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Germany did not fully mobilize her available resources in the early war years, a fact I have been discussing in other threads, most single-mindedly here. She did not mobilize earlier because Hitler didn't take the SU seriously. Here he does (he was close to this realization anyway).
This is not a revival of the old "Blitzkrieg economy" hypothesis: Germany's domestic margin of undermobilization was small but, as we will see, decisive. Her biggest failure to mobilize regarded foreign labor, where German "recruitment" lagged a maximal effort until early 1942 (more discussion here). Neither did Germany intentionally "choose" to be undermobilized, as Millward's Blitzkrieg Economy thesis holds. Instead, a perception that he lacked sufficient political capital caused Hitler not to take well-known measures to ensure private firms' compliance with war economy requirements (discussed here) and to close inefficient firms (discussed here). Here Hitler balanced internal vs. external threats to his regime, seeking (in an intuitive way) to maximize his chances of power and survival. When it emerged that the Soviet Union's power (combined with coalition allies) threatened his regime more than internal resistance to mobilization, he took the previously-avoided mobilization measures in late '41 and early '42 (see Germany and the Second World War, vol. 5/1, "The Winter Crisis of 1941-42").
The point of departure for earlier German mobilization in this thread is Hitler's earlier understanding that the SU was a formidable enemy; that greater mobilization was required. By May 1940, when he begins seriously planning his post-France moves, he orders greater mobilization - foreign and domestic.
In another thread I have analyzed the feasible impact of earlier maximal mobilization; I will summarize its points here and refer to that post (and the preceding) for further details. A critical point is that German armaments expenditure was a low portion of German military spending and GDP - around 1/5th of military spending and 1/10th of GDP. So shifting merely 10% of German national resources to armaments in 1940-41 would have roughly doubled armaments output.
My economy-focused thread shows that, had Germany added ~80k more foreign workers per month in 1940-41, and had it clamped down on known misallocations of supposed war workers, it could have increased production nearly 50% by the end of 1940 (relative to OTL) and nearly doubled it by Fall '41 (vs. OTL). I give a breakdown of potential usages of that additional production:

...and this is the breakdown I will use for further discussion in this thread. The table assumes a 50% delta to OTL panzer production from May '40, 50% to motor vehicle production from July, and 20% to army weapons production from August. In September '40, I add an army ammunition delta worth 10% of total OTL armaments output (ammo was highly variable OTL so I just used a big chunk to replace the OTL ammo nosedive around that time). With these additional items, achievement of my "One More Panzer Group in Barbarossa" ATL is over-determined. The Ostheer can have at least 10 more mechanized divisions (5 manned by new drafts, 5 converted from standard inf.divs). In addition, it has at least twice as much ammo as OTL and the rail system to deliver it (discussed further below).
Note that the added production is sufficient to improve Ostheer's tank and truck parks qualitatively, in addition to quantitatively. 50% more Pz III/IV's means a greater portion of medium tanks in Ostheer than OTL, even after creating 5 new Panzer divisions. I won't get into the details because it's not a point on which I'll rely for now.
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Stronger Germany - not just in the East
As the spreadsheet makes clear, earlier mobilization will give Germany additional resources beyond what was needed to ensure victory over Russia. By October '40 she can afford doubling all shipbuilding (inc. Uboats). Thereafter, the spreadsheet specifies that all resource increments - ATL vs. OTL - are applied to aircraft production. By mid-41, LW is receiving ~50% more planes than OTL.
Obviously the additional air/sea production opens strategic vistas for Germany's war with the West. In the remainder of this post, I will get us to discussing the wider war by first summarizing (and linking to) my fuller explication of 1MPG's Eastern Front course. In that thread I have reached 1942, at which point strategic interplay between Eastern and Western wars is fuller - so it's best to proceed on both fronts thereafter.
Please do not take the spreadsheet projection literally. No war program goes exactly to plan; it's an indication of the shape of expanded German output.
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Catching up on 1MPG. Recap, summary, peak into the ATL '42 campaigns.
Clarifications/Renunciations:
Unlike in 1MPG's OP, I now see the necessary PoD falling in mid-'40 rather than prewar. I suspected as much back then; with further research my earlier caution is no longer necessary. Germany can begin preparing a stronger Barbarossa as laid out in this thread, not 1MPG.
Initial forces:
- The primary initial force delta is still as 1MPG specified: 5 more panzer divisions (85k more recruits into Heer); 5 more motorized divisions converted from existing units.
- Besides the mechanized divisions, Ostheer also earlier receives some of the ID's transferred later - only these are upgraded using our additional army weapons production. The additional ID's support ATL PzGr5 in Romania, as in 1MPG's OP.
- LW and KM support are as in OTL.
As in 1MPG, initial centerpiece is a Kessel in Galicia, using our one more panzer group to encircle and destroy Southwest Front. Detailed discussion here.

Next stage (July '41), discussed here, looks like this:

August '41, also discussed here, looks like this:

September '41, discussed here, looks like this:

...leaving Moscow, Leningrad, and Ukraine all in German hands. As discussed in the linked September post, what follows is mostly a slower, infantry-focused push over the late-Fall and early winter to these lines:

...the yellow-dashed area being taken in geographically-limited, but otherwise full-speed, offensive (basically Blau 3-4) employing only a part of Ostheer's mechanized forces.
LOGISTICS!
I discuss improved ATL Ostheer logistics here and here (and definitely elsewhere...).
As with everything Barbarossa, it's critical to understand that its logistics sucked because its planning sucked. As my logistics posts lay out, Germany possessed ample resources and expertise to support the Ostheer competently on a longer campaign, had she actually planned such a campaign.
Fuel
Discussed here.
SU's status at the end of ATL Barbarossa
ATL Spring '42 will see the SU roughly 40% weaker than OTL Spring '42, accounting for greater demographic, military, political, and economic damage. More details here and here.
Critical point: A better Barbarossa makes ATL '42 SU a smaller, poorer country than OTL. Smaller, poorer countries have smaller, poorer armies.
Ostheer's status at the end of ATL Barbarossa
Spring '42 will see the Ostheer's net casualties (i.e. casualties properly accounting for returning wounded) ~300k lower than OTL. Because of better Barbarossa logistics and production, its material state will be vastly improved as well.
I have put together a spreadsheet to track these things; available on request as a Google doc. Here's one version of the calculations:

The underlying arithmetic is only:
[casualties at Time 2] = [Enemy force at Time 2 ATL] / [Enemy force at Time 2 OTL] * [OTL casualties]
Where
[Enemy force at Time 2 ATL] = [Enemy Force at Time 2 OTL] - ( [Casualties at Time 1 ATL] - [Casualties at Time 1 OTL] )
...which applies the basic intuition that encircling more of RKKA at Time 1 means getting shot by fewer RKKA at Time 2. In addition, the spreadsheets assumes parameters for degradation of SU's weapons stock (lower production from earlier, greater territorial losses) and soldier quality (forces have to be fielded earlier, before training complete. And/or more militia used - else Germany can actually do something like the "railway advance" after most of RKKA is destroyed). Some discussion here.
Ostheer's plan for 1942
Plow ahead to the Urals and Baku, leaving Stalin with a rump state of maybe 50mil population, completely lacking oil resources and major industry. Stalin is expected to make peace to preserve his regime. Otherwise Germany conquers the important parts of Siberia in '43 and spreads insurrection in Central Asia, leaving Stalin an impoverished duchy west of Baikal that falls in '44 (if not earlier).
Japan
She doesn't join Barbarossa in this ATL (though she should have). Rather, in Spring '42 she perceives that the SU is no longer a serious threat to Manchuria and tightens the blockade on Vladivostok. She announces, helped by German inducements (below), that no Allied-originating or financed goods are permitted through. If SU attacks Japan, it's worse for Stalin. So let's assume he doesn't. As SU is truly collapsing in Fall '42, Japan probably plays the jackal on Primoskiye and Khabarovsk. Maybe all the way to the Amur and parts of Mongolia too.
The German inducements are: (1) surplus Heer material - MG's and obsolete tanks, say. These would greatly enhance IJA's war in China. Japan can get them by forcing SU to accept its reduced status as a purely Asian power, and resume German-Japanese trade over the TSRR. (2) full cooperation on a MidEast-India strategy after Japan seals SU's fate by cutting the main LL lifeline. Japan wanted this strategy OTL, Germany couldn't deliver while facing a powerful SU.
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BACK TO THE GLOBAL WAR
Having caught everyone up on how ATL Barbarossa went, it's time to look at the wider war and German prospects.
Germany's main post-SU goals will be like those in Directive 32:
Move into the MidEast, involving:
- A pressure campaign on Turkey followed (hopefully) by her acquiescence (otherwise invasion).
- Operations from Caucasus into Iran and Iraq.
- From Turkey, attacks on Iraq and Suez via Levant.
- Reinforce Rommel to help with Suez.
- Get Spain in the war one way or another to eliminate Gibraltar.
Redirect production to KM and LW. ATL this is already happening, as all production increments are going to the LW and army armaments share is shrinking (though absolute level remaining steady).
In addition, Germany will want to help Japan. She wanted to OTL also, here the TSSR makes that possible already in late '42.
Invading the Mideast
As I've been discussing elsewhere, the Allies OTL shipping situation makes defending the MidEast in '42/'43 a very difficult proposition. As Harry Hopkins said when tasked to analyze dealing with something like this ATL (SU falls, Rommel stronger), "The sea lines of communication are long and vulnerable, presenting an impractical proposition for military operations against strong enemy movement out of the Mediterranean." Cite.
I've produced various quantitative analyses using US official histories to determine what the US could deploy/maintain in Mideast during 1943 or 42.
TL;DR: Using ALL US Army shipping, it's hard to get 5 divs in the Mideast by '42's end. By 3Q '43, maybe 15 divs can be supported. Both scenarios assume passivity in the Pacific and no buildup in England.
That's using OTL Allied shipping. In this ATL, Germany doubles its shipbuilding and deploys >400 more Uboats during '41-'42 (20/mo OTL for most of '41-'42). If we assume these sink, on average, just 30k tons each by May '43 (i.e. much less than average OTL Uboat loss/kill ratios before May '43), Allies lose 12mil more tons of shipping in the BoA. That's ~30% of global Allied shipping:

Those losses would absolutely preclude any significant military additions in the MidEast and might make supporting even a 2nd-Alamein-sized force in Egypt (or Palestine) impossible. Why? Because allotments to military shipping came after satisfying Britain's basic import requirements; therefore military shipping was highly sensitive to the margin remaining after that essential minimum. As my spreadsheets show, US Army shipping (in measurement ton - miles) increased by a factor of ~150% between early '43 and mid-'44, when global Allied shipping pools increased by only ~50%. With global Allied shipping levels at an all-time low, US (and British) Army shipping space will be miniscule. This is the true shape of feasible Uboat victory: not to starve out Britain, rather to torpedo Allied strategic mobility.
So the MidEast is lost, Allies can't get there in any decent strength to check Germany in or south of Turkey, nor in Iran.
North Africa
Recall that Ostheer net casualties are ~300k lower up to Spring '42. The additional forces - call it 20 divs - redeploy to Norway, France, and North Africa in Spring '42 because Ostheer doesn't need them to finish a 40% weaker SU. To get more divs to North Africa requires suppressing/taking Malta. That's easy in this ATL, considering a much-stronger LW and doubled German shipbuilding (inc. MFP's for landing an ID on Malta or Gozo).
8th Army's rear is collapsing by early '43 anyway, as Heer moves from/through Turkey.
Torch is not an option either: Spain will be forced into the war by a German buildup on its borders and Gibraltar taken. If Spain resists - perhaps with Allied commitments of aid - then in '43 Germany bags an Allied expeditionary force with Iberia.
Asia-Pacific
SU's fall and, assuming Stalin behaves rationally, opening of the TSRR, allows Japan to finish Chiang's forces with German weapons (and perhaps training) and with the Kwantung Army redeployed to China (it was still very strong in OTL '43). This removes the rear threat from Japan's armies in Burma and opens a logistical line on the Burma Road from Kunming. India will shortly (1944) be in grave danger regardless of what happens in the Pacific (where Allied shipping shortages hamper their OTL offensives anyway).
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That's the setup so far: Germany "Vichy's" the SU in fall '42, conquers MidEast by mid-'43, Mediterranean is an Axis lake. On the economic front, Germany has >5mil more men shifted from army/graves into industry, recruits millions more (10mil?) from occupied Europe and its greater PoW hauls. Total German armaments production is >2x OTL and goes ~70% LW (vs. ~45% OTL): LW is >3x stronger. Bombing Germany is non-viable, invading Europe unimaginable. Germany is building MFP's, E-Boats, Destroyers, training more LW naval specialists - everything it needs to control the Channel and put an army over it. What next?
...to be discussed.