Perhaps many this year watched live on an attempt to land the first Israeli probe on the moon. It was quite convenient to track this, since telemetry data on the speed and position of the station above the Moon were often displayed in the broadcast.
The total amount of telemetry shown is such that, as a whole, it was possible to evaluate many of the nuances associated with both the design of the station and the features of its landing. This is really interesting. The fact is that landing on the moon is a very difficult process, the nuances of which are rarely published. In particular, real telemetry is usually not published at all.
Here, if you look at the published data, you can get the station’s height above the Moon, horizontal and vertical speeds, axial accelerations and the mass of the remainder of the fuel with an oxidizer with a time reference. All these data allow not only to evaluate the station landing pattern, but also to determine which sensors correctly reflected the reality. Since all parameters must be related to each other.
It is only necessary to pull them out of the broadcast and bring them into one table. The only thing holding back was the need to process a large amount of data. It was hoped that someone would do this work earlier, or SpaceIL would publish the original telemetry and a detailed description of the accident.
Alas, no one created the table, and a detailed description of the accident did not appear. As far as I know, it was only released a message that the shutdown of the main engine was triggered by the command sent by the dispatchers to the probe to restart one of the measuring sensors.
Personally, this information was not enough for me. In the end, all the same, I made a tablet in Excel.
It covers the period from 22:36 to 37:00 (according to the clip’s own time). 872 lines. In order to better analyze the data and understand the station’s flight algorithm, a mathematical model of the motion of an object with traction in the gravitational field of the moon was created. It was impossible otherwise. At the speed with which the station flew, this cannot be ignored. The Excel file with telemetry and processing can be downloaded at the end of the article.
For example, here is how a change in the overall speed of a station over time looks like:
The stage of orbital flight is also visible (the platform is from 22:36 to 25:00), the stage of regular braking (from 25:00 to 33:18) and the stage of falling onto the moon (from 33:18 to 36:45). White gaps are moments when data could not be obtained. This is either a problem with receiving data from the station, or telemetry during the broadcast was closed with a different picture.
Now let's see how the moment the braking starts. He is on the chart below. The blue line is the congestion data obtained from the change in station speed. Since the determination of speed went with some error, you can focus only on the overall picture. The dark red line is the data from the overload sensor along the Z axis.
It’s immediately obvious that there were some problems with the overload sensor. For some reason, he showed significant overload even at the moment when the engines were completely turned off. But after turning on the marching engine, he began to show information close to the truth. Moreover - he clearly did this further. Until the death of the station. It is a pity that all the same, it is practically useless for analysis. Overloading to one tenth is too coarse data. It would be much more informative if it were known with an accuracy of one hundredth.
According to the blue graph, you can already try to evaluate the operation parameters of the station's engines. Three plots are clearly visible on the chart. A plot near zero is the period of orbital flight. The first site in the region of 0.5 m / s2 is the inclusion of orientation engines for fuel sediment. The last platform is the inclusion of the main marching engine.
For some reason, secrecy unfolded around the marching engine. For a long time they did not write about its characteristics and manufacturer. But soon after the launch, it turned out that it was the British LEROS.
Some of its variants with different thrust / specific impulse are indicated. 407N / 318, 460 N / 325s, 640 N / 318 s, 1120 N / 323 s.
Let's try to more accurately evaluate the characteristics of the station.
The graph above shows that when the engine was turned on, the acceleration changed a little more than 1 m / s2. This means that the total mass of the station at this moment should be close to 407, 460, 640 or 1120 kg. The mass of fuel is known from telemetry and is equal to 216 kg. This means that the dry station should be slightly less than 191, 244, 396 or 904 kg.
The last figures are clearly too high. The problem is that for the dry mass of the station, the figures of 195 and 160 kg were mentioned. And you need to analyze telemetry in detail. Again, if there were normal data on overload, then this would be easy. But since they are not there, I had to go the hard way. The station descent dynamics was analyzed depending on the dry weight of 160 and 195 kg and, under stationary conditions, the total thrust values were obtained at 668N (of which 470N main engine), rods - 198N for 195 kg and 616N / 441N / 175N for dry mass of 160 kg.
Somewhere in parallel, I saw that on this slide, published during the flight of the station, there was indicated a thrust of 450 N for the mid-flight and, apparently, 25 N (total 200 N) for the rudders. But it was already clear that this is rounded data.
Knowing the cravings, one could try to estimate the specific impulse. It is known that in 340-342 seconds of flight, the station lost 70 kg (213.06-143.06) of fuel.
With a thrust of 668 N, this means an integral impulse of 330 seconds, and with a thrust of 616 N - 305 seconds. The first impulse clearly looks overpriced. But this becomes more obvious if you try to evaluate the specific impulse of the steering engines.
There are two specific impulse options for the LEROS remote control, depending on the fuel components. 326 and 318 seconds. Then, for the remote control parameters corresponding to a dry mass of 195 kg, the specific steering impulse should be 342 or 365 seconds. For a similar class of engines, these are unattainable parameters. So, far closer to the truth, the parameters for the dry mass of the station in 160 kg are 262 or 276 seconds.
However, it can also be immediately noted that these engines, like the marching ones, are two-component. Initially, I thought that they might work on the decomposition of hydrazine. But the momentum is too high for a single component.
For example, you can see the options for small thrust engines developed by KBKhM named after Isaeva.
As a result, a dry mass of 160 kg is much closer to the truth than 195 kg. Most likely, and this figure is approximate. And the real mass is, say, 164 kg. But this is not so important.
Summarize the initial data. Dry weight 160 kg. The mass at the start of braking is 376 kg. The thrust of the sustainer engine is 441N. The thrust of the correction engines is 175N. Total thrust - 616N. The initial overload is 616/376 = 1.63 m / s2.
Staff descent
In the graph below, you can see how the vertical speed of the station changed during a regular descent:
Very indicative schedule. It clearly shows how the station works out the pitch angles to compensate for the lunar attraction, at the end reaching a constant descent speed of 24.8 m / s. That is, the station rotates so that the vertical component of the thrust compensates for most of the attraction of the moon, and the horizontal, meanwhile, extinguishes the remainder of the orbital velocity.
This is how it should have looked at the end of the regular flight
Of course, the absolutely correct algorithm. The only problem is that the station had a very weak engine. Because of what, you need to spend as much on vertical speed compensation as on braking. Because of what gravitational losses grow. I generally have a suspicion that Bereshit had the smallest possible thrust-weight ratio for solving this problem. On the other hand, this is also one of the possible solutions, because its developers were clearly limited when choosing engines. Moreover, its descent was quite successful until at 33:00 the inertial sensor number 2 failed (judging by the description, this sensor controlled the rotation of the station around one of the axes). Then the following dialogue occurred:
33:14 - Controller 1 suggests trying to turn it on.
33:22 - Controller 2: - And its inclusion will not lead to the loss of the first?
Interestingly, telemetry from the station ceased to be updated at 33:17. Of course, loss of telemetry does not necessarily mean loss of signal. Moreover, there is evidence that JPL completely lost contact with the station at 33:32. This is a fairly important statement, as we will see below. Receiving telemetry from the station was restored only at 34:22. And during this time something obviously happened to the station.
Accident
Again, look at the vertical speed graphs:
And horizontal speed:
From this data, several unexpected discoveries can be made.
Firstly, the station was operating normally for a long time after the termination of telemetry. Otherwise, it cannot be explained that the horizontal speed fell from 901.7 m / s to 880.2 m / s, and the vertical speed during this time gained only 23 m / s. Engine shutdown occurs at approximately 33:37. Interestingly, this figure is quite close to the announced loss time in JPL of the signal from the station. So it is very likely that at first there were only partial failures. But part of the board worked as usual until the system was completely rebooted.
The second fact is even more interesting. During this time, the station not only turned off, but completely lost its orientation. The fact is that after the restoration of telemetry, she no longer extinguished the horizontal speed, she began to increase it! This is possible only if during the time of failure she noticeably unfolded. What the new orientation looked like can be seen in the diagram:
Perhaps the fact is that after the reboot, the station recorded the current orientation. At the same time, I would like to note that determining the current orientation of the station from an arbitrary position is not an easy task. Especially if you need to do this very quickly.
You can also evaluate the overall thrust of the engines. The data above is derived from telemetry and corresponds to overload data. By the magnitude of the thrust, it is clearly visible that the marching remote control did not work, only the steering wheels.
And all this data, alas, suggests that the station at the time of the restoration of telemetry was already doomed. Even if I could turn on the marching remote control. There is not so much fuel and oxidizer at the station, and due to orientation, the station constantly increased the speed, which, on the contrary, had to be extinguished. And spent the last fuel on it. Also, without marching thrust, the thrust of orientation engines is too weak to compensate for the attraction of the moon. So the station began to fall on the moon.
Why did the marching remote control fail? Moreover, it can be seen from telemetry: fuel consumption has remained unchanged. In other words, fuel was still supplied to the engine, only for some reason the engine did not create traction.
A few words about why fuel sediment is needed. During engine operation, the fuel in the tank is located in the usual way: below the fuel, above the boost gases. When gases are pumped into the tank, fuel is displaced from it into the pipelines, and then into the combustion chamber. But this only works if there is overload. As long as the station flies in zero gravity, fuel and boost gases can be located in a completely arbitrary way. To separate them again (to besiege), and turn on small thrust engines. True, such a scheme is usually used only on the stages of missiles or large booster blocks. At interplanetary stations, special bags are usually used that prevent the fuel from mixing with boost gases and allow you to turn on the engines even without preliminary precipitation.
You can see how it was done at our E-8 station:
Apparently, to simplify the overall design, the creators of Bereshit chose the option with preliminary draft fuel. It seems that this is exactly what finally destroyed the station.
When the mid-flight engine turned off due to a reboot of the system, zero gravity occurred. That is, the fuel mixed with boost gases, forming a gas-liquid suspension. And it was this suspension that went into the combustion chamber when the engines turned on again.
At first, I thought that it was this: the suspension kept coming into the combustion chamber all the time, which did not really mix and burn. But, having analyzed telemetry, I had to refuse this version. The steering worked quite confidently, and the time seems to be sufficient for fuel sediment. Apparently, something happened to the engine when this mixture was first fed into it. Personally, I can’t say how the engine will behave in this off-design mode. Moreover, LEROS proved to be quite gentle. And it was not in vain that for the first time before it was turned on, specialists first besieged the fuel.
Final stage
Unfortunately, a rather large part of telemetry immediately before the fall is absent. The broadcast simply switched from telemetry to other pictures. She was returned back just 5 seconds before the collision with the moon. That is, we have only 5 points with a height of 678 m to 149 m, which are very difficult to analyze, since the relief of the moon in this section of the flight could change. Moreover, it is a pity that during this time the station was “rebooted” several times, and it obviously changed its orientation, even if only slightly. She fell to the moon a little later than she should, maintaining the braking mode in which she was after the restoration of telemetry. At the same time, in the last 5 seconds it even fell a little faster than it should under the influence of lunar gravity. That is, the orientation of the station was already completely abnormal. However, the horizontal speed has already begun to decrease slightly. But, in any case, nothing could be changed. The station was doomed long before that.
conclusions
In the end, I decided to summarize a little. Actually, the version of the problems at the station that caused the reboot is also confirmed by telemetry data. And precisely because of the reboot, the station entered a mode in which it could no longer land on the moon. Only the problems were not only with the inclusion of the main engine of the station, but also with the orientation of the apparatus. After switching on, the station was fixed in the mode when it began to accelerate rather than slow down.
In general, with the current station scheme, a reboot at any stage of braking would seem to lead to a similar accident. In my opinion, if you begin to develop a new landing stage based on the current one, then you need to change the logic of the computer. Either provide redundancy for the landing time, or ensure that the station does not lose orientation and does not turn off the engine during a system reboot. Well, change the boost scheme so that it is possible to turn on the engines without preliminary fuel upset.
The resulting Excel spreadsheet file can be downloaded here . In the first tab telemetry, in the rest - the analysis of the stages of flight.