Launching in the Sky with Diamonds

Mach Diamonds are the faint row of ovals in the exit gasses from a rocket nozzle. In this zoomed crop, you can see what looks like four of them them on my son’s rocket launch…

He put a high impulse motor in a lightweight rocket, and successfully tested the strength of his build. =)

This was an experimental motor from the Aerotech labs. It has a carbon fiber casing which can take higher pressures than the aluminum we typically use in high-power rocketry.

For the curious geeks, here is the commentary from my rocket mentor, Toma: “The Mach diamonds are formed as a result of the motor nozzle configuration, and throat exhaust exit velocity. For any rocket motor, the fluid velocity at the throat cannot exceed Mach. Ideally, the fluid flow is isentropic at the shock wave boundary that forms as the fluid departs the throat, into the expansion nozzle.

The shock wave forms at the surface and end of the nozzle of the motor, and then extends beyond the nozzles edge, forming a boundary layer with the freestream airstream fluid flowing over the rocket. You saw this in your prior photo, with the condensation trail.

Depending on the chamber pressure and exit velocity, the exit gases will stagnate as they re-approach mach again after exiting the nozzle throat as they depressurize more to the venting atmosphere. Just as the nozzle widens, the pressure drops, and the energy is converted into kinetic energy, by increasing the velocity, until it reaches the mach number of the fluid characteristics. At this point, the fluid re-pressurizes, and then the whole series starts again.

This pressurization at the nozzle throat, reacceleration of the fluid stream, and then restagnation at the mach number again, forms a single diamond. This process repeats outside the nozzle, within the shock envelope, until sufficient energy is lost through the exhaust plume expansion to entropy, that it can no long reach mach again. Mach is a property of the air density, so is affected by pressure and temperature thermodynamically outside the motor nozzle closure.

You can see the diamonds in the motor plume, because of the radiative photonics emitted by the hot exit gases. The density changes associated with the supersonic exhaust changes the optical properties of the gas, and thus, the diamonds are visible because the light emitted within them is concentrated and diffracted. You will see them in a clean burning propellant in most cases, like double base propellants, and some motors with little metals that are composite AP motors. Mostly, you see them in fluid motors. Ethane-LOX, Ethanol-LOX, F-18’s (Jet turbines are actually ducted rocket motors. Most just don’t know it).

So, yeah. Those could be mach diamonds. Especially, given the small throat of the motor. It has a carbon fiber casing, which is also a sign. Aluminum hobby motor casings cannot take the pressures and temperatures a CF casing can, and so you usually do not see mach diamonds with them, because they can not take the pressures required to produce them in the exhaust.”

And for those who just want the equations, NASA has a good page on Isentropic Flow with a rocket nozzle.