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.