What will be velocity of the lander at impact

The lander during this phase had to carry out the imaging process of the lunar surface to identify the most suitable landing site in the region. The process was under operation till the 13th minute after which the screen at mission control suddenly froze. The Navigation Guidance and Control System which was working in automatic mode performed according to the plan. Though the rough braking phase significantly reduced the velocity of the lander.

The imager onboard the Vikram was switched ON at around 9. The breaking of the Vikram lander to reduce the velocity was being done using four onboard N liquid fuel engine.

Each of them had eight thrusters and the new throttleable technology of ISRO was being used. Like us on Facebook and follow us on Twitter. Financial Express is now on Telegram. Click here to join our channel and stay updated with the latest Biz news and updates. Answer 6. Topics Motion Along a Straight Line. Physics Chapter 2 One-Dimensional Kinematics.

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Recommended Videos Problem 2. Problem 3. Problem 4. Problem 5. Problem 6. Problem 7. The shock tube has a certain mass and can fall freely along the vertical slide rail at a certain velocity to impact the soil site in the model box, as shown in Figure 5 a.

The specified impact velocity is obtained by adjusting the drop height. The shock tube is composed of a cylinder, fixed lever, weights, and footpad, as shown in Figure 5 b. The footpad, made of hard aluminum, is fixed on a fixed lever and the weights are fastened by the fixed lever and bolts in the cylinder to avoid collision, one with the other.

The impact mass is controlled by changing the numbers of weights. As shown in Figure 6 , there are three kinds of high precision transducers in the impact test. It can be used to measure the changes of velocity and displacement of the footpad simultaneously.

Figure 6 b shows the piezoelectric dynamometer produced by Jiangsu Lianneng Electronic Technology Co. Figure 6 c shows the uniaxial piezoelectric accelerometer produced by Kistler Group in Switzerland, type A The accelerometer and dynamometer are arranged, as in Figure 5 c , to measure acceleration and impact force.

Two accelerometers are set along the radial direction for mutual checking. In the mixed-measurement system, studies have shown that there is a phase delay between the records of different sensors [ 33 ]. The system controls the state of motion and collects the real-time dynamic response data relating to the footpad. It has four bit timers that are built in to share clocks for the mixed-measurement systems.

In the experiment, digital analog converter will record the sampling time, up to 0. The footpad used in the experiment is modeled after some simplification on the NASA footpad mentioned by Bendix Corporation [ 2 ], as shown in Figure 8. Before the experiment, each sensor was calibrated and showed good linearity. Because of space limitations the relevant curves are not given in this paper. The relationship between the drop height and impact velocity was also confirmed by carrying out drop tests.

The results are shown in Figure 9 and illustrate good repeatability. The drop height and impact velocity relationship fits a quadratic relationship. Owing to the uneven distribution of lunar soil simulant particle sizes, the dry pluviation sample preparation method causes coarse and fine particles to segregate, leading to various and undesirable relative densities [ 34 ].

For each relative density, soil with a specified mass was uniformly placed into each layer and aligned with the scratch lines as shown in Figure 5 d.

According to the mass of the lunar lander being simulated, the shock tube mass was variously set at 1. Table 3 presents the impact velocities in the impact model tests, values that can be reached in the real landing process. The scheme of the impact model tests is detailed in Table 4 , which mainly includes the influencing factors of relative density, impact velocity, and impact mass.

The steps taken in each test are as follows. Repeated tests were conducted under the same conditions to verify the reliability of the test results. Figure 10 shows the time-history curves of axial force and penetration displacement, which show good repeatability, proving that the test results are reliable. The results of 27 groups of tests indicate that the shapes of impact craters are similar and resemble a basin.

The sizes and depths of the craters, however, are different due to changes in test conditions. Larger impact velocities generate dramatically larger and deeper craters.

The shapes of the dynamic response curves are similar even for different testing conditions. It can be seen in Figure 12 a that the footpad reaches the maximum penetration depth at 25 milliseconds.

With the time increasing, the penetration depth initially decreases, increases later, and eventually reaches stability. This indicates that the footpad rebounds after it reaches the maximum depth, then again impacts the simulant lunar soil site, and after further small vibrations tends to finally become stable.

It then fluctuates weakly on the horizontal axis and trends to zero. Figure 12 c indicates that the axial force in the footpad reaches its maximum value in the initial 5 milliseconds before reducing and creating a second peak. The resultant impulse is found to be A comparison of Figures 12 c and 12 a indicates that the displacement response lags behind that of the axial force. As shown in Figure 12 d , the two acceleration time-history curves recorded by the two accelerometers set on the footpad as shown in Figure 5 c are in good agreement.

A comparison of Figures 12 d and 12 c shows that acceleration and axial force responses are in phase. The force the footpad bears during the impact process is critical for a safe landing. Figure 13 shows the time-history curves of axial force for various relative densities, impact velocities, and impact masses. These curves indicate that the various modes of axial force are similar; in the initial instant contact force grows quickly to its peak value in only a few milliseconds.

It then declines to a lower level and tends to be finally equal to the weight of the shock tube. Figure 13 a shows the axial force response to the impact for soils of 3 different densities, which indicate that the denser the site, the larger the peak axial force and the shorter the impact duration time.

Figure 13 b illustrates that the axial force increases approximately linearly with increasing impact velocity but the impact duration time increases little. Figure 13 c demonstrates that the bigger the impact mass, the larger the peak axial force and the longer the impact duration time.

It is noteworthy that the axial forces remain almost unchanged in some cases in Figure 13 between the two peaks over quite long periods with respect to the whole process. A similar phenomenon was found in the footpad impact study made by NASA [ 2 ]. From the present experiment, the occurrence of this phenomenon is conditioned. When the relative density of the simulant lunar soil site is low, the flow failure is more pronounced.

For a specified relative density, the larger the impact velocity and the impact mass are, the easier it is for flow failure to occur.

It can be deduced that there exists a critical impact momentum or kinetic energy value for a simulant lunar soil site of a specified density. When less than that critical value, the impact will not cause flow failure of the simulant lunar soil site. The explanation is that, with the footpad penetration depth increasing, if the underlying soil of the ground is not able to bear the impact, the soil will exhibit plastic flow failure; otherwise, if the underlying soil has a relatively great strength which is enough to carry the impact force, flow failure will not occur.

Penetration displacement is another major factor affecting landing safety. The time of the first impact all begins from the 0 point. The variations in penetration displacement patterns are similar, that is, a quick increase once the lander touches the site, a rebound after reaching the peak value, followed by a slight further impact before reaching an ultimate stability. The larger the impact mass, the larger the peak value and the ultimate stable penetration depth and the longer the rebound duration time.

The curves shapes are similar. The whole curve can be divided into 4 stages, denoted by the characters , , , , as shown in Figure 15 a. The curve in stage AB is approximately linear. The axial force on the footpad is generated by the dynamic interaction between shock tube and the compressed soil.

The penetration displacement mainly is one of elastic compression deformation of the soil during this stage. In the shearing stage BC , part of the soil element under the footpad reaches failure, and the soil resistance decreases allowing shear deformation to occur.

That is why the slope of the curve becomes negative. In the flow failure stage CD , due to the expansion of the affect zone surrounding the footpad, the resistance of the soil remains stable or increases a little, but large vertical deformation occurs and the footpad is deeply pierced.

In stage DE , because of the weak elastic properties of the lunar soil simulant, the footpad rebounds even off the surface, and the axial force decreases sharply and even turns negative. The velocity variation of the footpad on the vertical motion track is shown in Figure 15 b. The velocity then decreases gradually until reaching the maximum penetration displacement point when the velocity equals zero. After fluctuating several times, it finally reaches the ultimate penetration point N.

Other than the time-history characteristics of the footpad dynamic response in the instant of contact, the peak values themselves are essential for the design of the lander buffering system, especially the extent of penetration which is the stable penetration displacement. Peak values of axial force and acceleration are also essential.

Figures 16 and 17 show the effect of relative density on peak axial force and penetration depth, which indicates that peak axial force increases significantly as relative density increases in all test conditions, while penetration depth is reduced.

Figure 18 demonstrates that peak axial force is little affected by impact mass. Figure 21 shows that the penetration depth also increases significantly as impact velocity increases in all test conditions. In general, the peak axial force is influenced more significantly by relative density and impact velocity than by impact mass. In order to comprehensively consider the influence of all control variables, the impact kinetic energy was set as an independent variable and the relationships between peak value dynamic responses of the footpad and kinetic energy are drawn as dots in Figure It can be concluded that, for different relative densities, the larger relative density leads to greater axial force and acceleration but smaller penetration depth; for the same relative density, the responsive peaks axial force, penetration, and increase steadily as impact kinetic energy grows.

The relationship can be expressed in the following exponential form: where are , , and , respectively, and , are material parameters related to the relative density of lunar soil, as listed in Table 5. For a given impact kinetic energy and site relative density, the dynamic responsive peak can be calculated using 1.

From the test results, the constants are given below. The curves employing the following constants are shown highlighted in the solid lines in Figure Since impact experiments are costly and the environmental conditions on the Moon are difficult to fully simulate, numerical analysis is commonly adopted to help understand the impact process consequences and make further predictions [ 42 ].

Considering the special granularity and interparticle attraction of lunar soil, it is of great interest to simulate lunar soil by discrete element method DEM [ 43 ]. However, the finite element method FEM is still used in this paper for the relatively mature commercial software and more understanding of the parameters required for analysis. In this paper, the numerical simulation is carried out on the commercial software Abaqus, for its good capabilities in analyzing nonlinear, transient dynamics problems.

The impact experiment model is taken as the prototype of the numerical FEM analysis. Then the results of the numerical analysis were compared with those of experiment, so as to verify the validity of the numerical model. The brief description of the numerical modeling and the simulation is given below; some details can also be seen in [ 44 ].

The appearance of the footpad model is shown in Figure 23 a. Due to the irregular shape, the shock tube is represented as thousands of four-node, 3D tetrahedron elements.

The mass of the shock tube is controlled by adjusting the height of the cylinder. Using the artificial truncation boundary, a cube with side length was taken as the finite element analysis area, discretized into 8-node hexahedron elements.

The site area was divided into two meshing zones as shown in Figure 23 b. Zone 1, where stress is concentrated and large plastic deformation occurs under impact load, is meshed into even smaller and denser grids than those of Zone 2. The shock tube and simulant lunar soil interact at the soil-footpad interface. As shown in Figure 24 , the contact face transfers interaction forces in both tangential and normal directions.

The contact stresses are applied to the following restrictions. When the footpad and the simulant lunar soil are not in contact,. Normal stress is generated as the two sides make contact. The stresses on the nodes of the contact surface satisfy the following relationships: is not allowed tensile stress; when tensile stress appears it is considered the separation which appeared. For , when the shear stress in the interface is less than the limiting value, the two sides bond, and when the limiting shear stress is reached, the two sides begin to slip.

The critical value is given by where is the friction coefficient, determined from interface shearing tests of the footpad made aluminum alloy and the TJ In the Abaqus software, the master-slave interface model was adopted to simulate the interaction. The bottom surface of the footpad was set as the master surface and the top surface of the simulant lunar soil sites as the slave surface, shown in Figure Through face-face mesh generation method and setting the friction coefficient, the aforementioned contact model is established.

Figure 25 shows the interface friction characteristics between the lunar soil simulant and the hard aluminum the same material as the footpad gained from direct shear tests. The interface shear behavior can be regarded as ideal elastoplastic. The range of friction coefficient at the contact surface is 0.

In this study, the friction coefficient has been taken as 0.