Theorical vs practical range of Air Defense systems. I've seen a few people saying that the S-400 systems bought by India would allow the IAF to target PAF planes as they take off from their bases, thanks to the 400km-range of the system. It's not the case.
We don't know yet where will the S-400s be based precisely, but according to indian news outlets, three of the five systems will cover the Indian border with Pakistan.
Because these are plausible options, I decided to set up two systems at the Bikaner and Ambala airbases, and an additionnal one is the south to cover the gap.
Now, two small details:
1- The 400km missile of the S-400 is the 40N6. This missile is not designed to intercept fighters. Its role it to engage ISR platforms, tankers and other non-maneuvering targets at very long range.
The missile is probably not available to India yet, as it barely entered russian service. It'll come to India eventually, but not now. In the meantime, the longest-range missile available will be the 48N6DM (formerly the 48N6E3), with a 250km range.
2- The pictures and infographics released by Indian authorities do not depict the 91N6E Big Bird D as the long range search and acquision radar of their S-400s. Instead, pictures of the less powerful 96N6E Grave Stone are used.
This might be done on purpose to confuse people, or India might have not bought the more expensive Big Bird at all.
Without the 40N6 and the 91N6E, the maximum range of the S-400 is significantly reduced, as illustrated here.
For the sake of this discussion however, let's assume that both the 40N6 and 91N6E are available to India today. Does that means that the S-400s will be able to extend their engagement bubble over Pakistani territory? Well, it depends.
The IAF is lucky in that there is barely any relief on India's western flank, so radars are able to work without any terrain masking issue. This is great for long range systems.
However, the Earth is still a sphere, and this does cause some problems related to radar horizon. The further you want to detect something, the higher it has to be. This is because otherwise it is hidden behing, well, the Earth.
In order to detect a target at its maximum range (600km), the 91N6E would need to be looking at something flying at around 20.000 meters. This is really high. Like, MiG-31-high. For a more reasonnable cruise altitude of 10.000m, the pratical range falls to approximately 370km.
Tactical fighters can fly much lower than that. At 1000m, the radar range has fallen to 150 kilometers. And for cruise missiles flying even lower, well, you guessed it, the range is lower as well.
This is what the radar ranges are for all three systems for a target altitude of 8.000 fts (~2450 m). Note the open corridors and the non-overlapping coverage.
Because of this radar horizon issue alone, indians S-400s will not be able to shoot down pakistani fighters on take off. They will however be a significant threat as the planes are getting closer to the border.
Now, all of this is nice and cool, but there's another elephant in the room. These ranges I just gave are theorical ranges. Just because you *can* detect a target flying at 1000m at 150km doesn't mean that you *will*.
Small-sized or low-observable aircrafts can reduce the pratical range even further, so let's make some very (VERY) basic testing.
A small disclaimer here: while the radar horizon problem is well understood and modelled in CMO, radar stealth is much complex to get right. Unlike with the radar LOS calculations, anything done w/r to stealth is indicative at best and should not be taken at face value.
Let's start by putting a Boeing 747 in front of the S-400. The starting altitude is 11.000m. As soon as the plane gets above the radar horizon, at 388km, it is detected, tracked and engaged with a 40N6. Well played.
