Monday, September 28, 2015

Superspeed and Other Powers I Wish I Had: A Report

In the chapter Flash Facts - Friction, Drag, and Sound, James Kakalios examines the possibility of the crazy physics of the Flash, the supersonic superhero who, after lightning strike laboratory incident, gains the ability to travel incredible speeds. This in turn opens up a surprisingly diverse set of talents for him..

The most basic one is building-scaling. The author found that it is actually possible for the Flash to run up the side of a building. If you disregard the insane speed necessary to perform the feat, the physics mostly check out....mostly. In order to travel the vertical distance of the building, he needs to have a high enough velocity to overcome the gravity that pulls at him in the opposite direction, which can be put into the equation v2=(2gh). James Kakalios compares this to an earlier chapter on Superman, where to reach a height of 660ft, he would need to have an initial velocity of 140mph. This wouldn't be a problem for the Flash who can run near light speed.

However, one of the most important forces to the Flash in order for his power to be relevant is friction. Without friction, he could windmill as much as he liked and wouldn't get anywhere. One particular villain with ice powers was able to incapacitate him this way. In order to travel up the side of the building, he needs enough friction to propel him forwards, vertically. However this in itself is a problem because friction is proportional to the weight being exerted perpendicularly on a surface, and as the Flash runs up a wall, none of his weight is acting down into the wall. Technically there can't exist any friction and so his powers are negated.

This problem is solved by examining his stride length for the speed he's traveling. Friction becomes barely relevant when you realize that his feet would only touch the ground once every 660ft if he's traveling a mere 3600mph or 5250ft/s. This alone is enough to cover the height of the building in the Superman problem, between footfalls.

Regardless, he would get smashed into the side of the wall from the force of the sudden 90 degree change in direction.

Another thing the author examines is the realism in the physics of the Flash's famous ability to run on water. It turns out that water has a high enough viscosity that it doesn't have time to move out of the way of his feet. Similar to how falling into water from a height is always described as feeling like hitting cement, the impact is so sudden that it creates a high density region where there is contact with the water. It acts more like a solid at the speed that the Flash travels at. There is still the issue of gaining momentum through friction, but it could be possible if he created backwards spinning vortices similar to how a water-strider propels itself.

Kakalios, James. "Flash Facts - Friction, Drag, and Sound." The Physics of Superheroes. New York: Gotham, 2005. 57-68. Print.

Sunday, September 20, 2015

Avoiding Death by Shockwave

A major meteor impact event is inevitable in Earth's future. There's 150 million asteroids over 100m orbiting just in the inner solar system. Luckily for us, thanks to NASA's NEAR program and other scientific efforts, all asteroids over 1km have been cataloged, and they're working to track all asteroids over 140m by 2020. However, to give perspective on this, the Tunguska event's object, which leveled over 80 million trees over an area of more than 700 miles is estimated to have only been 30m. Something of a relatively minor size compared to what is tracked could easily devastate a large area. Given, the Earth is mostly water, and chances are that it would never hit anywhere remotely populated, but if 30m can devastate an area that large, the 150 million over 100m are a considerable threat.
There are several legitimate asteroid deflection strategies that have been proposed by NASA, ranging from nuclear detonations to gravity tractors.

Despite the ridiculous plot of Armageddon, they kind of got right the part that nuclear detonations are the most effective logistically out of all the methods. Depending on the situation, it could work better to either detonate it by flyby, on the surface, or subsurface. The important part is to not fragment it though--we have good enough detection systems that it would (likely) never be as close of a call as it was in Armageddon, and the point is to push it off trajectory, not split it into several pieces of matter that have several different paths. The "astronauts" in Armageddon were lucky that their space rock was not in fact a collection of space rock rubble held together by gravity, which would have exploded and become atmospheric buckshot.

The point of the tracking systems is to have warning enough to change the course of a dangerous object. We don't currently possess anything that could release the amount of energy required to significantly alter the course of a large asteroid if it's already close to Earth. A nuclear detonation could best be used to change the change slightly change its path that over time it would miss our little planet.

Kinetic impact would be the next most effective. This is essentially launching something at the object to knock it off course. Of course, it has to have enough mass and velocity to even affect the object. The average asteroid orbits at a speed of 25km/s, or 55,900mph. The fastest spacecraft we have to date, New Horizons, reached a top speed of 40km/s after being assisted by Earth's orbital motion, but quickly dropped off in speed to around 19km/s by the time it reached Jupiter.

However, its mass is only 478kg, which would be utterly useless in stopping a medium asteroid such as 25143 Itokawa, which is has a diameter of about 400m and a mass of 3.5x1010kg. It would barely change its course.

The Deep Impact mission, which drove a 370kg impactor into Temple 1, a comet with a mass of 7.2x1013 at a speed of 28.6km/s affected the comet as to cause a 0.0001 mm/s change in its velocity and decrease its perihelion by 10m. However, if this same impact had been delivered to a comet 125m in diameter, in 10 years it would be moved by one radius of the Earth, or 6741km. So kinetic impact would be an effective deflection method, and we have the technology to execute it, if we have enough warning. The larger the object, the more time we need to significantly alter its course.

However, any unexpected celestial bodies and we're screwed.

Sunday, September 13, 2015

A Study of the Messiness of Death by Rail Gun

The year is 1996. The movie, Eraser. The muscles and guns hero....Arnold Schwarzenegger.

So Arnold is at the warehouse, and decides to give the Bad Guys a taste of their own creation. That is, violent death by railgun. But how realistic is the violence, for both parties involved?

First, we want to find out exactly how much firing one of those hurt.

With the law of conservation of momentum, we can use the equation:

Where a=Arnold and b=bullet

So for the values, I found:

Ma= 113kg (the Governator is reported to weight about 250lb)
Mb= 0.1kg
Vi,a= 0m/s
Vi,b= 0m/s
Vf,a= ?
Vf,b= 1.80x108m/s (I interpreted "near the speed of light" as 60% of the full 3x108m/s)

To calculate Arnie's final velocity:

Since the left side zeroes out, we can rearrange the equation to
Vf,a = -MbVf,b M

Fill in the fun parts
Vf,a = (0.1kg)(1.80x108m/s) / 113kg
the kgs cancel out to give the final units of m/s

And this is his final velocity
Vf,a 1.6x105m/s

While only traveling at 0.05% of the speed of light, that's still 356,078mph and probably won't feel good even in his smithereened state.

yeah that's gonna hurt

Next, we find out what this feels like to be on the receiving end.

Where v=Victim and b=bullet

Mv85kg (these guys didn't look too hefty)
Vf,v/b= ? (determined as one value if we're assuming the bullet stuck and they traveled together)

The equation for this
V(Mv + Mb) = MvVi,v+MbVi,b

Arranges down to
Vf  = MbVi,b Mv + Mb

And with the values plugged in
Vf  = (0.1kg)(1.80x108m/s) 85.1kg

Vf  = 2.1x105m/s
The victim is sent flying by the projectile from the rail gun at a speed of 2.1x105m/s, or 472,819mph......ouch.

Conclusion: This movie was not depicted nearly as violently as it should've been.

Saturday, September 5, 2015

Mission Impossible: Trying to refer to Tom Cruise as anything other than Tom Cruise is pointless

1. In the bridge attack scene, Tom Cruise quickly assembles his G36 just in time to shoot down the drone that's coming in for a second pass at him, after missing the first time to annihilate his car. He looks over a large hole blown in the road, the only ground remaining obstructed by a flaming wreck, to see The Bad Guy about to escape onto a helicopter. He takes off on a short running start, tosses his gun, and barely clears the gap, sliding and catching the edge. While Tom Hunt is known for performing many almost certainly impossible feats, is this one of them? Useful things to know are his velocity at takeoff and the distance of the gap. Tom Cruise claims he can run 17mph and while this is almost certainly not true, it's plausible for his character. As an athlete it is possible to reach maximum speed within 4-6 strides and he takes about 7. The gap is about the width of 7 tires, assuming they're about 26" in diameter that makes it 4.6m wide. In this past olympics, 11th place in the women's long jump was given to one Ivana Spanovic with a distance of 6.35m. Another thing to consider is that while Tom Cruise may occasionally act like a tank or some sort of invincible armored car, he doesn't behave like one in accelerating straight over drop-offs. His jump gives him a little more vertical lift as he crosses. Given this, the amount of acceleration he has, and as an adult male in good physical condition, it is possible that he would have made this jump.

2. Another question of physics comes up with the jump/swing scene. Tom Cruise is desperate to get his wife back, desperate enough to do some literal sketchy math and decide he can reach the top of his target building simply by swinging from a taller building next to it, effectively making all of Bad Guy's security measures useless. We're given all sorts of relevant information, such as his target building (B) is 162m, his swing point (A) 226m, and the buildings are separated by the strangely exact distance of 47.55m. The difference in height is 64m. With some basic trigonometry you find that to reach a cable in a straight line from the fulcrum point of building A to a point straight across on the roof of building B would require it to be 80m. Tom Cruise most likely calculated for it to be a little shorter so that he didn't become abstract window paint. The physics question remaining out of this would be: can he reach a high enough speed from his starting angle, when the rope first snaps taut after his jump, to carry him far and high enough to not simply fall short and slam back into building A? Important factors for this would be his speed, the distance along the path of the arc that the angle (about 130 degrees) creates, and possibly his mass? With some more math I found that the arc length is about 216m. At this point I'm fairly sure this turns into a 2D kinematics problem (hopefully for Tom Cruise's sake not a collision one) where you treat his initial freefall and the swing separately to calculate the speed, however attempting this I got straight up lost so I'll leave it as a posed question. To the inexperienced eye he appears to impossibly speed up in the second half of the arc on the upswing when they cut between shots but only physics can truly determine exactly how stupid desperate Tom Cruise was here.

3. The last scene I chose was the helicopter chase scene. They are escaping after a successful rescue mission of soon-to-be creepy-eyes-dead-lady, but are being pursued through a field of wind turbines by an Apache helicopter armed with among other things, heat-seeking missiles. After several close calls the pilot of Tom Cruise's helicopter decides to kill them all by flying through a turbine, just kidding, it's a tricky evasive maneuver and the Bad Guys fall right for it, flying through after them and not being able to perform a similar not-dying stunt. So the question is: can they really be that stupid or is there some typical movie trickery going on that makes the Bad Guys always lose? And the actual physics question is: at the velocity they were following at, and the timing of the blades, should the Apache helicopter also have made it through the turbine? Appropriate values to find would be the velocities of both helicopters, the distance through the turbine, and the speed of the blades. None of these are available or easily calculable in standard measurements so I will be using approximations. Up until this point, the Apache has been matching team TC's copter, never more than 2-3 seconds behind. The speed of the blades is approx. one rotation per second. The first helicopter takes exactly this second to fly through, the next blade actually looks like it should come down on the tip of the tail. The Apache, approaching the turbine at an identical velocity, takes almost three full seconds to pass through from the exact same point. The third blade crunches with a satisfying explosion directly into the middle of the helicopter. It's not possible for the helicopter to have slowed down that quickly from the speed they were pursuing at (Apache top speed is 182). If I had actual values to plug in I would find this clearly violates some kind of minorly super important stuff, like the basic laws of motion.