I think the answer is a bit more nuanced than simply saying that heavy bombers weren't grounded and the workload shifted to medium bombers. Here is how I understand the strategic air campaign in 1943 leading into 1944. (since the many of the members of the forum have better knowledge on this topic, I encourage your corrections)
1) The opening strategic bombing campaign was built on a theory that heavily armed bomber formations would overwhelm defensive fighter forces and be able to carry out a campaign to cripple a country's war industry and force surrender. As soon as the USAAF had placed a sufficient number of bombers in England they began to test this theory. As the USAAF gained experience executing this campaign there was a transition to ever longer missions that began to leave the umbrella of GB based fighter cover. Ultimately in September/October the 8th Air Force carried out a series of raids in Germany intended to cripple what was seen as a weakness in the industrial supply chain - ball bearing production. These raids were disasters for USAAF with the loss of over 30% of aircraft, including crews as well as additional wounded. Following these raids, the USAAF suspended all raids that exceeded the limits of fighter coverage.
2) Following what was perceived to be a defeat, USAAF reassessed its approach to strategic bombing and used the end of 1943 to:
a. Build infrastructure - Its often forgotten that the growth in USAAF presence in England also included one of the largest building campaigns of the 20th century including a whole string of airfields, fueling depots, repair shops etc to support its efforts.
b. Grow the bomber force
c. Grow the fighter force - especially aircraft capable of escorting the entire duration of an air assault
d. Build competency - This was crucial to the future success of the air campaign. In addition to losses in the face of the Luftwaffe, the air force had to learn how to manage large coordinated air assaults. This was done through a series of raids largely over France that targeted U-Boat pens, French factories contributing to the Nazi war effort, and shipping chokepoints. These were limited objective missions, but were really for building skill in the air and organizational competency.
3) While USAAF was reformulating its strategy and tactics, the Luftwaffe was also studying the air campaign of 1943 and reorganizing itself to better combat future air assaults. This included relocating fighters dedicated to attacking the bomber stream further east out of range of existing escort aircraft. Importantly, the Luftwaffe increased the potency of "bomber destroyers" by adding heavy cannons to several aircraft types. (Me 110, FW 190A) A key point in the LW plan to attacking bomber streams was the expectation that they would not face opposing bomber escorts. (see the chart attached below regarding escort range)
4) Having gained competency and the availability of new aircraft capable of long range escort, USAAF set a new priority, the destruction of the Luftwaffe rather than the destruction of industry. Officially titled Operation Argument, but commonly called "Big Week" the campaign to establish air superiority over Europe was conducted at the end of February 1944 and lasted through March, although the critical dates are 2/20 - 2/25. Anecdotally, I had a relative who was ground support then who called it the Air Corps D-Day. Big Week consisted of a series of raids intended to force the Luftwaffe to engage the bomber stream and more importantly, longer range escort fighters. Earlier in this thread, someone posted kill percentages for Big Week breaking down Mustangs vs Thunderbolts vs Lightings. The relatively higher kill percentage by Mustangs makes sense when you consider that these raids were of a distance where only the Mustang was escorting and the Luftwaffe was flying "bomber destroyers" that had so much added armaments as to lose their ability to dogfight. The Mustang was a huge surprise to the LW and the calculation that you could operate overloaded fighters against bombers without opposition was a major miscalculation.
The success of Big Week then allowed for the combined USAAF/RAF to transition to the Transport Plan and the assault on western Europe in preparation of D-Day.
5) You asked about medium bombers in Europe and from what I can tell, the numbers were fairly limited in GB until late in 1943. It appears from the unit histories that I have been able to track down that the majority of MB's were assigned to the MTO until November/December. Then, in late 1943 and especially in early 1944, there is a huge increase in the number of medium bomber groups based in England. This makes sense as they would have a significant role in the Transport Plan, but not in the strategic bombing campaign. It also makes sense from an infrastructure standpoint as you will also need new air bases for medium bombing groups and you need time to establish that infrastructure.
Thats a long response to give better context to the question about the suspension of heavy bombing in 1943.
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