Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ames!ncar!noao!asuvax!enuxha!kluksdah
From: kluksdah@enuxha.eas.asu.edu (Norman C. Kluksdahl)
Newsgroups: sci.space
Subject: Re: Sanger
Summary: advantages of speed vs. altitude
Message-ID: <78@enuxha.eas.asu.edu>
Date: 15 Mar 89 22:47:52 GMT
References: <1989Mar14.172237.29235@cs.rochester.edu <7234@thorin.cs.unc.edu>
Organization: Arizona State Univ, Tempe
Lines: 65

In article <7234@thorin.cs.unc.edu>, symon@lhotse.cs.unc.edu (James Symon) writes:
> In article <1989Mar14.172237.29235@cs.rochester.edu,
> dietz@cs.rochester.edu (Paul Dietz) writes: 
> > . . . Sanger would use turboramjet engines to propel a winged 
> > first stage to Mach 5, at which point a LOX/LH2 propelled second stage 
> > -- either an unmanned expendable cargo rocket (like Pegasus) or a 
> > reusable winged manned vehicle -- would be released to ascend to 
> > orbit.  
> 
> I would think that the greatest advantage an air launch would have
> over ground launch would be initial altitude not initial speed. Mach 5
> is pretty tough to achieve with a cargo vehicle and is only about 20%
> 
I have done some back-of-the-envelope calculations to check out the
advantages of speed at release of the orbital vehicle.  (Note:  these
are only rough calculations, intended only to demonstrate a point).

In all cases, it is assumed that the payload is released at an altitude
sufficiently large to neglect most air frictional effects.  (Note 2.  This
perhaps implies use of rockets to provide the final acceleration of the
carrier vehicle.)

Assuming Isp = 400 (which gives exhaust velocity of 4000 m/sec)

   Mach # at launch       Mass Ratio
         1                  5.27
         2                  4.90
         3                  4.56
         4                  4.24
         5                  3.96
         6                  3.68
         7                  3.43
         8                  3.19

Mass ratio is the ratio of fuel and structure at launch to the mass of
the structure delivered to orbit.  

A few important features stand out here.  First, if you can get to
altitude where air resistance is negligible, the usable payload becomes
a large fraction of the launch weight ( 19% - 31% ).  Of course, you
have to then figure what fraction of the vehicle can actually be devoted
to payload and what is structural weight.  Second, like all chemical
rockets, trade-offs are an integral part of the game.  Accelerating the
'aircraft' carrier to a decent Mach number will eat fuel, which means that
the structural weight of the carrier becomes non-negligible.  Higher Mach
numbers require technology like air-turbo ramjets or such, which aren't
exactly off-the-shelf items, or rockets, which means dual power sources
and more parasitic weight.  In addition, atmospheric heating of the carrier
will necessitate some form of heat shielding, which increases the parasitic
weight.  Counting the carrier, the usable payload fraction is quickly 
diminishing to single digit percentages (or less!!).

As with all rocket design, the final configuration will inevitable be a
compromise.  Still, air launch does promise something--I read that OSC's
Pegasus gains about 15% in usable payload by air launch at Mach 0.8. 
Just imagine the gain if they had an XB-70 to launch from... :-) :-) :-)


**********************************************************************
Norman Kluksdahl              Arizona State University
            ..ncar!noao!asuvax!enuxha!kluksdah

standard disclaimer implied

Useful criticism always appreciated.  Senseless flames always discarded.