Two things.
There are multiple types of radar, you have not specified which one you are talking about. Guessing by the range, you're talking SJ-1 (not SJ, that's a different set) though?
Second, 40 miles even under perfect conditions seems to me to be *really* dubious due to simple line of sight. Radar line of sight beyond the horizon is defined by this formula:
rangeNM= 1.23 * (sqroot radar height + sqroot detected object height)
If I recall, the height of the sj-1 antenna is 33 feet. The top of the superstructure of an IJN BB, which is about as tall as it gets, is going to be in the ballpark of 130 feet (depending on class obviously, but this should be a fair approximation).
The math there yields a maximum theoretical detection range of 21 miles under ideal conditions. Honestly, I don't know if the power output of the radar set could even reach out that far, but supposing it could, that is still around half of 40 miles you're talking about.
I guess what I'm saying is that I would need to see a credible source to even believe a 40 mile number when everything else I've seen is saying that detection of a battleship is more realistically around 11-16 miles (depending on conditions).
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