From: Doug Jones (random@qnet.com)
Date: Sat May 27 2000 - 13:15:35 MDT
Brian Atkins wrote:
>
> First off can you explain to me what the difference is between Isp and
> Fsp, thanks.
Isp is specific impulse, the amount of momentum delivered per unit
propellant mass:
Isp = Ft/M m/s
This has the units of a velocity, but in the american provincial unit
system the distinction between pound mass and pounds force is often
swept under the rug, so the equation becomes
Isp = Ft/(Mg) seconds
Their "Specific Thrust" is just the engine thrust over the burning area
and chamber pressure:
Fsp = F/(ApPcCF),
(The real figure of interest is the thrust/burning area, but they throw
in the Pc to make the units dimensionless and make low-pressure
operation look good.) The only real significance is that, if the
burning rate is high enough, the burning area need not be much larger
than the nozzle throat and an end-burning geometry will work.
> First in the marketing section they claim to have validated their
> orders of magnitude improvement in thrust through something called
> The Aerospace Corporation. Ever heard of them?
AC is a tame think tank set up by the USAF about 45 years ago. Beltway
bandits who are called in to do due diligence and give a thumbs up or
thumbs down. They tend to come up with the answers they're paid to
produce. In this case they carefully pointed out that yes, this is a
good solid rocket fuel, but did not endorse the nozzleless
configuration.
> In the technology section they show a graph of how in different kinds
> of explosions (conventional explosions vs. thermite) the reactant
> diffusion distance is inversely proportional to reaction velocity.
> Farther away reactants have to move to get to each other, the slower
> the reaction velocity.
Yeah, with better mixing the propellants burn faster.
> They show a picture of a typical chunk of fuel/oxidizer from regular
> fuel- about 200 microns wide (they relate it to a table salt grain),
> and then make the claim that whereas in regular fuel this would be
> a single pair of materials, in their fuel this would contain tens of
> billions of fuel/oxidizer pairs.
Yeah, with better mixing the propellants burn faster.
> Next page is a table showing burn rates and chamber pressures of three
> technologies: stinger (.33 inch/sec and 1300 psi), boeing delta II
> (.23 inch/sec and 800 psi), their end burning rocket (6.8 inch/sec and
> 25 psi). Below that is a graph showing Fsp of various rocket types along
> with their burn rates. What that seems to show is most conventional stuff
> such as Shuttle SRB, Titan IV, sidewinder are all grouped near each other
> at around .4 burn rate and .005 specific thrust (psi/psi). Meanwhile
> they show their caseless motor up close to 8 inch/sec burn rate and a
> specific thrust of 1. Assuming this graph is correct, what are the
> consequences? The graph also shows a different version of their system
> which is apparently not caseless... this would be used in sidewinders
> and such I guess. This one has multiple points along the graph line,
> from much slower than the others to about the same point as the caseless.
> So I guess they are saying they can control the reaction rates pretty
> well.
Yeah, with better mixing the propellants burn faster. Look, I know a
bit about making rocket propellants burn faster- the proprietary liquid
injector technology we use achieves an Fsp (as they define it) of about
6. The more customary measure of combustion speed is the characteristic
length of a combustion chamber, the volume divided by the throat area:
Lstar = Vcham/Athroat
This is an easily measured figure of merit closely related to the
residence time of the propellants in the combustor. Our competitors are
happy to get good combustion efficiency with Lstar of about 40 inches;
our engines are twenty or less, and for certain propellants we can do
about 5. Since the chamber mass is almost directly proportional to
Lstar, XCOR is doing mighty good :)
> On the next page they show a cutway pic of a regular solid rocket motor
> vs an end burning. Both show nozzles. They point out that their motors
> with the highest specific thrust are nozzleless and sometimes caseless,
They haven't *built* any rockets- they're only doing propellant
combustion tests in open-ended tubes. The highest Isp they've
demonstrated is less than half of the state of he art for solids, little
more than a third of liquid fuel engines.
> and they make the claim that a caseless rocket would be capable of SSTO.
> But no real details on how that would work. :-)
And it _wouldn't_work_. In the Aerospace Corp report, they wrote: "The
highest observed Isp is 114 s." Without a nozzle, it ain't gonna get
better. If you plug an Isp of 130 (to be generous to further
development) into the rocket equation,
v = g Isp ln(M/M0)
and solve for v = 9000 m/s to get into orbit, the mass ratio needed is
about 1200. Thus if the entire stack is propellant with no parasitic
mass (such as some means of *steering* the damn thing!), you'll need
1200 kg of propellant for each kg delivered to orbit. A monster the
same mass as the space shuttle stack (2,000,000 kg) would deliver less
than 1700 kg to orbit. Conventional solid propellants cost several
dollars per pound, and gas-condensed Al isn't likely to make it cheaper-
this comes to several thousand dollars per pound of payload.
> I guess what I would like to know is what impact if any do these Fsp
> and other numbers above have?
The high Fsp makes an end-burning solid motor theoretically possible.
It also makes it inherently vulnerable to cracks and disbonds which
would lead to overpressurization and case failure.
> > Here they are flat-out wrong. Without a de laval nozzle to efficiently
> > expand the hot gases to supersonic velocity and collimate the exhaust
>
> Well it seems that their reaction rates alone are fast enough to create
> the supersonic velocities without having to do anything else.
No joy- without high combustion pressure, there is no way to extract
enough work from the hot gases to accelerate them up to high velocity.
Either a nozzle with a restricted throat must be used to provide that
pressure, or a pulsed detonation cycle can produce high pressure by
constant-volume combustion. With neither, the hot gases cannot do work-
and a rocket engine is ultimately a heat engine that does its work on
the exhaust gases.
> Interesting, but what if you were using their super-well-mixed nano
> aluminium fuel. Could you get an effect like this?
No, not with a continuous-combustion process.
> > The one big bad ugly thing is that any sort of disbond or crack in the
> > grain would be even more dangerous than for a center-burning motor.
> > Titan SRMs have a bad habit of blowing up when the buring area increases
> > by a few percent from a crack- imagine how critical propellant integrity
> > would be at 100x the burning rate. A small void that would make a
> > slower burn rate motor merely hiccup would double the burn rate of the
> > end-burner... instant pretty fireworks.
>
> Would this really be a problem if you are burning at the end rather than
> inside a case with a nozzle? At any rate on the web page I cite above
> they claim that their fuel has stable burn rates to over 1600 psi.
Without a case, you could probably get away with it- but since the
performance would suck, why bother? Put that propellant in a case with
a nozzle, and sometimes it will work, but often you'll get fireworks.
-- Doug Jones Rocket Plumber, XCOR Aerospace http://www.xcor-aerospace.com
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