Question for you aerodynamic types

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Sep 22, 2014
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Here is a question for you aerodynamic types.

Can an object (dart or other) free fall from zero initial velocity and transition into the supersonic speeds only under the influence of gravity ? This means a rocket or dart with no initial means of thrust, falling from a high altitude toward the Earth, can ultimately increase in speed until it goes supersonic.

I have had this discussion with coworkers over the years and always get two opposite answers:

1. NO. The transonic Cd is too great and it will limit the free fall velocity prohibiting the object from ever going into the supersonic region.

2. YES. If the object is properly designed to quickly get throught the transonic region, then yes it will.

Any definitive answers from anyone ?
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Felix Baumgartner did it, so I'm going to go with a yes. And man is not very aerodynamic.

Speed of sound is a function of temperature and viscosity. Go high enough where the air is cold and thin, going supersonic is relatively easy even for a dude in a space suit. It would probably not sustain supersonic speeds all the way through freefall though, as it would slow down as it enters the warm thick air.
You accelerate from standstill (out in the wispy atmosphere or space somewhere) to the point where atmospheric drag equals gravity pull. Your peak speed is at that point and if you are faster than the speed of sound you have done it. That altitude in the atmosphere depends on your drag coefficient and mass, surface area and starting altitude. Basically if you are far enough out you can come in almost as fast as you want. Baumgartner's limit was the height (128k') a balloon could lift him. Caution: don't exceed human physical limits :wink:
It takes a long way, iirc a minimum of 16,000 feet (I didn't do the math, just number I remembered)
Ejection failures on heavy minimum diameter rockets will come in supersonic.
was thinking that the 'tallboy' and 'grand slam' bombs could do it but, the wiki states they topped out at 750 mph. on the other hand they were dropped from 18k...wonder what they could do from a higher drop height.
IIRC Two humans have reached supersonic speeds by jumping out of high altitude balloons.
You can watch supersonic falling happen every time SpaceX lands a booster. Once it hits the troposphere it slows down a lot.

So it is safe to say that gravity can easily accelerate an object beyond the speed of sound, so long as it is in thin air. The jury is still out as to whether this can happen at ambient air pressure.
A regular skydiver will have a terminal velocity of only a few hundred mph at best.

You need to go seriously high to get the drag down enough for supersonic peak speed.

As was said, SpaceX do it all the time. Watch the deceleration figures on the telemetry from the flights. The velocity goes up as the booster is falling, and then it abruptly washes off speed somewhere around the 30km mark IIRC.

Here is a nice artilce on Baumgartner's jump: