🚀 go-pugleaf

This posting consists of two parts:

1) A reply to the comments of Edward Wright on a previous posting on this
subject

2) An expanded description of the concept of using a LOX/kerosene booster as
a first stage for the DC-1


In reply to my posting attempting to show the potential virtues of building a
LOX/kerosene booster stage for the DC-1, Edward Wright writes:

Dunn:
>        If a DC-1 in SSTO mode can launch 10 tons to LEO and the two stage
>vehicle using the DC-1 as an upper stage can launch 50 tons to LEO, then we
>have the following costs for launching 50 tons:

>DC-1 in SSTO mode:  5 flights needed, incurring 5 DC-1 stage turnaround
costs

>DC-1 in 2 stage mode:  1 flight needed, incurring 1 DC-1 stage turnaround
and
>1 lower stage turnaround cost.

Wright:
The 2-stager is a *much* larger vehicle, so your vehicle fabrication
costs will be much larger.

Reply:
Larger is a slippery word.  Measured by dry mass, the lower stage is four
times larger than the DC-1.  Measured by fueled mass, it is two times larger.
Measured by linear dimensions, it is actually smaller than the DC-1 (it uses
much denser propellants).

Fabrication costs are not only affected by size, but also strongly affected
by complexity and by how closely material limits are pressed.  A petroleum
supertanker weighing 1000 times the weight of a Boeing 747 does not cost 1000
times as much.  In fact therefore, the fact that the lower stage has a higher
dry mass than the upper stage (even though it has smaller linear dimensions)
is an indication that it is likely to be less expensive than an upper stage.
For more details as to the proposed lower stage, see below.

Dunn:
>       I will assert that turnaround cost of the lower stage will not exceed
>the turnaround cost of the upper stage (the lower stage is much less
stressed
>than the DC-1 upper stage, and uses cheap kerosene and LOX as propellants).

Wright:
Think again.  The SSTO recovers back at the launch site.  Your first
stage will splash-down or land somewhere downrange.  It needs to be
retrieved, safed, and returned to the launch site before it can be
used again.  This is not only expensive, it's time consuming.  You're
going to need a lot of extra stages to make up for the down time.

Mating the two stages will take time and manpower also.

Using a different propellent in the first stage means you're
going to have to invest in another set of propellent storage
and loading facilites.  Fueling will be more complex, requiring
more time and manpower.

Reply:
I am assuming that the first stage will return to the launch site under its
own power.  This was described in the original posting a couple of weeks ago,
although in fairness, I did not repeat it in my most recent posting.  This
subject is further discussed below.

Mating the two stages will take time and manpower, but if the system is
correctly designed the actual labor need not be too much.  The DC-1 will have
to be transported in any case from its landing spot to its launch cradle.
The use of a lower stage would merely mean that the DC-1 would be placed on
the lower stage, rather than on the launch cradle.

The lower stage uses LOX and kerosene.  The LOX delivery facilties are
already available (the DC-1 uses LOX) - it would be merely necessary to beef
up the storage facilites for LOX.  The kerosene storage facilities are
off-the-shelf items (RP-1, a refined kerosene used in rockets, can be handled
by the same equipment as your local airport uses for jet fuel).  Fueling a
two stage vehicle ***will*** be more time consuming than fueling a single
stage, but since refueling 1 lower and 1 upper stage will deliver 5 times the
payload as 1 refueling of the upper stage in SSTO mode, there is still a
lowering of the man power needed per ton orbited.


Dunn:
>Therefore, as far as turnaround costs go, the two stage vehicle costs 2/5,
or
>40% as much as the SSTO.

Wright:
That doesn't follow from anything you've said up til now.  Your second
stage is a DC-1, so that's 100% right there.  The first stage, being
much larger, will be a lot more.

Reply:
I am talking about turnaround costs per unit of cargo orbited - I think that
this was clear in my posting.  Of course the single flight turnaround cost
for a two stage vehicle is greater than that of a single stage vehicle.
However, when you figure out the turnaround cost per ton of payload orbited,
the two stage system requires only 1 flight and 2 stage turnarounds to match
the payload delivered by 5 SSTO flights (hence the 2/5).

Dunn:
>        A final advantage to the two stage design comes from the time
>necessary to perform turnaround.   Since the lower stage can be inspected
and
>prepared for another flight while the upper stage is making an orbital
>delivery, the frequency of flights will be governed by the turnaround time
of
>the upper stage after it gets back.

Wright:
Only if the first stage can teleport.

Reply:
I am assuming landing at the launch site - see below.

Dunn:
>Say that turnaround time is 1 week.  If you spend your money on two DC-1
>vehicles and operate them in the SSTO mode, then it will take 5 weeks to
>put 100 tons in orbit (two flights delivering 10 tons each per week).

Wright:
Or 5 days, flying two flights per day.

Reply:
OK, in this case two flights of the two stage vehicle can deliver the desired
total payload in a time of 2 days, as compared to 5 days and 10 flights for
the DC-1.  The advantage remains - what is your point?

Dunn:
>If you spend your money on one DC-1 and 1 lower stage, then the same
>100 tons can be put into orbit in two weeks (two flights, each
>delivering 50 tons).

Wright:
Of course, you'll only have enough money to pay for half the first
stage.

Reply:

Developing a first stage will obviously be costly, and the two stage scheme
would be most attractive if large quanties of material have to be delivered
to LEO (for example, to fuel a Mars expedition).  Once development costs are
"sunk" (or are spread over a large number of vehicles), there is no reason to
believe that a 200 ton dry mass LOX//kerosene stage should cost any more to
fabricate than a DC-1.  Remember, the first stage is build with very large
margins and low technology, and does not have to survive a high speed
ballistic re-entry.


The following is an adapation and expansion of two previous postings on the
concept of a two stage DC-1.


The design margins on the hypothetical DC-1 are quite tight.  Consider the
following performance model, which approximates a DC-1  (1 ton = 1000 kg, LEO
assumed to require 9300 m/sec, gravity and air resistance losses included)

DC-1:

Isp (LOX/LH2)                              430
Usable Ascent Propellant Fraction          0.91
Liftoff Mass (exclusive of payload)        500 tons
Ascent total propellant mass               455 tons
Structure, landing propellant              45 tons
Oxidizer/fuel mixture ratio                5.0
Ascent LOX mass                            379 tons
Ascent LOX volume                          332 cubic meters
Ascent LH2 mass                            76 tons
Ascent LH2 volume                          1083 cubic meters
Payload to LEO (SSTO mode)                 11 tons

Note that overall Isp at 430 is less than that of the engines in vacuum
(assumed to be 450), as the engines will have to spend part of their time
operating in air.


Hypothetical first stage:

Isp                                        300
Usable Ascent Propellant Fraction          0.80
Liftoff Mass (exclusive of upper stage)   1000 tons
Ascent total propellant mass               800 tons
Structure, landing propellant              200 tons
Oxidizer/fuel mixture ratio                2.3
Ascent LOX mass                            558 tons
Ascent LOX volume                          489 cubic meters
Ascent kerosene mass                       242 tons
Ascent kerosenevolume                      303 cubic meters
Payload to LEO (with DC-1 upper Stage)      58 tons


This stage is heavier than the DC-1, but is actually smaller in physical
dimensions as the LOX/kerosene propellant combination has a much higher
density than the LOX/LH2 propellants of the DC-1 (look at the tank volumes).
This can be a really low-tech vehicle with no pushing of material limits.
Add lots of redundancy, and a large fuel margin for landing.  Use 6 ex-Soviet
RD-170 engines running at partial throttle for lift (even at liftoff, four
engines at full throttle are sufficient).  Engines are in a hexagonal
arrangement, and any single engine failure and most two engine failures are
not fatal as the other engines can take up the slack. For launching the  DC-1
goes on top of the first stage.  The first stage climbs in a largely vertical
trajectory (to avoid getting too far from the launching point), accelerating
to approximately 1100 m/sec (and incurring about 1000 m/sec gravity losses
during the time).  The DC-1 is then staged, and the first stage returns to
the launch site and lands vertically.  The DC-1 then tilts over to a more
conventional ascent trajectory and continues to orbit.  Should the DC-1 have
engine ignition trouble on staging, it has both the fuel and thrust to land
at the launch site.  With only some engines working, it can burn off fuel
until it has a thrust to weight ratio of greater than 1, hover to get its
weight down further,  and then land.

Because of the necessity of keeping the first stage near the launch site, it
does not pay to build up a large horizontal velocity increment.  For this
reason, the first stage follows a more vertical trajectory than normal,
causing more gravity losses than normal.  In calculations of the payload for
the two stage vehicle therefore, I have assumed an additional 250 m/sec
penalty over the "normal" orbital requirement of 9300 m/sec.  On the positive
side, the DC-1 only has to operate in a vacuum, and its specific impulse is
therfore 450 rather than the flight average of 430 assumed for SSTO mode.

For the sake of using simple numbers in comparing the operating costs of the
DC-1 used in SSTO mode and in 2 stage mode, consider the payload of an SSTO
flight to be 10 tons (vs. 11 calculated), and a two stage flight to be 50
tons (vs. 58 calculated).

        If one assumes that development costs are "sunk" and not to be
applied against flights (or alternately assumes that large amounts of
material are being launched and thus development costs can be spread over
hundreds of flights), then the cost of launching revolves around the cost of
refueling and refurbishing the reusable vehicles.  As pointed out by many
posters, this is largely driven by manpower requirements.

        If a DC-1 in SSTO mode can launch 10 tons to LEO and the two stage
vehicle using the DC-1 as an upper stage can launch 50 tons to LEO, then we
have the following costs for launching 50 tons:

DC-1 in SSTO mode:  5 flights needed, incurring 5 DC-1 stage turnaround costs

DC-1 in 2 stage mode:  1 flight needed, incurring 1 DC-1 stage turnaround and
1 lower stage turnaround cost.

       I will assert that turnaround cost of the lower stage will not exceed
the turnaround cost of the upper stage (the lower stage is much less stressed
than the DC-1 upper stage, and uses cheap kerosene and LOX as propellants).
Assuming, as a worst case, that the turnaround costs of the lower stage equal
the turnaround costs of the upper stage, then turnaround of the two stage
vehicle costs 2/5, or 40% as much as the SSTO per ton of cargo orbited.  This
will be offset somewhat by the fact that facilities, spares etc for two
different stages must be maintained, but I doubt that this will eat away all
of the apparent advantage of the 2 stage design.

        I will further note that using the DC-1 as an upper stage does not
prevent it being used in SSTO mode for lighter payloads when this would be
desirable.  It also offers the opportunity to boost individual payloads 5
times greater than that achievable in SSTO mode.  A two stage design is thus
more flexible than the SSTO.

        A final advantage to the two stage design comes from the time
necessary to perform turnaround.   Since the lower stage can be inspected and
prepared for another flight while the upper stage is making an orbital
delivery, the frequency of flights will be governed by the mission length and
the turnaround time of the upper stage after it gets back.  Say that the
overall time per launch is 1 week.  If you spend your money on two DC-1
vehicles and operate them in the SSTO mode, then it will take 5 weeks to put
100 tons in orbit (two flights delivering 10 tons each per week).  If you
spend your money on one DC-1 and 1 lower stage, then the same 100 tons can be
put into orbit in two weeks (two flights, each delivering 50 tons).  This
same 2 to 5 ratio holds no matter how rapidly the stages can be turned
around.  This ability to put up a lot of payload in a very short time may be
of advantage for situations such as trying to fill the propellants tanks of a
lunar or Mars expedition vehicle with cryogenic propellants.







--
Bruce Dunn    Vancouver, Canada   Bruce_Dunn@mindlink.bc.ca