Fall from 24 miles -- terminal velocity?

[Bullgrit]

I'm sure everyone knows about Felix Baumgartner's jump from 24 miles above the earth, and his breaking the sound barrier during the fall. How does this jibe with terminal velocity?

Bullgrit

 

[Hussar]

Terminal velocity wouldn't actually apply since there's so little wind resistance. What would be the real difficulty would be the heat and friction caused by dropping into higher wind resistances as you fall. That would slow you down considerably.

 

[Umbran]

I'm sure everyone knows about Felix Baumgartner's jump from 24 miles above the earth, and his breaking the sound barrier during the fall. How does this jibe with terminal velocity?

"Terminal velocity" is not "the fastest something can move through the air." An object reaches "terminal velocity" when the force of gravity upon it is matched by the drag from the atmosphere - it stops speeding up or slowing down and falls with constant speed.

The drag is dependent upon many things - it is a complicated problem of fluid dynamics, really - including the object's current speed, shape, and the density of the air. Baumgartner broke the sound barrier while the air was still very, very thin. Practically vacuum, the air was unable to put up much resistance at all, so he just accelerated.

 

[Bullgrit]

All this time, I thought terminal velocity was the max velocity an object would move towards the pull of gravity. I didn't know resistance played any part in it. I never even thought to look up the term because I already knew what it was. Silly bull.

Do D&D lied to me. 20d6 shouldn't be the max damage for falling!

Bullgrit

 

[Scott DeWar]

he actually slowed down as he went through thicker air.

 

[Man in the Funny Hat]

The drag is dependent upon many things - it is a complicated problem of fluid dynamics, really - including the object's current speed, shape, and the density of the air. Baumgartner broke the sound barrier while the air was still very, very thin. Practically vacuum, the air was unable to put up much resistance at all, so he just accelerated.

I was actually wondering that he did in fact break the sound barrier AT THAT ALTITUDE, or if he simply exceeded the speed of sound as it is more typically measured at sea level. If I understand it (and I may not) the speed of sound would be a significantly higher velocity at very high altitudes, and at some point simply ceases to be measurable or meaningful in what increasingly approaches a vacuum.

Not that it detracts a whit from the cool factor of what he did, just pondering on the technicalities.

 

[Someone]

I was actually wondering that he did in fact break the sound barrier AT THAT ALTITUDE, or if he simply exceeded the speed of sound as it is more typically measured at sea level. If I understand it (and I may not) the speed of sound would be a significantly higher velocity at very high altitudes, and at some point simply ceases to be measurable or meaningful in what increasingly approaches a vacuum.

Not that it detracts a whit from the cool factor of what he did, just pondering on the technicalities.

You're right; the speed of sound is IIRC inversely proportional to the square root of the fluid density, so in very thin air it should be significantly higher than at sea level.

 

[Hussar]

I believe that Mach is measured at sea level.

 

[Umbran]

If I understand it (and I may not) the speed of sound would be a significantly higher velocity at very high altitudes, and at some point simply ceases to be measurable or meaningful in what increasingly approaches a vacuum.

You're right; the speed of sound is IIRC inversely proportional to the square root of the fluid density, so in very thin air it should be significantly higher than at sea level.

Sorry, guys, but you're misremembering. The speed of sound is *not* strongly related to the density or pressure of the gas. It is strongly dependent on the temperature.

For an ideal gas, the speed of sound c = sqrt(g*k*T/m)

Where:
g (actually gamma) is the adiabatic index - the ratio of specific heats of the gas.
k is the Boltzmann constant
T is the absolute temperature
m is the mass of a single molecule of the gas

Now, most gases are not quite ideal, but air is quite nearly so, and the effects of it being non-ideal are small. The speed of sound changes with altitude because the temperature changes with altitude.

 

[El Mahdi]

I believe that Mach is measured at sea level.

Actually, Mach is measured at whatever altitude you're at. Sea Level isn't used as the "reference" for Mach, altitude is just a variable in its computation. However, aircraft pitot/static indicators are calibrated using a standard day as a reference (more below). Mach 1 is simply the speed of sound at whatever pressure (usually altitude) and temperature (as well as density and viscosity) of the medium in which you're checking it. However, aircraft Mach indicators only use inputs for temperature and altitude (static pressure), as well as the requisite airspeed (pitot pressure) to determine Mach. Mostly for purposes of practicality as real time measurements of viscosity and density aren't possible with aircraft instrumentation, and the effects in air of those factors are negligible for aircraft stability purposes.

As far as the effects of breaking the sound barrier (on an aircraft or a human body), Mach 1 is Mach 1 no matter what altitude you're at. If an aircraft becomes unstable at certain Mach numbers, then the aircraft will experience instability at those Mach numbers regardless of the altitude. In other words, if an aircraft's mach limit is .86 (the Mach limit of a KC-135), and above that it can suffer control issues, then this will occur for this aircraft at aproximately 654 mph (568 knts.) True Airspeed at sea level, and at 567 mph (493 knts.) True Airspeed at 40,000 ft...as both of those speeds are .86 Mach for their specific altitude (and considering a standard temperature for that altitude, which is actually variable and why it's compensated for realtime).

When people ask what the speed of sound is, the answer is usually the speed of sound at sea level. Or more specifically, the speed of sound at sea level on a standard day. A standard day is defined by a specific value in pressure, density, temperature, and viscosity...though for aircraft usage, only pressure and temperature is actually used. A standard day pressure is 29.92" hg (inches of mercury) at Sea Level, and a temperature of 59° F/15° C. Technically, humidity plays a part also, affecting viscosity and density (as Umbran talked about), but as stated before, for practicality purposes aircraft Mach instrumentation only corrects for temperature and static pressure (altitude).

If I understand it (and I may not) the speed of sound would be a significantly higher velocity at very high altitudes, and at some point simply ceases to be measurable or meaningful in what increasingly approaches a vacuum.

You're right; the speed of sound is IIRC inversely proportional to the square root of the fluid density, so in very thin air it should be significantly higher than at sea level.

The speed of sound actually decreases as you climb in altitude.

The denser the medium, the faster sound travels. Sound actually travels faster through solid masses (like the Earth) than it does through air. However, energy is dispersed differently, limiting the range at which the sound can travel, and the attenuation of frequencies (which is why low frequencies travel through ground and water more effectively than high frequencies).

For example, the aproximate speed of sound in salt water (for a standard salinity, depth, and temperature), is about 1560 m/s (or just shy of 3,500 mph).




*I'm an Avionics Specialist.