Supersonic Freefall

[Mushroom_Farmer]

So what is the approximate maximum altitude or minimum air density, and speed needed, to create a sonic wave strong enough to create a sonic boom?

That is an excellent question. I know sound pretty well, but that's out there... I'd imagine there's a theoretical limit for sound-friendly air density, but there would be many variables, including the volume of air involved in the shock wave.

Well, the reason I ask is because the space shuttle creates a sonic boom when it re-enters the atmosphere. I've never seen the telemitry on re-entry, so have know idea what the velocity/altitude is. And the time it takes for sound to reach a the surface of the earth so a person could hear the boom would have to calcualted in too, I suppose.

[beaky]

So what is the approximate maximum altitude or minimum air density, and speed needed, to create a sonic wave strong enough to create a sonic boom?

That is an excellent question. I know sound pretty well, but that's out there... I'd imagine there's a theoretical limit for sound-friendly air density, but there would be many variables, including the volume of air involved in the shock wave.

Well, the reason I ask is because the space shuttle creates a sonic boom when it re-enters the atmosphere. I've never seen the telemitry on re-entry, so have know idea what the velocity/altitude is. And the time it takes for sound to reach a the surface of the earth so a person could hear the boom would have to calcualted in too, I suppose.

It builds that shock wave and creates a boom after intitial re-entry...a quick search for the average altitude tells me it's somehwere around 30,000 feet. Which seems pretty low... at the incredible speed that big thing is moving when it comes in, you'd think it'd pile up a lot of air even in the very thin upper reaches.

But here's an interesting tidbit I also found: the SR-71 produces a shock wave at Mach 3 at 80,000 feet, but it's (estimated?) to have an "overpressure rating" of less than a pound, whereas overpressures of anywhere from 20 to 144 lbs have been recorded coming from aircraft flying supersonic at 1000 feet and below.
I'm sure the force of the wave varies with speed and mass as well as altitude, so I'm still not sure if I'm right or wrong in thinking a freefalling human would create such a wave at +80,000 ft. Hard to find a straight answer on this one.

[Xyn_Air]

About terminal velocity, velocity in free-fall for any object is going to be governed by three things: the relative gravity between the two objects (obviously, the gravity of the larger object, i.e. the planet, is of most significance, but all physical objects have gravity); the distance between the two objects for gravity to accelerate the two objects toward one another; and, anything that would produce additional forces, such as friction due to atmosphere.

When it comes to friction caused by an object moving through an atmosphere, both the density of the atmosphere and the properties of the object (density, volume, and surface area, for starters) are going to influence the effect friction has on decelerating the falling object.  Density will also affect whether or not the object is so buoyant as to be unable to "fall" (be pulled through by gravity) through whatever constitutes the atmosphere.

Surface area (both quantity and geometric shape) really influences friction a great deal.  If you take a pebble that weighs 1 gram and a mass of crumpled paper that weighs one gram, the friction via air resistance that the surface area of the paper experiences is much greater than that of the pebble causing it to fall more slowly, that is, have a lower terminal velocity.

Now, in determining the terminal velocity of a person, you can toss right out mass and density, as neither vary enough from human to human to affect terminal velocity to any significant degree.  But, how a person's body is configured (flailing about, straight as a rod with arms tucked in, rolled into a 'cannonball', etc.) is going to significantly change the nature of their surface area and thus significantly impact their terminal velocity.  Also, changing clothes from say jeans and an angora sweater to a rubber suit is changing the nature of the surface area, again affecting terminal velocity.

It is these differences that I suspect are the reason there have been so many varying answers posted about what is the terminal velocity for a human in free fall.  As for the maximum speeds that have been mentioned, those represent very specific circumstances where everything was done to ensure the highest possible terminal velocity.  As for the 150-200mph range that has been oft-quoted, I can only imagine that this is perhaps the terminal velocity for a person dumped into free fall and just sort of flopping their way down to the ground.  Seeing as I am all out of bodies/willing test subjects to toss out of aircraft to test this theory, it would be great if someone could verify this for me.

But, the important thing to remember is that terminal velocity is not fixed for all humans no matter what.  It would be fixed for a specific set of conditions.  For example, the same person always jumping from 10,000 feet, always wearing the same rubber suit, and always in the same head down position with arms tucked alongside the body could expect to reach roughly the same terminal velocity each time.

Now, the million dollar question is, if all conditions were optimal, what then would be the maximum terminal velocity for a human free-falling towards the Earth?  My guess is that whatever that velocity is, the conditions to achieve it would likely prove fatal to the person attempting it.  Thank goodness there is no shortage of humans with giant cajones and a few cards short of a full deck.  

As a preemptive edit, I stopped studying physics about 2 1/2 years ago as a regular activity (it's amazing how graduating university will make a person lazy), thus I had to do a fair measure of this from my memory, and that just isn't what it used to be.  So, if there are any physicists out there, feel free to knock my explanation into shape.  I am interested in this sort of thing, but I would not claim to be an expert.

[Fozzer]

Quote:
"With air resistance acting upon an object that has been dropped the object will eventually reach a terminal velocity (around 120 mph (200 km/h) for a human body)."
Unquote.

Which is what I suggested earlier in the discussion?.....>>>>

http://en.wikipedia.org/wiki/Free_fall# ... _Mechanics

Paul....just fallen out of bed to prove the point... ...!

[Nick N]

all I have to say is he better have a change of underwear and not eat for 24-hours before    

I know that jump would force quite a bit to the other end if it were me

[Chris_F]

It builds that shock wave and creates a boom after intitial re-entry...a quick search for the average altitude tells me it's somehwere around 30,000 feet. Which seems pretty low... at the incredible speed that big thing is moving when it comes in, you'd think it'd pile up a lot of air even in the very thin upper reaches.

I think there's some misunderstanding here about sonic booms (not necessarily by you rotty).  Any object traveling faster than the speed of sound will create a shockwave in its "wake".  Actually it is similar to a boat wake in some respects.  This shockwave is the compression of the air around the object.  

If a supersonic object were to pass you you'd hear this wake as a crack or a boom.  Common mis-conseption being that the boom only occurs at the moment the object crosses the sound barrier.  Not true, it occurs any time the object is supersonic.  So the shuttle will create a sonic boom from the moment it encouters the atmosphere (where it is traveling well over the sound limit).  And our free-faller will as well.  But, like the old puzzle "if a tree falls in the forrest and nobody is around to hear it, will it make a sound?", in this case nobody will be around to hear the boom.  In fact at really high altitudes the boom is very quiet because there's so little air up there.  And in the case of the shuttle, nobody on the ground can hear the boom until it hits 30,000 feet.  Then it's close enough to the ground and encountering dense enough atmosphere.

I don't know what's typical for sonic boom audibility for other craft.  The shuttle is a big, big aircraft and likely makes quite a pressure wave.  But it's also a very clean design (supersonically) and therefore may not make as much wake as, say an F15.  I wonder how high the concorde used to be when its report was audible.

[TacitBlue]

Also, keep in mind that the shuttle is pretty massive and carries a lot of momentum. By the time it reaches air that is dense enough to create an audible boom, it is still carrying a lot of velocity because it simply hasn't slowed down enough yet despite all of the friction from the air. I wonder if our "supersonic" jumpers do the same thing?

[Chris_F]

Also, keep in mind that the shuttle is pretty massive and carries a lot of momentum. By the time it reaches air that is dense enough to create an audible boom, it is still carrying a lot of velocity because it simply hasn't slowed down enough yet despite all of the friction from the air. I wonder if our "supersonic" jumpers do the same thing?

Doubtful.  I suspect their velocity slows dramatically as they enter thicker air.  The low mass makes for rapid deceleration, so I doubt a supersonic jumper would remain supersonic very long as altitude winds down.

[TacitBlue]

Also, keep in mind that the shuttle is pretty massive and carries a lot of momentum. By the time it reaches air that is dense enough to create an audible boom, it is still carrying a lot of velocity because it simply hasn't slowed down enough yet despite all of the friction from the air. I wonder if our "supersonic" jumpers do the same thing?

Doubtful.