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From: (Henry Spencer)
Subject: Re: Ideal ISP's, why the variation?
Date: Wed, 24 Jun 1998 21:51:26 GMT

In article <>,
Robert Lynn  <> wrote:
>The LH2 LOX engines can thus get within perhaps 40 s of ideal - an
>efficiency of about 92%.  The Kerosene LOX engines only get within about
>100s of ideal or an efficiency of about 76%.  Why is there this huge
>disparity between the two fuels?  Is it because the Kerosene exhaust
>contains a wide variety of gas molecules with different molecular masses
>and thermal equilibrium gives these gases different velocities?

Others have mentioned some reasons for this, but nobody has mentioned the
big one.  Different exhaust-gas mixes differ in how well they convert
thermal energy to kinetic energy.  It's not a matter of the variety of gas
molecules -- LOX/LH2 exhaust isn't all H2O, it has a lot of H2 in it --
but of the way energy gets bled off into internal rotation and vibration
in the more complex molecules.  This is particularly important for engines
built to run at sea level, as a lot of LOX/kerosene engines are; its
importance diminishes with the very high expansion ratios found in engines
built to operate only in vacuum (like a lot of LOX/LH2 engines).

A lot of the exhaust of LOX/kerosene engines is CO2 and H20, which as
triatomic molecules have several places to squirrel away energy.  They are
run a bit fuel-rich to get some CO and H2 into the exhaust, but you can't
do much that without running down the energy release per unit mass too far.

By contrast, LOX/LH2 engines run *very* hydrogen-rich, because hydrogen is
so light that you can get a lot of H2 into the exhaust without paying a
big mass penalty.  (You do pay for it in tank size, which is one reason
why modern LOX/LH2 systems tend somewhat toward higher mixture ratios and
less hydrogen excess.)  All those diatomic molecules help a lot.
Being the last man on the Moon is a |  Henry Spencer
very dubious honor. -- Gene Cernan  |      (aka

From: (Henry Spencer)
Subject: Re: Exhaust speed
Date: Tue, 17 Aug 1999 02:18:15 GMT

In article <7p4epk$o1$>, MA Lloyd <> wrote:
>>...why rocket engines often run fuel-rich, because the exhaust products
>>of a fuel-rich mix often turn out to have more of their energy immediately
>How big is this effect?  I thought you usually ran fuel rich
>to lower the average molecular weight of the exhaust (CO, or unreacted H2
>is ligher than CO2, H2O or unreacted O2) with consequent improvement
>in specific impulse.

That's the account you can find in a lot of textbooks, which is more than
a little embarrassing because it's *wrong*.

The textbook derivation concludes that specific impulse is proportional to
the square root of temperature over molecular weight.  But those two
numbers are *not* *independent*.  (Not in a chemical rocket, anyway -- in
nuclear and solar systems, the rules are different.)  In fact, if you
study the details carefully, temperature over molecular weight is simply
combustion energy release per unit mass of propellant.  There is no way
you will *increase* that by adding extra mass which does not take part
in the reaction.  Equivalently, there is nothing you can do to lower the
molecular weight which will not also lower the temperature.

So why run fuel-rich?  Two reasons.

First, some of the simplifying assumptions in the textbook treatment are
not exactly correct.  In particular, dissociation can (effectively) limit
the maximum temperature, which lets you adjust molecular weight without a
temperature penalty.

Second, and more important, there's another term in the specific-impulse
equation, to do with nozzle efficiency, which the textbook treatment tends
to ignore.  In it, you will find an expression taken to the power
(gamma-1)/gamma.  Now the textbook will explain that gamma is not a very
strong function of gas composition, which is true, but (gamma-1)/gamma is
different -- it's quite a strong function of gas composition.  It's
equal (with a simplifying assumption or two) to R/Cp, which is roughly
inversely proportional to the number of atoms per molecule in the gas.
And the reason for that is exactly what I quoted:  the complex molecules
have more places to hide energy, to make it unavailable for expansion.
(Monoatomic exhaust would be ideal, but is hard to arrange...)

The textbook mistake actually looks plausible if you look at system
performance, because energy release per unit mass *tends* to go up, and
atoms per molecule *tends* to go down, as the molecular weight goes down.
You need a propellant chemist, not a rocket engineer, to spot the error...
and indeed, the only place I've ever seen this discussed *correctly* is in
John Clark's priceless book "Ignition!".
The good old days                   |  Henry Spencer
weren't.                            |      (aka

From: (Henry Spencer)
Subject: Re: Exhaust speed
Date: Mon, 23 Aug 1999 02:26:11 GMT

In article <>,
Del Cotter  <> wrote:
>If I understand what Henry's saying, then this applies only to chemical

Correct.  Systems where the energy source and the propellant are separate
actually do follow the textbook derivations; for them, the lower the
molecular weight, the better.

>NERVA-type engines, which heat a working fluid with an
>external energy source, really can increase kinetic energy per molecule
>by reducing molecular mass, else the NERVA people would have no reason
>to choose hydrogen over other, denser working fluids such as, say,
>oxygen or nitrogen.

Right general idea, although wrong wording:  the kinetic energy per
molecule is fixed by the temperature, that's what temperature *is*.  But
what counts in a rocket exhaust is momentum, and that can be maximized --
for a given kinetic energy -- by using the lightest possible molecules.
Nuclear-thermal, solar-thermal, and electric-thermal rockets are hurt
badly by running on anything other than hydrogen (although, as Doug points
out, ammonia is an interesting halfway point since it decomposes easily
and a lot of the result is hydrogen).
The good old days                   |  Henry Spencer
weren't.                            |      (aka

From: (Henry Spencer)
Subject: Re: SPS chemical reaction
Date: Sat, 2 Oct 1999 05:33:48 GMT

In article <>,
Gregory Pribush  <> wrote:
>    Why the there is a high percentage of H2 and CO ? I thought that
>Aerozine-50 and N2O4 are burned in stochiometric proportions.

No, almost any fuel/oxidizer combination in the CHON chemical system gets
best performance slightly fuel-rich.  H2O and CO2 are noticeably inferior
to H2 and CO at converting thermal energy into exhaust kinetic energy, so
it is worth skewing the mixture ratio a little, accepting a bit less
energy release for the sake of more efficient energy conversion.

>Can you give the fuel/oxidizer ratio for the maximum Isp.

Depends somewhat on conditions, and I don't have good data on that
combination.  As examples, the Titan II first and second stages run at 1.9
and 1.8 respectively (mixture ratios are always quoted as O/F), and if I'm
not mistaken, the stoichiometric ratio for N2O4/50-50 is 3.0.

>    P.S. My guess is that UDMH/hydrazine and nitrous tetroxide are not
>burned at the stochiometric ratios to increase Isp by lowering average
>molecular weight.

You have the right general idea, but that explanation is actually wrong
(even though you will find it in many textbooks).  It's true that Isp is
proportional to sqrt(temperature/molecularweight), but T and MW are not
independent -- if you convert units carefully, you find that T/MW is
essentially the energy released per unit mass of propellants, which
*cannot* be increased by adding non-participating mass.  The real issue,
as noted above, is energy conversion efficiency:  more complex molecules
have more places to hide energy where it can't come out quickly, so they
aren't as good at converting it.

The mistake comes about partly because the books are written by rocket
engineers -- as opposed to propellant chemists -- who don't think hard
about the meaning of the equation, and partly because there is in fact
a *correlation* between low exhaust molecular weight and high Isp.  But
as any statistician will tell you, "correlation is not causation".

>I think, that the hydrocarbons and hypergolics are burned at stochiometric
>ratios, however...

Nope, sorry.  Hypergolics I'm not too familiar with, but LOX/hydrocarbon
combinations are *always* run fuel-rich, usually around 3.0 (stoichiometric
being 3.4 for CH2, 4.0 for CH4).

There are some combinations which are run pretty much at the stoichiometric
ratio, e.g. fluorine/hydrazine, but they're rather less common.
The space program reminds me        |  Henry Spencer
of a government agency.  -Jim Baen  |      (aka

From: (Henry Spencer)
Subject: Re: Optimal LOX/LH2 mixture ratio
Date: Sun, 17 Oct 1999 16:46:25 GMT

In article <>,
Jukka Neppius  <> wrote:
>> Optimal LOX/LH2 mixture ratio is about 4.0...
>Is fixed mixture ratio really optimal?

No, but relatively few rockets have been capable of varying their mixture
ratio in flight.  The Saturn V upper stages were capable of it, but only
because it was seen as a good way to ensure simultaneous depletion of fuel
and oxidizer.

(You want fuel and oxidizer to run out at the same time, because any
excess of (say) oxidizer when the fuel runs out is dead weight, like
having that much lead ballast aboard, and the flow rates are high enough
that a second or two of extra propellant is a lot of mass.  The idea was
to adjust the mixture ratio in flight, based on data from tank gauges, to
ensure that fuel and oxidizer would run out at exactly the same time.
However, it turned out that more traditional methods (careful measurement
and loading) of ensuring near-simultaneous depletion were adequate, and so
the mixture ratio could be varied to optimize flight performance instead.
This was done on the S-II stage after the first flight or two.)

>Wouldn't it be better to use 6.0 or higher at start of the flight:
>more thrust & lower isp
>And closer to 4.0 at end of flight before reaching orbit:
>lower trust & higher isp

Yes, that's basically the right idea, although the variations actually
used by the S-II weren't quite that large.
The space program reminds me        |  Henry Spencer
of a government agency.  -Jim Baen  |      (aka

From: (Henry Spencer)
Subject: Re: Optimal LOX/LH2 mixture ratio
Date: Sat, 23 Oct 1999 21:35:13 GMT

In article <>,
Jukka Neppius  <> wrote:
>> >Wouldn't it be better to use 6.0 or higher at start of the flight...
>> >And closer to 4.0 at end of flight before reaching orbit...
>> Yes, that's basically the right idea, although the variations actually
>> used by the S-II weren't quite that large.
>Why is this not used? What is isp of LOX/LH2 with 4.0 and 7.0 mixture
>ratios?  (8.0 is probably too dangerous:)

There's no great problem with 8.0 if you've got proper wall cooling.  The
RL10 has been run, briefly and experimentally, even leaner than that with
no damage.

Isp depends a whole lot on assumptions.  As a case in point, though, the
J-2s on the early Saturn Vs had roughly linear change in Isp and thrust
over the mixture range they used:  430s and 178klb at 4.5, 423s and 225klb
at 5.5.

As for why it's not used... there have been proposals to use it.  But for
modern systems, the tradeoffs usually seem to favor running lean all the
time, to minimize tank mass -- a problem whose severity was not fully
appreciated at the time the Saturn hardware was designed -- even at the
cost of slightly lower Isp.

>SSTO has to adjust its engines anyway, because its mass drops to
>1/20th of start mass during flight.

Yes, but the range of throttling needed is much larger than the small
changes you get from tinkering with mixture ratios.  Partial engine
shutdowns are usually needed.

>Variation of same idea is to use kerosene & LOX at start and switch to
>LH2 later.  Did somebody study this?

Yes, at considerable length.  Along with a number of other variations,
like using a bit of LH2 for pump drive and chamber cooling during the
LOX/kerosene part of the flight.  In general, the extra complexity does
not look to be worth the trouble.  Depending on what figures of merit you
use for evaluation, the optimum percentage of LH2 generally turns out to
be either 0% or 100%.  (If you use *sensible* figures of merit -- none
of this gross-liftoff-mass nonsense -- it's generally 0%.)
The space program reminds me        |  Henry Spencer
of a government agency.  -Jim Baen  |      (aka

From: (Henry Spencer)
Subject: Re: Optimal LOX/LH2 mixture ratio
Date: Sun, 7 Nov 1999 19:33:35 GMT

In article <803jq0$9to$>,
Jens Lerch <> wrote:
>>Actually i wanted to calculate effect of changing MR for H2/O2 engine.
>>Density with MR 13:1 is 550 kg/m^3, but perhaps isp is too low.
>At a MR of 13:1 preventing the oxygen from oxydizing (i.e. burning) the
>walls of the thrust chamber and the nozzle is very difficult.

Not impossible, though.  What matters is that the "curtain cooling" layer
near the walls must be cool; despite Western superstition, it doesn't have
to be fuel-rich.  There's at least one small Russian engine which uses an
oxidizer curtain.

The RL10 has been fired at 13.5:1 -- briefly and experimentally -- without
any damage.
The space program reminds me        |  Henry Spencer
of a government agency.  -Jim Baen  |      (aka


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