Basically a big lawn dart, so I hope you have lots of liability insurance.
Nah, the liabilities from lawn darts come from little kids chucking them carelessly. No little kid’s gonna carelessly chuck one o’ these suckers in a hurry.
Gravity, like the centrifugal force on a spinning space station, is entirely the result of us being in an accelerated reference frame. As I sit at my desk right now, I’m accelerating upwards at almost ten meters per square second. One need not invoke curvature of spacetime at this point.
Now, you, partway around the world, are also accelerating upwards, at the same rate. As is someone in Australia, or India, or Chile. Despite not moving relative to each other, we’re all accelerating in different directions. This is where we need curvature of spacetime, to reconcile this.
If it helps, you can think of an accelerometer. Really, all Einstein is saying is that your accelerometer is correct. When you’re standing on the surface of the Earth, your accelerometer reads 1 g. If you were in deep space with your rocket engine turned off, your accelerometer would read 0 g. And if you were in the vicinity of the Earth, but falling, your accelerometer would also read 0 g. In which of these cases are you not accelerating? In the cases where your accelerometer reads 0.
What does an accelerometer use for reference?
While my friends and I were contemplating this for fun we were stuck with trying to work out the fastest animal
We started with cheetas, then falcons then we got to the big balloon in the sky
We were going along fine until we got scuppered by not understanding terminal velocity becasue pgymy shrews had been at that stage a good bet but now reading this a blue whale with gold fillings (can’t spell tungston) might be a good bet now
But I do have possibly a minor point, since the mass of your projectile can’t effect the earth choose a bigger planet to drop, Jupiter
And we’ve gone that far (must be an amazing balloon but… :)) find a huge planet with little atmosphere
And if we used a sun can you ever get a “sucking” (? ) effect, I know fires can pull things in.
Any use to anyone with actual facts?
So, we get a rod of tungsten (~10% heavier than U) about 100 ft in diameter and 1000 ft long.
This really got me thinking. See if you find the mistake I am making, because I get an amazing answer.
V=3.14rrl (can’t do squared or pi here)
And we’re going metric here, sorry.
100 ft = 30.5 m
1000 ft = 305 m
V=3.14 * 15.25 * 15.25 * 305
222 725 m3
Density of tungsten at 20 degrees C is 19.3 g/cm3
1 m3 = 100 * 100 * 100 cm3 = 1 000 000 cm3
so your projectile would weigh
222 725 * 1 000 000 *19.3 g
4 298 592 500 000 g
4 298 592 500 kg
4 298 592 tonnes
Quite a heavy object.
Round off one end, bolt some fins on the back and let 'er go. 25-30 seconds later … WHUMP!!
I wouldn’t want to be around to see it happen.
Four and a quarter **million **tons in a thousand foot long bit of tungsten?
Just seems too much…
Would it destroy the Earth? Certainly create a ripple or two…
Really[sup]2[/sup]?
When come back, bring π.
What you want to maximize for this problem is the ballistic coefficient, defined C[sub]B[/sub] = W / (C[sub]D[/sub]*A) Where A is the area of interest, C[sub]D[/sub] is the overall drag coefficient, and W is the weight.
Terminal velocity can be expressed as a function of ballistic coefficient and nothing else. This isn’t news to this thread, we already know that you want something both heavy and low-drag.
To increase this ratio, one easy way is to make the object big. Larger objects can have more volume (hence mass) per unit of surface area. A javelin will fall faster than a sewing needle with the same proportions, even if you could keep them both stable. Similarly, a cannonball will have a higher terminal velocity than a BB. So we want to have te biggest practical object. Get large enough, and your balloon isn’t going to take off.
The other critical thing is making that weight fit in a package with the least drag. A lot of people seem to keep coming back to a teardrop or airfoil shape. It’s important to realize that an airfoil isn’t designed to minimize drag as much as it’s designed to maximize lift. Drag is a necessary by-product of lift production, and while minimizing it is desireable, there are more important things to design to.
A javelin shape would probably be the best option. This minimizes cross-sectional area, which is the most important. Lowering the frontal area kills two main sources of “pressure” drag: the drag of air impacting the front surface, and the wake in the rear (the hole something punches in the air creates low pressure behind it which slows it down). There will be a corresponding increase in skin friction drag. After all, a javelin will have more surface area than a sphere of the same volume. But skin friction drag is a very minor contributor to overall drag. If, as a designer, I could reduce pressure drag by 10%, but were forced to increase friction drag by 10 times, I’d probably still come out ahead in most cases.
Stabilization efforts won’t be necessary as long as you make the javelin nose-heavy. Keeping the center of gravity ahead of the aerodynamic center (right in the middle for a symetricaly-shaped javelin) ensures positive stability. It will fly straight down with no problem. No fins necessary.
The other reason for the javelin is the inherently sharp nose. If you’re able to get this thing’s terminal velocity above the speed of sound, you’ll want a sharp nose so that it creates an attached shock wave, which is less draggy than a detached shock off a blunt body. Small cross-sectional area will also reduce create weaker shock waves (again, only important at supersonic speeds). It’s a non-issue in this scenario, however, as it’s not possible to get to supersonic speeds in free fall from 10000 feet on Earth, even with zero drag. But if you were dropping from, say, 100000 feet, it might be important.
So the short answer: the biggest, densest javelin you can get up in the balloon, with sufficient weight bias keep it nose-heavy. Perhaps a big, long spear of osmium.