# P-51 crit Mach-figure?



## delcyros (Oct 25, 2006)

Despite having read elsewhere that the P-51 Mustang could exceed Mach 0.8 I found those comments of an encounter report:

Pilot: Lt.Col. Thomas L. Hayes
date: 28th of may 1944
unit: 364 Fighter Squadron, 357th Fighter Group
time: 14:00 DST
area: NW of Magdeburg, Germany
Weather: Clear
Circumstances: Dogfight

quote:"(...)Taking up pursuit again, I was able to get on one of the Me-109, which now began to dive (now following details of the kill...) I WENT OUT OF 
CONTROLL INDICATING 500 MPH @ 20.000ft. AND SO DID MY WINGMAN"

At 20.000ft altitude, Mach 1.0 is normally encountered with 706.6 mp/h
(699.5 Mp/h with temps. 5 degrees below normal and 713.7 mp/h with temps 5 degrees above normal), so both Mustangs went out of controll at Mach 0.71 instead of the often quoted 0.82 figure.
Altough I also read several accounts of Mustang Pilots swearing they hit 650 mp/h at low altitude, implying Mach 0.85.
Any ideas anyone?
Thanks in advance,


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## prentice672 (Oct 25, 2006)

I have the flight manual for the P-51H (1954 version) and it lists 0.75 as the limiting Mach. The "H" was a little cleaner than the earlier versions but I seem to recall the limiting Mach was about the same.

Ron


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## mad_max (Oct 26, 2006)

According to my P-51D Handbook limiting max speeds:

All speeds are IAS.

40,000 ft. = 260 mph
30,000 ft. = 300 mph
20,000 ft. = 400 mph
10,000 ft. = 480 mph
5,000 ft. = 505 mph

From Robert Gruenhagen's book on the Mustang.

Maximum diving speed is 505 mph under 7,000 ft. and that the max. mach
number as .75.

Hess's book states dives were done to 650 mph; but most likely once compressibility
started to show it's ugly head, the pitot tube would be varying wildly showing wrong airspeeds.

I also understand that out of trim airframes and even how a pilot reacts to his airframe
will also have effects on max dive speeds.

Hope this helps.


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## Mike Williams (Oct 26, 2006)

Hello "delcyros":

Please see Hayes' Encounter Report for 28 May 1944. Here’s the relevant section:

_Taking up pursuit again I was able to get on one of the Me-109’s which now began to dive. I fired three short bursts. After the first burst he skidded, I suppose to look back. I fired again seeing debris and canopy come off. Just as the third burst was fired it looked like the pilot started out, however at that instant strikes were noticed on and around what looked like the pilot. Then the ship actually disintegrated. I went out of control indicating 500 mph. at 20,000 ft. and so did my wing man. I picked up my element leader, Lt. Howell, quickly and covered him as he nailed a Me-109 with the pilot parachuting. We climbed back to the bombers from 12,000 ft. and continued the escort. How the enemy pilot came out of his plane at 700 mph is beyond me._

Please take careful note that Hayes records his speed as *indicating* 500 mph. He then concludes his account of this combat by noting that the enemy pilot came out of his plane at *700 mph*. Now it just so happens that 500 mph indicated at 20,000 feet is approximately 700 mph TAS. 700 mph TAS at 20,000 is approximately Mach .989. It’s not plausible that the dives actually reached those speeds. One possible explanation is that Hayes failed to account for instrument and compressibility errors when he did his quick calculation to arrive at 700 mph TAS from 500 IAS. Certainly Hayes and his wing man exceeded the P-51's recommended dive limits, and fortunately for them, their aircraft apparently were no worse from it as they went on to complete their escort mission. The Me 109 wasn’t as lucky since it "actually disintegrated" during the dive. We’ll never know if it was the bullets or structural failure.

Please see Encounter Reports of P-51 Mustang Pilots, in particular the section titled Dive, for more comments from Mustang Pilots relating to the speeds recorded during a dive while engaged in combat. 

Please see also Army Air Forces, Air Technical Command report on Dive Tests on P-51D. The report records the highest speed obtained during a test dive was a maximum true Mach Number of 0.85; concluded that the standard P-51D airplane may be safely flown to a Mach Number of 0.80; and in extreme war emergency the airplane can be dived to a Mach Number of 0.83. Read the full report for all the details.

Mike Williams

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## delcyros (Oct 26, 2006)

Thanks all, particularely Mike for the source!
A crit Mach figure of 0.75 is also closer to my equitation table.
I also expect that the racks for the underwing racks do imply some slightly lower crit Mach figure for the P-51 as used over Berlin.
505 mp/h at 20.000ft altitude imply something between 550 and 565 mp/h TAS (recalculated, factoring compressability effects), which also very well fit to Mach 0.8.

again thanks for Your comments.


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## Soren (Oct 27, 2006)

*Robert C.Curtis, American P-51 pilot:*
_"My flight chased 12 109s south of Vienna. They climbed and we followed, unable to close on them. At 38,000 feet I fired a long burst at one of them from at least a 1000 yards, and saw some strikes. It rolled over and dived and I followed but soon reached compressibility with severe buffeting of the tail and loss of elevator control. I slowed my plane and regained control, but the 109 got away. 
On two other occasions ME 109s got away from me because the P 51d could not stay with them in a high-speed dive. At 525-550 mph the plane would start to porpoise uncontrollably and had to be slowed to regain control. The P 51 was redlined at 505 mph, meaning that this speed should not be exceeded. But when chasing 109s or 190s in a dive from 25-26,000 it often was exceeded, if you wanted to keep up with those enemy planes. The P 51b, and c, could stay with those planes in a dive. The P 51d had a thicker wing and a bubble canopy which changed the airflow and brought on compressibility at lower speeds."_



*Thomas L. Hayes, Jr., American P-51 ace, 357th Fighter Group, 8 1/2 victories:*
_"Thomas L. Hayes, Jr. recalled diving after a fleeing Me-109G until both aircraft neared the sound barrier and their controls locked. Both pilots took measures to slow down, but to Hayes' astonishment, the Me-109 was the first to pull out of its dive. As he belatedly regained control of his Mustang, Hayes was grateful that the German pilot chose to quit while he was ahead and fly home instead of taking advantage of Hayes' momentary helplessness. Hayes also stated that while he saw several Fw-190s stall and even crash during dogfights, he never saw an Me-109 go out of control."_


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## Crumpp (Nov 1, 2006)

Measuring speeds in the transonic realm in the late 1940's was problematic at best. I would be highly suspect of any propeller driven aircraft achieving anything higher than Mach .8.

All the best,

Crumpp

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## delcyros (Nov 2, 2006)

> Measuring speeds in the transonic realm in the late 1940's was problematic at best. I would be highly suspect of any propeller driven aircraft achieving anything higher than Mach .8.



That´s exactly, what I think, too, Crumpp! Altough I would rather add "...other than in terminal dive" even in case this was more a problem for jet driven aircraft in this timeframe.


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## HealzDevo (Apr 2, 2007)

I think this is questionable, however the only way to really prove one way or the other would be to try to design replicas using the original methods install the computer equipment in a way that doesn't change overall weight and then conduct the testing. I still remain sceptical though that the resultant force wouldn't have ripped off the wings, and tail...


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## Zipper730 (Apr 6, 2019)

Mike Williams said:


> Please see Encounter Reports of P-51 Mustang Pilots, in particular the section titled Dive, for more comments from Mustang Pilots relating to the speeds recorded during a dive while engaged in combat.
> 
> Please see also Army Air Forces, Air Technical Command report on Dive Tests on P-51D. The report records the highest speed obtained during a test dive was a maximum true Mach Number of 0.85; concluded that the standard P-51D airplane may be safely flown to a Mach Number of 0.80


So 0.75 is like maximum safe speed in peacetime, 0.80 in wartime, 0.83 if you're in for the fight of your life and gunfire is a more certain threat to your life than the high-risk of losing your wings from high speed (a gradual pull out was needed, though), with mach 0.84 being the fastest speed that the test pilots dared go.


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## soulezoo (Apr 9, 2019)

IIRC, a KC-10 _cruises_ at .87 mach. It has thick wings too... 

Nice necro post!


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## drgondog (Apr 9, 2019)

delcyros said:


> Despite having read elsewhere that the P-51 Mustang could exceed Mach 0.8 I found those comments of an encounter report:
> 
> Pilot: Lt.Col. Thomas L. Hayes
> date: 28th of may 1944
> ...


BIG difference between IAS and TAS - both for normal reasons dealing with pressure altitude and temperatures as well as Mach corrections.

Mcr for the NAA/NACA wing was ~.75 but in comparison with P-38/F6F/F4U/Fw 190 NACA 23-016, never achieved uncontrollable 'pitch down' control forces.

The highest M no. for dives was ~ .85M and the issue was the structural damage due to Q forces.

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## grampi (Apr 10, 2019)

Soren said:


> *Robert C.Curtis, American P-51 pilot:*
> _"My flight chased 12 109s south of Vienna. They climbed and we followed, unable to close on them. At 38,000 feet I fired a long burst at one of them from at least a 1000 yards, and saw some strikes. It rolled over and dived and I followed but soon reached compressibility with severe buffeting of the tail and loss of elevator control. I slowed my plane and regained control, but the 109 got away.
> On two other occasions ME 109s got away from me because the P 51d could not stay with them in a high-speed dive. _



I can't imagine a 109 being able to outdive a P-51...


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## fliger747 (Apr 10, 2019)

Critical Mach number would be when some part of the aircraft begins to generate shockwaves. This is different than the limiting Mach number. For instance with the B747-400 one could see shockwaves standing up about 10' inside the winglets at M .90 though the certified Mach was .92. A little light shaking at M .90. My understanding the aircraft was flight tested to plus M .99 and several Asian carriers have "field tested" it in service to plus M 1.0. A limiting Mach number would exist when adverse aerodynamic effects such as shift of CL begin to arise.

Just as a guess, the D model with the bubble canopy might begin to generate a shockwave off of the canopy at a lower speed than the B model.


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## Joe Broady (Jun 2, 2019)

Mike Williams said:


> Please take careful note that Hayes records his speed as *indicating* 500 mph. He then concludes his account of this combat by noting that the enemy pilot came out of his plane at *700 mph*. Now it just so happens that 500 mph indicated at 20,000 feet is approximately 700 mph TAS. 700 mph TAS at 20,000 is approximately Mach .989. It’s not plausible that the dives actually reached those speeds. One possible explanation is that Hayes failed to account for instrument and compressibility errors when he did his quick calculation to arrive at 700 mph TAS from 500 IAS.



We can't make any accurate computation of the true airspeed or Mach at 500 mph *indicated *airspeed because we don't know the P-51 correction for "position error". That is the error due to the inaccuracies in the pitot and static pressures supplied to the airspeed indicator. Usually most of the error is in the static pressure, since it's difficult to find a place on the skin where a sample port experiences true freestream pressure.

An example was the Hellcat. At a moderate cruise speed of 140 knots *indicated* airspeed, the F6F-3 read 12 knots low and the F6F-5 reads 7 knots high with respect to *calibrated* airspeed (the speed you would see if the instrument were provided perfect samples of pitot and static pressure, and the instrument itself responded to those pressures exactly as designed). That's almost 20 knots discrepancy between two variants of the same basic airplane! The reason is that Grumman relocated the static pressure port on the -5. According to their long time test pilot Corky Meyer, that was to silence Navy complaints of the Hellcat's slow speed relative to the Corsair, and it worked. (See the book on the Hellcat he co-wrote with Steve Ginter. He says Grumman flew an F6F-3 and an F4U-1D on loan from the Navy in formation to compare top speed. It was practically a tie, but the Hellcat consistently indicated 20 knots lower, so Grumman found a new static port location which made the Hellcat match the Corsair reading.)

Getting back to the P-51, without knowledge of its position error at 500 mph we have no basis to convert IAS to CAS, the latter being the correct route to TAS. My Jeppesen CR-2 "whiz wheel" says 500 mph (435 kt) CAS and 20,000 feet pressure altitude = .92 Mach = 650 mph (565 kt) TAS.

On the other hand, the E-6B slide rule says 500 mph CAS at 20,000 feet = 685 mph TAS. That's 35 mph high because the CR-2 is designed for jet speed, while the basic design of the E-6B is from the WW2 era and ignores compressibility. The error is trifling until about .5 Mach.

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## tomo pauk (Jun 2, 2019)

Joe Broady said:


> ...
> An example was the Hellcat. At a moderate cruise speed of 140 knots *indicated* airspeed, the F6F-3 read 12 knots low and the F6F-5 reads 7 knots high with respect to *calibrated* airspeed (the speed you would see if the instrument were provided perfect samples of pitot and static pressure, and the instrument itself responded to those pressures exactly as designed). That's almost 20 knots discrepancy between two variants of the same basic airplane! The reason is that Grumman relocated the static pressure port on the -5. According to their long time test pilot Corky Meyer, that was to silence Navy complaints of the Hellcat's slow speed relative to the Corsair, and it worked. (See the book on the Hellcat he co-wrote with Steve Ginter. He says Grumman flew an F6F-3 and an F4U-1D on loan from the Navy in formation to compare top speed. It was practically a tie, but the Hellcat consistently indicated 20 knots lower, so Grumman found a new static port location which made the Hellcat match the Corsair reading.)
> ...



An informative post.
I do have a thing sticking out there, however - even when F6F-5s went through the USN and British tests, they were still ~20 mph slower than F4U-1 on same horsepower. We have USN and British data sheets where -3 and -5 are within a few mph true air speed when using same horsepower.
The XF6F-6 was slower by 20 mph than F4U-4, both used same engine and prop.


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## fliger747 (Jun 2, 2019)

Manufacturer's and service test data for WWII planes is usually at variance. In fact I generally suspect the number of significant figures one should trust. Much data was recorded on the test pilots knee board, subject to all sorts of error. Yes I could probably find a location for the static port on a Hellcat that would increase the IAS... However the point should be to produce accurate data. Individual planes varied a lot, especially ones pulled off the ramp at random.

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## Joe Broady (Jun 2, 2019)

Joe Broady said:


> On the other hand, the E-6B slide rule says 500 mph CAS at 20,000 feet = 685 mph TAS. That's 35 mph high because the CR-2 is designed for jet speed, while the basic design of the E-6B is from the WW2 era and ignores compressibility. The error is trifling until about .5 Mach.



What I should have said was "... 500 mph _EAS (equivalent air speed)_ ..." At light plane speeds EAS and CAS are practically the same, but at the speed we're talking about CAS is significantly greater than EAS, this "inflation" being due to compressibility. The more sophisticated CR-2 device compensates for that, but the E-6B doesn't. So to convert IAS to TAS with an E-6B when compressibility is significant: 1) look up IAS in the airplane's position error chart and apply the correction to obtain CAS, 2) subtract compressibility error from CAS to obtain EAS, 3) enter EAS and pressure altitude in the E-6B to obtain TAS.

USAF flight manuals from the jet era often include a graph of compressibility error. (This is purely a function of airflow physics and the same for all airplanes.) From one such chart I get a correction of 24 mph at 500 mph CAS and 20,000 feet. Thus EAS = 500 - 24 = 476 mph. When I enter that in the E-6B it says 655 mph TAS. With the CR-2 I got 650. That's better than 1% agreement, not bad for slide rules and a chart.

Someone expressed skepticism about Corky Meyer's claim of speed parity between the Hellcat and Corsair. I had the same reaction. However, his is a first hand account from a pilot who participated in the tests. Admittedly Grumman received only one exemplar of the Corsair. Meyer says it was brand new, but maybe it was a "runt of the litter"? One interesting thing I omitted was that he said the Corsair was definitely the faster at low altitude, when neutral blower was in use. The reason was that the Hellcat inhaled hot unrammed air from the accessory section in this mode, while the Corsair blower was fed cold rammed air. This was no oversight by Grumman. They chose to make the performance sacrifice in exchange for freedom from induction icing even in bad weather.


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## tomo pauk (Jun 9, 2019)

Joe Broady said:


> ...
> 
> Someone expressed skepticism about Corky Meyer's claim of speed parity between the Hellcat and Corsair. I had the same reaction. However, his is a first hand account from a pilot who participated in the tests. Admittedly Grumman received only one exemplar of the Corsair. Meyer says it was brand new, but maybe it was a "runt of the litter"? One interesting thing I omitted was that he said the Corsair was definitely the faster at low altitude, when neutral blower was in use. The reason was that the Hellcat inhaled hot unrammed air from the accessory section in this mode, while the Corsair blower was fed cold rammed air. This was no oversight by Grumman. They chose to make the performance sacrifice in exchange for freedom from induction icing even in bad weather.



In one corner we have recollections of a company's test pilot, and we can accept them in good faith. However, in another corner we have test results and official data sheets issued by two main users - USN and RN/FAA. Whenever a simmilar situation arises, I tend to believe the 1st hand data, here it will be the papers issued by USN and the British. Those papers do show 20 mph (give or take) speed advantage for Corsair at all altitudes.

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## michael rauls (Jun 9, 2019)

Another possible explanation for variations in the reported critical mach of the same type of aircraft might be that the speed of sound changes rather substantially not only with altitude but with temperature and humidity as well. A little while back I went poking round the internet about the speed of sound looking for an explanation for why in warmer/ dryer theaters the p38 seemed to have little trouble with compresability but in colder/ wetter ones compresability became a hindrance.
Three factors changed the speed of sound in the order of greatest to least; altitude( as I'm sure everyone here is already aware), temperature, and last and least influence humidity. While altitude had by far the greatest influence on the speed of sound the combination of hotter and drier or colder and more humid could change the speed of sound as much as about 25 m.p.h.( doing this from memory so that 25m.p.h might not be exactl but it's pretty close if not).
Add this to some of the other explanations others have posted like a change in pitot tube positioning and if all the variables were working in the same direction it doesn't seem like a stretch that you could have pilots reporting getting into trouble at 50 or 60 m.p.h mach reading differences at the same altitude in the same type of aircraft.


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## michael rauls (Jun 9, 2019)

tomo pauk said:


> In one corner we have recollections of a company's test pilot, and we can accept them in good faith. However, in another corner we have test results and official data sheets issued by two main users - USN and RN/FAA. Whenever a simmilar situation arises, I tend to believe the 1st hand data, here it will be the papers issued by USN and the British. Those papers do show 20 mph (give or take) speed advantage for Corsair at all altitudes.


That certainly makes sense. I'm certainly no aerodynamics expert but just eyeballing the two planes it's hard to imagine speed parity between them with the same power.
The corsair, at least in appearance, is much more streamlined.


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## swampyankee (Jun 9, 2019)

While air is not a perfect gas, it is quite close; speed of sound in air is predominantly affected by temperature: speed of sound (in meters per second) is 20.05 times the square root of the temperature (in kelvin). It is affected by humidity (mostly as water vapor has a lower molecular weight than most of the other gases that make up air); the affect of pressure is probably measurable only with really good equipment at the pressures WW2 aircraft could operate.

In warmer climates, the P-38 would be operating at lower Mach numbers.

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## llemon (Jun 13, 2019)




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## drgondog (Jun 13, 2019)

llemon said:


> View attachment 541632



This is a good representation of the individual CD vs Mach, but one must also take into account that the Spit IX CDo was about .025 to Mustang .019 at the same low RN speed of 100mph... Additionally, the CD to RN slope is steeper for the Mustang - which is why it was 20-40mph faster at all altitudes with the same engine, including up in the 0.65M range The above plot represents the *CDm/CD* drag factor to account for compressibility as shown below.

The equation kinda looks like CD = (CDp + CDcl +CDcool) *CDm/CD* + CDind. The stuff in between the ( ) is much lower for the Mustang, the Induced Drag CDind is lower for the Spit. At high speed CDcool =0 for the Mustang and varies in level flight for the Spit at ~ 0.0040.

So, one needs to take the Entire drag relationships into context.


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## BiffF15 (Jun 14, 2019)

drgondog said:


> This is a good representation of the individual CD vs Mach, but one must also take into account that the Spit IX CDo was about .025 to Mustang .019 at the same low RN speed of 100mph... Additionally, the CD to RN slope is steeper for the Mustang - which is why it was 20-40mph faster at all altitudes with the same engine, including up in the 0.65M range The above plot represents the *CDm/CD* drag factor to account for compressibility as shown below.
> 
> The equation kinda looks like CD = (CDp + CDcl +CDcool) *CDm/CD* + CDind. The stuff in between the ( ) is much lower for the Mustang, the Induced Drag CDind is lower for the Spit. At high speed CDcool =0 for the Mustang and varies in level flight for the Spit at ~ 0.0040.
> 
> So, one needs to take the Entire drag relationships into context.



Bill,

I’m trying to gonkulate your reply into layman / Biff terms. The Mustang had lower drag at “lower” Mach numbers but the drag rise eventually becomes steeper at higher Mach than the Spit? Or, why did the Mustang have a lower Mach crit than the Spit?

The Mustang is lauded as having one of the or best “mileage” numbers of WW2 piston fighters. With that in mind was it mostly contributed to the wing and the radiator “scoop” / housing being so efficient or is it more a combination of details large and small (wing, radiator installation, fit and finish)?

Cheers,
Biff


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## Peter Gunn (Jun 14, 2019)

drgondog said:


> This is a good representation of the individual CD vs Mach, but one must also take into account that the Spit IX CDo was about .025 to Mustang .019 at the same low RN speed of 100mph... Additionally, the CD to RN slope is steeper for the Mustang - which is why it was 20-40mph faster at all altitudes with the same engine, including up in the 0.65M range The above plot represents the *CDm/CD* drag factor to account for compressibility as shown below.
> 
> The equation kinda looks like CD = (CDp + CDcl +CDcool) *CDm/CD* + CDind. The stuff in between the ( ) is much lower for the Mustang, the Induced Drag CDind is lower for the Spit. At high speed CDcool =0 for the Mustang and varies in level flight for the Spit at ~ 0.0040.
> 
> So, one needs to take the Entire drag relationships into context.


Geez Bill...

My head hurts now...

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## pbehn (Jun 14, 2019)

Peter Gunn said:


> Geez Bill...
> 
> My head hurts now...


It can be summarised as "The Spitfire holds complete superiority in the propeller falling off speed range, the P-51 superior in all others".

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## drgondog (Jun 14, 2019)

BiffF15 said:


> Bill,
> 
> I’m trying to gonkulate your reply into layman / Biff terms. The Mustang had lower drag at “lower” Mach numbers but the drag rise eventually becomes steeper at higher Mach than the Spit? Or, why did the Mustang have a lower Mach crit than the Spit?
> 
> ...


Hi Biff - The primary contribution to onset drag rise leading to Mcr is the wing for both airplanes. The Spitfire delayed Mc due to thinner wing, the Mustang delayed Mcr due to the Low Drag/High Speed profile even though the wing T/C > Spit. The actual increase in the Ration of CDm/CD (incompressible flow) favored the Spit as shown in the plot above. That said, the Parasite Drag of the Mustang a.) started at a much lower value than the Spit for the same Reynolds Number, and b.) as a result would cross over around 0.83-.85M where the Mustang was in dangerous territory due to Q loads. Recall that the Mustang did Not fail in tests up to .85 Mach but suffered significant damage to flap and some rivet popping/skin buckling. At .9M the Spit lost its prop and suffered major damage to cowl for a dead stick landing.

The Plot in context is strictly the RATIO of Drag Rise over Incompressible Speed range to account for incompressibility. The Rate of CD increase was greater for the Mustang but the cumulative Total Drag was lower than the Spit until the 0.8-0.85M envelope.

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## drgondog (Jun 14, 2019)

pbehn said:


> It can be summarised as "The Spitfire holds complete superiority in the propeller falling off speed range, the P-51 superior in all others".



What you said... LoL


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## pbehn (Jun 14, 2019)

drgondog said:


> What you said... LoL


The picture of the spitfire that actually did mach 0.9 (or there abouts) is not good viewing.

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## special ed (Jun 14, 2019)

This kind of math is exactly why I don't have a degree today.

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## Zipper730 (Jun 14, 2019)

special ed said:


> This kind of math is exactly why I don't have a degree today.


Yeah, I never was all that spectacular at math...


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## soulezoo (Jun 14, 2019)

My Degree says DD214 at the bottom.

Thanks Drgondog, your posts always leave me having learned something... even if it makes my head hurt as well.

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## special ed (Jun 14, 2019)

I have discovered I am left brained in logic and organization but right brained in art and possibly language. I have always envied those who could look at an equation and come up with the answer in their head. An example was my last roomie at USAFA. The graded reviews lasted 4 hours and after returning, having only answered about 2/3rds , my roomie is resting on his bunk, staring at the ceiling. I asked," How did you do?" He answered, 'You remember question 38? I think I put the decimal point in the wrong place."

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## pbehn (Jun 14, 2019)

special ed said:


> This kind of math is exactly why I don't have a degree today.


I was always told by my maths teacher that maths is a language, a beautiful language. To me it is a second language so I have to translate the expressions back to English. If you transpose the mathematical expressions for an English description you get a beautiful and elegant explanation but without the precision or absolute truth that mathematics has. To me the discussion based on the graph is misleading to laymen like me, it took me a long time to realise that it is largely theoretical, but discussions in mathematics always tend towards limits, calculus is used to find and define limits. Mach 0.7 is 532 MPH at sea level, below that the P-51 held all the aces not only for the wings but also cooling drag, drag on the fuselage/cockpit and actual fit finish of the non theoretical plane in service. Not shown on the graph, which is about the limits of speed, faster even than the speed in most combats, is that at any given speed the P-51 used less fuel, and for any cruise setting it went faster and therefore further for a given amount of fuel. That is the area of the graph below M0.6

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## drgondog (Jun 14, 2019)

michael rauls said:


> That certainly makes sense. I'm certainly no aerodynamics expert but just eyeballing the two planes it's hard to imagine speed parity between them with the same power.
> The corsair, at least in appearance, is much more streamlined.


The F4U-1 in 'as delivered/unsealed' condition to Langley for full scale wind tunnel testing had a CDo of 0.0284, the F6F-3 had a CDo of 0.0293 (Compared to P-51B at 0.020. Notably the Mustang CDo is overstated due to zero Meredith effect of the exiting heated radiator heat in a contracting plenum. 

For the purposes of the Plot above of P-51 CDo vs Spitfire, if you peek back in the .1 to .5M range the CDo (scale model wind tunnel results) of the Mustang is 0.017 to the Spit value of ~0.023

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## Peter Gunn (Jun 17, 2019)

drgondog said:


> The F4U-1 in 'as delivered/unsealed' condition to Langley for full scale wind tunnel testing had a CDo of 0.0284, the F6F-3 had a CDo of 0.0293 (Compared to P-51B at 0.020. Notably the Mustang CDo is overstated due to zero Meredith effect of the exiting heated radiator heat in a contracting plenum.
> 
> For the purposes of the Plot above of P-51 CDo vs Spitfire, if you peek back in the .1 to .5M range the CDo (scale model wind tunnel results) of the Mustang is 0.017 to the Spit value of ~0.023


See... there you go again...


ASPIRIN... STAT!


Wait! Some dim light clicks on in my noggin... Mustang slippery, Spit, not AS slippery, Mustang use less fuel, go farther faster with same fuel, maybe even able to go faster with same power... grunt... Peter begin to understand... also forget use pronouns...

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## Shortround6 (Jun 17, 2019)

Peter Gunn said:


> .. Mustang slippery, Spit, not AS slippery, Mustang use less fuel, go farther faster with same fuel, maybe even able to go faster with same power... grunt... Peter begin to understand... also forget use pronouns...



Too much Star Wars you watch, think I

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## Snowygrouch (Jun 17, 2019)

I dont know enough about aerodynamics to contribute directly, but if anyone (who can read German) wants this I can forward via download link.

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## BiffF15 (Jun 17, 2019)

Shortround6 said:


> Too much Star Wars you watch, think I



Or Mongo from Blazing Saddles.

😉

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## wuzak (Jun 18, 2019)

pbehn said:


> The picture of the spitfire that actually did mach 0.9 (or there abouts) is not good viewing.
> View attachment 541921



Several test flights were undertaken to 0.9M, this was the result of one of them.

There were successful flights to 0.9M and some where other failures occurred, such as when the supercharger blew up. In the above picture it was a reduction gear housing failure which led to the propeller parting ways with the fuselage, after which the aircraft experienced some violent manoeuvres.

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## wuzak (Jun 18, 2019)

BiffF15 said:


> The Mustang is lauded as having one of the or best “mileage” numbers of WW2 piston fighters. With that in mind was it mostly contributed to the wing and the radiator “scoop” / housing being so efficient or is it more a combination of details large and small (wing, radiator installation, fit and finish)?



Biff, while the wing profile and the radiator installation were big factors, overall it was a combination of many factors that saw the P-51 have superior speed by 20-40mph than the Spitfire IX.

An example is that the 20mm cannon barrels protruding from the leading edge of the Spitfire's wing cost as much as 8mph.

Fit and finish was certainly a factor, as was the cockpit canopy (Spitfire's was steeper).

The Spitfire's radiator(s) could have worked better, even in the historical location under the wings (Supermarine did propose an under fuselage radiator).

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## pbehn (Jun 19, 2019)

wuzak said:


> Several test flights were undertaken to 0.9M, this was the result of one of them.
> 
> There were successful flights to 0.9M and some where other failures occurred, such as when the supercharger blew up. In the above picture it was a reduction gear housing failure which led to the propeller parting ways with the fuselage, after which the aircraft experienced some violent manoeuvres.


Some accounts say in addition to losing the prop the wings were distorted backwards. My point was that the discussion is mainly a theoretical one about air flow. When you actually test it physically all sorts of things happen because the air frame is beyond what it was designed for. It may pop some rivets, or bend something or something fall off. To get a plane to go to M0.9 and guarantee being able to land with no damage would need a complete re design of almost everything.

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## tomo pauk (Jun 19, 2019)

wuzak said:


> Biff, while the wing profile and the radiator installation were big factors, overall it was a combination of many factors that saw the P-51 have superior speed by 20-40mph than the Spitfire IX.
> 
> An example is that the 20mm cannon barrels protruding from the leading edge of the Spitfire's wing cost as much as 8mph.
> 
> ...



We can also recall that wartime Spitfires were mostly with uncovered main wheels wells, plus there is rear view mirror to steal a few mph.

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## DarrenW (Feb 4, 2022)

drgondog said:


> This is a good representation of the individual CD vs Mach, but one must also take into account that the Spit IX CDo was about .025 to Mustang .019 at the same low RN speed of 100mph... Additionally, the CD to RN slope is steeper for the Mustang - which is why it was 20-40mph faster at all altitudes with the same engine, including up in the 0.65M range The above plot represents the *CDm/CD* drag factor to account for compressibility as shown below.
> 
> The equation kinda looks like CD = (CDp + CDcl +CDcool) *CDm/CD* + CDind. The stuff in between the ( ) is much lower for the Mustang, the Induced Drag CDind is lower for the Spit. At high speed CDcool =0 for the Mustang and varies in level flight for the Spit at ~ 0.0040.
> 
> So, one needs to take the Entire drag relationships into context.


At first glance one wouldn't believe that the FW 190A had less parasitic drag than the Spitfire, giving it less total drag with both having roughly the same induced drag. Greg (not GregP but the one on YouTube) however performed calculations which proved that this was indeed the case.

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## drgondog (Feb 5, 2022)

DarrenW said:


> At first glance one wouldn't believe that the FW 190A had less parasitic drag than the Spitfire, giving it less total drag with both having roughly the same induced drag. Greg (not GregP but the one on YouTube) however performed calculations which proved that this was indeed the case.



I listened to the entire presentation. Several of Greg's assumptions were well reasoned but collectively made his conclusion subject to questions. 

Further, he didn't quite grasp what Lednicer's methodology of CFD yielded with respect his drag analysis. Nor was it particularly elegant to make assumptions about Exhaust Gas Thrust - 

but I can't disagree his conclusions that the FW 190A had less total drag than the Spit IX at medium to high speeds where parasite drag dominates. 

The major difference maker was the Cooling System drag arrangement of the Spit IX attempting a Meridith System design to reduce the drag of the inlet and arrangement of the oil/glycol radiators. 

The Wing of the Spit IX (save the cooling system and 'open' wheel well) should have less profile drag due to thinner wing as well as significantly less Induced Drag. I suspect that the Spit IX may have less total drag at speeds up to optimal cruising speed for distance, but because the oswald efficiency factor should be much higher for elliptical wing Spit, the Induced drag must be much lower for the Spit - But *Drag total = Drag (parasite , profile) + Drag (induced)*. For given speeds equal to each other, this alone strongly favors the Fw 190A as having less Parasite/profile drag if their total drag values are nearly equal for a given speed and altitude.


Max L/D= CL/CD, is at the Velocity for which CDtot=CDi. The drag polars should have notable difference for minimum velocity required for level flight (lower for Spit)

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## DarrenW (Feb 5, 2022)

drgondog said:


> I listened to the entire presentation. Several of Greg's assumptions were well reasoned but collectively made his conclusion subject to questions.
> 
> Further, he didn't quite grasp what Lednicer's methodology of CFD yielded with respect his drag analysis. Nor was it particularly elegant to make assumptions about Exhaust Gas Thrust -
> 
> ...


Thanks Bill for chiming on on this. I knew you could help dissect this further and give credence for or against Greg's hypothesis.

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## Snautzer01 (Feb 7, 2022)



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## Snautzer01 (Feb 7, 2022)



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## drgondog (Feb 7, 2022)

Snautzer01 said:


> View attachment 657234


I had Hoerner's Fluid Dynamic Drag as one of my Aero Textbooks in undergrad. Still have the book. 

Clark Millikan PhD at CalTech (along with Von Karman) had more influence in the development of assumptions and calculations for Performance Estimates at NAA, largely because of his 'disciple' Ed Horkey who was hired right out of CalTech.. 

I still occasionally draw on both Hoerner and Millikan's "Aerodynamics of the Airplane' when I am pondering what I have forgotten over 55 years.

Millikan was a key advisor on Arnold's technology Board and frequently served as a conduit to Arnold.

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## Snautzer01 (Feb 7, 2022)

Both are pdf so if anybody has use for it ? 

 Wurger
please advise if it is ok?. P-51 is from 1945 ( should be good Hoerner 1965 i am not sure about.


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## Wurger (Feb 7, 2022)

Snautzer01
both pics work. I can see them if you meant that.


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## Snautzer01 (Feb 7, 2022)

Wurger said:


> Snautzer01
> both pics work. I can see them if you meant that.


No full books as pdf i can put up.


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## Wurger (Feb 7, 2022)

Due to the possible copyrights I wouldn't post them here.

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## drgondog (Feb 8, 2022)

Snautzer01 said:


> Both are pdf so if anybody has use for it ?
> 
> Wurger
> please advise if it is ok?. P-51 is from 1945 ( should be good  Hoerner 1965 i am not sure about.


The NACA report should be reproduceable but credited.


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## tomo pauk (Feb 8, 2022)

That NACA report for the P-51B is here: link

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## msxyz (Feb 9, 2022)

An interesting question regarding the reports mentioned in this thread. Were the speeds measured with 'modern' probes? The instruments available at the time gave incorrect readings once the speed climbed above 500mph/800kmh; a typical example was the diving speed of many Italians planes that the tester pilots enthusiastically reported. Ing. Castoldi (of Macchi fame) was one of the first that desumed that the probes of the time ceased to report accurate airspeeds above Mach 0.75-0.8 (hence the 'true' airspeed was somewhat lower than what the instrument would show)

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