[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

starship-design: Lox kerosine SSTO numbers



Subject: LOX/KERO v LOX/LH2 SSTO
From: "Steven S. Pietrobon" <steven@sworld.com.au>
Date: Mon, 23 Jun 1997 09:17:55 +0930
Message-ID: <33ADB9AB.54A2@sworld.com.au>

This is a multi-part message in MIME format.

[Mod note: I am bending the usual no-MIME encoded messages rule
for this one; it's got a postscript ascii document in the second
part which is of reasonable, smallish size and which seems to add
to the utility of the message quite a bit.  Those without MIME
capable newsreaders can extract the contents with a text editor
if they so desire.  Any complaints to gherbert@crl.com - gwh]


--------------367E49BE69E4
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit

I think it is worth investigating the use of LOX/KERO as propellants
for single stage to orbit (SSTO) vehicles. Attached is a postscript
file which shows delta V versus propellant volume/final mass ratio.
As can be seen, in terms of propellant volume LOX/KERO (or H2O2/KERO)
is significantly better than LOX/LH2 (all the way to orbital speeds
of 9000 to 10,000 m/s).

The numbers I used were

                   v_e (m/s)   d_p (kg/l)    MR   Mass (kg)  Engine
H2O2/KERO     3042       1.314         7.2   8755       RD-170 (calculated)
LOX/KERO        3305       1.025        2.6   8755       RD-170
LOX/LH2          4441       0.3611      6.0   3177       SSME

where v_e is the exhaust speed, d_p is the propellant density, and
MR is the mixture ratio.

The VentureStar has the following specifications (1 t = 1000 kg)

m_e  =   89.8 t (empty mass)
m_p  =  875.0 t (propellant mass)
m_c  =   26.8 t (cargo mass)
m_t  =  991.6 t (total liftoff mass)
F_s  = 13,419 kN (sea level thrust)
v_es =   3403 m/s (sea level exhaust speed)
v_ev =   4462 m/s (vacuum exhaust speed)
V_p  =   2423 m^3 (propellant volume)

The total delta V for the vehicle is

dV = 4462 ln(1+ 875.0/(89.8 + 26.8)) = 9551 m/s

The liftoff acceleration (ignoring gravity) is

a = F_s/m_t = 13,419/991.6 = 13.53 m/s^2

Let us assume that the propellant volume flow rate through the
LOX/KERO and LOX/LH2 engines is constant. Then the liftoff thrust
for an equivalent LOX/KERO engine is

F_s2 = (d_p2/d_p1) (v_e2/v_e1) F_s1
     = (1.025/0.3611) (3032/3403) 13,419
     = 33,938 kN

The sea level v_e of the RD-170 is 3032 m/s. This thrust is about the 
same as the Saturn V. Let us assume that the liftoff acceleration is 
the same, thus

m_t2 = F_s2/a = 33,938/13.53 = 2507.8 t

Assuming the same delta V (the actual delta V will be lower due
to the larger thrust and thus smaller gravity losses) we have

9551 = 3305 ln(1+ m_p2/m_f2)
2507.8 = m_p2 + m_f2

where m_f2 = m_e2 + m_c2. Solving we have m_p2 = 2368.4 t and
m_f2 = 139.4 t. The tank volume is V_p2 = 2368.4/1.025 = 2311 m^3
which is 112 m^3 smaller than VentureStar. The final mass of
VentureStar is m_f1 = 89.8 + 26.8 = 116.6 t. Thus, the new design
will have a final mass that is 22.8 t greater than VentureStar.
Unfortunately, this greater mass can not be converted into payload
mass since the engine mass for the new design is greater than for
VentureStar.

For the RD-170 the engine mass to sea level thrust ratio is
8755/7259 = 1.206 kg/kN. I don't know this ratio for the VentureStar
engines so I'll take the figures for the SSME which are
3177/1668 = 1.905 kg/kN. Thus the engine mass for the new design
is 33,938 x 1.206 = 40.9 t and for the VentureStar the mass is
13,419 x 1.905 = 25.6 t. Thus, the new design requires an increased
engine mass of 40.9-25.6 = 15.3 t which reduces the extra payload
mass to orbit to 22.8-15.3 = 7.5 t. Let us use this mass for the
stronger thrust structure. Thus, with a 26.8 t payload (the same
as VentureStar) we have that the empty mass of the new design is
139.4-26.8 = 112.6 t (of which 36.3% is engine mass). This compares
to the empty mass of 89.8 t of VentureStar (of which 28.5% is
engine mass). Despite the higher empty mass the new design will be
slightly smaller dimensionally due to the smaller tank volume.

So there you go. If reduced gravity losses reduce the delta V by
500 m/s (Mitchell Burnside Clapp showed that a H2O2/KERO powered
SSTO reduces delta V by 595 m/s) then the empty mass can increase
to 135.4 t (of which 30.2% is engine mass) with a 26.8 t payload.
The tank volume is 2288 m^3 (135 m^3 smaller than VentureStar).

So, I think a LOX/KERO SSTO is technically feasible but the large
engine mass could be a problem. Still, it may be desirable to make
a LOX/KERO SSTO work due to the operational advantages it offers. KERO
is much easier to work with than LH2. The propellant costs will also
be less which in a resuable system (like airplanes) will hopefully
be a large part of the cost of a launch.
-- 
Steven S. Pietrobon, Small World Communications, 6 First Avenue
Payneham South SA 5070, Australia           fax +61 8 8332 3177
mailto:steven@sworld.com.au           http://www.sworld.com.au/