What is 737's Critical Mach no.?

[sam_airman]

Mrit

Dear Pilots,

first of all: there is no specific Mcrit for ANY airplane!

Definition:
The Free Stream Mach number at which the local velocitey first reaches Mach 1.0 (SONIC) is called the Critical Machnumber (Mcrit). Mcrit is the highest speed at which no parts of the aircraft are SUPERSONIC.
Increased thickness/chord and increased angle of attack cause greater accellerations over the top surface of teh wing; so the critical Mach number will DECREASE with increasing thikness/chord ratio or angle of attack. Which means, that the aircraft will reach Mcrit at a lower Mach number.

At speeds just above the critical Mach number there will be a small region of supersonic airflow on the upper surface. This area is terminated by a shock wave. As the aircraft speed is increased the region of supersonic flow on the upper surface extends and the shockwave (marking the end of the supersonic region) moves rearwards.

When the aircraft speed reaches Mach 1.0 tha airflow is supersonic over the whole of both upeer and lower surfaces. the shockwave (also to be found on the lower wing surface) has moved all the way rearwards to the trailing edge of the wing.

And remember!: LSS (local speed of sound) varies with changes in absolute Temperature! So if temperature rises LSS will increase. And as temperature decreases LSS will decrease as well.

Now let's get back to that question.
Mcrit is not always the same TAS/IAS for a given aircraft. One always has to take into consideration the angle of attack and therefor consider aircraft mass, CG position and wander.

[Milt]

Remarkable story yesterday from an ex RN TP who was tasked at BD to determine the effects of an F-86 Sabre going through Mach 1.0 without a cockpit canopy.

He flew several flights to gradually approach Mach 1.0 eventually becoming confident to accelerate through to supersonic in a steep dive.

The remarkable observation was that he could physically feel the effects of a shock wave pass slowly past his head. The Orenda powered Sabre remained controllable.

In some light conditions I have been able to see the shadows of shock waves dancing around on the wings of a Sabre. It sort of gets your attention.

This was during investigations into aileron hydraulic jack stalling which limited the amount of aileron one could apply supersonic. It's an offputting feeling to have the stick lock up as the jacks stall. It would have been too difficult to fit higher powered jacks so the limitation had to be accepted.

Would like to know if the Sabre pilots in combat in Korea found jack stalling to be a problem when chasing a target.?

[SR71]

I'll have a go.....

Using the relationship for incompressible lift from elliptical wing theory and Prandtl Glauert (or even better von Karman and Tsien) relationships, along with the tables here:

http://books.elsevier.com/companions...le-2/table.htm

you can work out a compressible lift coefficient assuming the lift curve slope of the two dimensional wing is 95% of the theoretical value and an angle of attack of 4 degrees in the cruise.

Suffice to say, lets call it 0.4 - because I can't be bothered to work it out otherwise.

You can then look in some magic tables which plot M_crit (zero sweep) against t/c ratio for various C_L.

The tables in the html file above give t/c ratio for 733 as ~12.9 and sweep as 25 degrees.

M_crit (zero sweep) is thus 0.69 according to my magic table.

Since M_crit (with sweep) is equivalent to M_crit (zero sweep) divided by the cosine of the sweep angle, I'm going for

M_crit (25 degrees sweep) = 0.75.

A good approximation of M_{drag divergence}, assuming that this is the Mach number where the gradient of the C_d versus Mach number curve reaches 0.05, is:

M_{drag divergence} = M_crit*[1.02 + (1-cos(sweep angle))*(0.08)]

This assumes two dimensional wing theory and applies only exactly to a wing of infinite span. It should be good for wings of high aspect ratio.

This gives

M_{drag divergence} ~= 0.77

We know

Mmo = 0.82 and

M_ne should be about 5% higher: ~= 0.86

I have observed Mach Tuck in a 737 sim before but I can't remember what Mach number it manifest itself at.

Someone tell me my guesses are right!



PS: The other good time to see shock waves is in humid conditions at TO which only serves to illustrate Sam_airman's point about how dependent M_crit is on C_L.

[flymax]

I think that the Mcrit is a figure that you never need to carry an airplane, because it varies witha a lot of factos. The definition of it you have more that one time in this topic, and says that the Mcrit is the the mach number at wich any part of the aircraft first meet mach 1, so it depends on the angle of attack, bank, gust, and it could be on the wing surface or even the fuselage, so the only parameters regarding mach numbers are the MMO, adverse weather or turbulence Mach target, andthe buffet onset for given weight and FL, in airplanes with efis you can find it so easy.

[Centaurus]

Remember the Silk Air crash? The initial dive was extremely steep (50,000 ft per minute approx by the transponder read-out I recall) I wonder what final Mach that aircraft achieved before it came apart around 5-7000 ft and especially, at what estimated Mach, recovery would have proved unachievable?

[SR71]

Centaurus,

In the instance when I was shown Mach Tuck in the sim, the aircraft gradually nosed over into an unrecoverable dive.

Even with full back stick and application of nose up trim and with the thrust levers at idle, the aircraft continued to slowly nose down further into the dive.

Not a pleasant feeling.

I have no idea of the fidelity of the sim aero model in this region of the flight, nor can I remember exactly what the Mach number was at the time, but surely someone (i.e., a TRI/TRE) here can have a go in the sim and report back.

[CaptainSandL]

SR-71,

When I tried to reproduce the Silk Air crash in the sim I could not hold the aircraft in the dive at anything like the speeds achieved because the lift was such that the aircraft wanted to pitch up more than I could hold it down without excessive nose down trim.

Moral of the story - don't believe simulators when outside the normal operating envelope.

S&L

[john_tullamarine]

CaptainSandL has it right re sims .. only a fancy computer and not to be trusted too much once outside the comfort zone ..

However, when Milt sees the last few posts he possibly may relate a tale wherein he was in the sharp end of a big military bird which was caught in this situation in the real world .... goes back a few years ago now but still a valid scenario to consider ... it made a quite fascinating tale over dinner some time ago ..

[Old Smokey]

I fully endorse John_Tullamarine's remarks with respect to excessive trust in simulator fidelity, as compared to 'real aircraft' data. Typically, simulators are programmed to provide a reasonable representation of the aircraft's flight characteristics within the normal flight envelope, with little attention given to charasteristics outside the normal envelope.

The normal envelope considered for simulator fidelity is from stick shaker at the low speed end, up to Mmo at the high speed end. Within this band, simulator response can be considered as quite reasonable, outside the band, most of the data is simply 'off the shelf' generic code applicable to most aircraft. Pilots are trained to respond to the stick shaker and overspeed alerts appropriately, and, as a training tool for normal operations, little attention is usually given to flight characteristics outside this band.

I have had some insight to how in-flight test data is incorporated into simulators, having done flight testing, and taken the resultant data onwards to the simulator (usually on the same day). A lot of it is 'hard' data, but a lot of it is the testing pilot carrying over his own subjective response to the simulator programmers.

On one aircraft type that I did this for, the launch customer for the type wanted to incorporate some realistic data beyond the normal range, as this aircraft was to be the operator's junior aircraft where trainees would be exposed to their first jet aircraft. In achieving this, I am able to provide the following general summary -

(1) Up to Mcrit, control response is conventional, i.e. with increasing speed, the aircraft tends to pitch up, and forward elevator and trim are required to maintain stable flight.

(2) Mach Tuck begins to manifest itself after Mcrit, in the initial stages it is rather mild. The aircraft continues to pitch up due to increasing speed, but Mach Tuck begins to counterract this. At or about the Mach Number where the pitch up and the pitch down forces are equal, the "MACH TRIM INOP" speed limit is imposed. Full elevator authority (or close to it) is available. This Mach Number is usually about 0.02 above Mcrit, BOAC has indicated that the "MACH TRIM INOP" limit speed for the B737 is M0.74 (reinforcing my assertion that Mcrit is about M0.72 for the B737).

(3) Beyond the "MACH TRIM INOP" speed, the Mach Trim system progressively makes greater input. The upper limit of allowable Mach Number is determined when UP elevator authority (without assistance from the stabiliser) is at a point where just sufficient is in reserve for recovery. MMO is established about 0.02 to 0.03 below this speed. (It must allow for Mach Trim fail right up to MMO and the aircraft recoverable, with an elevator authority margin, using Elevators alone).

(4) Beyond the upper limit speed (MMO + 0.02 to 0.03), elevators alone cannot effect recovery, and UP stabiliser is required to regain control in addition to Elevator input. SR71 has indicated this in his last post. For certification purposes, the aircraft must be able to recover without resort to stabiliser use. In a MMO exceedance case, where elevator control is insufficient, stabiliser use is imperative. Our flight testing terminated (to my relief) when we had passed the threshold where stabiliser use was necessary for recovery. As our simulator response was quite realistic in the area of MMO exceedance (proven), crews were taught the absolute necessity of stabiliser use to effect a recovery. The secondary unpleasant aspect of this was that as the aircraft then pitched up and reduced speed, it was trimmed well nose up, often (always) resulting in a large zoom upwards requiring down elevator and assertive forward stabiliser trimming.

Centaurus, the Silk Air B737 was supersonic, although I do not know to what degree.

BOAC has come up with some good info here, I agree with him that the first portion of the B707/B727/B737 to pass mcrit was the nose/cockpit region, probably also the case with other aircraft too. Although increasing drag will always be a concern to us, increasing control problems are of far greater concern, and thus, Mcrit is typically quoted for the wing (even though other non-control portions of the airframe have already passed M1.0).

Getting back to simulator fidelity, modern fly by wire aircraft normal responses are very well emulated in the simulator, as the same computer/commands/logic of the Primary Flight Control (PFC) system is used in the aircraft and the simulator. When we turn the PFCs off during training, the same old "is it real?" question arises.

We never did get the low speed end of the envelope right, the simulator stalls like a Tiger Moth, but the fully developed full back stick stall in the aircraft is a wildcat!

Hachiouji-shi, I can't help but think that you're confusing Mcrit (a mild encounter) with the very adverse effects of gross MMO exceedance

Regards,

Old Smokey

[Centaurus]

Milt will recall this better than me but in around 1951 the RAAF lost three Vampire Mk 30 aircraft (Rolls Royce Nene's instead of Goblins). In each case the aircraft were in normal high altitude dives (from aerobatics and the other from practice quarter attacks) when the pilots reported getting into compressibility. I suppose severe case of Mach tuck is today's description.
They were unable to recover from these dives and with no ejection seats in those aircraft the pilots were killed. The problem was the installation of two additional engine air intakes that were installed on top of the engine behind the pilots canopy. Shock waves formed above these intakes (called Elephant Ears) at high speed - 0.73 or thereabouts I believe - and these caused reduced elevator effectiveness. At 10,000 ft in their dives the aircraft were vertical leaving insufficient room to recover. The fix was to relocate the intakes under the engine and the Vampire would recover unassisted after that.

[SR71]

My suggestion is that the simulator fidelity is questionable only outside the phase space captured by the stability derivatives.

If you have the relevant dependent variables in the multi-dimensional matrices, just because you are outside the normal operating envelope, does not necessarily mean the simulator will respond inaccurately. The test phase space should obviously be larger than the operating envelope.

However, I agree you need to be far more conscientious when extrapolation is the name of the game.

Interpolation is easy.

In actual fact it is quite easy during wind tunnel testing to acquire stability derivatives outside the normal operating envelope of the aircraft.

The characteristics for a commercial aircraft may be fairly benign as the operating envelope is fairly small.

I would hazard a guess that in the 737 aero model, outside the tested phase space, the stability derivatives are merely set to the values at the extreme ends of the test matrix.

In general for more manoeuverable aircraft with greater control power and authority the derivatives become highly nonlinear.

When you start solving the equations of motion, associated with such systems is the problem of sensitivity to initial conditions - just like any nonlinear system.

Normally the pitching moment is the hardest to model.

I spent years attempting to extrapolate F-18HARV performance at high rates of pitch using the existing quasi-steady aero models.

In the end, I had to move away from stability derivative methods to nonlinear indicial response methods.

Unsteady effects are one case where even interpolation may yield incorrect results because in the case of unsteady effects, the instantaneous aerodynamic loading is actually a function of the whole past history of motion.

Its only my opinion, but Mach Tuck is a relatively simple problem to model. Whilst it is obviously a transonic effect, and the transonic regime is notoriously difficult to model, I would be surprised if Boeing had not tested slightly beyond Vne.

I'd have faith in the model until at least slightly beyond Vne.

Because, of course, there are probably very few people, if any, that are able conclusively to substantiate the corollary! If there are, I'd like to know what they were doing at the time...

[john_tullamarine]

I keep thinking back to a 73 box which had a not at all convincing rudder response model at low speed ...

Then, as a couple of customers were FAA AOC airlines, the FAA dictated that the model be updated for the rudder hardover research .. I was the slowest getting away the night the boffins wanted to do some box testing so I was the bunny .. strange .. the box went from being totally unrealistic to very convincing ..

I am long convinced that a significant problem is computing power in the earlier boxes and where the tweaking efforts are concentrated .. but I stand willing to be corrected by those who have had far more experience in sim design etc., work ...

[Mad (Flt) Scientist]

Originally Posted by SR71

My suggestion is that the simulator fidelity is questionable only outside the phase space captured by the stability derivatives.
If you have the relevant dependent variables in the multi-dimensional matrices, just because you are outside the normal operating envelope, does not necessarily mean the simulator will respond inaccurately. The test phase space should obviously be larger than the operating envelope.

Given the demands on development time, I'd have doubts over any simulator manoeuvre not EXPLICITLY validated during the sim qualification.

For example, sims are usually validated ffor OEI cases at low sideslip angles, and for AEO cases at high sideslip angles. Without evidence that there was a match, I'd take any OEI high sideslip data with a pinch of salt - even though it would appear to be simply a case of adding together two sets of known data, it never quite works out that way ...

Non-QTG manoeuvres aren't guaranteed to be wrong, of course. But nor are they necessarily right.

In actual fact it is quite easy during wind tunnel testing to acquire stability derivatives outside the normal operating envelope of the aircraft.

Well, static derivatives aren't TOO difficult - though there are always tunnel model limitations which may restrict what you can get - but dynamic derivatives are a whole other question.

[Milt]

Ok Centaurus - here is the Vampire story.

Back in the 50s we didn’t know too much about compressibility and shock waves. I converted from Mustangs to single seat Mk30 Vampires which had been re-engined with Nenes which needed increased airflow over the original Derwents. Two scoops above the engine were fitted. Flight testing did not explore the high Mach corner of the envelope and three RAAF pilots were lost leading to the aircraft’s Mach tuck being seriously examined.

We used to take the aircraft to compressibility with some apprehension as the ‘shake, rattle and roll’ and inconsistent elevator effectiveness was quite startling. Years later as a TP at BD I was to find a similar edge of the flight envelope with the Vulcan.

‘Black Jack’ Walker was a very experienced WW2 RAAF pilot who was given the responsibility for factory production flight testing following some intense coaching by De Havilland’s pilots at Hatfield. His description of his exploratory flights is an extract from his book “Black Jack”.

“By early '49 the first Australian Vampire was beginning to take shape and I was taking more than an academic interest in its progress. In fact it was not ready for its first flight till late June of the same year. We had very little trouble with that first Vampire. Its Mach number was limited to Point Seven Five and I had only ever taken it to near Point Eight which I thought was sufficient margin. This could have been, in hindsight, the cause of a problem.
After we had delivered half a dozen to the Air Force and they appeared to be functioning quite well from the station at Williamtown, two Vampires, after flying in formation at altitude near Newcastle, went into the ground in an almost vertical dive. Apparently they had never even looked like recovering. So De Havilland, to whom the matter had been referred, told me, "You, Mr Test Pilot, had better take the next Vampire up and see what happened to those two aeroplanes."
Well do I remember that flight. I knew it must have something to do with compressibility. I took it up to well over forty thousand feet and put it into a very steep dive, as steep as I dared, with not too much power, about three-quarters, because if anything was going to happen I wanted it to happen fairly quickly. I soon found out. Once the aeroplane went over Mach Point Eight, the nose got heavier and heavier and the aeroplane kept on endeavouring to go past the vertical and the controls were largely ineffective. So I closed the throttle and put on the dive brakes immediately and this would have been somewhere around twenty-seven thousand feet. The aeroplane obviously had to be got out of a very sticky situation. As it got into the lower, denser atmosphere the dive brakes started to slow it up. I was even thinking of throwing the undercarriage out, which would probably have destroyed the fairings, but -- anything to slow it up. Otherwise I would not come back with any answers.
Fortunately, as I descended to twenty-thousand feet I could feel the controls slowly becoming a little more effective and I was able to lift the nose up from almost vertical to an attitude where the Mach number was slowly decaying and recovery was becoming possible. We eventually came out of that dive at about thirteen thousand feet and though it was a fairly cool day, I was dripping with perspiration. It was pretty close and as the characteristics were so different to the English Vampire at high Mach numbers, it seemed to me it must have something to do with those wretched Elephant's Ears on the upper surface of the fuselage.
As it happened, the design team came to the same conclusion -- we tended to generally agree -- and they quickly did a switch around and took the auxiliary intakes from off the top of the fuselage and placed them on the bottom of the fuselage. This redesign took several days but our production rate was not that high and a few days later they said, "All right, check it out and try again."
On this occasion I still wasn't taking any chances and I took it up to as far over forty-thousand feet as I could reach comfortably and this time put it into a dive of about seventy-odd degrees with a bit of power on. I was ready for it this time. If it kept on ducking its nose down when it hit high Mach numbers, I intended to haul out of it as quickly as I could. But imagine my relief when, instead of ducking its nose down, once I reached Point Eight the nose began to rise. This was 1951 and Point Eight Four was high. Today aeroplanes cruise at that rate. We still had much to learn but that solved that problem with the Vampire and thereafter they all had their auxiliary intakes underneath the cowl, in spite of the fact that on a grass aerodrome the engine could suck in tufts and dust.”

[john_tullamarine]

... c'mon, Milt, tell us about the Vulcan as well ...