Vikram Lander Soft Landing Experiment − Event Analysis

We all have been anxiously waiting to know what has happened to Vikram Lander during the last few minutes before its touch down on Moon's surface. Here I'm going to take up a small exercise to deduce whether or not Vikram Lander will ever be communicable. This attempt is to decode the event to study possibilities from the perspective of a curious student of science. It's not a failure analysis or root cause analysis as such analyses need a more detailed event data that has been obtained till loss of communication.

The experiment by ISRO is an extremely challenging one. Great missions bring greater challenges. Naturally, at each stage, there involved the risk of falling short somewhere. Despite that what ISRO's team has been able to achieve is truly incredible. They have taken a leap of faith. The interest that this experiment has kindled in young minds is invaluable and its intangible benefits will remain unparalleled in near future.

In true sense, the exercise at hands today is more about dispassionately appreciating the basic physics of the event based on limited data available through live telecast and of course wikipedia.

Mass 1471 kg (source: wiki)
Last velocities reported
Horizontal velocity Vh 48.1 mps,
Vertical velocity Vv -59 mps,
Altitude 0.335 km, 1.09 km left before touch down. (Source: recording of live telecast of the event from mission control room by DD National)

Absolute velocity V 78.84 mps, 276.6 kmph
Lander moving at an angle of 51° with moon surface.

Kinetic energy KE possesser by lander = 0.5mV2
= 4,342,392 J = 4242.392 kJ

Moon's gravity 1.62 m/s2 (mostly not used in calculations being a small value)

Approximate time to descend to surface at constant vertical velocity
= 335 m/59 mps = 5.68 s

Required time with available thrusters is way higher than available time if no resistive force is present to reduce velocity of the descending lander.

Required magnitude of constant force opposing the motion of lander in bringing the lander to rest in 5.68 seconds
= 4242.392 kJ ÷ 335 m = 12.66 kN
Force needed at each thruster
= 12.66 kN ÷ 4 = 3.17 kN

Required acceleration (negative)
= −12.66 kN ÷ 1471 kg
= − 8.61 m/s2, which is plausible if orientation of lander is proper.

Considering the information that is coming in recently, the lander lost the orientation and leading to less effective braking. Also the horizontal velocity was seen to have diminished fast and vertical velocity had seen a significant rise. This was evident from the trajectory deviation. They probably assisted descent also. The last visual of the graph of trajectory showed the descent was fast going close to vertical. This reinforces the suspicion that the lander had lost orientation and thrusters were becoming less effective. This means the lander dived into moon surface at a velocity of around 280 kilometres per hour (approximately adding effect of moon's gravity) thus leaving hardly any hope for its equipment to remain undeformed and functional - communication antennas included. Imagine a formula one car crashing into a large concrete block at 280 kilometers per hour. Will we consider repairing the remains, that once made the car seen before impact? More likely than not, the answer will be No. After eliminating least probable scenario, the only scenario is left with us according to which the lander dug into moon's surface to some extent if the surface at point of first contact was soft enough. Also it's likely that it would have tumbled along surface several times before coming to halt.

It's a sure thing that ISRO's team, which is in possession of telemetry data till 335 meter, in my opinion, doesn't expect to establish communication with lander. It'll be a miracle if they do!

...

The woods are lovely, dark and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.
- Rober Frost (1874-1963)

Musings on flood affected brothers and sisters

Western Maharashtra is facing extreme flood situation and almost half a million population is directly affected. There is a great deal of anxiety and anger present in the affected region over the hardship these people are undergoing. On the other hand these people have shown remarkable resilience in facing such hardship and loss and have joined hands with each other and government machinery in rescue and the first stage relief operations. Countless people in affected and unaffected areas are working round the clock behind the scene; sometimes even putting their health at risk. There is growing debate on why the problem of such extreme flooding has arisen and which factor is responsible for this.

From illegal constructions and farming near rivers, clogging by plastic waste, excessive rainfall, presence of Alamatti Dam on River Krishna to lack of coordination between governments of Maharashtra and Karnataka are being discussed as some of the main reasons behind these floods. In this brief article, we will go through some of these reasons in order to assess their role in causing the floods.

Among these reasons, the claimed reason of alleged lack of coordination between the governments has a political connotation and hence it is not considered within the scope of present discussion.

On the onset, I would like to say that no single factor alone can lead to the calamity of such scale. It is always a combination of a few or several factors result in such event od such magnitude.

The effect of Alamatti Dam can be ignored in case the level was maintained as per studies carried earlier. Or, to say the least, effect of the presence of Alamatti Dam can be considered less significant though I personally believe otherwise. In my opinion, every resistance to flow on the downstream side potentially increases swelling on the upstream side in the requisite amount. However I do not have quantitative insight and I hereby go with the outcome of hydrological studies reportedly carried out by a joint team of experts in the past. And also unprecedented rainfall in catchment area, which is upstream of flooded region, is another factor which supports the argument of not treating the construction of a dam on the downstream side as a significant reason.

Other major factors for flooding are amount of rainfall, depth and width of riverbed, slope of plains with other geographical aspects.
Now the most important aspect is the population affected by flooding. Wise way to deal with this is to keep population out of the floodline marked by historically highest flood water level. And this is where we are failing time and over again. And when I say population I also mean the use of land within floodline for agriculture as it has potential to raise hydrodynamic resistance to water flow.

Now let us look specifically at the flooding that has taken place. Here we are talking about six to eight hundred percent excess rainfall within a span of six to eight days. This sounds to be the most significant single reason behind the flooding of such catastrophic scale. This factor is unstoppable for ordinary mortals. At the maximum, a qualitative intimation of very high rainfall can be given to the people living near rivers. However in absence of localised judicial studies, exact area under influence of floods cannot be predicted precisely.

Hence the unprecedented rainfall became the cause for extreme hardship that people in rural area underwent in last two weeks. Most of them were living inside their respective village boundary which was in most cases a couple of kilometers away from river. They had not done anything wrong. Just that the flood water breached the long trusted border between human and the river and they were trapped badly.

It must be borne in our mind that no matter how strong you are, you cannot stand the fury of nature. Only way to save yourself is to stay away; far away! That is why certain rules and regulations in town planning are put in place. This is where the role of construction between 100 year floodline and 25 year floodline (red line and blue line respectively) comes into picture. This construction exposes its inhabitants to deadly flooding. Builders and inhabitants look at this risk of suffering from flood based on their knowledge of probability of occurrence of flood at their property. Often this knowledge is shallow and is based on hearsay and never on facts. But the old guard's ways, i.e. planning for the worst, is overlooked. Worldly wisdom is forgotten. Construction plans in risky and restrictive zones are proposed. They are somehow approved by local authority. This local authority usually is oblivious to the involved risk. The nexus straightaway puts the people residing in buildings in restricted zone into grave danger of facing hardship due to flooding at least once in their life time. This increases the flood affected population.

Going by the recent reports, 20 to 25 percent people affected during the current flood situation in Western Maharashtra lived in the restricted zone. This is certainly alarming. Had such illegal constructions been avoided, the number of flood affected population would have reduced to its three fourth.

In this context, government, at least now, should ensure strict enforcement of rules by local authority. On the other hand, citizens need to be sensitized for not purchasing properties in restricted zones and create backward pressure on the builders so that they realise that their buildings if not legally located in safe zone will not be sold. No builder will overlook this aspect if this awareness of potential customers becomes reality.

Also important is the issue of lack of awareness in population of the potential risks of severe flooding. This was the reason why a large number of people across the affected region when requested by volunteers, local administration and NDRF refused to vacate their houses. The reluctance of these people to move to safer area or relief camps multiplied the hurdles in rescue work. This also delayed rescue efforts. However timely and voluntary evaluation done by a large section of flood affected people, those who have shown reasonabilty and courage of the highest order is commendable. Their patience in getting relief or in getting essential provisions and food made the giant effort by rescue teams and volunteers worth the risk.

There is discussion among general public how such flooding can be altogether avoided by construction a canal network that bypasses excess water from catchment areas away from the populated places. This idea reached many people through interview of widely respected social worker Shri Sambhaji Bhide, popularly known as Guruji, given to a few television channels wherein he appealed the state government to explore such means after due studies. It is to be seen how much traction such suggestions can gain in bureaucratic functioning of governments. But if proven feasible in this region, idea of canal network remains an attractive flood mitigation measure in case of extreme high rainfall like this month.

Now relief operation by government is in full swing. Assessment of loss itself will take some time. Chief Minister of Maharashtra has announced immediate release of financial aid to flood affected people. However the next stage of relief and rehabilitation is going to be an uphill task. I strongly recommend voluntary contribution to CM Relief Fund through its official website. Considering a large number of people from some places in states likes Karnataka, Kerala and Gujarat also are suffering from floods, considering The Prime Minister's Relief Fund for making contribution also is a welcome idea.

In the end, it needs to be emphasized that calamity arising out of such flooding can be faced only with a firm control on building plan approval process, proactive town planning, creation of new settlements at safe places and creating more awareness on how a common man should respond to such calamity. At a time when rainfall pattern is changing, if appropriate steps are not taken now, this region is bound to see such calamities only more often.