```Date: 5 Jul 87 00:07:09 GMT
From: ssc-vax!eder@beaver.cs.washington.edu  (Dani Eder)
Subject: Re: Launch Vehicle Size

In article <452@telesoft.UUCP>, roger@telesoft.UUCP (Roger Arnold @prodigal) writes:
> > A typical value today is 2500 lbs total for this set of hardware.
>
> Typical?  I'll take your word for it.  But hardly representative of
> what ought to be feasible.  Otherwise, your own plans for a small
> demonstration model catapult fired launch system are infeasible.

That is correct.  Perhaps I should restate that more clearly:
A typical value for a rocket that flies today, with 1 year
old electrical systems, is 2500 lb.  For example, the computer
on the IUS built by Boeing is smart enough to control a Titan
launch vehicle.  The computer is an 8-bit processor with 48k of
ram (= about an Apple II).  It weighs 40 lb, not counting
batteries.  There are two of them on the IUS.  Of course, the IUS
was designed in 1973.  For a new rocket, we can do much better
with today's electrical equipment.  But, at any given time, there
will still be a constant weight component to a rocket design.

> excludes fiber based composites.  There is no optimal shape for a
> tank made from a fiber based composite, so long as the fibers are
> laid up in a manner that places them all under equal stress in the

But there is a minimum gage.  Let us take the case of very good carbon
fiber/epoxy with a tensile stength of 400 ksi.  We design to 300 ksi to
allow some factor of safety.  Available materials are 7/1000 inch thick
per ply of fibers.  Assume the internal tank pressure is 10 psi.  Since
stress=pD/2t for a cylindrical thin shell, we can calculate the D that
corresponds to 1 ply of composite.  It is
(stress/p)*2t=d=(300,000/10)*2*0.007=420 inches.  Thus, any tank smaller
than this would waste some of the strength inherent in 1 ply of
composite.  In a realisitic design there would be at least 2 plies
oriented,say at +-20 degrees from horizontal, to give longitudinal
strength, so this is even worse.

In response to the engine inlet pressure issue, the trade is usually
tank weight vs engine pump weight, the lower the inlet pressure, the
bigger the low pressure pump inlet has to be to avoid sucking vacuum
(cavitation).  Cavitation is death to rocket engines, because they are
not normally designed for (1) the vibrations on the pump blades (2) the
vibrations caused inside the combustion chamber when you burp gas rather
than fluid and (3) the loss in wall cooling of bubbles in the coolant
lin.  All of these have caused engines to fail in the past.  Solving
these types of problems keeps propulsion engineers employed.  Of course,
you could design your engine to survive these problems, but then it
weighs twice as much.

> For a given chamber pressure, the nozzle
> area required is directly proportional to the mass being lifted.  A
> certain nozzle area can only supply lift for a certain mass, which
> translates to a certain height of rocket.  You can't make a rocket
> arbitrarily tall; to make it bigger, you have to make it wider.

This is incorrect.  The nozzle area = throat area x expansion ratio of
the nozzle.  Most of the thrust in a rocket arises from the thrust
imbalance between the throat and a corresponding area on the top of the
engine.  In a converging-diverging nozzle, the flow becomes supersonic,
and thus is effectively zero pressure as seen from inside the combustion
chamber.  For example, in the SSME, the chamber pressure is 3000 psi.
The liftoff mass is 4,500,000 lb.  Hence, only 1500 square inches, or
10.42 square feet of throat area is required for liftoff.  The actual
SSME nozzles have an expansion ratio of 77:1.  This expansion against
the nozzle walls has an upward component, which provides thrust in
addition to the throat component.  I belive in this case it adds 40%
more thrust.  The solid rocket boosters, on the other hand, have an
expansion ratio of only 10-15:1 (I'm at home and don't have my refernce
books handy).  This is because they work at 700 psi pressure.  In both
cases the expansion is limited by when the gas reaches 15 psi in the
nozzle (= sea level pressure).  The sea-level back pressure in the SSME
nozzle causes it to lose 23% of vacuum thrust.

> But there is one area that you didn't mention where skinny tanks
> (and small vehicles) eat it: tank insulation efficiency.  I don't
> know how much of a problem that really turns out to be.

It is non-trivial.  A typical value is 0.2 inches of cork insulation
required on the forward part of a rocket to protect it from aerodynamic
heating.  Propellant boiloff is generally not a problem, since you are
using it very quickly.  The main reason to insulate a cryogenic tank is
to prevent ice (water, CO2, even air) buildup on the ground.

> For the sake of argument, let's accept your implication that a system
> sized for 10,000 lb. of payload would be only 55% as efficient, in
> terms of fuel consumed per pound of payload, as one sized for 100,000
> pounds.  That represents a cost penalty of something like \$2.00 to
> \$3.00 per pound.  If the high launch rate, the steady production of
> vehicles, and the confidence attained from an extensive track record
> enabled the small system to achieve operational costs as low as 10
> times its fuel costs, then it would be more than twice as economical
> as a larger system whose operational costs were 50 times its fuel
> costs.  (For comparison, I think that operation costs for airlines run
> about 3 times their fuel costs, while for the Shuttle, they're on the
> order of 500 times, or more, depending on how one does the accounting).

In the aerospace industry, we experience a production 'learning curve'
as the quantity of production goes up.  Typically the reduction is
15% in unit cost per doubling of cumulative production.  So if we have
10 times as many units made, we would expect the unit cost to be
58.3% as much.  Since 1.82 times as much vehicle dry weight would
be required, the total cost would be 1.06 higher for the small
rocket IF costs were proportional to dry weight.  In practice, much
of the cost of a rocket is in the fixed weight items, rather than in
the tanks and other structure, so the cost/lb of dry weight goes up
for small rockets.

Another way of looking at this, is that, roughly, we use up the same
number of pounds of engines and tanks in 10 10,000 lb launches as we do
in 1 100,000 lb launch, but in the former case we use up 10 times as
many sets of electrical equipment.

The key measure in determining space launch cost is the number of pounds
of hardware thrown away per pound of payload delivered to orbit.  In an
expendable rocket it is about 2 lb hardware/lb payload.  In the shuttle,
it was not much lower.  We threw away 1 lb of external tank per pound of
payload.  Allowing for reuseable element comsumption at weight/life, we
use up 15,000 lb of SRBs and 3000 lb of orbiter per flight, giving a
launch system we are about to start work on, the figure will be 0.56 lb
hardware/lb payload.  I agree that propellant is cheap.  My dream is a
launch system where I have to worry about propellant cost.  Even on the
ALS, it only is 1% of the total costs.
```

```From: jtkare@ibm.net (Jordin Kare)
Newsgroups: sci.space.tech
Subject: Re: Do small engines have higher T/W ratios? (was mini-engines,
candles)
Date: Fri, 03 Dec 1999 18:35:06 -0800

In article <38471859.3F8B9EB3@primary.net>, jimdavis2@primary.net wrote:

> Andrew and Henry's discussion got me to think about whether small
> engines can be demonstrated analytically to have a higher thrust to
> weight (T/W) ratio.
>

> Thrust chamber weight scales with size squared, thickness, and material
> density
>
> W = k2 * g * t * r2 * rho
>
> where
>
> W = thrust chamber weight
> g = acceleration of gravity
> t = chamber thickness
> rho = material density
> k2 = constant of proportionality

This assumes a constant engine shape.  Engine shape may vary with size,
especially if constrained by required combustion chamber length for
complete combustion.

>
> This indicates that T/W ratio is directly proportional to material
> strength to weight
> (s / rho) ratio (well, duh!) and inversely proportional to engine size.
> Now I realize there is more to the engine than the thrust chamber but I
> wonder whether this crude analysis holds any water in the real world.

When we did the Mockingbird minimum-scale SSTO design at LLNL, Rod Hyde
went through a bunch of scaling relationships, with results similar to
yours.  Note that T/W proportional to 1/r means T/W proportional to
1/(sqrt(thrust)) so it's not as fast a gain as it might seem.

In practice, as I note above, there are some factors which limit the
scaling of the chamber so the advantage of small engines is reduced.  A
larger factor in the "real world" is that turbopumps scale badly to small
sizes, so T/W for turbopump-fed engines, including the pumps, tends to
improve for larger sizes.  Overall, historical data gives better T/W for
large engines.

Mockingbird got around the turbopump problem by using reciprocating pumps,
whose specific mass *improves* at smaller sizes, with a crossover relative
to turbopumps somewhere in the general ballpark of 20,000 N (~4000 lbf)
thrust (highly implementation and technology dependent).  Mockingbird
baseline engine design was regen-cooled peroxide/kerosene with a
pump+chamber mass (8 chambers) of 13.3 kg and a vacuum thrust of 3.2 kN
per chamber (25.6 kN total) for a T/W of 188.  (Sea level thrust was 2.5
kN per chamber, 20 kN total, T/W 147)

Jordin Kare
```