# Throats, Nozzles and Shock Diamonds

All rocket engines feature a “throat”, a narrowing of the exhaust nozzle. In the photographs above this throat is obvious at the top of the images.

A de Laval nozzle (also known as a convergent-divergent nozzle) as used in rocket engines.

The question of why rocket engines all feature throats might seem like it has an obvious answer: just try blowing air out of your mouth with your mouth wide open. But the physics behind rocket throats is a little bit more complicated than that.

The nozzle of a rocket engine is designed to accelerate exhaust gases to Mach 1 at the throat, causing a process known as choking or choked flow.

Normally the rate at which a gas can flow out of a pressurised container, such as the combustion chamber of a rocket engine, is limited by the difference between the pressure of the interior of the container and the pressure of the atmosphere surrounding the container: the container tries to push gas out, and the atmosphere tries to push the gas back in. In choked flow, this dependence disappears: the outside pressure has no effect on the rate at which gas is ejected, external pressure cannot force its way past the supersonic shockwave that forms at the throat. Choked flow produces the greatest rate of flow of exhaust gases, and therefore the highest possible thrust: you cannot get the exhaust gas particles to move any faster, but you can push through more of them per second.

As a gas passes through a narrowing in a pipe its pressure decreases and its speed increases; and as the pipe expands the pressure increases and the speed decreases.* This is known as the Venturi effect.

$\frac{dv}{v}=\left( \frac{1}{M^2-1} \right) \frac{dA}{A}$

Where $\frac{dv}{v}$ is the rate of change of the velocity of the gas, $M$ is the speed of the gas as a fraction of the speed of sound (i.e. the gas’s Mach number) and $\frac {dA} {A}$ is the change in the area that the gas is flowing through.

There is a limit to the Venturi effect, and that is when the fluid reaches the (local) speed of sound, as happens during choked flow. At this point, the Venturi effect is reversed: instead of the gas slowing as the nozzle expands, its velocity increases (because the $\frac{1}{M^2-1}$ term becomes positive rather than negative).

Thus the shape of a de Laval nozzle is designed to first accelerate the gas (by narrowing) to sonic speeds at the throat, and then because the Venturi effect has been reversed, to accelerate the gas further (by expanding) to supersonic speeds. The faster the exiting exhaust gas is, the more thrust that will be produced.

Once the gas has exited the throat, the shape of the diverging (widening) part of the de Laval nozzle is such that the exhaust gases are directed backwards parallel to the body of the rocket (as shown in the middle diagram below), giving the maximum possible thrust in the direction that you want the rocket is to travel in.

An underexpanded nozzle (top) is inefficient because some of the exhaust gas is propelled backwards at an angle to the rocket’s direction of travel, i.e. pushing it right/left and back/forth rather than up. An overexpanded nozzle (bottom) is more efficient than either of the previous two, but the jet of exhaust that it produces is unstable, which could lead to your rocket veering off course.

The degree of expansion of your nozzle depends on the ambient pressure, and so nozzles are often overexpanded at low altitudes and underexpanded at very high altitudes, giving a “sweet spot” during its journey where it operates at the best possible efficiency.

When a nozzle is over- or underexpanded, a complex process can cause shock waves to form in the exhaust flow. Unburnt fuel passing through these shock waves is compressed and burnt, causing bright “shock diamonds” to form.

Shock diamonds in the exhaust of the XCOR Liquid Oxygen-Methane engine.

Shock diamonds in the exhaust of an F-16 during takeoff.

* This is an interesting example of the conservation of energy: the energy of the fluid is a combination of the fluid’s kinetic and potential energies, and as the speed (and therefore the kinetic energy) of the fluid increases, the potential energy (i.e. its pressure) must decrease.

# Where is the best place to launch a rocket from?

NASA has quite often had to “scrub” (cancel) launches from the Kennedy Space Center (KSC) in Florida because of inclement weather. But why build a Space Centre in Florida in the first place? It’s location makes it particularly vulnerable to hurricanes and other weather “events” so there must be a significant advantage to its location.

The paths of the eighty-three Florida hurricanes that occurred between 1975 and 1999.

Florida is a good location for rocket launches because it is both on the east coast of the US and because it is close to the equator.

Launching from the east coast of the US means that the rocket can take advantage of the Earth’s west-to-east spin. If a rocket were launched from the west coast it would either have to fly right across the continental US, which would be dangerous if it malfunctioned; or it would have to take off east-to-west, flying against the spin of the Earth.

At the North or South pole the speed at which you are moving, relative to a stationary observer not on Earth, is zero. As you move closer to the equator this speed increases, until at the equator you are travelling at a speed of 465 metres per second (1040 mph). At KSC, which is at a latitude of 28°N, this speed boost is reduced slightly, to about 410 m/s (916 mph). This is the best possible location in the continental USA, presumably more suitable (i.e. more southern) locations in Hawaii, Puerto Rico or one of the US’s other territories were discounted because of their remoteness.

The closer to the equator you can get, the greater the speed boost you receive. This reduces the amount of energy required to get into space and means that less fuel is required. The European Space Agency makes its launches from the Guiana Space Centre in French Guiana which is only 5° north of the equator. The commercial space launch service Sea Launch uses a mobile launch platform that sails nearly 5000 kilometres from Long Beach in Los Angeles where the rockets are assembled, to a location actually on the equator where the launches take place.

# Remembering Challenger

(A guest post from Leila Johnston.)

It’s almost exactly 25 years since one of the most tragic incidents in the history of space flight. Mission STS-51-L was to be the 25th Space Shuttle mission, an event surrounded by tremendous excitement and optimism. Children around the world knew that a schoolteacher was on board – a thrilling prospect that made the whole thing so much more human. But Sharon Christa McAuliffe never made it into space. With the world watching, the craft disintegrated just 73 seconds after launch, and all seven crew members perished in a twist of smoke. The story of Challenger is so tragic that it still feels very difficult to even look at the pre-flight footage or publicity shots. It was also avoidable.