Even with the drag of a stabilizing chute he was going 6 times ground level TV of a naked human. A naked human falling at that height would be entering thicker zones of atmosphere already having achieved that zone’s TV and being slowed down.
Kittinger was performing high altitude jump tests to see what kind of problems pilots ejecting at high altitude would face. On the third jump his right hand glove lost pressure and immobilize his hand from exposure to near vacuum. He didn’t report this till after was on the ground for fear it’d scrub the mission.
You’ve taken my sentence out of context, which is perhaps my fault; I should have left it connected with its preceding paragraph.
My point was that it’s possible to have a very large, very dense, very aerodynamic object with a sea-level TV greater than 25K mph. For such an object, it will not achieve its SLTV before reaching sea level.
Clearly the pressure-suited Captain Kittinger was neither large enough nor dense enough (nor aerodynamic enough) to fit that description.
But a solid osmium cylinder six inches in diameter and five feet in length (weight: ~1400 pounds), with an aerospike nose and modest tail fins, might conceivably perform as I described.
Sure it can. Supersonic means more drag, but there’s nothing magical about it. Fighter planes with a thrust-to-weight ratio of 1:1 - that is, propulsive force equal to the vehicle’s weight - are able to go supersonic in level flight. such an aircraft in nose-down freefall with the engines off (i.e. gravity pulling down with the same force with which the engines had been propelling the aircraft in level supersonic flight) should be able to exceed the local speed of sound without any difficulty.
Now carve the same exterior body shape from a solid block of osmium, and watch what happens. Now the weight goes from 40,000 pounds to (WAG) 400,000 pounds, with no change in drag. This thing is gonna fall pretty fast, much faster than Mach 1.
I’m sorry for the delay in responding - I’m afraid life got in the way.
I get what both of you are saying, and they are quite valid responses. I guess I’m still uncomfortable with the claim that terminal velocity is never reached when in practice it will be. I take the point though that the expression “terminal velocity” itself could be seen as meaningless.
After posting, I was thinking of a skydiver. For the sake of the argument let’s assume the equation is perfect. If a skydiver assumes the “delta wing” configuration (arms back alongside the hips) he will be approaching a certain terminal velocity. Further let’s assume that close to this terminal velocity he changes his position to the standard one (don’t know how to describe it, but it’s with the arms above the head in a V position), which has a slower terminal velocity than the delta wing one.
Then we presumably have someone approaching terminal velocity from above it - i.e. he will always be going faster than terminal velocity, but decelerating towards that figure. Is this correct? If so, it’s certainly possible to exceed terminal velocity - you just need to change your configuration from one which has a higher terminal velocity.
I’m sure when Joe Kittinger made his jump from the edge of space he actually slowed down during some phase of his fall.
If considering a non-deliberate (non-human) example, it would surely be easy to think of an object falling from space which has a bit fall off, changing the shape in such a way as to make the terminal velocity slower than the speed it had already attained.
You don’t even need a skydiver who changes his body shape. Just take any skydiver (or a cinder block, for that matter falling in a fixed configuration at his terminal velocity (~120 MPH), and have him deploy his parachute. The new configuration has a much lower sea-level terminal velocity, something like 5-10 MPH instead of ~120 MPH.
In either case, you’re changing the conditions that were supposed by the OP and everyone else here - namely, an object that does not change its basic aerodynamic configuration during the freefall.
It certainly is possible to exceed terminal velocity as you describe. It’s also possible to exceed local TV by falling from a great height (a la Capt. Kittinger), accelerating to very high speed in thin high-altitude air before reaching the thick, juicy air at lower altitudes, where you then get slowed down.
I gather you’re looking for the most specific, precisely expressed, carefully laid-out idea, one that accounts for all the possible exceptions one might think of to controver the basic concept of a freefalling atmospheric projectile. I’ll attempt a first draft here:
**For an object:
-of fixed mass;
-fixed shape;
-falling through a quiescent atmosphere in a stable orientation with respect to gravity;
-under the influence of gravity and aerodynamic drag, and no other externally applied forces,
the net force exerted upon said object - that is, the sum of gravitational attraction and aerodynamic drag - tends toward zero as the object approaches its local terminal velocity.**
By “local,” I am referring to the conditions (gravitational attraction to the earth, as well as atmospheric pressure/temperature/humidity/viscosity/chemical composition) in the immediate vicinity fo the object.
Since acceleration of the object is proportional to net force exerted upon it, it stands to reason that as the object approaches its local TV, its velocity will change less and less rapidly. Suppose its velocity differs from TV by 0.001 MPH. Is it at TV? Strictly speaking, no, it’s still accelerating (or decelerating, as the case may be) very, very slightly. Check in a while later, and its velocity now differs from TV by 0.000000000001 MPH, and it’s accelerating even more slowly.
It should be obvious now that actual velocity of our freefalling object will never reach TV unless you change local conditions; that would include changing local air density, object configuration, and/or gravitational attraction. If you change one or more of these things such that local TV changes (as with our skydiver) then the object may, depending on what’s changed, find itself either above or below (or possibly exactly at) its local TV; in either case, the object will still slowly (asymptotically) approach its new TV.
For every TV calculation, there is an error on uncertainty based on the fact that none of the input variables are known exactly. And this is even ignoring things like the slight change of gravity, wind, temp variations, brownian motion, quantum physics, turbulent flow, the random bug, and increasing air density.
IMO ONCE the falling object’s speed is closer to the asymptotic limit than the error range in calculating the TV due the imprecise nature of the calculation it has reached TV. The second set of complicating factors makes that error range even larger.
IMO anybody saying that TV isnt reached for normal things under normal conditions is being pendantic, and without good cause.
Sure, it’s pedantic, but the point is, there’s no simple answer. If you don’t invoke uncertainties in the input quantities, Brownian motion, etc., then the only answer you can give is the pedantic “It never reaches TV”, but on the other hand, there’s also no way that you can invoke things like that without also being pedantic.
But either the definition is supposed to have some use and real meaning, which it certainly can, or its an excuse to be pedantic and doesnt really mean anything because you by definition cant define it, because that would require you to know every single value with perfect precision. IMO of course.
I know where I stand (fall heh) on that one.
And I dont know why folks are wanting to use gold or expensesium or rareium or whatever. Depleted uranium would be plenty cheap and available and dense enough to build the MACH 10 falling lawn dart from hell.