## Tuesday, October 27, 2009

### The Stick Does Not Pogo

With the upcoming test flight of the Ares IX, there is lots of talk about high vibration levels and design problems with the big solid first stage. One common misconception I've noticed (and pointed out) a couple times is that folks think Ares I might have pogo oscillations. Pogo oscillations are a specific type of propulsion-structure interaction that occurs in liquid rockets, not solids.

Here's a succinct description of what pogo is (Rubin, 1970, emphasis mine):
Many liquid rocket vehicles have experienced longitudinal vibration because of an instability arising from interaction of the vehicle structure with the propulsion system. The vibrations, nicknamed pogo'' after the jumping stick, have occurred principally in the first longitudinal structural mode during operation of the first liquid-propellant stage of a launch vehicle.

From the same report, here's a figure of the accelerations characteristic of pogo.

The dynamic instability being described here is not simply resonant forcing. There is a positive feedback loop.
A block diagram of the positive feedback process which can lead to instability is shown in figure 2. Structural vibratory accelerations induce the propulsion system to generate forces which can then intensify the original vibration. When the system becomes unstable, oscillations will appear spontaneously.

--Rubin (1970), emphasis mine

Rubin gives a further description of the two types of pogo.
Two basic kinds of propulsion-system behavior have produced pogo instability. The common form of pogo, called engine-coupled pogo, has been experienced to a significant degree on certain configurations of the Thor, Titan, and Saturn space vehicles. This form results from the action of the tank-to-engine propellant feed-lines and the engine itself (fig 3.) When the vehicle vibrates longitudinally, the pump and the propellant in the flexible tank undergo oscillatory motions. These two motions produce oscillating flow in the feed-line and in the pump's discharge line. The flow oscillations lead to oscillations in engine thrust and in pressure at the pump inlet, which then act as regenerative forcing functions on the vehicle structure. The feedback loop is thereby closed. Although a pump is included in figure 3, pogo can also occur in pressure-fed systems.

A much less common form of pogo results from the pneumatic behavior of an active pressurization system for the propellant tank ullage. This form is known as ullage-coupled pogo, and has been experienced only on Atlas vehicles immediately after liftoff. It has also been referred to as pneumatic-coupled pogo, or bloating''. A simplified schematic of an active pneumatic system for pressurizing a tank is shown in figure 4. When the vehicle vibrates longitudinally, the tank ullage pressure oscillates because of oscillation of the ullage-volume boundaries. The sense line transmits the pressure oscillation to the regulator. The regulator responds by producing an oscillatory flow of pressurant (i.e., the pressurizing gas) into the supply line which regenerates the ullage-pressure oscillation that acts as an axial forcing function on the vehicle structure, and again the feedback loop is closed.

The big SRB being contemplated for use in Ares I probably does have lots of combustion instabilities which will cause some wicked forcing on the rocket. It may even couple well to the rocket's lower longitudinal modes, but that is not pogo. There is no positive feedback there, just lots of hammering on the structure (and the astronauts).