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Old 5th Oct 2000, 20:30   #1 (permalink)
v1rotate
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Question Mcrit with altitude and Local speed of sound

Can anyone tell me why does Mcrit increase with altitude? Also, What is the speed of sound at Sea Level and at 40,000? (The formula behind them?)

[This message has been edited by v1rotate (edited 05 October 2000).]
 
Old 5th Oct 2000, 23:12   #2 (permalink)
nugpot
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Hi V1,

Local Speed of Sound (LSS) is directly proportional to the square root of the absolute temperature. Using the relationship between pressure and density you can get a constant to represent them in a formula.

LSS (kts) = 39 x sqrt(Temperature in Kelvin)
For Kelvin just add 273 to Celcius.
Ex. LSS = 39 x sqrt (15 + 273) = 662 kts at ISA sea level.
and LSS = 39 x sqrt (-56.5 + 273) = 574 kts at ISA above 29 000 feet.

Mcrit is the speed at which the first part of airflow (boundary layer) goes supersonic. This usually happens on the wings and be dependent on camber (and obviously various other factors to do with the shape of the airfoil section). Another name for Mcrit is Mcdr (Mach critical drag rise) and this occurs with the formation of the first shock wave. I can't immediately think why Mcrit should rise with altitude. I always thought it to be pretty constant, but I can be wrong.

The danger of subsonic wings at Mcrit is that the center of pressure moves rapidly with the formation of shockwaves and this can cause tuckunder.

I'll pull out my books when I next go home and phone you with some more info.



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Old 5th Oct 2000, 23:41   #3 (permalink)
Tor
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Mcrit is constant as it is related to the design of the wing - only. However, the actual speed is lower in high altitudes as the speed of sound also is lower.

The aircraft is limited by two speeds. One is a certain indicated airspeed and the other is Mcrit. The limiting indicated airspeed is not to overstress the airframe and is typically around 330 kts. At mean sea level that would be apprx. mach .50 (330/662 = 0.5 *).

The indicated airspeed decreases with altitude since the air gets thinner. That means that two aicrafts flying at same groundspeed (in no wind), then the one at mean sea level will have a higher indicated airspeed than the one at 40000'. At some point (around 20-25000') the crew will fly a machspeed rather than an indicated. The aircraft will now reach Mcrit (say .92) before 330 kts, therefore Mcrit is now the limiting speed, and the aircraft can now go faster than at mean sea level (.92 as oposed to .50).

Tor

* = note: the indicated 662 is also indicated airspeed, as trueairspeed = indicated at mean sea level.

[This message has been edited by Tor (edited 05 October 2000).]
 
Old 6th Oct 2000, 00:17   #4 (permalink)
v1rotate
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Thanks nugpot and tor, I appreciate the info. I've left my books back on the other side of the world so I needed some expert help with a couple of questions. That, I did have.

Thanks once again
 
Old 6th Oct 2000, 07:22   #5 (permalink)
Oz_Pilot
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Isn't Mcrit just the speed at which the first local flows become supersonic? Wing sweep is designed to increase Mcrit, but knowing Mcrit doesn't help with operating the aircraft... Mmo is another story.

Agreed on Mach tuck with shifting centre of pressure (which is why Concorde has fore and aft fuel tanks with transfer pumps, to alter CoG position).

Not too sure about Mcdr and Mcrit being interchangeable either??
 
Old 6th Oct 2000, 15:40   #6 (permalink)
nugpot
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Oz_Pilot

I may be wrong about Mcrit and Mcdr. I am digging into my notoriously unreliable memory for this, but will check when I go home and get to my books.

V1, you still overseas? I see the 125 standing at DN every day and always pointing the same way. Hope you get enough work for it.

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Old 8th Oct 2000, 04:35   #7 (permalink)
AICUS
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Reading from "Aerodynamics for Naval Aviators", the Mcdr is the mach number which produces a sharp change in the drag coefficient and usually exceeds Mcrit by at least 5-10%.

I also have a note in my notes (???) that says Mcdr is when the drag increases out of proportion to the lift (by a factor of something like 20%)

Anyway i hope that helps
 
Old 8th Oct 2000, 12:56   #8 (permalink)
Oz_Pilot
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Cool bananas.
 
Old 12th Oct 2000, 16:40   #9 (permalink)
aerostude
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Simple really. Mcrit increases with altitude as Mach number is a ratio of velocity of flight and local speed of sound. Speed of sound decreases with altitude therefore, as you go up, you are dividing by a smaller value. Hence for constant airspeed, Mcrit will get bigger as you go up.

As for formulas:
Speed of sound at sea level is near enough
340 m/s which is 660 kts
at 40000' which is in the stratosphere, so you can assume a constant temperature of 216 Kelvin, gives speed of sound to be 295 m/s which is 572 knots.

The formula is:

M = squareroot(1.4*287*temperature)

M is the Mach number
1.4 is the ratio of specific heats for air
287 is the gas constant, R in J/KgK
and the temperature must be in Kelvin
 
Old 13th Oct 2000, 03:03   #10 (permalink)
alosaurus
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My regional turboprop is limited to 0.52 above 15,000-is this related to mcrit of the props?

[This message has been edited by alosaurus (edited 14 October 2000).]
 
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