Dave Saxton wrote:One thing working against the Germans successfully renewing an Atlantic surface offensive going into 1942 was the proliferation of Type 273 centimetric radar aboard British cruisers. Luetjens was mistaken in his report at the time that the enemy had surface search radar effective to 35km. By 1942 it was a fact. However, I'm drifting off topic.
no problem but even with 35km detection , sweep rates are going to be very poor indeed. The simplified calculation I remember was the detection range x 2 width [~ 40nm] was multiplied by the ship cruising speed. So a RN/USN cruiser is going to manage 15 knots x 40nm or about 600nm^2 per hour. A similar sweep for U-Boat would be 10nm x 15 knots or 150nm^2 per hour.
Next review target area to be searched GIUK . Nominally a 1000nm wide area, but more like 700nm- when you remove land. This is multiplied by day cruising speed of the target ; which was 20 knots x 24 hours or ~ 480nm x 700nm or 336,000nm^2 sea to be swept.
The RN cruiser can manage a day patrol of 24 x 600= ~ 14,400nm ^2 per day. So in short- based on ship detection alone - you need ~ 23 such cruisers sweeping spaced equidistant to have a 100% sweep success. If it was U-boats [252000nm/3600nm] you'd need about 70 search platforms to get 100% success .
If the weather is moderate to good you can sortie the sea planes which can sweep ~ 1250nm per hour against U boats and maybe 3 times this against larger ships. With a margin- they can patrol two planes for 3 hours each day adding > 22,000nm^2 to sweep area increasing the cruiser sweep to ~ 37,000nm^ 2 per day [weather permitting] . In that case the numbers required reduces to 9 search platforms for the GIUK gap. If a Rheinubung operation is attempted in May they will be detected [although historically the 1941 mission was only 5 cruisers], however if Operation Berlin is attempted in November -March the weather in this area is so bad the Raiders will likely not get detected in time and break through.