Back in the early 30's bombers were still crude: The were meant to take off, cruise, drop bombs, cruise possibly fend of fighter with machine guns and land. This was quite the same approach as in the First World War. In fact, night bombing (which happened to small extent in WW1) was included, but not exactly popular due to poor accuracy. This dominant bomber concept was so crude that Ju 52/3m passenger aircraft were adaptable as auxiliary bombers.
This primitive model of a bomber was shaken in the 30's by two new concepts; the dive bomber (for better accuracy of bomb drops; notably the Ju 87) and the fast bomber (for avoiding fighters; notably the early Blenheim, early Do 17 and SB-2).
Tupolev SB-2. Skin by Karel Chvojka, 3dz by Captain Kurt mod. by Karel C.
The machine gun defence proved to be unsatisfactory. It was difficult to add more defensive machine guns, while fighters increased their weaponry from two to up to eight machine guns. Armour plating, armoured windshields and self-sealing fuel tanks plus the increasing strength of airframes reduced the effectiveness of normal machine guns. Fighters were able to cope by adding 20 mm autocannons, while the same calibre was very unwieldy in movable installations for bomber defences.
Bombers needed better survivability than armour and machine guns could afford. Four approaches promised relief; flying higher, flying faster, flying in darkness and flying with escort fighters.
To fly higher was no good solution (for bombers) because of the inherent accident and reliability issues (due to freezing temperature), added aircraft cost, low payload and poor accuracy of bombing runs.
To fly faster was a questionable solution (for bombers) because it was a time of rapid improvements of top speeds in aviation. A bomber prototype could easily fly faster than all contemporary fighters and still find itself to be much slower than hostile fighters during a war only a few years later. The Mosquito was later on successful with this approach, but only so because it faced opposing forces that were limited in their performance (especially at high altitude) in part by an inferior raw materials base. Propeller aircraft were also bound to meet the limit of their potential at about 800 km/h, and without the introduction of turbine engines we'd have seen an air war scenario in which almost all aircraft would have had a very similar top speed again (as they had already in WW1).
To fly in darkness meant high training and avionics costs, a high accident rate and a typically poor accuracy.
To fly with escort fighters proved to be most successful, but that wasn't about bomber design itself.
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Reconnaissance aircraft of the late 30's looked still a lot like First World War reconnaissance aircraft, but they had badly fallen behind fighters in both cruise and top speed. The Hs 126 is a typical example. The poor survivability of such recce aircraft called for new approaches.
One approach was to fly higher - this proved less problematic for (photo) reconnaissance than for bombing, and the Ju 86P was one of the extreme examples.
Another approach was to fly faster, and this worked for recce better than for bombing simply because air forces needed fewer recce aircraft and the fast fighters could be adapted to photo reconnaissance. The Spitfire PR versions are a good example, also the F-4/-5/-6 U.S.A.A.F. aircraft and the Bf 109 and Fw 190 with recce kit (a specific "Rüstsatz"; mission module). There were also successful two-engined reconnaissance aircraft and even some dedicated fast photo recce aircraft.
The highly successful Japanese Mitsubishi Ki-46 III high speed photo reconnaissance aircraft
To fly in darkness proved to be a niche escape, for both illumination/flash bombs and infrared photography were apparently not fully satisfactory.
To fly with escort fighters - a typical WW1 approach - was unsuccessful because it was both uneconomical and because the ground control for interceptors enabled the defenders to face such a recce package with altitude and numerical superiority just about every time. This in combination with the fact that a single recce aircraft suffices to make photos while a single bomber doesn't suffice to bomb a target properly defined the recce aircraft as unique. They were usually alone on their missions. This influenced which survivability strategies did work and which didn't.
A unique alternative for battlefield recce aircraft was to fly too slow. Fighter had advanced in top speed at the cost of aerodynamics that led to a high stall speed. The Fi 156 was very successful as a short range battlefield reconnaissance aircraft in part because even fighter aces had difficulties to get a Fi 156 into their crosshairs if they managed to do it at all. It was just too damn slow and agile. The same effect was observed in trial mock dogfights against Fl 282 helicopters. Very slow recce aircraft were only suitable for very short range aerial recce and very vulnerable to anti-air weapons, though.
The next analysis is about fighters. There were basically two directions for fighter philosophies in the 30's; the manoeuvrability school (Italians, Japanese, Czechs) that emphasised dogfights and even aerobatics (overall a similar philosophy as in WW1 air combat) and the high speed school (Germany) that emphasised a superior speed. The Russians initially followed both schools with their I-16 (fast monoplane) and I-153 (more agile biplane).
The high speed school was typically combined with low drag liquid cooled engines that were less powerful than radial engines (during the 30's) and did thus initially lack a superiority in climb rate over the more agile fighter designs. Liquid-cooled engines caught up with radials when radials grew to the limits of single radials (the solution was the double radial engine, but that brought cooling issues) at the end of the 30's. By 1939/1940, both liquid and air cooled engines were at about 1,000 to 1,300 hp. By this time liquid cooled engine-driven fighters had caught up with comparable radial-driven fighters in climb rate.
The whole competition changed during WW2. The high manoeuvrability school lost out in Europe; faster fighters were dominant because they chose when to fight and only they were able to cope with fast bombers. The Japanese stuck to the manoeuvrability school with few exceptions, Italy did too (and failed for several reasons) and the British did at least keep a better manoeuvrability than Bf 109 fighters.
The new conflict was different than the 1930's conflict between fighter philosophy schools: All fighters had to have a similar top speed to be competitive, but they proved to have different manoeuvrability strengths.
The vertical air combat manoeuvrability school emphasized climbing and diving and in some cases also a high roll rate. The horizontal air combat manoeuvrability school emphasized tight turns and a low stall speed. The vertical school won, as evidenced by the Fw 190's success over Spitfires and the 1943-1945 success of U.S. fighters against most Japanese fighters. The reason was simple; the vertical school was again dominant, for it was the key to offensive manoeuvres. The horizontal manoeuvring was only at its premium in defensive manoeuvring and at very low altitudes.
Vertical air combat manoeuvre example: A Bf 109 expert vs. defensive fighter ring
To fly tight turns was mostly about shaking off a pursuing fighter (and had little chance of success if employed offensively), while climbing and diving was mostly about attacking a fighter (often with the deadly advantage of surprise). Defence may be stronger than offence most of the time, but offence is decisive. The vertical air combat manoeuvrability school was furthermore still potent in numerical inferiority situations.
Another division between fighters was between fighters for high altitude and for low altitude. Eastern Front and Pacific air wars were mostly about low altitudes, while Western European air combat was mostly about high altitudes. There was a spiral for ever greater practical flight ceilings whenever high altitude combat became dominant in a theatre. The Allies won this race in 1942-1944 thanks to the British lead in two-stage superchargers and the American ability to supply the necessary heat-resistant alloys for turbochargers. The Germans trailed in both regards, but jumped far ahead in 1944 with turbojet engines (even though they lacked heat-resistant alloys and had a very short lifespan, poor reliability and handling characteristics).
It's also possible to divide between short range and long range fighters; long range was important for escort fighters and over the vast expanses of the Pacific theatre, while short range was sufficient for interceptors and fighters supporting ground warfare.
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The post-WW2 period saw competing philosophies for fighters as well:
# Short range ("WVR") vs long range ("BVR") air combat
# Short range fighters vs. long range fighters
# high performance vs. huge numbers
# pursuit of superior speed and altitude performance after the first Mach 2 generation (mostly MiG-25, later F-22)
# low visibility to sensors ("stealth") vs. much external hardware
# avionics with finesse vs. brute power avionics (example for the latter: MiG-25 radar)
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It's interesting stuff (to me), but I'm not so sure about the lessons.
Aircraft kept becoming more capable, more refined, more oriented at their purpose.
There's an eternal development for better survivability.
Superior offensive qualities tend to dominate over the superior defensive qualities in air combat.