German-Allied loss ratios in aerial combat, Western theaters

[Richard Anderson]

I don't know why it is needful to spell this out, but if an aircraft is lost to accident, be it in the Z/I or in a theater of war, while on a non-combat mission, then by definition it is a non-combat accident and would not and should not be included in an accounting of "German-Allied loss ratios in aerial combat".

So nice to see when someone can follow the breadcrumbs, but no, I don't worry about other posters misusing sources, I worry about them misusing my work that I derived from those sources, especially the data tables I used to freely share. Given I freely shared sources with this particular poster in the past, their whining is an interesting commentary on their motivation and attitude in posting. If I don't see a request for sources from this poster any more, it may have something to do with the fact that their previous conduct and lack of interest in their postings caused me to put them on ignore, so that I infrequently, like this morning, bother to review their posts.

[David Thompson]

Two uncivil posts from TheMarcksPlan were removed, pursuant to the forum rules.

[PaulEwaldvonKleist]

Strategic vs. Tactical Analysis, using Mackay and Price's findings

To repeat, neither side in the BoB could choose to have bigger air forces. In the Battle of Germany ("BoG"), aka basically the Combined Bomber Offensive ("CBO"), however, either side could have had different forces: Germany could have devoted more resources to fighter production or could have freed/obtained more resources by defeating the Soviet Union. Britain and America could have spent more on air forces and/or could have sent less to the Pacific.

These are strategic choices that have implications for tactical attrition ratios: A larger ATL tactical attacking force (B for Allies) would inflict kill percentages of enemy forces in proportion to (size delta)^1.2 * (OTL kills); same for a smaller tactical attacking force. A larger ATL defending force (G for Germany) would inflict kill percentages in proportion to (size delta)^.9 * (OTL kills). Mathematically we have:

dB/dt ~ [(size delta)*(OTL G)]^.9

dG/dt ~ [(size delta)*(OTL B)]^1.2

Note: dB/dt and dG/dt represent percentage loss of each force

This gives us a defender kill percentage that is sublinear with tactical strength and an attacker kill percentage that is supralinear with its tactical strength.

Now let's put some numbers to it, using my "defeated Soviet Union" counterfactual wherein opposing LW strength is 5x OTL.

OTL Allied losses = X ATL Allied losses = X * 5^.9 = 4.26X

OTL German losses = Y ATL German losses = 5Y

ATL attrition ratio = (4.26/5)*X/Y

note: X and Y represent absolute, not percentage, values

At the tactical level, this actually contradicts my working assumption that ATL attrition ratios would be at least as favorable to LW as OTL. ATL attrition ratio moves against Germany by 15% (Germany loses 5x the fighters, Allies lose 4.26x OTL).

That's not the whole story, however, as we move from tactical to strategic level of the entire BoG or CBO. Holding Allied European air resources constant, for now, the size and/or number of Allied air raids - their size in tactical engagements - would have to decline. If tactical strength declines, we can solve for when OTL attrition ratios by solving for Z in the below equation:

Z = (OTL Allied tactical strength) / (ATL Allied tactical strength)

( (5^.9) / 5) = Z ^ 1.2

Z = .875

...this is the crossover point where, on the Mackay/Price BoB model/data, the attrition ratio effect of smaller attackers (Allies) equals the effect of larger defenders (Germans).

Would Allied losses in this counterfactual environment (i.e. 5x initial LW strength) imply at least 12.5% smaller Allied tactical strength as the campaign wore on? Pretty clearly yes. To see why (if it's not intuitive already), let's look at OTL 8th/15th bomber strength:



Then let's look at OTL AAF heavy bomber losses (to fighters) in Europe:

Hi, trying to understand your model (I am EwaldvonKleist from the Reddit discussion, btw).

dB/dt ~ [(size delta)*(OTL G)]^.9

dG/dt ~ [(size delta)*(OTL B)]^1.2

Is this some variation of the Lancaster differential equation? OTL=Original time line? Where do the exponents 0.9 and 1.2 come from, how is size delta calculated?

[ewest89]

Losses in the United States need to be considered. These include aircraft that never made it to the war zone due to their being lost in the U.S.

https://www.amazon.com/Forces-Aviation- ... 0786421061

[Richard Anderson]

Is this some variation of the Lancaster differential equation? OTL=Original time line? Where do the exponents 0.9 and 1.2 come from, how is size delta calculated?

You will not get an answer here since that poster was banned last spring. Yes, I suspect they meant OTL to be "original time line". That is a common abbreviation with the What If crowd. I have no idea where they thought those exponents were from.

[Richard Anderson]

Losses in the United States need to be considered. These include aircraft that never made it to the war zone due to their being lost in the U.S.

Why? See my post from last December.

"I don't know why it is needful to spell this out, but if an aircraft is lost to accident, be it in the Z/I or in a theater of war, while on a non-combat mission, then by definition it is a non-combat accident and would not and should not be included in an accounting of "German-Allied loss ratios in aerial combat"."

Accidental losses in the Z/I have no relationship to aerial combat losses in Western theaters.

[Carl Schwamberger]

Yes, theres been a bit of topic drift there. Referring back to the OP the subject question was "..analysis of German-Allied loss ratios in aerial combat. "


I suppose theres legit reasons to compare of gross or overall losses from all reasons, but the remarks are not clearly labeled or in clear context. Reviewing the thread I had the usual obstacle of having to reread multiple times many posts to grasp the intended context.

[Sid Guttridge]

What are we trying to measure here? Who had the better pilots?

Cheers,

Sid.

[Carl Schwamberger]

I don't think so. My take is a attempt to quantify the better Air Force or fighter force in general?

[paulrward]

Hello All ;

I noted Mr. PaulEwaldvonKleist had a question:

Hi, trying to understand your model (I am EwaldvonKleist from the Reddit discussion, btw).

dB/dt ~ [(size delta)*(OTL G)]^.9

dG/dt ~ [(size delta)*(OTL B)]^1.2

Is this some variation of the Lancaster differential equation? OTL=Original time line?
Where do the exponents 0.9 and 1.2 come from, how is size delta calculated?

While I have not sat in my Calculus Class for nearly five decades now, I believe that the exponents
come from regression analysis in the article cited in the post you quote. Apparently Mr. TheMarcksPlan's
analysis applies the article's Battle of Britain framework to an ATL Battle of Germany in which the Luftwaffe
was much stronger (because Germany has defeated the USSR, focuses its production on increasing the size
and strength of the Luftwaffe, and has much greater overall production due to demobilization of soldiers
who had been fighting on the Eastern Front, and also benefited from a greater foreign labor "recruitment").

You're welcome to discuss the topic with the OP here, as I am certain he will be more precise in his
explanations than I could ever be.


https://www.tapatalk.com/groups/ww2analysis/


I heartily reccomend the site, as the Group is both congenial and convivial and the discussions are at
a very high level.

Respectfully :

Paul R. Ward