# The Trestle

The Trestle (or more formally the Air Force Weapons Lab Transmission-Line Aircraft Simulator) is a unique structure built by the US government in the Albuquerque desert and which was used to test aircraft’s resilience against the electromagnetic pulses created by nuclear weapons.

The Trestle is three hundred metres long and nearly two hundred metres tall and made entirely from wood and glue. The presence of any metal would distort readings from EMP testing and therefore The Trestle does not even use metal nails or braces. It was built from more than fifteen thousand cubic metres of Douglas Fir and Southern Yellow Pine and was strong enough to support the weight of a fully loaded two hundred tonne B-52 Stratofortress strategic bomber.

Source

The Trestle was equipped with a two hundred gigawatt, ten megavolt Marx generator and was used to test bomber, fighter and transport aircraft and even long-range missiles. The Trestle programme was shut down in 1991 when computer simulations became good enough to simulate the effects of EMPs and the dried-out, creosote-soaked wood now poses a serious fire hazard.

Efforts are being made to have the Trestle site declared a National Historic Landmark, but these efforts are being hampered by the fact that The Trestle is located on Kirtland Air Force Base. Kirtland houses a number of Top Secret units such as the US Air Force Nuclear Weapons Centre, the 498th Nuclear Systems Wing and the Air Force Research Laboratory and therefore access to the site is highly restricted.

# Leap smear

For reasons I have discussed before it is occasionally necessary to add* a leap second to the time, in order to keep the time on Earth in line with Earth’s inconsistent rotation.

Many systems require an accurate time to function correctly and the addition of a leap second can cause these systems to malfunction. In June 2012 the addition of a leap second caused a number of major websites such as Reddit, FourSquare, Yelp, LinkedIn, Gawker and StumbleUpon to malfunction and crash, but Google came up with a unique workaround – the Leap Smear – that prevented this from happening.

Google, like many others, uses the Network Time Protocol (NTP), to synchronise time across a network.† In order to cope with the leap second problem they configured their NTP servers to gradually add a small fraction of a second over a long period of time (in this case one day) so that at the end of this period their NTP servers’ time would have caught up with the adjusted time.

$t \left(\textnormal{Google}\right) = t + gain \left( 1 -cos \left( \pi \left( \frac{t}{window} \right) \right) \right)$

Where t(Google) is the time according to Google’s NTP servers; t is the actual UTC time; gain is the desired amount of gain time (in this case one second); and window is the time over which this gain should happen (in this case twenty-four hours).

The effect of using the cosine function is such that the time offset is small at first (in the first hour only four milliseconds are added) and gradually increases (to sixty-five milliseconds per hour at most) before decreasing again towards the end of the window.

This prevented servers and devices connected to Google’s NTP servers from “noticing” that something was wrong and applying their own corrections.

As they say in their blog post,

The leap smear is talked about internally in the Site Reliability Engineering group as one of our coolest workarounds, that took a lot of experimentation and verification, but paid off by ultimately saving us massive amounts of time and energy in inspecting and refactoring code. It meant that we didn’t have to sweep our entire (large) codebase, and Google engineers developing code don’t have to worry about leap seconds.

I wouldn’t be at all surprised to see others employing Google’s Leap Smear technique in the future.

* There are also provisions to subtract a leap second, but this has never yet happened.

† The NTP does contain a “leap indicator” but Google decided to force their NTP servers not to apply this.

# The Roche limit and planetary rings

As a satellite orbits around an object (a primary), the gravitational force on the side closest to the object is greater than that on the side opposite the object. This difference in gravitational attraction gives rise to a tidal force (so-called because it is what causes the tides on Earth). As a satellite approaches closer to the body it orbits this tidal force will eventually become greater than the gravitational forces holding the satellite together. The point at which this occurs is known as the Roche limit (named for Édouard Roche who first calculated it).

The Roche limit d depends on the radius of the primary RM, the density of the primary ρM and the density of the satellite ρm.

$d = 2.44\; R_M \sqrt[3]{\frac {\rho_M} {\rho_m}}$

If we take our Earth-Moon system as an example, with the radius of Earth being 6370 kilometres, the Earth’s density as 5520 kilograms per cubic metre and the Moon’s density as 3350 kg/m3 this gives us a Roche limit of 18 400 km. The Moon’s actual orbit is 385 000 km, so luckily we don’t have to worry about the Moon breaking up any time soon.

The Earth-Moon system, to scale. The area beyond the Roche limit is shaded red.

When an orbiting object passes through the Roche limit it begins to break up, with the material closest to the object moving faster than the material behind it. This eventually leads to the formation of rings.

# The composition of nuclear electromagnetic pulses

When a nuclear weapon is detonated at high altitude the effects are very different to those created by a low-altitude detonation. Aside from creating a much larger, much faster-expanding fireball, the nuclear detonation also creates an electromagnetic pulse (EMP) that can damage electromagnetic equipment on the ground.

A nuclear EMP differs from other EMPs such as those generated by lightning strikes or by conventional EMP weapons (such as flux compression generators) in that it is much more powerful* and is composed of three different pulses called E1, E2 and E3.

## E1

The E1 pulse is the most destructive, occurring far too quickly for protective equipment to activate. It is the component that destroys computers and communications lines by causing the insulating components of these devices to become conducting and allowing electrical current to flow between regions that are not supposed to be connected, effectively short-circuiting all circuits simultaneously.

The E1 pulse is created when the intense gamma radiation from the nuclear detonation ionises atoms in the upper atmosphere (Compton scattering); releasing electrons which travel downward at relativistic speeds, about 95% of the speed of light. Any charged particle in a magnetic field will experience a force (the motor effect) and the Earth’s magnetic field causes the electrons liberated by the gamma radiation to follow a spiral path around the magnetic field lines. As the electron oscillates back and forth it creates an electromagnetic field and as there are about 1025 electrons doing this simultaneously, this creates a very powerful (about 50000 volts per metre, 6.6 megawatts per square metre) but very short-lived electromagnetic pulse. The E1 pulse typically reaches its peak value in about five billionths of a second (five nanoseconds) and ends after about one millionth of a second (one microsecond) as the scattered electrons are stopped by collisions with air molecules.

The shape of the region affected by the E1 pulse depends on latitude, due to the changing orientation of the Earth’s magnetic field. Away from the equator the region is U-shaped, and towards the equator it is more symmetrical.

## E2

The E2 component is caused, like E1, by Compton scattering when scattered gamma rays, gamma rays produced by interaction of fission neutrons with atoms in the air and gamma rays produced by radioactive decay of fission fragments ionise air particles.

The E2 component lasts from about one microsecond after detonation to one second after detonation and is very similar to the pulses created by lightning strikes. The E2 component is easy to protect against using conventional lightning protection equipment, but this protective equipment is likely to have been damaged by the E1 component and will therefore not function correctly, allowing the E2 component to cause further widespread damage.

## E3

The E3 component is very different to the E1 and E2 components. It lasts tens to hundreds of seconds and is caused when the Earth’s magnetic field “snaps” back into place after being pushed out of the way by the ionised plasma created by the expanding nuclear fireball. This induces electrical currents in conductors on the ground such as pipelines, power lines and transformers.

The E3 component is similar to the pulse created by a geomagnetic storm, when a severe (X-class) solar flare pushes on the Earth’s magnetosphere and is sometimes referred to as “Solar EMP”. In 1989 a solar EMP-type event caused the collapse of the Hydro-Québec power grid when a huge coronal mass ejection followed a X15-class solar flare.

* During a Soviet nuclear EMP test called K-3 the E3 component of the pulse fused the entire length of a 570-kilometre overhead telephone line (with currents reaching up to 3400 amperes) and the E1 component caused all of the attached overvoltage protectors to fire. The test also started a fire that caused the Karaganda power station to burn down and penetrated nearly a metre into the Earth to burn out 1000 km of buried power cables.

# Hypnic jerk

Have you ever been lying in bed, trying to get to sleep, and suddenly felt like you were falling? If you have, then you’ve experienced a hypnic jerk.

A hypnic jerk is a positive myoclonic twitch that occurs during hypnagogia, the state between being awake and being asleep. Myoclonus is a sudden, involuntary muscle twitch and a positive myoclonic twitch is one that causes a muscle, or a group of muscles, to suddenly contract.* A hiccup is a myoclonic twitch affecting the diaphragm.

The exact cause of hypnic jerks is unknown, though I have heard it suggested that it is linked to human beings’ origins as tree-dwelling primates, or that it is a defence mechanism designed to jerk you back into consciousness if the body thinks it is “shutting down” too quickly as you fall asleep.

* A negative myoclonic twitch causes a muscle or muscle group to relax.