was taken as an example. The manipulator consists of a base platform, a mobile platform and three chains, and every chain is a 5-DOF serial manipulator with only 1-DOF being active. The algorism is based on dual quaternion and DH method and contains a total of 78 geometric parameters, and hence it is able to be used for accuracy analysis, accuracy synthesis, accuracy calibration and accurate kinematic simulation of parallel manipulator. Finally, the precise, stability and rapidness of the algorism were verified through iterative calculation. The forward kinematic algorism of 3RPS, 3_5R, 3_RPUR, 3_RPRRR,and so on can be expressed in a same form on the basis of the proposed algorism.
Fighter maneuver control method of radar range tracking interrupt
Li Fei, Yu Lixin, Wang Long, Sui Yonghua
2014, 40(4): 467-472. doi: 10.13700/j.bh.1001-5965.2013.0317
Abstract:
The maneuver trajectory control strategy that can interrupt the radar range tracking loop was proposed based on the system characteristic of auto range tracking system. The transfer function of auto range tracking system was developed, and the error production mechanism was researched. Taking the missile attacking on two-dimensional plane as example, the second order relative motion model was analyzed. And then, the fighter control method used to interrupt the radar range tracking loop was put forward based on close-loop feedback control. The analytical form of maneuver trajectory control law was derived. The application range was analyzed through digital simulation. The results provide the fighter pilots reference when making decision.
Mass estimation method and its application for horizontal takeoff horizontal landing two stage to orbit system
Jiang Yazhong, Jiang Chongwen, Gao Zhenxun, Lee Chunhian
2014, 40(4): 473-478. doi: 10.13700/j.bh.1001-5965.2013.0299
Abstract:
Aiming at transportation missions to low global orbit, a mass estimation method was proposed for horizontal takeoff horizontal landing two stage to orbit (TSTO) transportation systems considering thrust-drag characteristics in different flight stages and specific impulse variations in different engine modes. Three schemes of turbine based combined cycle-reusable rocket (TBCC-RR), rocket based combined cycle-reusable rocket (RBCC-RR), and reusable rocket-reusable rocket (RR-RR) were designed and compared for a mission to deliver 8 t payloads to a 200 km orbit. Influences of several parameters on design results were analyzed, including the separation point, throat-drag ratio and structure mass fraction of the first stage vehicle. The position of separation point has a great influence on TSTO schemes. If a RBCC vehicle is used as the first stage, it's recommended that the separation take place when the scramjet is turn off. Though TBCC-RR scheme leads to a smaller gross takeoff mass, RBCC-RR scheme has a smaller structure mass. The most effective way for gross mass reduction is to cut down the structure mass fraction and another approach is to improve throat-drag ratio of the vehicle.
Attitude dynamics and control of spacecraft with fluidic ring actuator based on the refined model
Guan Hong, Xu Shijie
2014, 40(4): 479-485. doi: 10.13700/j.bh.1001-5965.2013.0316
Abstract:
The influence of nonlinear disturbances to model's precision and control accuracy were studied after considering the viscous of the flow flied and the friction in the pump control system. For the former, the momentum loss caused by the viscous of flow was studied. The equivalent momentum loss depth in boundary layer and the momentum loss model of fully developed flow in curved rectangular tubes were obtained. For the latter, feedback compensation law of friction loss was designed under the consideration of friction nonlinearity influence, which improves the performance of pump. The precise dynamic and control models of fluidic ring actuator (FRA) for the high accuracy attitude control missions were deduced by adding the above two nonlinear feedback models to FRA dynamic model functions.
Nonlinear leakage model of rotary vane actuator
Wang Zeng, Jiao Zongxia, Wang Chengwen, Shang Yaoxing
2014, 40(4): 486-493. doi: 10.13700/j.bh.1001-5965.2013.0584
Abstract:
Rotary vane actuator is a high-precision actuating mechanism. Internal structure of seals is more complex than the other actuators. Nonlinear leakage model of rotary vane actuator was put forward based on the analysis of the character of seals of rotary vane actuator. Rotary vane actuator's total leakage consists of three parts. Each part of leakage was analyzed. The key factors of leakage were found. The method of decrease leakage of rotary vane actuator was applied via analysis. In operation, the problem of seal failure existed. The reason of seal failure is about shaft shoulder seals. Increase the compression quantity of O-ring of shaft shoulder seals could prevent seal failure. Leakage of rotary vane actuator not only related to load pressure and velocity of actuator, but related to the rotary angle of vane. The nonlinear model provided the theory proof for electro-hydraulic servo system for rotary vane actuator.
Spacecraft attitude estimation based on attitude-weighted kernel regression
Zhang Haopeng, Jiang Zhiguo
2014, 40(4): 494-499. doi: 10.13700/j.bh.1001-5965.2013.0298
Abstract:
An attitude estimation method for monocular vision imaging systems was proposed to solve relative attitude estimation problem of spacecrafts. On the basis of the original kernel regression model, the similarity of training data in the attitude space was used to weight kernel functions of the original kernel regression model in the visual input (image feature) space. A joint probability distribution function of input variables (image features) and target variables (attitudes) was learned, which was called acceptance function. Given images containing spacecrafts with unknown attitudes, the estimated attitude of the target spacecraft can be obtained by maximizing the acceptance function in the attitude space. The proposed method just needs training data to learn the model, so it has fewer limits than other vision based methods. Comparison experimental results show the advantage of the proposed method in attitude estimation. The effectiveness of the proposed method for spacecraft attitude estimation was also validated by the experimental results on satellite image dataset.
Stiffness characteristics distribution of 3 PRS/UPS parallel manipulator with actuation redundancy
Guo Jiangzhen, Wang Dan, Fan Rui, Chen Wuyi
2014, 40(4): 500-506. doi: 10.13700/j.bh.1001-5965.2013.0304
Abstract:
A three degree of freedom (DOF) 3PRS/UPS parallel manipulator with actuation redundancy was designed and investigated. The architectural model was constructed and the kinematic analysis was presented based on screw theory. The overall Jacobian matrix including redundant actuation was derived through respectively establishing the actuation and constraint Jacobian matrices. The overall stiffness matrix was derived by virtual work principle, in which the compliances subject to actuators and constraints were involved. The deformation of manipulator under static load was calculated, and its distribution rule was established. Utilizing the extremun eigenvalue of stiffness matrix and kinematic stiffness index (KSI), the stiffness performance of the manipulator was evaluated. The influence to the stiffness characteristics distribution of the manipulator after introducing redundant actuation was compared and analyzed. It was concluded that the redundant actuation can increase the stiffness along specific axis and improve its stiffness characteristics distribution, which will be valuable for the architecture design of a parallel manipulator with actuation redundancy.
Tipping calibration method for K-band hyperspectral microwave radiometer
Xie Yan, Chen Jingxiong, Miao Jungang
2014, 40(4): 507-511. doi: 10.13700/j.bh.1001-5965.2013.0315
Abstract:
The K band ground based hyperspectral microwave radiometer can be applied in the atmospheric sounding field, and it can improve the profile error and the vertical resolution of the moisture profiling from Earth's surface to the atmospheric troposphere. For the purpose of reducing the fluctuations of the atmospheric mean radiant temperature in different frequencies and different elevation angles, an improved tipping calibration method was proposed under hyperspectral microwave condition based on atmospheric profiles of Beijing in previous years and Liebe millimeter propagation model (MPM)(1993). Compared with the traditional tipping calibration, the proposed tipping calibration method can improve the prediction accuracy of the atmospheric mean radiant temperature based on the priori meteorological data in the current area. Analysis results show that the impact of the atmospheric mean radiant temperature on calibration errors can be effectively reduced with the improved tipping calibration method for the K-band ground-based hyperspectral microwave radiometer.
Robust optimization of coupled structural-acoustic systems based on sensitivity analysis
Wang Chong, Qiu Zhiping, Wang Xiaojun, Wu Di
2014, 40(4): 512-516. doi: 10.13700/j.bh.1001-5965.2013.0328
Abstract:
An interval finite element method and an interval robust optimization model were proposed for the coupled structural-acoustic field prediction and structural design with uncertainties both in the inherent parameters and external load. Based on the central difference method, the response sensitivity with respect to the system parameters was derived from the structural-acoustic dynamic equilibrium equation. Interval variables were used to quantitatively describe all the uncertain parameters with limited information. In terms of the first-order Taylor expansion, the lower and upper bounds of the uncertain structural-acoustic field could be quickly obtained. In the structural robust optimization, the original uncertain single-objective optimization problem was transformed into a deterministic multi-objective one by introducing a sensitivity index. To ensure a more stable performance of the structural design, the interval possible degree was adopted to describe the robustness of the constraints. Numerical results about a bomb bay were given to demonstrate the effectiveness of proposed robust model and algorithm.
State space theory and NR-LMS algorithm based method for structural dynamics parameter identification
Wang Yunfeng, Cheng Wei, Chen Jiangpan
2014, 40(4): 517-522. doi: 10.13700/j.bh.1001-5965.2013.0285
Abstract:
A parameter identification method for structural dynamics system based on state space (SS) theory and normalized robust least mean square (NR-LMS) algorithm was proposed. By using this method, the identified dynamic system's input and output data were used to build its Hankel-Toeplitz model based on the state space theory. Iterative NR-LMS algorithm was applied to achieve parameters' estimates and Hankel matrix for this model. Singular value decomposition (SVD) method to Hankel matrix was employed for quantifying the order of this dynamic system. Modal parameters and the state space model's parameters also could be achieved from the Hankel matrix by certain calculation. A simulation of 3-DOF(degree of freedom) spring-mass system was employed to validate this method and experiment of identifying cantilever's parameters was studied. The results demonstrate this method can identify structural parameters accurately and quickly.
Precise configuration of mixed message sets’ transmission mode in network partition
Tu Xiaojie, He Feng, Wu Qing, Xiong Huagang
2014, 40(4): 523-528. doi: 10.13700/j.bh.1001-5965.2013.0286
Abstract:
It was indicated that configuration of message transmission mode among network partition method in distributed integrated modular avionics was uncertain. Through formal description the problem was transferred into an optimal problem with constrains including real-time, bandwidth and buffer. Then the transmission mode configuration algorithm was proposed based on genetic simulated annealing algorithm; the objective function was aimed to balance of end-to-end delay of system messages. Effectiveness of the algorithm was verified based on two experiments, and performance of the algorithm was compared with that of traditional genetic algorithm. The results show although the algorithm is 18.1% slower, the fitness value is 28.7% higher. This algorithm provides a reference for the network partition application in avionics systems.
Hexahedral mesh generation method for geometric features
Chen Ruizhi, Xi Ping, Wang Shuai
2014, 40(4): 529-535. doi: 10.13700/j.bh.1001-5965.2013.0296
Abstract:
In order to guarantee self-adaptability of geometric features and coordination between meshes of geometric features and overall structure, a hexahedral mesh generation method for geometric features was proposed which focuses on generating high-quality hexahedral meshes for local complex features having regular structures. Firstly, types of geometric features and meshing processes of geometric features were analyzed, based on which parameters relevant to meshing processes of geometric features were separated into two categories, real and virtual parameters. Subsequently, through integrating the design thought of parameterization into geometric features' three typical meshing processes including entity separation, feature decomposition and mesh generation, a parameter-driven mechanism transferring information from geometric features into meshing details (such as numbers of elements of edges, specific meshing strategies, etc) was built. Also, meshing database for geometric features was established so as to solidify the parameter-driven mechanism corresponding to geometric features into meshing programs. Finally, film-cooling holes and spoiling posts of turbine blades were meshed under different designated element sizes. Meshing results reveal the applicability and stability of the method proposed.
Method optimization of optimum measurement point selection in experiential modal analysis
Rong Shuanglong, Li Chuanri, Xu Fei, Ma Tian
2014, 40(4): 536-543. doi: 10.13700/j.bh.1001-5965.2013.0292
Abstract:
As an important basis of the validation of the finite element model, the result of experimental modal analysis is influenced by various aspects, one significant aspect is the measurement point selection. A new optimal measurement point selection method, namely effective independent-coefficient variance of modal kinetic energy (EI-CVMKE) method was proposed based on the effective independent (EI) method and the modal kinetic energy (MKE) method. Besides, a new criterion called the coefficient variance of modal kinetic energy (CVMKE) was presented. The obtained optimal measurement points using the new method were compared with those gained by EI method and MKE method. The advantage and disadvantage of those three methods were demonstrated by three evaluation criteria which are CVMKE, modal assurance criterion (MAC) and singular value decomposition ratio (SVD ratio). A computational simulation and a modal test on an aluminum alloy plate were carried out to demonstrate the feasibility of the optimal measurement point selection method. The result shows that EI-CVMKE method can not only make the truncated mode shapes as linearly as possible but also enable the measured MKE to maintain the maximum value. The new method is most feasible in the three methods.
Adaptive recovery algorithm for compressive sensing based on Fourier basis
Lü Fangxu, Zhang Jincheng, Wang Quan, Wang Yu
2014, 40(4): 544-550. doi: 10.13700/j.bh.1001-5965.2013.0332
Abstract:
In order to improve the recovery accuracy of compressive sampling, an algorithm of modified sparsity adaptive matching pursuit based on discrete Fourier transform (MSAMP-DFT) was proposed. In the course of reconstruction, not only the correlation, but also the conjugate symmetry on discrete Fourier transform was used to control the process of adding the index value into support set. The double threshold, residual energy and changing rate of residual energy were used to stop loop iteration. Lastly, the reconstructed signal was obtained by inverse discrete Fourier transform. The experiment results verify that, the method introduced can converge to the signal sparsity without any prior information and the recovery accuracy of the arithmetic introduced is better than others under the same rate of signal to noise.
Oblique flying wing supersonic airliner aerodynamic configuration parameters selection method
Hu Shuyao, Jiang Chongwen, Gao Zhenxun, Lee Chunhian
2014, 40(4): 551-557. doi: 10.13700/j.bh.1001-5965.2013.0291
Abstract:
The method is capable of providing the basic geometry of the flying wing simply by given certain bulk parameters, such as the passenger number, range, cruise velocity and height. Discussions were paid to the selection of the appropriate symmetry plane chord, the constraint of the wing span caused by the aspect ratio and take-off wing loading, the range identification of the aspect ratio and take-off wing loading, as well as the dimension derivations of the fuel tank and passenger cabin. In order to demonstrate the correlation between configuration parameters and design demands, several designed points were calculated using the present method under the conditions of 250-550 passengers and 6 500-10 000 km flight range, with lift-to-drag ratio of 11-12. The results yield that there exists a take-off weight threshold of the designed wing. When the take-off weight is less than the threshold value, minimum aspect ratio defines the wing area; whereas the take-off weight is larger than the value, maximum wing loading determines the wing area. Improvements on the cruise lift-to-drag ratio would lessen the wing area which can be decided by the maximum wing loading.
Camera calibration from geometric feature of spheres
Zhao Yuntao, Sun Junhua, Chen Xu, Gong Zheng
2014, 40(4): 558-563. doi: 10.13700/j.bh.1001-5965.2013.0293
Abstract:
Camera calibration with spheres has little demand on image number, camera shooting angle and high adaptivity to occlusion, which has an obvious advantage in applications. A novel camera calibration method was proposed based on geometric feature of sphere projection model. This algorithm used two projection conics of spheres and solved the intrinsic parameters of the camera. The projection conics were obtained from image of two spheres at different positions. The symmetry axis and common tangent of the projection conics were used to solve the principal point and the projections of sphere centers. Then normalized focal length was computed based on geometric relationship of the principal point and projection of sphere center. Finally intrinsic parameters were obtained using optimization algorithm. Simulation data experiments analyze the main error factors and real data results show that the proposed method is reliable and the error is less than 5% comparing with planar target method.
Anti-coking performance of nozzle materials’ surface chemical modification
Li Fan, Zhu Yuelin, Huang Yanfei, Liu Yajie
2014, 40(4): 564-568. doi: 10.13700/j.bh.1001-5965.2013.0326
Abstract:
Based on the problem of technical performance and service life of the aero-engine with a mass of coking on nozzles, steady rich chromium oxide layer was prepared on the aircraft engine nozzle materials' surface through the chemical oxidation-cathodic reduction method. The sample surface was characterized by scanning electron microscope, energy dispersive spectrometer and contact angle measuring device. Static coking quality determination and dynamic aero-engine bench combustion test was carried out. The anti-coking mechanism of chemical modification was discussed. It is found that the materials' surface is flat, and oxidation film particles closely arrange. Nozzle materials' anti-coking performance is closely related with surface composition and interfacial tension. The highest static anti-coking rate is up to 12.5%. Dynamic combustion experiment has more significant effect.
Probabilistic flutter analysis with uncertainties in structural stiffness
Tang Jian, Wu Zhigang, Yang Chao
2014, 40(4): 569-574. doi: 10.13700/j.bh.1001-5965.2013.0336
Abstract:
A probabilistic flutter analysis method was proposed to evaluate the structural stability and flutter risk of the rudder, which was subject to uncertainties in structural parameters with stochastic distribution. Monte Carlo simulation (MCS) and non-intrusive polynomials chaos (NIPC) method were used. A typical 3-D rudder with nonlinear factors, whose steering gear has two uncertain variables, that is bending rigidity and torsional rigidity, both satisfying Gauss distribution, was selected to examine the present method. A large amount of flutter information was obtained by flutter calculations of massive samples when using the MCS method, while which was gotten by surrogate models with point-collocation method when using the NIPC method. After that, the dangerous regions of velocity and the probability of flutter under certain velocity were obtained. Then the comparisons of the confidence level, analytic precision and efficiency of calculation were conducted. The results suggest that the probabilistic flutter analysis method based on uncertainty quantification is effective in the flutter risk assessment of structures using the probability information of the uncertain parameters.
Calculation and selection of sequentially truncated test scheme
Yu Chuang, Wang Xiaohong, Li Qiuxi
2014, 40(4): 575-578. doi: 10.13700/j.bh.1001-5965.2013.0295
Abstract:
The method for calculating the two types of risk's real value under sequential test scheme was researched, and software for calculating the truncation scheme of test was programed. Then test scheme was analyzed and the relationship between truncated sequential test and fixed number test was studied. Two methods to select the test scheme in the specimen number limited conditions was put forward, the first method is to modest relaxation of risk requirements, and the second is to adjust the test's reception line and reject line which could decrease the maximum required number of trials and keep the two types of risk unchanged. These two methods could determine the testing program flexibly under the specific test requirements, which allow the maximum required number of trials decrease about 30% with the two types of risk or minimum required number of trials increase less than 10%.