It might be a good idea to mine mars - the crust could be substantially thicker than that of earth allowing a much higher volume of mineable mineral.
Lunar Mining
The liquid core of the moon, unlike earth comprises only about 25% of its diameter. (link) This means that the solid crust is, on average, about 1400 km thick. A lunar mine-shaft could stretch 800 miles straight down before it could reach liquid core. On earth the deepest recorded shaft is only 12 kilometers, about 7.4 miles, about 1% of the depth that it could reach on the moon.
As the core cools the denser material stays inside toward the center and the lighter material floats at the surface where it can cool. This is interesting because the moon is arguably made of the same "stuff" as the earth (link) so the kinds of materials that can be mined deep in the crust of the moon are substantially not acessible on earth. Not only is the material of the moon able to be mined much more extensively than earth but there is stuff "there" that isn't "here".
Why is the moon so non-liquid while earth is less than 1% as much cooled? The intensity of energy incident on the earth and the moon is arguably the same over their shared history. The atmosphere of the earth reduces the amount of heat that can escape - the greenhouse prevents the surface of earth from exposure to the radiative thermal sink of outer space.
Mining Mars:
Although earth has a "nice warm blanket" the moon does not. Mars also does not. It is farther from the sun, and has less of a "blanket'. Mars should have substantial core thickness.
Mars does not necessarily have the degree of similarity of composition that the earth-moon system does. Although it planets form by core accretion and tidal downsizing (link), the idea of ballistic coefficient for particles during nova implies an inhomogenous distribution of the accretion disc. Denser atoms have a greater capacity to store kinetic energy, and will (ceteris paribus) have to travel farther through the same resistive medium to dissipate the energy. Ballistic coefficient comes into play - a measure that accounts for gravity, dissipative interactions, and average velocity in an accretion disc.
The mantle of Mars is estimated to have a core radius that is around 1700 km (link). Mars has a planetary radius of 3376.2 km. This gives a worst case accessible crust depth of 3376.2 - 1700 = 1676.2 km. While mars has a crust thickness comparable to the moon, it has a diameter that is about 1.95x larger (link), or a volume ratio of 7.425x.
Bottom line:
While mining earth is a developmental requirement, the moon has a much larger mineable volume. While mining the moon is likely not a bad idea in the short term, there is a lot more mineable (and possibly habitable) volume in Mars.
Update (2020):
It seems others are thinking about this now.
https://phys.org/news/2020-07-lava-tubes-exploration-priority-worlds.html
Tuesday, May 15, 2012
Saturday, January 28, 2012
Curving a bullet
So Mythbusters Season 6 Episode 6 is titled "Curving Bullets". They conclude it is busted - humans can't aim and even if they could the bullets don't curve. Even machines cannot make modern bullets curve.
Could a "smart bullet" follow a non-linear trajectory? If there were a microchip and fins on the bullet, or even tiny rocket motors - what would be required to make the bullet change its target?
Question: A curveball follows a curved path in the air, why couldn't a bullet?
Short Answer: The aerodynamic forces acting on the ball are large enough that they can influence the path of the ball during its flight.
Law: There are 5 laws in physics that are never broken, and the one that applies here is balance of linear momentum. The rate of change in momentum of the ball equals the vector sum of the instantaneous acting forces.
Analysis:
A non-curved regulation ball has a mass of about 5 ounces (0.142 kg) and flies 60 feet (18.28 m) at around 100 miles per hour (44.7 m/s). It travels the path in about 0.4 seconds and its momentum is the mass times the velocity or about 6.34 kg*m/s.
A curveball can deviate from the path by about 1 foot (0.3 m). In order to travel that distance in the same amount of time the ball must be traveling an average of 0.75 m/s (1.67 mph) perpendicular to its initial line of motion. That means that the average momentum imparted by aerodynamic forces is going to be 0.105 kg*m/s, therefore the average perpendicular force is about 0.2625 N. Peak values may be higher.
The mass of a 32 grain 22 caliber bullet (long rifle bullet) is about 2.1 grams (0.0021 kg). It travels at about 500 meters per second. This means that the parallel momentum is going to be 1.05 kg*m/s. The time to act, however is much smaller. The bullet traverses the path in 0.03656 seconds therefore the required average externally (aerodynamic or other) force acting perpendicular must be such that the bullet is displaced 0.3 meters in that time therefore its average perpendicular speed must be at least 8.2 m/s (18.34 mph). Using this value the change in momentum per time must be 0.471 Newtons, or about 1.8x the force from the curveball.
The frontal area of the baseball is 6.47 square inches while that of the bullet is 0.038 square inches. Aerodynamic forces are usually proportional to these areas so all things being equal the ratio of an aerodynamic force acting on a baseball is 6.47/0.038 = 170.26 times larger. Given the ratio of the forces needed is 1.8x and the impact of the frontal areas ... one needs to amplify the aerodynamic force acting on a curveball by about 1.8*170.26 = 306.47 times larger to get the same effect on the bullet.
Conclusions:
I think that if there were conventional means to do that without active/powered help then a good pitcher (like Randy Johnson) would have figured that out and used it in his curveballs to make it fly in circles.
The same powder that makes the bullet go one way could make it go another ... so a small amount of powder stored inside the bullet could conceivably be triggered in-flight by an on-board chip, to make the bullet slightly change direction. The real challenge there would be to get the bullet to behave in a controllable manner. Guns use big steel barrels and rifling in order to channel the energy from the gunpowder into the bullet in a controlled way and miniaturizing that is not going to be simple or cheap.
Whatever it is that makes the bullet change it's target - it is not a passive system. It is active and complex.
Addendum:
It might be easier to make a bullet that doesn't change its trajectory due to wind than it would be to make one that uses the air to change its aim.
Update (02Feb2012):
Sandia Labs Makes Smart Bullet (link, link). They take out spin. The make it long, put the cg way front, and put electromagnetically actuated fins on it (meaning it is naturally stable in orientation). It is meant for the far field, thousands of meters away using a laser-designator - this is a sniper weapon, or at least a weapon requiring an informed illumination of the target for the duration of the flight.
Update (28Apr2014):
DOD now says that (EXACTO) - Extreme Accuracy Taked Ordinance - now works. (link, link) The claim is that they can turn a newbie sniper into a better shot than a veteran sniper. This likely has large implications for drone-mounted weapons.
Could a "smart bullet" follow a non-linear trajectory? If there were a microchip and fins on the bullet, or even tiny rocket motors - what would be required to make the bullet change its target?
Question: A curveball follows a curved path in the air, why couldn't a bullet?
Short Answer: The aerodynamic forces acting on the ball are large enough that they can influence the path of the ball during its flight.
Law: There are 5 laws in physics that are never broken, and the one that applies here is balance of linear momentum. The rate of change in momentum of the ball equals the vector sum of the instantaneous acting forces.
Analysis:
A non-curved regulation ball has a mass of about 5 ounces (0.142 kg) and flies 60 feet (18.28 m) at around 100 miles per hour (44.7 m/s). It travels the path in about 0.4 seconds and its momentum is the mass times the velocity or about 6.34 kg*m/s.
A curveball can deviate from the path by about 1 foot (0.3 m). In order to travel that distance in the same amount of time the ball must be traveling an average of 0.75 m/s (1.67 mph) perpendicular to its initial line of motion. That means that the average momentum imparted by aerodynamic forces is going to be 0.105 kg*m/s, therefore the average perpendicular force is about 0.2625 N. Peak values may be higher.
The mass of a 32 grain 22 caliber bullet (long rifle bullet) is about 2.1 grams (0.0021 kg). It travels at about 500 meters per second. This means that the parallel momentum is going to be 1.05 kg*m/s. The time to act, however is much smaller. The bullet traverses the path in 0.03656 seconds therefore the required average externally (aerodynamic or other) force acting perpendicular must be such that the bullet is displaced 0.3 meters in that time therefore its average perpendicular speed must be at least 8.2 m/s (18.34 mph). Using this value the change in momentum per time must be 0.471 Newtons, or about 1.8x the force from the curveball.
The frontal area of the baseball is 6.47 square inches while that of the bullet is 0.038 square inches. Aerodynamic forces are usually proportional to these areas so all things being equal the ratio of an aerodynamic force acting on a baseball is 6.47/0.038 = 170.26 times larger. Given the ratio of the forces needed is 1.8x and the impact of the frontal areas ... one needs to amplify the aerodynamic force acting on a curveball by about 1.8*170.26 = 306.47 times larger to get the same effect on the bullet.
Conclusions:
I think that if there were conventional means to do that without active/powered help then a good pitcher (like Randy Johnson) would have figured that out and used it in his curveballs to make it fly in circles.
The same powder that makes the bullet go one way could make it go another ... so a small amount of powder stored inside the bullet could conceivably be triggered in-flight by an on-board chip, to make the bullet slightly change direction. The real challenge there would be to get the bullet to behave in a controllable manner. Guns use big steel barrels and rifling in order to channel the energy from the gunpowder into the bullet in a controlled way and miniaturizing that is not going to be simple or cheap.
Whatever it is that makes the bullet change it's target - it is not a passive system. It is active and complex.
Addendum:
It might be easier to make a bullet that doesn't change its trajectory due to wind than it would be to make one that uses the air to change its aim.
Update (02Feb2012):
Sandia Labs Makes Smart Bullet (link, link). They take out spin. The make it long, put the cg way front, and put electromagnetically actuated fins on it (meaning it is naturally stable in orientation). It is meant for the far field, thousands of meters away using a laser-designator - this is a sniper weapon, or at least a weapon requiring an informed illumination of the target for the duration of the flight.
Update (28Apr2014):
DOD now says that (EXACTO) - Extreme Accuracy Taked Ordinance - now works. (link, link) The claim is that they can turn a newbie sniper into a better shot than a veteran sniper. This likely has large implications for drone-mounted weapons.
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