Why Clouds can’t help hide Planes from Radar — Coz Physics
Prime Minister Narendra Modi was not wrong to suggest that we could make use of the clouds to protect the Indian Air Force Jets from the Pakistani radars during the Balakot attacks. Developed in the 1930s, the quintessential Radar, uses Radio waves to detect and determine the approximate location of an aircraft. Radar achieves this by measuring the time taken for the radio waves emitted from the source to be be reflected by the body of the aircraft to return back to the source, from which the radio waves originated (such as a military base or another aircraft).
Radio waves used in radars (with applications ranging from air traffic control, moderate surveillance to missile guidance) are electromagnetic waves with frequency ranges between 1–12 GHz. Like any electromagnetic waves, radio waves as it comes in contact with a medium (air in this case), is capable of three things :
- It is transmitted through the medium
- It is absorbed by the medium
- It is reflected by the medium.
Most often than not what occurs is a combination of all these three phenomenons. The extent of each would vary depending on the nature of the media that is incident upon and the frequency of the electromagnetic wave.
So the Prime Minister was right to have an intuition that the added cloud cover (Higher concentrations of dust particles and water vapour) in the atmosphere, might help increase the extent of absorption of the radio waves thereby reducing the amount that will be available for reflection, reducing the chances of detection.
His “Raw Wisdom” (which I am guessing he gained on his padayatra across the Himalayas in his youth) might have been in the right direction.
But quite like his policies of Demonetisation and GST, it was rolled out without much further thought or due diligence.
Had this come up as a question from an eight year old, we would have all been impressed at his/her intuitive grasp on electromagnetic theory. But the fact that this was put forward by the ‘de facto’ ruler of the nation, one who has taken the Air India One more than 44 times since he took office to various foreign countries spending upwards of 400 crore rupees of tax payers money on his travel should not have ever suggested it. Did he never see clouds when he looked out of the window of the plane ?
As a Physicist I find this very troubling, personally a bit insulting even. If this remark is an indication of the scientific understanding of our nation, I cannot even begin to imagine the damage it does to the image of Indian scientists on a more global level.
For the past couple of days since he gave that interview to News Nation my social media feed has been filled with Bhakts defending the statement by using the qualitative arguments that I had raised in the first part. So I decided let’s move beyond that and put some numbers on it.
Discarding all the complex physics behind the propagation of an Electromagnetic Wave (Diffraction, Scattering, Doppler Effect and so on), and just using 12th standard Physics (which you expect Modi to understand, after all he is an engineer), the Math does not seem to agree to the Prime Minister’s statement.
Assuming that Modi meant that more clouds cover would absorb more of the radio waves emitted by the radar, the absorption of an electromagnetic wave while passing through a medium is given by the Beer-Lambert Law . The law is given as :
where,
I(x) = Intensity of radiation at position x
Io = Intensity of radiation at the source (x=0)
n = Density of medium
σ = Amount of energy absorbed by water molecules in a particular frequency
x = total distance covered (twice including the reflected round trip)
The maximum range of ROHINI, Indian Air Force’s Surveillance radar is about 200 km. Let’s assume that Pakistan has something similar with the same maximum range. The Indian Air Force used the Spice 2000 missiles to target the terrorist camps in Balakot. It has a maximum range of about 50 km.
The intensity of the radio wave decreases exponentially with an increase in distance. The intensity of the reflected radiation at the maximum range is the minimum detectable intensity for a radar, any further the signal is reflected from the signal will become too weak.
If the Prime Minister’s “Raw Wisdom” is to be true, the minimum intensity seen for the reflected signal at 200 km must be observed at 50 km (the maximum range of the Spice 2000 missiles). Then, the aircraft would effectively hide from the radar as there wont be a signal strong enough to be detected.
Removing all the common terms on both the right hand side and left hand side we are left with :
which boils down to :
Thus, in order for the Prime Minister’s idea to work out the density of a cloud has to be four times its normal value.
Considering that there were intense rains and clouds on the day of the attack, it will be safe to assume that they are Cumulonimbus clouds, with densities between 1 and 3 grams per 1000 litres. So for his idea to work, we expect the density of the clouds to be somewhere between 4 and 12 grams per 1000 litres.
But here is the problem there are no clouds that have such high densities. Even if it is the lighter Cumulus clouds, the clouds present in the effective path of the radar would be at most 2 percent of its total path length, offering nowhere near the necessary density to mask the planes from the radar.
Prime Minister Modi might have had the right intuition. His heart was there, but his thought did not back it up and as it has happened to the country many times in the past 5 years, his ego got the better of us.
What I am finding even more troubling is not his ignorance, it is the sheer thoughtlessness and ardent defensiveness his followers abide by. But the amount of trolls and satirical scoffs that have also erupted in social media in the aftermath does help breathe a sigh of relief. It only goes to show that the only thing that is cloudy is Modi’s perspective that Indians will treat every word he utters as ‘Amrutham’ and blindly take it in.
Assumptions:
- Also bear in mind I have assumed that the radar is located at Balakot.
- There is continuous cloud coverage of the same density all the way from Balakot till the aircraft, 50 kms out.
- The reflectivity of the radar waves by the clouds is minimal and only absorption plays a major role.
- Have avoided a large proportion of the complex physics for the sake of simplicity.
