I want to find out the absolute max speed for an object that you could drop from a ballloon at 10,000 feet.
What is the best shape, size, and weight?
What materials would it be made of?
What would its terminal velocity be?
Something like a cannonball would fall pretty fast but something in the shape of a downward pointed rocket would probably be better. I have no idea what the best size would be. There are also stability issues to take into account to keep the object at the optimal aerodynamic position.
Do you have any other ideas or know of any other issues to take into account?
Note: This is a theoretical rather than a practical question for now.
I don’t know much about aerodynamics, but I’d guess that the shape they use for the bombs they drop from planes would be pretty close. You could probably squeeze out a few more m/s because you aren’t limited by the space and shape needs of a particular payload.
The slipperiest shape is the teardrop shape. The secret to its low drag is the pointy end, which minimizes turbulence of the trailing air stream. I am no aerodynamics engineer, though.
I can’t tell you why cars, airplanes, the Space Shuttle, and bombs are not shaped like that, however.
I’m confused by the Question. Didn’t Newton of Galieleo prove that all items fall and hit the ground at the same time, regardless of what the objects are?
(It was Galileo.) In a vaccum, yes, but you have to take wind resistance into account. A feather and a ball bearing won’t hit the ground at the same time.
Dropped from a great height, some objects will attain a higher terminal speed because they have lower wind resistance. That’s why I suggested the javelin, which I think would reach a higher speed than any of the other shapes suggested.
IANA physicist or any other kind of cist, but several issues come to mind. There is no payload requirement, so there’s no need for the somewhat bulbous shape of a conventional air-dropped bomb. That leads me to consider a needle shape, dropped point downward of course, as the best possible shape.
In my mind the question would be if some area of stabilizing fins would be necessary to minimize the cross-section cutting through the air resistance.
I am assuming you mean dropping through 10,000 ft. of the earth’s atmosphere. And to be even more specific, I will assume you mean dropping from 10,000 feet above sea level. Can we rule out dropping from 100,000 ft and measuring the speed when it reaches 90,000 ft., for example. In this latter case, gravity-induced acceleration would be slighly lower, but atmospheric friction would be drastically lower. Can we rule out crosswinds, or limit them to within some parameters? What if you drop it through a tornado? Or… find a storm system generating strong localized down drafts?
As I write this I’m already rethinking the needle idea and veering toward a sphere, which would have the sane cross-section regardless of orientation, and would therefor have no need of stabilization fins.
So now I’m going with a sphere, made as small as possible out of the densest possible material.
So we have to be able to actually create it using today’s technology? If not, It seems to me a black hole would be the answer. If not, what is the densest possible stable solid material? Depleted uranium, maybe?
There is a payload requirement of sorts - the more mass you can cram into the projectile, the stronger the gravitational force. So you first choose the most dense material that can hold its own shape (possibly depleted uranium), and then the problem boils down to: for the given volume, what is the most aerodynamic shape?
As I understand it, a long needle is not always the answer. Frontal area of a needle is tiny, but the surface area becomes large and that also creates drag. I believe the optimal shape also depends on speed and mass. It should be some type of a long pointy cigar shape, like the cross-section of an aircraft wing (but symmetric).
No way. A sphere has a terrible coefficient of drag. A teardrop/airfoil shape with tail fins would be faster.
I'm thinking quantum black hole. It would only encounter a very few air molecules on the way down and it would be too massive for those to noticeably slow it down.
Just imagine that this is a real sport (I think it would be kind of cool). A balloon will take the competitors up to 10,000 feet for a drop. The highest average speed on the way down wins. The object has to be made of materials available today but there are no other restrictions on that. You can assume that the air is relatively calm. There is a size and weight limit based only on how much the balloon can carry (it is a large sized hot air balloon that normally carries several people).
I will grant you that, in fact I recall that raindrops form themselves into the teardrop shape as a result of atmospheric interaction – they essentially form themselves into the most efficicent shape to fall.
However, we have a different situation here, bevause the shape is fixed. The mass of a raindrop can tumble and flow, but the shape will allso chane as it passes through the stmosphere to maintain a minimal drag. I don’t know that a teardop shape that tumbles is the best choice.
I suggest hailstones are a more apt natural model for this competition, and they are closer to spheres than teardrops.
Where in the OP does it say this object has to be solid?
A drop of mercury, it seems to me, would be the ideal easy and safe real-world candidate.
It’s metal, so it’s dense, so you’ve got the greatest mass for gravitational acceleration possible. But it’s liquid, so it will naturally assume the ideal shape and orientation for falling.
Nature’s solutions are often the best, I find. The raindrop shape exists for a good reason.
Of course, there are denser materials available which can be liquified. Gold, lead, uranium, etc etc. Not that mercury isn’t dangerous enough, but it’s quite a bit safer and cheaper than the others. Molten lead, depending on the circumstances, might be a safer choice.
As an aside regarding the post about mass, I believe the US military used old 8 inch howitzer tubes (damned heavy} for “bunker buster” bombs. They just bolted on “smart bomb” tech.
Kinetic energy was the key here, I understand, because they could penetrate somthing like sixty, eighty, a hundred feet before detonation.
The OP specifies a “design” and asks “what would be the best shape…” Perhaps I’m wrong, but in my minds that constitutes a fixed shape. Otherwise you simply have a competition of selecting the best liquid to spill from the balloon.
But I will agree, should a liquid be within the bounds of a “design”, then a teardrop is probably the best shape. But that shape is continuously reconfiguring itself based on several environmental factors.
If the object is unable to reconfigure itself, I’m not convinced that a teardrop is the best choice. But as I say this, I realize I am moving into IMHO territory, all the moreso because I lack the technical background to be authoritative in this area.
So I will shut up and wait for someone with genuine knowledge to come along with a more informed response. If any of you who’ve challenged my opinions can offer some credentials to suggest your opinion is more informed than mine, I invite you to post them.
I would guess that this shape was chosen for its aerodynamic properties. Yes, it was propelled, but I’d only guess that being propelled would have to overcome even more drag, so a gravity driven projectile would not experience this.
Could we have a reality check here? Just exactly what makes you think raindrops or hailstones are shapes optimised for maximum falling speed? Hailstones are the shapes they are because of the way they are formed. Raindrops are shaped by wind resistance (OK, that’s potentially relevant) and surface tension, which may or may not act to produce a shape that causes them to fall faster.
Agreed, there’s more than just drag operating on a raindrop. There’s surface tension too which yields some inappropriate rounding.
I think the best option here is just like the Bell X-1 without wings, and the bigger the better, milled from solid iridium. The bigger you get, the mass increases to the third but the cross section to the second.
What about a long thin rod 9,999 feet long oriented to point downwards? When you let go of the top end, it only has to fall a foot before it hits the ground, which has to be pretty much the shortest possible transit time.
[sub]Yes, I know it’s cheating, but someone had to do it.[/sub]