How Fast Is Mach 1?

The speed of sound was big in the news over the past couple of weeks as Felix Baumgartner prepared to jump out of a helium balloon gondola at 120,000 feet, or maybe higher. Calculations showed that he would accelerate to a speed above Mach 1 during the free fall from the highest human parachute jump ever.

The news media reported various speeds for Mach 1 which is accurate. Mach 1 is not a constant speed. But the media just handed out a number, usually somewhere around 750 mph, as though that speed is always Mach 1.

The fact is Mach 1 as speed—velocity—varies with temperature. It changes quite dramatically over the normal range of altitudes and air temperatures where airplanes operate.

So that airplane designers and pilots can have a uniform frame of reference the International Standard Atmosphere (ISA) was developed decades ago to account for Mach and other changes in the atmosphere that impact airplane operation. Under ISA the standard air temperature at sea level is 15 degrees C and the air pressure is 29.92 hg. Under ISA conditions at sea level Mach 1, the speed of sound, is 661.5 knots, or about 761 mph.

At 41,000 feet, a typical business jet cruise altitude, under ISA conditions, Mach 1 speed is down to 573.6 knots.

We all learned in private pilot ground school that air temperature drops approximately 2 degrees C per 1,000 feet of altitude gain. Those are ISA conditions. But there is an atmospheric phenomenon called the tropapause which is the altitude where the air temperature stops decreasing and remains constant, or even warms, as you climb.

Under ISA the “trop” is at 36,089 feet—don’t ask me why the 89 feet—where the air temp is -56.5 degrees C. ISA declares that the air temp remains at that value all the way up to 65,617 feet and above that level the air warms with increase in altitude.

In real world flying the “trop” can be much lower than 36,000 feet, particularly when flying in the far north or south latitudes. Near the equator the “trop” is typically much higher, sometimes above the cruise altitude of jets. Once you climb through the “trop” the air temp can increase instead of remaining steady and can be 10, 15 or more degrees C warmer than ISA. That warm air at cruise altitude robs engines of thrust and wings of lift because air density is reduced. In general, warmer than ISA conditions is bad for jet airplane performance.

There is an exception though, when you have plenty of reserve thrust, and can maintain maximum airspeed. Under those conditions warmer air increases the speed of Mach 1, so your indicated Mach cruise speed of, say, Mach .85 will be a higher true airspeed than if the air temperature were colder. In a cruel twist of aerodynamics colder air allows the engines to make more power so the airplane can fly up to its Mach airspeed limits, but the colder air reduces the actual speed of Mach 1 so the true airspeed will be slower than if the air was warmer. Since jet speeds at cruise are limited by Mach effects the same indicated Mach will be slower true airspeed in colder air, and faster in warmer air.

The whole ISA concept becomes somewhat vague above 65,000 feet because, well, there are so few air molecules left to feed an engine or to lift a wing at those altitudes. ISA does say that between 65,000 feet and 105,000 feet the air temp increases from  -56.5 degrees C to -44.5 degrees C. By 150,000 feet ISA air has warmed to -6.1 degrees C. At 65,000 feet under ISA the speed of Mach 1 is the same 573.6 knots that it was down at 36,000 feet. But at 150,000 feet under ISA the speed of Mach 1 rises to 636.8 knots.

I haven’t seen a reliable air temperature report for the 128,097 foot altitude where Baumgartner jumped, but the report of his maximum speed being Mach 1.24 implies the air temperature was around -48 degrees C, several degrees warmer than ISA predicts.

It’s been 65 years since Chuck Yeager “broke” the sound barrier, but the pesky Mach 1 still hangs around putting barriers in the way of fast airplanes, and rapidly falling humans. And Mach 1 is a speed limit that doesn’t remain constant under cruise conditions so our real true airspeed, the value that moves us over the ground, wonders around, too. You could say that Mach 1 imposes its limits on flying, but doesn’t limit itself to a single speed.

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31 Responses to How Fast Is Mach 1?

  1. Kayak Jack says:

    Nice job of explaining a subject that sounds simple on its face, but rapidly gets more complex with more knowledge.

    Just for the record, I usually cruise my 172 at about (just a minute here, doing long division with Roman numerals is kinda hard……. ahh – got it!) .114-.145 Mach.

  2. Mac says:

    Some of the test pilots who did the experimental development flying on Cessna’s model 162 Skycatcher LSA had also been flying in the Citation X program. That jet has a top speed of Mach .92. A little math showed that the Skycatcher could live up to its model number and zip along at Mach .162. The pilots had test flight program jacket patches made to celebrate the speed of the Skycatcher and its Mach bending performance. They gave me one of the patches to add to my collection after I nudged the Skycatcher that close to the sound barrier.
    Mac Mc

    • Swede says:

      True airspeed is the true speed going through the air mass not the speed over the ground. Ground speed is the speed over the ground and as you well know head wind /tail wind has a big -/+ with the same true airspeed.

      Mac, Thanks I have always enjoyed reading your material. Swede

  3. Cary Alburn says:

    All of that is interesting but definitely does not impact the cruise speed of my P172D, as she plods along at 115 knots TAS. :)

    Cary

    • Dan says:

      The same changes in altitude and temperature affect your TAS. It won’t always be 115kts.

    • Dan says:

      The same changes in altitude and temperature affect your TAS. It won’t always be 115kts.

      • Cary Alburn says:

        True, but that makes for a pretty good flight planning speed, at the usual 9,000 or 10,000 MSL altitudes I fly. Or 0.17 Mach (the next decimal numbers vary according to temperature, humidity, etc., in addition to altitude variations, right?).

        Still = “plods along” :)

        C

    • DEL says:

      Today, at 700′ QNH and 80 mph (the end of my green arc), I was overtaken by a train! What a shame! Since the ambient temperature was about 30 deg-C, I could state that that train ran faster than Mach 0.1025. This is pointless, however, as air compressibility effects, for which Mach numbers were invented, show signs of existence starting only with Mach 0.3. We, trainspotters and pool-side jumpers, should be content with our V-speeds.

  4. Dave Volker says:

    While the temperature of the air through which sound is passing may effect its velocity, the density of the air has the real effect.

    Felix was able to exceed the speed of sound during his free fall descent because the indicated air speed of mach 1 between 120kft and 100kft is lower than his free fall terminal velocity.

    Imagine that Felix had a pitot tube attached to his right index finger and an airspeed indicator attached to it within his sight as he took the big step. If he were able to point it into the relative wind and the direction of fall as gravity accelerated him toward the earth he would have seen his indicated airspeed climb until he reached his terminal velocity. (I am guessing, but a skydiver’s terminal velocity is somewhere between 120 and 160 miles per hour depending on the aerodynamics of his suit and other variables. ) It so happens that the mach is in that same speed range. ( see below)

    Why? Because the air, the medium through which the sound pressure wave passes, is so rarefied at that altitude that there is a lot of space between the molecules that make it up. Sound passes more slowly through the medium of air the higher you go. The following is an illustration I found on a thread devoted to this topic:

    http://www.airliners.net/aviation-forums/tech_ops/read.main/188932/

    The values are expressed as calibrated airspeed (closer to indicated than equivalent airspeed) are as follows. The spreadsheet I use I designed for lower altitudes (50,000 ft or less), so I’ve never tested it for higher stratosphere levels. Hopefully the figures are close enough.

    Altitude..CAS @ M=1.0 (knots)

    0,000 ft CAS = 661.41
    10,000 ft CAS = 561.21
    20,000 ft CAS = 475.12
    30,000 ft CAS = 389.87
    35,000 ft CAS = 349.93
    36,089 ft CAS = 341.50
    40,000 ft CAS = 312.52
    45,000 ft CAS = 278.71
    50,000 ft CAS = 248.27
    53,000 ft CAS = 231.53
    55,000 ft CAS = 220.96
    57,500 ft CAS = 208.40
    60,000 ft CAS = 196.51
    65,000 ft CAS = 174.66
    70,000 ft CAS = 155.17
    75,000 ft CAS = 137.80
    80,000 ft CAS = 122.33
    85,000 ft CAS = 108.58
    90,000 ft CAS = 96.35
    95,000 ft CAS = 85.49
    100,000 ft CAS = 75.84
    105,000 ft CAS = 67.28
    110,000 ft CAS = 59.68
    115,000 ft CAS = 52.93
    120,000 ft CAS = 46.95
    130,000 ft CAS = 36.93
    140,000 ft CAS = 29.04
    150,000 ft CAS = 22.84
    For example, Burt Rutan’s SS-1 was flying in these altitude ranges and was very supersonic for part of its trajectory but I personally heard Mike Melville said the indicated airspeed never exceeded normal maneuvering airspeeds at any time during his first X=Prize flight.

    • Patrik says:

      I was going to say the same thing about the density. In addition, though, the terminal velocity will be much larger at that low density, certainly much faster than a skydiver at more normal altitudes. This also goes in the direction of making it easier to cross the sound barrier.

    • Tim Austin says:

      Burt Rutan said that SS1 as it “exited the atmosphere” was mach 3.35 and and 18 kt IAS.
      Measuring airspeed close to and above mach 1 becomes a whole new complicated topic.

    • deadstick says:

      For the record, the speed of sound in air is given by V = 49.1*SQRT(T+459), where V is the speed in feet per second and T is the Fahrenheit temperature. Divide the result by 1.47 to get mph, or by 1.69 to get knots.

    • deadstick says:

      “Sound passes more slowly through the medium of air the higher you go. ”

      Only because the higher you go, the colder it gets. The speed of sound is a function of the temperature, period.

      Temperature is a measure of the kinetic energy of the air molecules, which is proportional to the square of the mean velocity of their random motion. Sound is propagated, quite literally, at that velocity. As I mentioned in another post here, the speed of sound in feet per second is 49.1*SQRT(T+459), where T is the Fahrenheit temperature.

      • Skydriver says:

        So given the exact same temperature the mach number is the same in both water and air?

        • deadstick says:

          No; it depends on the substance, too. If you were comparing, say, air and helium, you could just put different constants in that equation — but a liquid is a different phase of matter, with different mechanics.

          In sea level conditions, sound is over 4 times as fast in water as in air.

  5. Josh says:

    I believe the tropopause begins at the “odd” height of 36,089 feet because as an international standard, it is more commonly referenced by its metric equivalent of 11km (11,000 meters), which is nice and round.

    • Kari Seppanen says:

      Exactly correct. The International Standard Atmosphere is in fact metric and some of the values are nice and round, like the 11 km value for the tropopause. Other exact values: 15 deg C at sea level; 760 mm of mercury pressure; -6.5 deg C/km temperature lapse; geopotential feet to ignore change in gravity with altitude. Only some of the things you don’t get a choice in have any decimal places.

  6. Predrag says:

    No need to hide the reason for the “89 extra feet” in 36,089. The odd figure is a very nice round number of 11,000 metres.

  7. Predrag says:

    Apologies for saying exactly the same thins as Josh. For some reason, it didn’t appear on the page when I submitted my comment.

  8. David Money says:

    Oh! I’m so glad to be a member of EAA and get some sensible, correct data on this otherwise amazing jump. I tried to explain to quite a few non-aviators the difference between actual speed in the drop and TAS. Blank looks! As I recall SS1 never exceeded 130kt at any point in the flight, including being taken up to 50,000 ft for release. Our TV coverage ended with a LEGO re-creation of the whole thing – I don’t know where it originated but it was just brilliant!

  9. Loren says:

    Here’s a thought for y’all……
    Since sound is normally conducted in air, can there be sound at or above 328,000 ft (100km), which was the target altitude for SS1? Or in “deep space”? Further, since OAT (outside air temperature) is a measure of actual temperature of the air, can zero air exhibit any temperature?

  10. gig2000 says:

    My reading of deadstick is “Only because the higher you go, the colder it gets. The speed of sound is a function of the temperature, period. ”
    Mac in the original post writes: “Under ISA the “trop” is at 36,089 feet—don’t ask me why the 89 feet—where the air temp is -56.5 degrees C. ISA declares that the air temp remains at that value all the way up to 65,617 feet and above that level the air warms with increase in altitude.” They seem to disagree so both can not be right. Basic physics formula for an ideal gas is PV=nRT. Deadstick is ignoring the pressure which along with the density of air, decreases with increased altitude. Dave and Patrick have the right idea, density matters. For a given substance, speed of sound varies with temperature because the density varies with temperature. If you hold the temperature of air constant and increase the pressure, the speed of sound increases because the density increases. Or, if you hold the pressure constant, the speed of sound increases if the temperature goes down again because the density of air increases. As you go up in altitude through the “trop” it becomes a little more complicated because initially you have decreased pressure at higher altitudes combined with colder temperatures then decreased pressure at even higher altitudes combined with warmer temperatures. A truly accurate speed of sound would factor both pressure and temperature to give you a density which is truly what affects the speed of sound.

    • deadstick says:

      Yes, Gig, I’m ignoring the pressure because it doesn’t count. Please take a look at http://en.wikipedia.org/wiki/Speed_of_sound#Practical_formula_for_dry_air . The third equation in that paragraph is identical to the one I gave above, except it’s in meters per second and degrees Celsius.

      If you don’t trust Wikipedia, I refer you to Thermodynamics, an Engineering Approach by Cengel & Boles, McGraw-Hill. Equation 17-11 on page 852 in the 7th edition is the same equation again, this time using absolute temperature.

      • Skydriver says:

        As a layman it is hard to get over the density thingy. That is why I asked my question about water and air at the same temperature (above). The formula provide by deadstick is quite clear . . . density is not part of that formula. I also appreciate deadstick’s explanation of different materials with different constants . . . thank you 

        But it is hard to accept that density in not in the equation of something! So at the risk of thread drift (because this is a velocity thread) I must ask about amplitude. Sound is a pressure wave. It has both velocity and amplitude. Does density have an effect on amplitude or the decibel value of sound?

        • deadstick says:

          Yes, density comes into play when you’re talking about amplitude, but so do a couple of other properties.

          Dynamic viscosity is the resistance of a substance to being sheared. It’s high for molasses, low for air. Kinematic viscosity is the ratio of dynamic viscosity to density, and it represents the ratio of viscous forces to inertial forces.

          Viscous forces turn mechanical energy into heat, which means they rob sound of some of its energy, and the sound gets weaker.

          The attenuation (loss of amplitude) of sound as it travels through a substance is described by Stokes’s Law, which says it’s proportional to the kinematic viscosity.

          Now air is less “dynamically viscous” than water, but it’s also a great deal less dense: consequently, the kinematic viscosity of sea-level air is about 16 times that of water, so sound diminishes 16 times as fast in air as in water. That’s why whales and submarines can hear things going on a thousand miles away.

          • Skydriver says:

            Well if it ain’t speed at least we can say something happens to sound as altitude increases. Since kinematic viscosity changes with density we at least know sound amplitude decreases with altitude. :-)

      • gig2000 says:

        Thanks Deadstick,
        The wiki article is excellent,thank you, but, if you read it carefully you will note that the formula you give is an approximation over special conditions of temperature and pressure in the troposphere where aircraft fly. It is not correct to say “the higher you go the colder it gets” Look at the graph showing altitude, temperature, pressure, and density in the article you cite. Also below are paragraphs taken from the article you cite which show you to be correct only at lower altitudes but not correct at the higher altitudes discussed in the original post above 100,000 feet.

        “Density and pressure decrease smoothly with altitude, but temperature (red) does not. The speed of sound (blue) depends only on the complicated temperature variation at altitude and can be calculated from it, since isolated density and pressure effects on sound speed cancel each other. Speed of sound increases with height in two regions of the stratosphere and thermosphere, due to heating effects in these regions.”

        “This equation is correct to a much wider temperature range, but still depends on the approximation of heat capacity ratio being independent of temperature, and for this reason will fail, particularly at higher temperatures. It gives good predictions in relatively dry, cold, low pressure conditions, such as the Earth’s stratosphere. The equation fails at extremely low pressures and short wavelengths, due to dependence on the assumption that the wavelength of the sound in the gas is much longer than the average mean free path between gas molecule collisions.”

        File:Comparison US standard atmosphere 1962.svg

  11. Tom Miller says:

    Funny that no one is complaining about Mac now. Why not? This MACH 1 stuff, compressibility, and the speed of sound has almost nothing to do with my Lancair.

    I guess it just strikes me as odd that folks are fine with being aviation nerds on this topic, but get all in a huff when Mac discusses Mach tuck or similar issues as they relate to business jets. At least be consistent, people!

    • Dave Volker says:

      when i made my comment i did not consider it to be polite to strongly disagree with Mac. Even though i felt he was waaay off base in his premise I offered an alternative explanation that I could defend scientifically.

  12. Alex Kovnat says:

    It would be nice if NASA could work out the aerodynamics and come up with a design for a high-end business jet or a narrow-body, single-aisle airline aircraft that could cruise a little above Mach 1.0, i.e. Mach 1.05-1.10, yet require (for business jets) no more than a mile of runway for takeoff and landing, or no more than 10,000 feet (for airline operations). Problem here is, how to operate efficiently with shock waves wanting to leap to life while at the same time, having good low-speed handling to keep Vref low enough to meet said runway requirements.

    The B-1 bomber, the F-111 and the Navy Tomcat were designed with what for a while seemed a good solution to the problems of being able to operate supersonically, without too high a Vref while landing. Unfortunately variable sweep wings are not likely to be a hit with either bizjet operators nor airlines, what with all the structural complications and reliability/maintenance issues.

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