BF 109 Dive Rate

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Doesn't sound difficult drgndog, simply source the NACA report for Jan24 1939 pilot H Lloyd Child a/c P-36A, the flight was just before noon at Buffalo.

I couldn't source the report in the NASA/NACA records - do you have a copy?

The book is quite well presented, with plenty of primary source references and a glowing foreword praising it is by NACA test pilot Richard Collins.

Glowing Forwards are Nice

And the flight test itself is clearly explained and witnessed and published in the media as the dive that was "faster than a bullet," at the time it made Curtiss and the pilot Child quite famous. Hallion himself writes "one can have little doubt the Hawk exceeded 500mph during the dive but 600mph?"

Bold claims are Nice". A .45ACP at 830 fps is about as slow a bullet as existed in Gov't service - that would be .74M (830/1161) at SL. You think a P-36A could do .74M at SL (or any altitude) ? Did any of the reports specify what they meant by a 'speeding bullet"?

He also notes there was some controversy about the French recording instrumentation placed aboard the a/c as a result. In any case it is the pilot's testomony he exceeded 500mph by a count of seventeen seconds in a vertical dive. Child wrote "It was a good opportunity to see what the Hawk could do, if let out a little, and I gave the plane its head."
Child is one of the most respected test pilots who ever lived.

The world is full of great and respected pilots that looked at their instrumentation while diving. The world has seen infinite testimonials about Mustangs and Spitfires 'exceeding 600-650 mph' in dives in combat Encounter Reports. Would you consider those claims credible?

The facts to support the claims via calibrated instruments, compensated for stagnation pressure/temperatures induced under compressibility effects are Zero in the 1930-1945 timeframe.


He was also quite explicit that the F3F biplane routinely attained 400mph in dives. The reference to the XF4U-1 routinely achieving 550mph in dive tests is also quite explicit.

I would come closer to believeing 400mph for the F3F than 500 for P-36A. Ditto on the instrumentation questions but 400mph, at altitudes near 10,000 feet, is closer to .55M where the instrument readings (IAS) were corrected for altitude w/o much error. .55M is where compressibility becomes a factor in pitot tube reliability w/o Temp sensor corrections.

but I would more believe the F4U results as 'close' to 550mph TAS than a P-36A at 500 mph -


Since this book is mostly based on the commentaries of the test pilots themselves and their official reports, I can really see little manner in which to challenge its voracity.

I didn't question veracity - they believed what they saw. I question whether what they saw (instrument readings) was corrected for compressibiliy effects - and QED whether the claims matched reality.

It even goes so far as to directly challenge manufacturer listed technical specifications of aircraft, though again it uses test pilot reporting and service documentation (for example Lindbergh's contractual flights for the DoD in the P-47 and F4U) to do it.

I appreciate your personal disbelief, I find the challenging and controversial statements made by test pilots amusing and fascinating.

It is not only credible the P-36 achieved 500mph, it is really incontrovertible. Else you call the pilot, the French contingent, the airfield personnel, the testors, all liars, or a very detailed description of the test itself, referencing test pilot Child's own statements, obviously available official reports, media publication of the time, and with the support of Richard Collins on the general voracity of the author...complete fiction. Perhaps it could be, though I assure you I am more than satisfied.

Good for you.

I assume you are not only a fact driven rational person but also a technically competent individual.

To embrace the narratives in complete confidence that the engineering level compressibility calculations were made prior to and after the statements were published would suggest that you a.) understood the instrumentation, b.) understand the REQUIREMENT to both sense and record the stagnation temperatures when the free stream pressures are brought to a rest, along with the stagnation pressures, and c.) can point out that such instruments existed in 1940-1945 - much less in 1939?

Sources, Please!

I reiterate that I am willing to supend belief and examine the reports but I have a far better Engineering education in Aero than any of the aero engineers of the 30's and 40's (simply because far more Aerodynamics knowledge was available and taught in the 60's and 70's).

I am NOT saying smarter - just more knowledgable about compressibility and the effects to instruments, flow characteristics and stability and control of aircraft in that regime than the guys who were seeing it for the first time and scratching their heads... and sure as hell more than the test pilots of the 30's

I need to see the actual reports to better understand how they arrived at their conclusions regarding the speeds attained in the dive tests before I believe the conclusions.

Even a time/altitude and IAS series of data points would help but IAS would be significantly overstated at speed near .6 to .7M simply because of the significant temperature rise of the air brought to a rest, causing an error in the stagnation pressure reading.

If there was a camera mounted with time stamps to monitor altimeter readings versus time, they could could get an accurate true 'vertical' (perpendicular vector to ground) velocity. If they had that plus an accurate method to measure dive Angle - then they could finally plot the TAS along the angle of the dive .. but not with instruments of the day

Summary - Absent the camera/altimeter/dive angle verification, They REQUIRE temperature sensors within the pitot tube, to compare against the actual Temp at that altitude, to arrive at the Temp corrected density and therefore the corrected TAS.

If you have your hands on the Report see what it says about the instrument correction methodology.
 
The fact remains however disputed the French increased their order for the Hawks on the strength of a 500mph formal dive speed requirement which was satisfied to their sentiments and all others present on Jan24 1939.

Okay let's be honest here, I think you're tremendously uncomfortable about the fact a P-36A can dive exceeding 500mph in comparison to other a/c dive speeds irrespective of reasoning, but really it's a very solid little all metal a/c not entirely removed from the standards of late war production aside from airfoil thickness really.

Consider the DVL reports the BF-109 airframe as stable at 0.79 M dive. The Fw190 as "has trim change" at 0.78 M dive.
Why is it so difficult to believe that a P-36A can exceed or even reach 0.677 M in a power on vertical dive through 12,000ft altitude loss? Is it the year?

I'm not really in a position to argue with you, I'm not qualified, but the author who seems more qualified than me was perfectly satisfied the P-36 had exceeded 500mph as is the general consensus of all those directly related to the test. Naturally media exaggerates. And obviously there is tremendous controversy and outright challenge to the instrumentation readings of which were concluded 600mph had been touched, at the end of that day (it took most of the day to assess the results). Nobody I think believes that, though it was just too juicy for me to leave it out.

Your dispute is your own and you have your reasons, but we're discussing the annals of flight testing in the thirties, published in the 90s and the dispute is indeed your own. Maybe you're right, I'm just not in a position to accord you.

Might I point out that the aircraft dive speeds of the period you are satisfied with, performed by RAE for example, used much the same methods and instrumentation as those here, agreed the RAE in particular are noted for accuracy in adjusting results for compressability effect, this was recognised in the book (which gives British flight testing and test pilots in general a glowing accolade). But adjusted for compressability, look at the figures published, 0.82 M for P-51B on at least two occasions, 0.895 M for the Spit MkXI, etc. 0.677 M for a P-36 so hard to believe? Indeed the author would suggest somewhere around 0.7 M closer to actual speed attained, but that is indeed lax speculation, the satisfaction is in excess of 500mph at 9000ft in a power on vertical dive from 22,000ft.
Most of us would imagine the a/c would break up under those conditions regardless of actual speed, whether 450mph or what, 13,000ft altitude loss in a power on vertical dive just seems suicidal in a P-36, but surely at least that part is relatively indesputable. Or should we give a little accord there, too, be minimalists, say it was a 10,000ft altitude loss in a power on vertical dive (test conditions specified at the time in the US were zero lift dive, which as mentioned turned out to be dangerous by the war era and was changed as a result of designs like the XP-38 and XF4U-1, where the RAE tested their Spits for example in a 50-degree power on dive, the Hawk test preceded this change in flight test procedure).

What are you saying, it topped out at 400mph in the dive and just remained vertical down, power on for 10,000ft having reached terminal velocity with no ill effect? I'm not an engineer but I don't think it works that way.
 
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The fact remains however disputed the French increased their order for the Hawks on the strength of a 500mph formal dive speed requirement which was satisfied to their sentiments and all others present on Jan24 1939.

What has not been entered as a 'fact' is whether a.) the instrumentation gathering the data was of sufficient capability to accurately conclude the maximum dive speed attained, and b.) which set of recording devices were used.

Okay let's be honest here, I think you're tremendously uncomfortable about the fact a P-36A can dive exceeding 500mph in comparison to other a/c dive speeds irrespective of reasoning, but really it's a very solid little all metal a/c not entirely removed from the standards of late war production aside from airfoil thickness really.

"tremedously uncomfortable?" - no. "Skeptical, Cynical"?? - yes for the reasons I have cited.

The P-36A was a well built machine. So was a B-17. The P-36A was approximately the same speed as a B-17C (actually slower than the 320mph B-17C). You think the the B-17C would out dive a P-36A? If not, why not>

The XP-51 had the same hp engine as the P-36A (1120hp for the Allison 1710-39) but was 70mph faster than the P-36A. The total drag for the XP-51 and all subsequent variants was Far Less than the P-36A.. ditto the Me 109 and Fw 190 and the Spit.


Why is it so difficult to believe that a P-36A can exceed or even reach 0.677 M in a power on vertical dive through 12,000ft altitude loss? Is it the year?

Because of the comparisons above and the lack of information regarding the test methods and recording devices. Very Draggy airplane, no evidence of accelerometers or other sophisticated instrumentation in hand so far, and no reason to suspend belief based on instruments available in the cockpit.

It is Possible, but my opinions absent the data and methods is that it is Improbable until otherwise substantiated by data I can believe. Anecdotal recounts and research into newspaper articles or manufacturer's claims (trying to sell a/c) are less than compelling




Your dispute is your own and you have your reasons, but we're discussing the annals of flight testing in the thirties, published in the 90s and the dispute is indeed your own. Maybe you're right, I'm just not in a position to accord you.

Might I point out that the aircraft dive speeds of the period you are satisfied with, performed by RAE for example, used much the same methods and instrumentation as those here, agreed the RAE in particular are noted for accuracy in adjusting results for compressability effect, this was recognised in the book (which gives British flight testing and test pilots in general a glowing accolade). But adjusted for compressability, look at the figures published, 0.82 M for P-51B on at least two occasions, 0.895 M for the Spit MkXI, etc. 0.677 M for a P-36 so hard to believe? Indeed the author would suggest somewhere around 0.7 M closer to actual speed attained, but that is indeed lax speculation, the satisfaction is in excess of 500mph at 9000ft in a power on vertical dive from 22,000ft.
Most of us would imagine the a/c would break up under those conditions regardless of actual speed, whether 450mph or what, 13,000ft altitude loss in a power on vertical dive just seems suicidal in a P-36, but surely at least that part is relatively indesputable. Or should we give a little accord there, too, be minimalists, say it was a 10,000ft altitude loss in a power on vertical dive (test conditions specified at the time in the US were zero lift dive, which as mentioned turned out to be dangerous by the war era and was changed as a result of designs like the XP-38 and XF4U-1, where the RAE tested their Spits for example in a 50-degree power on dive, the Hawk test preceded this change in flight test procedure).


What are you saying, it topped out at 400mph in the dive and just remained vertical down, power on for 10,000ft having reached terminal velocity with no ill effect? I'm not an engineer but I don't think it works that way.

Carefully - I am saying I am skeptical regarding the 500mph (or greater) claim for an actual result for the P-36A. Nothing more, nothing less.
Too many statements to discuss w/o wasting a lot of time. Here are the keys.

1. RAE did not record or comment on P-36A dive tests, and the methods for testing and recording flight data in 1942-1945 was progressively more sophisticated as compressibility effects became known. If you have an RAE test report on the P-36A I would give it a lot of credibility.

2. A vertical dive, as was the practice in the late 30's would have been fine for an aircraft with sufficient drag as to prevent it from entering the transonic range (such as a P-36A) where compressibility dramatically alters stability and control as well as exceeding dynamic pressure levels above design ultimate loads - dangerous to the structure.

The fat wing of the P-36A would most likely have prevented it from even .67M. .67 M BTW is ~ 482mph at 15,000ft at STP and ~ 473mph at 20,000 feet at STP conditions for SL

.67M at 5000 feet is 501 mph. For a vertical dive in a P-36A at .67M at 5,000 feet means a recovery somewhere below ground level.

Until the P-38 the entire realm of compressibility was a glimmer in the theoretical aerodynamicist's eye. Von Karman and others were just touching on that boundary at NACA when the P-36A was being flown.

Enough on my part..
 
research into newspaper articles or manufacturer's claims (trying to sell a/c) are less than compelling
I'm sorry I haven't the slightest idea what you're talking about here. I've never done anything of the sort nor claimed to. I don't think you've taken the time to read my posts and having just scoured through them with cursory examination as if you were grading papers, you had formed an impression and argue against an impression you formed about me personally. All I did was reiterate what was written in a publication by an apparently well respected author on the subject of aircraft testing in the period, a book at least one NACA test pilot formally recognises in the foreword as accurate and well presented.
Perhaps you should send Richard Hallion a letter challenging his claims directly?

Carefully - I am saying I am skeptical regarding the 500mph (or greater) claim for an actual result for the P-36A. Nothing more, nothing less.
And carefully I will reiterate your own initial statement, in your very first response to my post as if it were some kind of personal correspondance between us: good for you.

You done?
I don't think I find you very balanced in your appraisal of things, engineer or no. I've met poor judgement with good qualification before.
For example you can't "cite" reasons for skepticism when you're talking about (even an educated) opinion. You "cite" sources when referencing a formal paper. I think you're being overbearing with what amounts to nothing more than a personal opinion, with no genuine evidence to challenge what even more qualified people (ie. the pilot of the plane in question) cite, and here is an appropriate use of the word cite just for future reference, is a matter of the historical record.

But hella cheers and thanks for the back and forth, it was really...special. Mate.
 
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Mike - That definitely is one I would like translated!

Did you get my April 24 Expansion/update?

Hi Bill:

Yes, I've read through your update of the 24 April 1944 article. It's very good, nice work!

FWIW, here's something I've been working on that may interest you:
Narrative of Operations, Intelligence Summary No. 276, 11 September 1944

That's the mission where your dad destroyed an Me 109, shared one Me 109 destroyed and damaged a third, as you no doubt know.

Back on topic; I'll send you a complete translation of the 109 dive report when I get around to cleaning up my current rough translation.
 
Snippets from a Finnish book "Pilots view":

Hawk 75A maximum speed in dive: 715km/h TAS (444mph)
Test pilot Lloyd Child was told to exceed 900 km/h TAS (559mph)

Of Fiat G-50 (plane of the same generation as P-36):
Harmaja (Finnish pilot) made a dive test in Italy . According a study of the chief designer Gabrielli the maximum speed achieved in that dive was 828 km/h (515 mph, 90km/h above the design limit speed, allowed speeed was 585km/h (364mph) indicated).

Fiat was a strong plane, the ultimate load factor was 14g.
 
Hi Bill:

Yes, I've read through your update of the 24 April 1944 article. It's very good, nice work!

FWIW, here's something I've been working on that may interest you:
Narrative of Operations, Intelligence Summary No. 276, 11 September 1944

That's the mission where your dad destroyed an Me 109, shared one Me 109 destroyed and damaged a third, as you no doubt know.

Back on topic; I'll send you a complete translation of the 109 dive report when I get around to cleaning up my current rough translation.

Its a bit of a cheek I admit but could I ask for a copy of this as well, better still load it onto your site and put a link on.

Please
 
Hi Bill:

Yes, I've read through your update of the 24 April 1944 article. It's very good, nice work!

FWIW, here's something I've been working on that may interest you:
Narrative of Operations, Intelligence Summary No. 276, 11 September 1944

That's the mission where your dad destroyed an Me 109, shared one Me 109 destroyed and damaged a third, as you no doubt know.

Back on topic; I'll send you a complete translation of the 109 dive report when I get around to cleaning up my current rough translation.

Mike - Definite interest on my part. Do you also happen to have either May 13, or November 26 in your files?

As you probably know, dad tried to share the score on that 109 (as reflected on the Report) but it was given to him 100% - you have the encounter report on your site. BTW - he met the pilot of the third airplane in a chance encounter in 1975. Amazing story.

Dan (Lesofprimus) Case did a fantastic IL-2 sequences of the 354FS mission on Sept 11, icluding dad shooting down the second 109, it crash landing and pilot running into woods while Johnson strafed the 109.

Its in the IL-2 Thread below - you ought to check it out Enjoy...

http://www.ww2aircraft.net/forum/att...-354-final.wmv

You have permission to use the April 24 story on your site if you want to replace the old one. The timelines and encounters are much better.
 
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I'm sorry I haven't the slightest idea what you're talking about here. I've never done anything of the sort nor claimed to. I don't think you've taken the time to read my posts and having just scoured through them with cursory examination as if you were grading papers, you had formed an impression and argue against an impression you formed about me personally. All I did was reiterate what was written in a publication by an apparently well respected author on the subject of aircraft testing in the period, a book at least one NACA test pilot formally recognises in the foreword as accurate and well presented.

That is true - you also posed that independent of any other questions regarding the performance for the reasons i 'posed' (if you like that better than 'cited') that the facts of a 500mph dive (versus opinions based on the methods applied) were in evidence by virtue of respected OPINIONS.

Perhaps you should send Richard Hallion a letter challenging his claims directly?

Perhaps I am consumed by indifference?

You are a little sensitive and I am sorry your feelings are hurt. I know all you did was re-iterate what you read. I can tell you from personal experience how disappointed I was when I heardmany first hand accounts of Mustangs reaching 620 mph in dives to shoot down me 109s by extremely well thought of and respected fighter pilots - only to find that while their observation of the instruments was probably true, the actual instrument readings were flawed - by simple but not well understood effects due to laws of physics.


And carefully I will reiterate your own initial statement, in your very first response to my post as if it were some kind of personal correspondance between us: good for you.

You done?

I don't think I find you very balanced in your appraisal of things, engineer or no. I've met poor judgement with good qualification before.

Good for you. we continue to share things in common

For example you can't "cite" reasons for skepticism when you're talking about (even an educated) opinion.

From the very beginning I shared a.) my skepticism, b.) the reasons for the skepticism for my opinions regarding the reasonable doubt that the P-36A attaining 500mph, and c.) focused my reasoning on the lack of knowledge regarding compressibility, the lack of instrumentation to calibrate dynamic pressure with temperature compensation, the doubt that accelerometers and other sophisticated devices were used in the test, the anlogous anecdote of comparisons of P-51 Drag and P-36A drag to demonstrate that it was a pig relative to Cdo, the fact that Drag rises rapidly in airspeeds >.55 for Fighters of the 30's (whicjh also affects airspeed instruments). These are reasons that are fact based - not opinion based.

Which ones do you discard as reasons I "can't" pose (as I dare not use "cite") for your elucidation or consideration?


You "cite" sources when referencing a formal paper. I think you're being overbearing with what amounts to nothing more than a personal opinion, with no genuine evidence to challenge what even more qualified people (ie. the pilot of the plane in question) cite, and here is an appropriate use of the word cite just for future reference, is a matter of the historical record.

Just so we can agree on common ground

Main Entry: cite
Pronunciation: \ˈsīt\
Function: transitive verb
Inflected Form(s): cit·ed; cit·ing
Etymology: Middle English, from Anglo-French citer to cite, summon, from Latin citare to put in motion, rouse, summon, from frequentative of ciēre to stir, move — more at -kinesis
Date: 15th century
1 : to call upon officially or authoritatively to appear (as before a court)
2 : to quote by way of example, authority, or proof <cites several noteworthy authors>
3 a : to refer to; especially : to mention formally in commendation or praise b : to name in a citation
4 : to bring forward or call to another's attention especially as an example, proof, or precedent <cited the weather as a reason for canceling the picnic>


But hella cheers and thanks for the back and forth, it was really...special. Mate.

You are of course welcome to your opinion.
 
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Snippets from a Finnish book "Pilots view":

Hawk 75A maximum speed in dive: 715km/h TAS (444mph)
Test pilot Lloyd Child was told to exceed 900 km/h TAS (559mph)

I do know this - our little debate above is all about 'observation' versus 'reality' of TAS versus IAS in near to fully compressible flow conditions. Thanks for the info below on the Fiat.

Of Fiat G-50 (plane of the same generation as P-36):
Harmaja (Finnish pilot) made a dive test in Italy . According a study of the chief designer Gabrielli the maximum speed achieved in that dive was 828 km/h (515 mph, 90km/h above the design limit speed, allowed speeed was 585km/h (364mph) indicated).

Fiat was a strong plane, the ultimate load factor was 14g.

Timppa - was 14g the design 'ultimate' load or was that the estimated threshold G force attained in that dive. The reason I ask is that 8/12 was the primary design/ultimate load factor for many aviation companies for fighters - not that I have insight to Fiat's design practice.

It would be unusual to build in the extra weight implied by having 8.7/14 g design philosophy for what should be a very rare perfromance threshold.
 
Not to muddy this debate up anymore, but, is there any definative dive tests that were performed on any of the P-40 series from Curtiss??

This is only a guess, but seeing as how most of the aircraft is unchanged (airfoil and fuselage), other than the engine, if there is a test on an early mark of the P-40 to the P-40 B/C maybe we could "guestimate" how it would compare to the P-36.

I would guess that the early P-40, with the smaller chin radiatior may be cleaner than the radial P-36. It may be a toss-up between the later marks of the P-40 with the much larger radiator and / or longer and changed fuselage.
 
Mike - Definite interest on my part. Do you also happen to have either May 13, or November 26 in your files?

Hi Bill:

I don't recall having much material on May 13, 1944 other than the Encounter Reports. I'll put that on my to-do list. I have been researching November 26, 1944, however, I still have much more work to do. Here's the field order for starters: Field Order No. 529-B. 26 November 1944


As you probably know, dad tried to share the score on that 109 (as reflected on the Report) but it was given to him 100% - you have the encounter report on your site. BTW - he met the pilot of the third airplane in a chance encounter in 1975. Amazing story..

Thanks for the clarification; that rings a bell.

You have permission to use the April 24 story on your site if you want to replace the old one. The timelines and encounters are much better.

Thanks, will do! I noticed the LW loss list was also much more complete.
 
Hi Bill:

I don't recall having much material on May 13, 1944 other than the Encounter Reports. I'll put that on my to-do list. I have been researching November 26, 1944, however, I still have much more work to do. Here's the field order for starters: Field Order No. 529-B. 26 November 1944

Erich and I have collaborated on 26 November for the big JG 301/JG 6 and JG 1 clashes with 355th, 361st and 339 - let me know if you need anything


Thanks, will do! I noticed the LW loss list was also much more complete.

Joerg Dietsch helped quite a bit filling in the last of the blanks. It does seem clear that no Ju 88 went down to 357FG and nothing about an Me 410 has surfaced as a possible ID mismatch either.
 
I made a graph of allowed dive speeds [mph, IAS]. Iin case of German and Russian fighters the limits are probably minimum requirements rather than their actual limits, because the speeds are the same (750 and 650km/h respectively).

The sources are mainly "America's Hundred Thousand" and Pilots manuals.

In case of F4F and Fokker the speeds are actually their terminal speeds.

dives.gif
 
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I made a graph of allowed dive speeds [mph, IAS]. Iin case of German and Russian fighters the limits are probably minimum requirements rather than their actual limits, becuse the speeds are the same (750 and 650km/h respectively.

The sources are mainly "American Hundred Thousand" and Pilots manuals.

In case of F4F and Fokker the speeds are actually their terminal speeds.

dives.gif

Very nice presentation - I was suprised at a.) low dive 'permissable' for 109 and Spit IX as well as the high P-63.

Absent the data it seems difficult to match reality versus observation for the values of 450mph and above for several reasons.

State to Instrumentation that existed through 1945, particulalry for conversions from IAS to TAS.

Consistent applied analytical methods applied to reduce and normalize the data to account for compressiblity as the reduced stagnation pressures for temperature became more problematical.

Manufacturer's standards for dive tests and structural engineers tolerances for exceeding limit loads (or using Limit load factors as their guideline for a very specific gross weight condition). In other words did "America's Hundred Thousand" researchers look only to Pilot's Manual for stated performance and limits, or the available test data the Engineers used to formulate theoretical limits?

Thanks for the work that went behind the plots
 
An additional note:

In many Pilot's manual only one IAS speed is given (e.g. for Typhoon).
Tempest limiting speed is given as 540mph below 10,000ft.
P47N:
564 mph at sea level
522 mph at 5,000ft
482mph at 10,000ft
So there are many caveats in this graph.
Btw. very big thanks to Micdrow for most of the pilot's manuals.
 
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Joerg Dietsch helped quite a bit filling in the last of the blanks. It does seem clear that no Ju 88 went down to 357FG and nothing about an Me 410 has surfaced as a possible ID mismatch either.

Hi Bill:

Girbig puts German casualties at 87 for November 26, 1944 and notes a loss of at least 90 machines. US claims were what, about 98 – 100 destroyed? Do you have a LW loss list in detail for 26 November 1944? Fwiw here's the 361st Fighter Group's Mission Summary Report of 26 November 1944. Interestingly their claims were adjusted up from 19 to 23 destroyed after review.
 

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