Fun With: Sonic Booms

[rhoenix]

This is a relatively simple question about biological stress limits.

Let's say an average man, 6'0" tall and weighing 180 pounds, is suddenly accelerated at a rate of 25 feet/second, with each second's acceleration being cumulative (e.g second 1, the person is moving at a rate of 25 feet per second - at second 5, said human would be moving 125 feet per second).

Given conditions of the area (calculate assuming that this is at sea level with a constant 70 degrees F air temperature), that person will break the sound barrier in about 46 seconds (if my math is right).

Now for the first question - what would that do to an unaided human body?

[Batman]

Given that acceleration is noticeably below a single g I predict nothing much until we get to speeds where friction becomes a concern, which Mach 1 definitely qualifies for, but I don't expect anything besides serious discomfort and the inability to keep you eyes open without harm prior to 400 kph (always barring FOD). Mach 1? I don't know if friction heat is already a concern at that speed but it's going to be seriously painful at the very least.

[JGregory32]

Wouldn't there be increasing pressure on the chest from forcing the air in front of the person to move aside?

[Cykeisme]

Let's say an average man, 6'0" tall and weighing 180 pounds, is suddenly accelerated at a rate of 25 feet/second, with each second's acceleration being cumulative (e.g second 1, the person is moving at a rate of 25 feet per second - at second 5, said human would be moving 125 feet per second).

Shouldn't the unit for acceleration be feet/second^2? That said, what is the actual rate of acceleration?
If the acceleration is in fact increasing (perhaps the propulsive force on the man increases), what is the rate of increase of acceleration?

Anyway, I think suffocation, and rupture of eardrums and other soft tissues (due to Bernoulli's principle and such) would become a problem long before drag-induced heating really starts to take effect.


Edit: After re-reading the question, I got it.. an accelration of 25 feet/second^2, in which case it is not the acceleration that is increasing.. the velocity is.. and that bit about cumulative stuff can be left out entirely without losing meaning.

[rhoenix]

Edit: After re-reading the question, I got it.. an accelration of 25 feet/second^2, in which case it is not the acceleration that is increasing.. the velocity is.. and that bit about cumulative stuff can be left out entirely without losing meaning.

Apologies; the inherent perils of posting whilst half-awake and having not taken a math class in quite a while. Thank you.

Now, the issues of friction and ruptured eardrums make sense, but would there be a separate effect as well for when this poor person becomes supersonic?

[Duckie]

If I remember correctly, planes had significant trouble breaking the sound barrier, and their wings would rip off for some reason (force of air hitting the wing at really high speeds?). I'm not sure what this means for the accelerating person, or if it would happen, but it's at least a manner of inquiry.

[Cykeisme]

Hmm after some re-thinking, you're right, in the ~45 seconds, there won't be enough time for a person to suffocate or bleed out from ruptured membranes.
We'll have to figure out of the drag will tear a person apart.

It's going to be important what direction our person is traveling in (e.g. straight forwards, or headfirst), and it may start to become important where the force is being imparted on the person (rocket boots, jetpack, or something else?).

And then that'll be some serious aerodynamic calculations that we'll need to check against anatomical information here, which are unfortunately beyond me.

[rhoenix]

It's going to be important what direction our person is traveling in (e.g. straight forwards, or headfirst), and it may start to become important where the force is being imparted on the person (rocket boots, jetpack, or something else?).

To keep things relatively simple for the time being, assume the person's moving in the least aerodynamic method possible - e.g. standing upright.

As for where the force is being exerted, let's assume for the time being that the force is being distributed more or less from the center of balance out (roughly the belly button area).

[Darth Yoshi]

At the speeds we're talking about, if the poor sod's essentially being dragged forward at supersonic velocities by his navel, air resistance is going to seriously fuck up his spine. If I remember my aerodynamics right, as you approach mach 1 the air practically forms a wall in front of you, sort of like how surface tension renders water effectively solid if Olympic divers hit the water wrong. It'll be like looping a rope through a hole in a solid wall and around the guy's waist, and then dragging him through the wall. Ouch.

This is, of course, in addition to friction burn on any exposed skin.

[Sky Captain]

What`s the highest survivable ejection speed from fighter plane? I guess that could answer the question whether human body can survive supersonic speeds.

[tim31]

I'm searching around, and there's no consistent or verifiable data on ejection, other than a consensus that there is no 'safe' ejection speed; an SR-71 pilot survived a mach 3 ejection, where others have died at takeoff speeds and less. Ejection systems are designed for pilot survival, not comfort, so broken bones, bruises, crushed vertebrae are not unexpected.

[Simon_Jester]

I'm searching around, and there's no consistent or verifiable data on ejection, other than a consensus that there is no 'safe' ejection speed; an SR-71 pilot survived a mach 3 ejection, where others have died at takeoff speeds and less. Ejection systems are designed for pilot survival, not comfort, so broken bones, bruises, crushed vertebrae are not unexpected.

He lived through that in large part because he was flying at around three times the altitude of the top of Mount Everest. The air is so thin up there that you get a lot less drag. At sea level... I doubt that would have been survivable.

Given how easily aircraft come apart at transsonic speeds if they aren't designed right, I really doubt that you could take a human being through the sound barrier without killing them, except in atmosphere so sparse that they'd asphyxiate instead.

Another point to remember here is that for a realistic Newtonian force, at some point the guy is going to stop accelerating because the drag he experiences balances out the force of 25 feet/s^2. Since 25 ft/s^2 is about 0.78g, he'll hit terminal velocity pretty quick. If he hits a physical object at that speed it will probably be fatal, but moving through the air itself won't kill him.

[Sea Skimmer]

I'm searching around, and there's no consistent or verifiable data on ejection, other than a consensus that there is no 'safe' ejection speed; an SR-71 pilot survived a mach 3 ejection, where others have died at takeoff speeds and less. Ejection systems are designed for pilot survival, not comfort, so broken bones, bruises, crushed vertebrae are not unexpected.

Keep in mind that on the SR-71, the crew wore fully sealed pressure suits not dissimilar from those designed for astronauts around the same time. It is only because of these suits that ejection even began to be possible at such high speeds and altitudes. On the B-58 and B-70 meanwhile, the crewmen did not use pressure suits but actually had ejection seats which a retracting cover that would enclose them during ejection. The B-58 was only meant to fly up to about mach 2.5 and 65,000 feet (much less then SR-71/B-70) so this gives an idea of when you start having lethal limitations.

Normal ejection seats for use by a pilot with a flight suit and helmet only are usually rated for more then mach 2.0, often less, and 50,000 foot altitudes or less. This was a serious problem for the design of the F-22 Raptor, and was one of the reasons why the pilots have to use a partial pressure suit. So basically if you get close to mach 2 or go faster, a human body becomes highly unlikely to survive. However death will be from the concussion or lung damage long before the body starts tearing apart. Injuries from successful ejections tend to come more from the 40+ gravity violence of the ejection moreso then the effects of the windblast though.

[tim31]

How hardy are these pressure suits? I had imagined that hitting slip stream and multiple times the speed of sound would have quite a concussive effect on the body.

I do recall that in US Navy Fighters and all of its offshoots ejection over about 4-500 knots would cause instant death

[Oskuro]

I do recall that in US Navy Fighters and all of its offshoots ejection over about 4-500 knots would cause instant death

The fact that this causes you to use such a gleeful smiley perplexes me.

On another note, if I recall correctly, the BlackBird would generate some serious heating on and around it due to air pressure at high speeds, wich I guess was a factor in high speed ejections (possibly mitigated with fire-proof gear).

[Sea Skimmer]

How hardy are these pressure suits? I had imagined that hitting slip stream and multiple times the speed of sound would have quite a concussive effect on the body.

Tough but judge for yourself
http://www.wvi.com/~sr71webmaster/press_suit001.html