View Full Version : Mach number Question

23rd Aug 2002, 08:11
Hi, i just have a question about the mach number. I have been told that an aircraft can not fly at Mach 1 at low levels. i am now reading the"Aeroplane performance,planning &loading for the Air transport Pilot(B727) from trevor Thom" book which i bought a while ago. now i am no airline pilot but just a student pilot but what i dont understand is that the book says that Mach number =
true airspeed
local speed of sound

It also says "the higher the temperature,the faster the speed of sound.conversely,the lower the temperature,(or higer the altitude) the slower the speed of sound". now my question is: if the temperature lowers as we get higher, than why are aircraft that do speed of sound, flying at such high levels. would this not make speed of travel possible at lower levels due to the higher temps? Please dont forget that i am a student pilot!


Captain Stable
23rd Aug 2002, 09:27
Mach number = Airspeed / Local Speed of Sound

Speed of sound = K * SqRt (Absolute Temperature)

Therefore, as you go up, the ambient temperature drops.

As the temperature drops, the local speed of sound drops. Your airspeed, remaining constant as measured in knots, becomes closer and closer to Mach 1.

So, on the first equation above, "Airspeed" starts off small relative to "Local Speed of Sound", so "Mach number" is small. The top of the fraction remains constant, but the divisor gets smaller and smaller as you climb. Hence the overall value of the equation increases.

Does that explain it?

23rd Aug 2002, 09:35

Mach number depends on temperature. For example, if you're flying along at Mach 0.98 and you pass through an area of much lower temperature, you can easily exceed Mach 1. Think of Mach number as an indicated measurement... this is valid at any altitude, i.e, flying at Mach 1 at FL360 @ -57 degrees Celcius would also be Mach 1 at 100ft AGL over the North Pole at
-57 degrees Celcius, but only, (for example) .65 Mach at 100ft AGL in the Sahara (+50 degrees Celcius).

In other words:

Low temp: Higher Mach number,

High temp: Lower Mach number.

Clear as mud? ;)


oxford blue
23rd Aug 2002, 11:06
You have also been misinformed if you think that aircraft cannot fly at Mach One at low level. Most can't, some can. It depends on whether they have been designed for high speed flight. Examples of aircraft that can exceed Mach One at low level (ie, 200 feet or so) are F15, F16, F18, Jaguar (believe it or not) and Tornado.

Tonic Please
23rd Aug 2002, 12:17
Saying that...is it possible for a 747 or A340 - (my favourite) to exceed the speed of sound depending on altitude and temperature?

Smooth skies

23rd Aug 2002, 13:01

In theory it's possible for an A340 or 747 to exceed Mach 1... however the temp would have to change a heckuva lot and you'd have to be cruisin' at a very high Mach number. I know that a 747 has exceeded Mach 1.3 in a spin recovery dive, but there's NO WAY the Airbus would let you do it. It's hardwired to keep you from doing things that you shouldn't! Unless you're in DIRECT mode of course! :P


Rhys S. Negative
23rd Aug 2002, 19:33

If I understand your original question, you are perhaps wondering why an airliner capable of cruising at say 0.8M (8/10ths of the speed of sound) chooses to do so at 35,000ft rather than at 5,000ft, where its true airspeed would be higher.

The answer is that it might be possible, but it wouldn't be economical. Air density increases as altitude decreases. As an exaggerated analogy, think how much more effort you expend walking across a swimming pool waist-deep in water, compared with walking along the poolside. Likewise the engines of an aircraft would need to produce more thrust at low altitude even to fly at the same true airspeed. Add to this that jet engines are more economical (low specific fuel consumption, ie less 'litres per 100km') at higher altitudes, and this helps explain why airliners climb to cruising altitude as quickly as possible, and stay there as long as they can.

Aircraft designed for high speed/low level are of course optimised for this with such features as highly-swept wings, buried engines with clever intake design, and engines with reheat (= large fuel bills).

A moderately-swept wing such as on most airliners experiences a large increase in drag as Mach number gets close to 1, and it just won't be able to accelerate; added to that, the engines need to breathe subsonic air, and a simple intake on a large-fan podded engine is not suitable to provide this.

Hope this is of help,


23rd Aug 2002, 23:06
In my humble opinion,
the last answer by Rhys is the one that holds the truth and perfectly answers the question. It is all a matter of looking at it in terms of increased TAS with altitude and higher air density (thus higher drag) with lower altitude.
Not to forget the aerodynamical difficulties encountered with airspeeds exceeding Mach 1 : high speed stall condition for the airlayer on the extrados of the wing, air intake of the engines which needs to reverse the speed of the incoming air to subsonic speeds.

Good question.

Captain Stable
23rd Aug 2002, 23:11
If one leaves out such factors as the development costs of Concorde, how much does it cost to operate compared to subsonic transcontinental airliners? (DOC's?) Can anyone answer?

26th Aug 2002, 04:24
The DC-8 broke the sound barrier.

Click Here To Go Super Sonic (http://www.dc8.org/library/supersonic/index.php)

Wednesday, August 21, 1961

Douglas Passenger Jet Breaks Sound Barrier

DC8.org Newswire

Edwards Air Force Base, Calif. - The Douglas Aircraft Company has broken yet another record with its DC-8 aircraft. Earlier today, during a routine certification test flight, Douglas Chief Pilot Bill Magruder flew the aircraft faster than the speed of sound, making the DC-8 the first Commercial Jet Transport to break the sound barrier. After climbing to an altitude of 52,090 feet, the DC-8-42 series aircraft attained a maximum speed of Mach 1.012 or 660 mph while in a controlled dive through 41,088 feet. The purpose of the flight was to collect data on a new leading-edge design for the wing.

A Lockheed F-104 Starfighter and a North American F-100 Super Sabre accompanied the record setting flight to confirm the data.
Upon completion of flight testing, the record setting aircraft will be delivered to Canadian Pacific Air Lines for regular scheduled service.

In June, the DC-8 set 3 speed records while being operated by Delta Airlines.

26th Aug 2002, 08:25
The highest TAS (and therefore groundspeed in still air) staying below the barber's pole (max IAS) for a given Mach number can be got at FL280/FL290. I regularly used to gain 15 minutes flying a 737-200 on a four hour flight flying at M0.74 at FL280 compared with M0.72 at FL350. Not the most economical way to fly but helped with schedule keeping and flight time limitations. In the early days of BKK-LHR and SIN- LHR I believe BA 747s flew home at FL280 at M0.86(?) this saved up to an hour on higher levels (although could be bumpy across the Bay of Bengal in the monsoon!) and meant less Cabin crew required, lower premium payments etc.