Defining and explaining "Corner Speed"

[drgondog]

exactly.
I don't see how anyone could be a fan of aviation, particularly WW2 fighters, and not have an understanding of mach tuck.

Knowing that 'mach tuck' results in a pitch down is different from understanding why it happens.

There are also some other contributing factors to the actual tuck, which may not actually be related to compressibility but instead the actual drag profile of the aircraft and how the air screw distributes air over the wing.

While the rotational flow in the stream tube contributes to turbulent flow over much of the inner wing and horizontal stabilizer - that is more about lessening the effectiveness of the hor.stab to recover than the cause of pitch down

If the pilot throttles back the slowing airscrew and this causes more drag. It was found that pilots could recover from tuck by increasing throttle in the dive, where decreases would cause a more severe tuck. Again, this is also outlined in the manuals, particularly in later manuals where they may have had a better understanding of emergency procedures and compressibility.
In reviewing a Wright Field test for the P-47 dive flaps, the amount of tuck was from 65 to 67 degrees,(4 seconds of dive) a mere 2 degrees. It may have steepened more if the pilot had not deployed dive flaps, but also test pilots may have also had a better understanding in how to combat mach tuck or to minimize its effects.

The dive 'flap', similar in design to P-38 device, had the same objective - namely slow the rate of descent by increasing drag..

I know the Mustang had specific variants with thinner wings and lower load limits.

The Mustang from XP-51 through P-51A and B/C/D/K all had the same airfoil with the same thickness. NAA/NACA 45-100 had a 14.8 thickness ratio with max thickness at 45% chord. the only difference was in the D/K model wing Root which was longer than the earlier versions. The P-51H actually had a Higher t/c with the NACA 66-(1.8)15.5 = 15.5% T/c ratio.

The load limits have nothing to do with the airfoil per se - It is all about individual component allowable stresses at design weights. The P-51D had essentially the same components as the original design. The XP-51 was designed to be an 8G Limit/12G Ultimate at 8000 pounds. The problem for the D/K is that the GW grew significantly with the additions of extra guns and ammo and internal fuel tanks - so, for a normal mission the Limit Load and Ultimate Load limits decreased significantly - as explained in my first couple of posts.

Its apples to oranges when comparing them to the wing thickness of the P-47, The P-47 had the Republic S-3 airfoil which is an 11% T/c so, like the Spit, it had a smaller thickness to Chord ratio which assisted in preventing onset of Mcrit for comparable design airfoils with max 'T' between .24 and .3 i only mention it because perhaps my reading was not in the context of the P-51D which had higher load limits and wing thickness than previous variants.

Not true as explained above. In fact all the earlier versions were more sound structurally due to lower Gross Weights. The P-51H was designed to 7.3 Limit and 11.0 G Ultimate at 8000 pounds but because the GW was less by 600+ pounds than the D/K, the 51H were pretty equal all around in structural integrity

So saying the P-47 was better suited to handle mach tuck, may not have included the P-51D.
It doesn't take long to find several examples of P-51 pilots diving from 20k ft in vertical dives while chasing or eluding enemy aircraft. It was certainly a very capable fighter in that capacity.

The Jug with the dive flap (-30? and above) would slow down faster than the 51 which could be an advantage when chasing a 109.

In various dive tests to compare the two fighters, they were extremely close on maxximum sustained dives - each around .85 which is ~ .8 to .9 above the placard for each in their respective manuals.

The Jug gets the edge but its not enough to make a difference in a chase.

 

[renrich]

I am not an engineer like youall but one thing that I don't hear mentioned in this most interesting dialogue you have posted about mach tuck is that I understand that because the speed of sound varies according to air temperature, and since air temp rises as the airplane gets lower, what might be mach .80 at 25000 feet is something less than that at 20000 feet and so on. Therefore it seems to me that if mach tuck occurs, for instance at mach .80, as soon as the airplane gets lower, where the air is warmer, even if his TAS is the same, his mach number is lower and the mach tuck goes away.

An example of this is in
"The Great Book of World War Two Airplanes". During the Korean War, Ensign Dan Bryla, launched from USS Valley Forge, was detailed to bomb a hydro electric plant in his Corsair. He nosed over into a steep dive from 17000 feet. Soon he noticed intense buffeting and vibration which he interpreted as the onset of compressibility. He jettisoned his bombs and brought back the throttle to reduce speed while pulling back on the stick. The Corsair rolled inverted and at the speed he was traveling the ailerons could not be deflected enough to roll back upright. Still in a dive and inverted Bryla tried to pull through a half loop but this steepened the dive, rendering the elevators almost as useless as the ailerons. Finally, at about 4000 feet, with both hands pulling back on the stick and one foot on the left rudder pedal, he managed to bring the AC through a partial loop and into level flight and subsequently landed on his carrier. This account is from a Navy report published in 1953 and the mission must have been over North Korea in the winter with very cold air temps.

Incidently, Bryla was in a great deal of discomfort flying back to the carrier. It was found that he had broken his left hip and strained back and shoulder muscles in his attempts to pull out of the dive. The Corsair returned to duty the next day.

 

[drgondog]

I am not an engineer like youall but one thing that I don't hear mentioned in this most interesting dialogue you have posted about mach tuck is that I understand that because the speed of sound varies according to air temperature, and since air temp rises as the airplane gets lower, what might be mach .80 at 25000 feet is something less than that at 20000 feet and so on. Therefore it seems to me that if mach tuck occurs, for instance at mach .80, as soon as the airplane gets lower, where the air is warmer, even if his TAS is the same, his mach number is lower and the mach tuck goes away.

Ren - true, during the course of the dive the air is denser and as a result drag is higher, which causes a steady reduction of velocity to below Mcrit (for WWII aircraft).. at the point where the airflow over the top of the wing goes below Mcrit and the wake turbulence reduces, the pressure distribution moves toward 'high speed' normal.

That means all the Stability issues associated with CMac dominating the contribution of the stab/elevator goes away.

It is in this region that P-38 and P-47 pilots would start to see their 'aft' stickforce being effective and start their dive recovery.

An example of this is in
"The Great Book of World War Two Airplanes". During the Korean War, Ensign Dan Bryla, launched from USS Valley Forge, was detailed to bomb a hydro electric plant in his Corsair. He nosed over into a steep dive from 17000 feet. Soon he noticed intense buffeting and vibration which he interpreted as the onset of compressibility. He jettisoned his bombs and brought back the throttle to reduce speed while pulling back on the stick. The Corsair rolled inverted and at the speed he was traveling the ailerons could not be deflected enough to roll back upright. Still in a dive and inverted Bryla tried to pull through a half loop but this steepened the dive, rendering the elevators almost as useless as the ailerons. Finally, at about 4000 feet, with both hands pulling back on the stick and one foot on the left rudder pedal, he managed to bring the AC through a partial loop and into level flight and subsequently landed on his carrier. This account is from a Navy report published in 1953 and the mission must have been over North Korea in the winter with very cold air temps.

Incidently, Bryla was in a great deal of discomfort flying back to the carrier. It was found that he had broken his left hip and strained back and shoulder muscles in his attempts to pull out of the dive. The Corsair returned to duty the next day.

Lucky guy. The 'do not' exceed velocity for an F4U in a dive was much lower than for a Jug or Mustang.

 

[renrich]

Bill, unless I am mistaken though, since the air gets progressively warmer at lower altitudes then the effects of compressibility go away if the same speed is maintained since the speed of sound varies only as the air temp.

An exaggerated example might be: a supersonic airplane can reach Mach one at 40000 feet AGL where the air temperature is minus 50 degrees F if he is making 500 mph TAS. That airplane at 500 mph is well into compressibility.

Another example is that I have read that the F80 at very high altitudes, around 40000 feet, had a very small envelope to fly in, because, since the speed of sound was so low at that altitude, if flown too fast it would feel the effects of compressibility. Yet, if flown to slow, it's wings could not maintain lift in that thin air and it would stall out. It did not have that problem lower down because the speed of sound was a lot higher.

That same airplane doing 500 mph TAS at 10000 feet over Texas in the summer where the air temperature is around 75 degrees F is not close to Mach one and therefore feels no effects of compressibility. I have seen unlimited class warbirds at Sherman, Texas( why would we name a town for that SOB?) doing around 500 MPH in a shallow dive beginning the pylon races and they obviously were not into compressibility.

What I am trying to say, (poorly) is that as an airplane into compressibility problems at high altitudes in a dive will automatically gradually get out of those problems even if he maintains his speed at lower altitudes because the air is warmer and the speed of sound is higher.

The Corsair, according to Dean was limited to Mach .72 at higher altitudes and at 10000 feet was limited to .70 Mach or less if a high G pullout was attempted.

 

[billswagger]

The Mustang from XP-51 through P-51A and B/C/D/K all had the same airfoil with the same thickness

In that case, then the P-47 was considered to be more structurally sound for compressibility dives than the Mustang, keeping in mind that the actual speed attained by the Mustang would be slightly higher before it entered compressibility.
They did make thinner winged mustangs with lower load limits but i don't have information on where they served. It was the thought of British designers to make a design that did not meet the requirements of the US load limits to see how the sleeker design benefited in speed.
That may have been where i got that idea from.

since the air gets progressively warmer at lower altitudes then the effects of compressibility go away if the same speed is maintained since the speed of sound varies only as the air temp.

True. Pilots usually reported compressibility problems above 25,000ft. Compressibility usually keeps the aircraft from falling faster because of the high increase in drag. In some ways its rare to see a plane gain enough speed to maintain compressibility through out the dive.

 

[drgondog]

In that case, then the P-47 was considered to be more structurally sound for compressibility dives than the Mustang, keeping in mind that the actual speed attained by the Mustang would be slightly higher before it entered compressibility.

Bill - recall that while the airfoil section of the P-47 was ~11% versus 14.8% for all versions of production P-51s (except 8) the P-47 had a 87.5 inch mean chord while the 51 had a 79.6" mean chord.

14.8% 79.6 of =11.8" actual max thickness on that portion of the wing while 11% of 87.5" = 9.6" actual thickness.

This gave the Mustang 2+ extra inches for a main spar which is signifiv=cant for a beam/torque box designed to take high bending loads.

There is no way to conclude that a P-47 was more structurally sound based on the wing dimensions. Only a detailed analysis would yield where the actual projected 'weakest' condition would be - but both were designed to the same 8G Limit/12G ultimate for a specific design gross weight - and both grew in GW throughout the war resulting in less 'structural integrity' when compared to lower gross weight. I do NOT know what the P-47M and N may have changed with wet wings.. but most of the comparisons are between P-51B/D and P-47D.

They did make thinner winged mustangs with lower load limits but i don't have information on where they served. It was the thought of British designers to make a design that did not meet the requirements of the US load limits to see how the sleeker design benefited in speed.
That may have been where i got that idea from.

Actually no. The P-51H had a NACA 66-(1.8) 15.5 which has a t/c ratio of 15.5 > 14.8 for the NAA 45-100 on all the earlier series P-51 through D/K.

What is correct about the H is that it was designed from the very beginning to be 7.33G (vs 8) Limit Load as a constraint on the weight reduction program - but at the end of the day, when you compare Mission GW for both variants the actual allowable loads were the same for all practical purposes.


True. Pilots usually reported compressibility problems above 25,000ft. Compressibility usually keeps the aircraft from falling faster because of the high increase in drag. In some ways its rare to see a plane gain enough speed to maintain compressibility through out the dive.

Practical compressibility occurs when the velocity equals M=1 at a local point on the airfoil ~ 25% chord for conventional wings and closer to 40% for Mustang. The Mustang Wing, because of the more gradual pressure gradient along the chord, reached M=1 and initiated separated later than say an equal t/c for a conventional wing of the day.

Having said this, the M=1 varies from 1116 fps (760mph) at SL, to 1077 fps at 10,000 to 1036 fps (706 mph) at 20,000 to 1016fps (692mph). That physical existance is the same for all the fighters. What is different is how the airfoil/airframe influences the local velocities, and in particular, over the wing. The P-38 experienced local M=1 at a much lower TAS than the Mustang (or the P-47).

If you go back to the NAA/Mustang Corner Speed/G Limit diagram on the first post - you will see the 'vertical line' out aroung 505mph. That is where the Dynamic Pressure Loads are so high that the airframe has reached 8g applied loading and begins to bend the airplane. At SL, 505mph is about .65 M

 

[billswagger]

There is no way to conclude that a P-47 was more structurally sound based on the wing dimensions.

Certainly, there is much more to structural stability than the wings. There is the tail section, the nose and canopy, etc.
It was the general thought of pilots that the P-47 could be dove more aggressively, where P-51s were found to fold a wing when attempting to dive like a P-47.

 

[drgondog]

Certainly, there is much more to structural stability than the wings. There is the tail section, the nose and canopy, etc.
It was the general thought of pilots that the P-47 could be dove more aggressively, where P-51s were found to fold a wing when attempting to dive like a P-47.

Yes - but if one a/c is designed to 8G Limit and compared to another a/c also designed to 8g Limit load - and both are at design Gross weight, or both are the same percentage overload - then both should behave similarly to the same applied loads. Every flight safety component/sub component was designed to 8G Limit with 1.5 safety factor for Ultimate.

The wing is the usual suspect for symmetrical loads and the tail is the usual suspect for asymmetric loads - there are examples of both ships failing in a dive. AFAIK there was no tendency of one over the other in number of incidents.

I know for example that the 355th FG had two fatal accidents (non-combat) due to eppenage loss of a P-47 in dives in Sept and Dec 1943. There were no such accidents for the Mustang in the 355th.

Having said that, the 8th AF P-51B/C had several structural failures traced to uplocks failing to restrain main gear in a high G pullout, popping the gear down and causing a catastrophic failure of the wing, as well as losing the tail in a high speed slow roll or snap roll. There were also suspected failures of the ammo doors popping open in a high speed dive causing the wing to fail.

 

[bobbysocks]

I know for example that the 355th FG had two fatal accidents (non-combat) due to eppenage loss of a P-47 in dives in Sept and Dec 1943. There were no such accidents for the Mustang in the 355th.

what was the reason the eppenage bent or broke from the 51s prior to the mod which re-inforced of the tail section on the later D models? was it what year did they add this? I do not know of fatalities but do know they had several instances of bending or breaking off....hence the mod.

 

[drgondog]

Bill, unless I am mistaken though, since the air gets progressively warmer at lower altitudes then the effects of compressibility go away if the same speed is maintained since the speed of sound varies only as the air temp.

Essentially yes

An exaggerated example might be: a supersonic airplane can reach Mach one at 40000 feet AGL where the air temperature is minus 50 degrees F if he is making 500 mph TAS. That airplane at 500 mph is well into compressibility.

Ren - M=1 @ 659mph at 40K. If the a/c is doing 500TAS, that is about .75. A Mustang is definitely in compressibility but an F-106 might not be because of the much thinner wing and whitcomb area rule fuselage.

Another example is that I have read that the F80 at very high altitudes, around 40000 feet, had a very small envelope to fly in, because, since the speed of sound was so low at that altitude, if flown too fast it would feel the effects of compressibility. Yet, if flown to slow, it's wings could not maintain lift in that thin air and it would stall out. It did not have that problem lower down because the speed of sound was a lot higher.

This is more of an air density issue than a Mcrit issue. For both the F-80 and say, the U-2 at their relaltive ceilings, their max speed is very close to the minimum speed to support level flight - so they are on ragged edge of a stall.. the same applies to a Me 109 or Ta 152 or P-51H at altitudes greater than 42000 feet.

That same airplane doing 500 mph TAS at 10000 feet over Texas in the summer where the air temperature is around 75 degrees F is not close to Mach one and therefore feels no effects of compressibility. I have seen unlimited class warbirds at Sherman, Texas( why would we name a town for that SOB?) doing around 500 MPH in a shallow dive beginning the pylon races and they obviously were not into compressibility.

Actually Ren - that big bore racer Dago Red doing 505 mph on the deck in a straightaway is in fact entering compressibility for a Mustang @ ~.65 M

What I am trying to say, (poorly) is that as an airplane into compressibility problems at high altitudes in a dive will automatically gradually get out of those problems even if he maintains his speed at lower altitudes because the air is warmer and the speed of sound is higher.

Yes

The Corsair, according to Dean was limited to Mach .72 at higher altitudes and at 10000 feet was limited to .70 Mach or less if a high G pullout was attempted.

The Mustang and Jug had limit dive speeds about 60mph (IIRC) above the F4U and more than that re: P-38 - but both the Jug and Mustang have been pushed close to .85M.

 

[renrich]

I was only using the the speed of 500 mph TAS at 40K feet as an example of the speed of sound being lower at high altitude where the air is colder. I knew it was probably inaccurate. My recollection is that at SL, it is about 750 mph.

Dago Red was one of the AC in that race and if I am not mistaken, it was the winner. I have photos somewhere. There was a Yak in the race but he did not get off the ground. The Super Corsair was also in the race as well as a number of Mustang types. We were told by the announcer that when the race was declared on and the planes were in this shallow dive toward the pylons that they were doing 500 mph. That may have been an exaggeration. This was about 1990-92. I think the pace plane might have been an L39.

I learned all about Mach tuck from the British film, "Breaking the Sound Barrier" The airplane was called "Prometheus" and it was a Supermarine "something" The pilot on the radio was screaming, "Nose heavy, trimming back!"

 

[billswagger]

Yes - but if one a/c is designed to 8G Limit and compared to another a/c also designed to 8g Limit load - and both are at design Gross weight, or both are the same percentage overload - then both should behave similarly to the same applied loads.

However, both did not behave similarly to the same applied loads, nor did either behave similarly in dives nearing or exceeding Mcrit other than tuck.

For that reason its safe to say that loads exerted on either airframe is disproportionate despite having similar limiting factors.
Yaw was found to be a dangerous factor in dives, even with the P-47 because it exerts tremendous pressure on the tail frame. Pilots were advised to center the ball during the dive otherwise there was eminent danger of breaking the tail frame. The p-51 experienced excessive yaw while entering Mcrit, and that could be the difference if such yaw could not be trimmed or countered with rudder force. Such yaw may have meant that the load amount was not symmetrical and one wing would be handling an excessive load amount compared to the other.
This is supported by more specific reports saying that the Mustang was found to fold a wing while matching dives with a P-47, while most pilots felt that exceeding or entering compressibility in a P-47 was not as dangerous and somewhat more predictable upon recovery.

To bring the thread back on topic, i would expect similar cornering speeds between the P-47 and P-51 given similar load factors.

 

[drgondog]

However, both did not behave similarly to the same applied loads, nor did either behave similarly in dives nearing or exceeding Mcrit other than tuck.

Oh, how were they different?

increased lift increases altitude, applying ailerons causes a rolling moment, etc, etc. As to dives nearing and exceeding Mcrit how disd they depart in behavior other than 'tuck' differences? I grant the Mustang had a tendency to yaw to the right, controllable by rudder - but what did you have in mind?

For that reason its safe to say that loads exerted on either airframe is disproportionate despite having similar limiting factors.

Disproportionate in what way? sources, metrics, examples?

Yaw was found to be a dangerous factor in dives, even with the P-47 because it exerts tremendous pressure on the tail frame. Pilots were advised to center the ball during the dive otherwise there was eminent danger of breaking the tail frame. The p-51 experienced excessive yaw while entering Mcrit, and that could be the difference if such yaw could not be trimmed or countered with rudder force. Such yaw may have meant that the load amount was not symmetrical and one wing would be handling an excessive load amount compared to the other.

Bill, the point is that both exhibited unpleasant yaw characteristics, both had solutions, and if the solutions were applied, the airframe survived. BTW there never was a dive envelope in which the P-51 rudder could NOT correct the resulting yaw. In fact the Reverse Rudder Boost kit was developed to INCREASE the rudder pedal force required to crank in rudder so as to not over stress the tail during the dive.

As to asymmetrical load - when either rudder is applied or yaw is experienced an assymetric load is being applied... be it trim in a dive, or a roll, etc.

This is supported by more specific reports saying that the Mustang was found to fold a wing while matching dives with a P-47, while most pilots felt that exceeding or entering compressibility in a P-47 was not as dangerous and somewhat more predictable upon recovery.

The 'fold a wing' experience was specifically caused during pullout when the early B/C models main gear dropped under the high g pullout and when forcing the gear door to open caused a huge spike in the Q load.. this was fixed with wheel uplock kits.

To bring the thread back on topic, i would expect similar cornering speeds between the P-47 and P-51 given similar load factors.

Only if CLmax is the same (which they are not) -

Given equal CLmax, then equivalent GW to Design Weight ratios and given the same design philosophy of 8G Limit/12G ultimate - then the corner speed profile betwen flight and accelerated stall is the same. The end state design limit as shown in forst post at 505 mph is based on Q load and presumably near the same for both ships.

 

[bobbysocks]

The 'fold a wing' experience was specifically caused during pullout when the early B/C models main gear dropped under the high g pullout and when forcing the gear door to open caused a huge spike in the Q load.. this was fixed with wheel uplock kits.

dr, what were the circumstances they dropped gear? were they trying to create drag in a high speed dive to slow down?

 

[FLYBOYJ]

, what were the circumstances they dropped gear? were they trying to create drag in a high speed dive to slow down?

The landing gear can be deployed if the G limit of the aircraft is exceeded, basically the wing structure twists to the point where the uplocks disengage and there is enough force to bring down the gear. If this happens at high speed, other things are quickly going to disintegrate.

 

[bobbysocks]

Oh... so this was an unintentional deployment?? structure flexing basically unlatched the gear from the up position? i thought hydraulics would have kept them in place..

 

[FLYBOYJ]

Oh... so this was an unintentional deployment?? structure flexing basically unlatched the gear from the up position?

Yes

i thought hydraulics would have kept them in place..

No - after the retraction line pressue in the up side of the hydraulic lines go to zero and the uplocks usually hold the gear in place. I don't think you want to fly around with 1500 psi inside the wheel well.

 

[Zipper730]

drgondog

Post #1: 12/21/10

All interesting topics and equally worth discussing - but this thread is about the huge dissemination of blivet on the subject of CORNER SPEED.

The first diagram is the Corner Speed Diagram prepared by North American Aviation to insert into the P-51D Pilots Handbook. Note carefully the message at the bottom which states that the Corner Speed calculation is for 8,000 pound Gross Weight and that the G load allowables for each condition must be factored by GWactual/64000 pounds.

And this determines the maximum g-load allowable?

Note the 'accelerated stall' area sets one boundary of the lower speed threshold.. so a 3G sustained turn at 160mph at 8000 pounds on the deck is on the threshold for departure but not structural limit and not corner speed.

Just to be clear, when you say sustained turn: Do you mean the ability to hold the g-load in a level-turn without a loss of speed, or the ability to hold it for more than a fraction of a second before immediately stalling?

I say this not to be pedantic, but some terms change a little over time: Modern day at least, it means the maximum g-load that could be pulled level without loss of speed.

Note that at 6G the sustained turn at ~230mph is at stall but NOT Corner Speed. Note@ 8G at ~ 260 mph at 8000 pounds at sea level the airframe has reached CORNER SPEED.

Is corner velocity the same as maneuvering speed, and isn't there a mathematical formula based on computing this by using the square root of the g-load times the stall speed?

More later - but Note for the second (conceptual) diagram that the Corner Speed at ~ 195mph is at the 6 "G" load for Design Limit and that Distortion (non elastic deformation) begins

When you say non-elastic I assume you mean permanent bending to the structure that does not contribute to failure?

BTW I have no idea why the left value indicators for 6G load has a +9 on the far right

I would have thought a different weight would have explained it.

Post #9: 12/21/10

Very True (although d/dt (mV) will take care of the change in mass with respect to time with greater precision than the change in Velocity for all the other reasons mentioned

d/dt (mV): Isn't that something like f=ma? I vaguely remember this formula, but I honestly don't know what units I'm supposed to put in.

Post #11: 12/21/10

The Pony started the drag rise around .65 M, the placard was for .75 and the highest achieved in dive was .83-85M depending on the belief system around the instruments.

Was the aircraft fitted with normal instrumentation used by the USAAF, the RAF, or specialized instrumentation?

The Jug with the dive flap (-30? and above) would slow down faster than the 51 which could be an advantage when chasing a 109.

Just do be clear

1. When you say -30, you mean P-47D-30 right?
2. Why would you want to slow down while in the dive? I thought the purpose of a dive was to speed up until the pullout at least.

In various dive tests to compare the two fighters, they were extremely close on maxximum sustained dives - each around .85 which is ~ .8 to .9 above the placard for each in their respective manuals.

I assume you're talking a P-51B/D normal and P-47D-30 with dive-flaps?

 

[fubar57]

Time to get more popcorn...

 

[Venturi]

Excellent info from drgndog