But what if the aft grain is small? It’d pack more propellant in the motor, but bad things could also happen. Common industry wisdom says keep a throat to port (thanks James!) area ratio of 0.5; McCreary is a bit sportier in “Experimental Composite Propellant“, going for a diameter ratio of 0.75 (and thus an area ratio of ~0.56). Of course, many rocketeers have been known to push this limit, even so far as to have a port the same size or smaller than the throat. And it works, sometimes. So what happens as the port size is increased?

There are some simple gas effects that we can model fairly easily using ideal rocket assumptions. The major item is a pressure differential that develops between the head end and the aft end of the grain. If you’ve ever bought an Aerotech 38/1080 motor and wondered why it needs a seal disk, while a 38/240 does not, it’s because of this pressure differential issue. (The seal disk keeps the gas leak from focusing over the edge of the liner, eroding it quickly and leading to forward end heat problems.) This pressure differential develops because mass is being added down the length of the rocket motor, and this mass needs to be accelerated by the gas flow to sonic velocity at the nozzle throat. Since temperature is constant throughout the motor, the energy lost to accelerating the gas shows up as a pressure loss.

How do we calculate this? The first thing to do is to figure out the gas velocity over the aft end of the grain. We can turn to our old isentropic flow friends to help us out — we know the port to throat area ratio Ap/At, so all we have to do is apply the area-Mach relation and we’ll have what we’re looking for there:

With the Mach number in hand, now we move on to using a simplification of the compressible flow god equation (topic for another post…) neglecting all terms except mass addition, to give the pressure ratio as a function of Mach number. (Think of this as the mdot version of Fanno flow or Rayleigh flow.) Considering the head end of the motor as location 1 and the aft end as location 2, we get:

So why does this matter, and how do you figure stuff out with it? Well, first of all, it affects the thrust of your motor — since there is energy lost in the system, neglecting erosive effects, you are losing thrust when compared to a simple lumped-parameter ballistic calculation. Calculating phi allows you to figure out exactly what your thrust loss is, since you want to be using the static pressure at the nozzle end to calculate thrust; in the words of my favorite propulsion professor, “no matter your vices and sins upstream, your thrust is determined by the pressure feeding the nozzle.” This also contributes to additional stress on the head end of the motor; if your have a burn that is already “on edge” in terms of your hardware strength, you could be in trouble here, too. (This is particularly important if you have a handle on the erosive behavior of the motor; though you might be designing in an erosive spike at startup, the combination of the spike and the increased head end pressure might be enough to blow the bulkhead.)

You can calculate the pressures at each end by simply using a conservation of mass flowrate — we’re still in steady-state ballistics land, so (mdot in) = (mdot out). Assuming a constant (conservative) burning rate for the propellant down the length of the motor:

Of course, this analysis does not take into account various propellant combustion effects. Having a port smaller than the throat will cause the choke point to be in the grain at startup, rather than in the nozzle throat. This can have a nasty effect on motor performance, what with shock waves forming and all, and can also lead to serious erosive burning effects as the gas velocity increases and the boundary layer thins. That’s the somewhat unpredictable part; it depends on propellant quality, composition, and rheology. But at least it gives us some insight into what exactly is going on when we tighten up the port in search of better performance.

SNPE Butacene® 800 is a liquid resin based on HTPB (hydroxy terminated polybutadiene) and grafted with a ferrocene derivative in the chain. It is used as a binder in high burning rate ammonium perchlorate based composite propellants. It leads to a higher burning rate with low pressure exponent without migration during aging.

It is manufactured by SNPE Energetic Materials (http://www.materiaux-energetiques.com/ — they also manufacture Ammonium Perchlorate and other chemicals for aerospace and defense) and imported by Mach I. The datasheet claims that the chemical structure of Butacene prevents migration of the catalyst, and still allows it to be fully miscible with standard HTPB.

I’m seriously thinking about adding a quote for a pail of Butacene to my list, as well. With 8% Ferrocene by weight, it would tremendously ease the path to a 1 in/sec (or higher) burn rate propellant for endburners, without the use of < 30mic AP, HMX, or other explosives, and without the processing qualms presented by GAP. Though the use of metallocenes has been derided by many manufacturers and consumers (most of the time seemingly without merit), they allow the simple chemical acceleration of a propellant, thus opening doors to new designs.

One of the most inspirational texts I’ve seen as of late was a copy of “Small Sounding Rockets” that I picked up from Paul Yarnold (thanks again, Paulie!). In the chapter discussing Atlantic Research sounding rockets was a page about a vehicle that was 3″ diameter and 5 feet long which reached 100,000 feet with the aid of a breech launcher and an 18-second burn duration endburning motor. With a high burn rate propellant, suddenly this vehicle becomes feasible to reconstruct.

Back in the day, high burn rate motors were made using Polysulfide binders, sub-mic AP and Al, addition of metal wires, and secret blends of catalysts. (Did I miss any?) Mark Clark successfully leveraged these techniques to successfully fire a 3-grain 76mm L5300. But Mark works for Universal Propulsion, so he’s got a bit of a head start.

CTI has also produced fast propellants without any metallocene products. Yes, metallocenes do migrate, so there is a concern there. But this sounds like a way to get around the migration and sensitivity issue (seriously though, if it’s so brutally dangerous to use metallocene compounds, someone show me a video of AT’s Warp 9 being set off with a hammer?) while simultaneously easing processing (no small amounts of catalyst to add) and avoiding the other — potentially more hazardous — methods of speeding up burn rate.

So, I’m thinking of storing this one away in the “high performance” toolbox with the other tricks I’ve gathered, and maybe one day taking a shot at the Black Rock waiver with something no bigger than a L1 cert rocket. Who knows. It just might work.

My other question is — how do you integrate the ferrocene molecule into the HTPB chain itself? Is there some sort of bonding agent that can be used to perform this bit of chemical wizardry, without relying on foreign sources? It may not be a panacea, but it sounds like a vast improvement in the mitigation of a potential hazard caused by “cene” catalysts. (I’m resisting the urge to make so many bad puns off of that…)

Either way, I think there’s some SNPE love coming my way on an invoice sheet in the near future.