Aerotech I357

TDK I300

OH YEAH. The one drawback was that this motor was not nearly as loud and generally “nasty” sounding as the higher pressure one. This was down at a Kn of 180, and operation was completely smooth, coming up to pressure and shutting down cleanly. I like this a lot. I have a 54/1050 and two 38/640s of this stuff ready to go next…

I’ve been working on a new blue formula as of late. Consider this the first “official release”. It was conceived in January, first fired in April, and first fired with data last weekend. It’s a smokeless variant of the typical blue I’ve flown in the past — 1% CuO, 2% Al — with the goal of getting something “Blue Thunder“-like. The story of the first flight is up in a blog post on OurPlanet.

First reactions from the flight were: (1) Not quite as fast as Blue Thunder, but certainly nice nonetheless, and (2) Oh my, look at that flame separation. Data from static testing showed that this burn was only at ~570 PSI, but the flame stands off nicely, even at low chamber pressures. It turns out to be about as fast as Kosdon fast, at least per the data. Here’s a typical curve from a Loki 38/480 firing:

Delivered Isp is somewhere around 200 sec, so nothing too special — just another “knob” propellant to add to the fray. Formula and rate data after the jump.

“SA Blue” (named such as I envisioned doing this in a C-slot for a Standard Arm I’m building) is 2% Al 400, 1% CuO, 80% solids with all 200 mic AP. Pretty much as simple as you can make it. But I like how it performs; not much to no slag on the nozzle, and a lot tamer than high CuO formulations (Amarillo Blue, I’m lookin at you…). Initial data says r = 0.0175P_c^0.42 (P_c in PSI) with a theoretical C* of 4632 ft/sec, safe to run between Kn = 200 and 300 in most situations. Maybe one day I’ll try it in a 2550 — right now it looks like just over 900 PSI and a 1.8 sec burn. L1500 anyone? Maybe after it’s better characterized…

The linear model for erosive burning (as posited in Zucrow & Hoffman, Green, and other sources) posits a direct linear correlation between local Mach number (or, assuming a homogeneous chamber temperature, local gas velocity) and increased burn rate, due primarily to compressibility. Several nonlinear models exist, too (Renie & Osborn, Lenoir & Robillard, King, Radzan & Kuo…), which are also related to gas velocity by way of mass flux. The

In small-scale metal-laden high solids loading propellant systems (as we in hobby rocketry build and fly), heat transfer effects seem to play a larger role in accelerating the burn than compressibility does, as simulations of pure grain length-induced erosivity achieve the greatest success using nonlinear methods. My gut feeling says the reasons for this are twofold. First, the physical properties of typical EX propellant allow it to withstand minor surface disturbance. Secondly, most EXers tend to follow very conservative design rules, ensuring the Mach number throughout the core of the motor is far below 1.

John DeMar’s simulations (and test data) shown above are based on the Lenoir-Robillard model. From Humble, Henry, and Larson:

Probably the best-known correlation for this effect is that of Lenoir and Robillard:

where and are new constants which must be determined experimentally, and is the length of the grain. In addition, the parameter is the bore mass flux (kg/m^2-s), and the 0.8 exponent comes from the effects of convective heat transfer. We consider the Lenoir-Robillard model as an erosion based on mass flux.

So that works. However, one of my strange long-term obsessions is the double-taper grain geometry. Ideally, the geometry is based such that the flow chokes in the core on its way to the nozzle to generate a large pressure (read: thrust) spike at startup. My concern is choking the flow for too long and ultimately blowing up the motor. Any simulations require a good erosive burning model, but I hesitate to jump straight to the Lenoir-Robillard equation, because it seems that compressibility is suddenly very important to the motor’s regression profile. (This is the part where I do more static testing so I don’t force my foot too far into my mouth.) Perhaps an appropriate course of action would be to modify Lenoir-Robillard with the aforementioned linear model proposed by Green, into something like

I might just go out, cast up a double taper motor, and fire it instead. If the motor works, it’ll help me figure out whether this is a reasonable train of thought. If the motor blows up, well at least I’ll have a little bit of pressure data to see how things were beginning to shape up!