From: ee00jc@unccvax.uncc.edu (John Childers)
Newsgroups: sci.space.shuttle
Subject: Re: One SRB...
Date: 10 Apr 92 20:22:30 GMT
Organization: University of NC at Charlotte

In article <1992Apr04.001636.25331@crash.cts.com>, gandalf@pro-electric.cts.com (Ken Hollis) writes:
> Greetings and Salutations:

> >From: mikemr@microsoft.com (Michael MRAZ)

> >It would be interesting to simulate this, however, and see if
> >the thrust vector controls could compensate. I've seen films
> >of an old Atlas lifting off after one of its three engines
> >failed. It actually flew fairly straight until the RSO destroyed
> >it.

> Each SRB weighs 1.293 Million Pounds, and generated 2.9 Million pounds of
> thrust.  At sea level, each SSME generates about 393,800 Lbs of thrust. 
> Assume the Orbiter Weighs 171,000 Lbs with payload of 30,000 Lbs ("Medium"
> weight assumption, Payload Guys could give you a better "Average" weight). 
> The ET weighs 1,655,600 Lbs.
> 
> Measurements:
> 
> Centerline from the middle of the orbiter to each SRB center is +/- 20.9
> feet in the Y direction.  Each SRB can gimbal up to 8 degrees.  Each SRB is
> 1790 inches Long, and 146 Inches in diameter.
> 
> SSME (Space Shuttle Main Engine) #1 is centerline in the Y direction, and
> 470 Inches in the Z direction.  SSME #2 is about 60 Inches from Center (to
> the left) in the Y direction, and 360 Inches in the Z direction, and SSME
> #3 is about 60 Inches from the right of the center and 360 Inches in the Z
> direction.  Each engine is hardware limited to +/- 10.5 degrees pitch, +/-
> 8.5 degrees yaw from null installation.  For E-2L, null is +3.5 Degrees Yaw
> (away from centerline), and E-3R is -3.5 degrees Yaw (away from
> centerline).  E-1C is null.  For Pitch, E1C is -16 degrees "Up", and E-2L &
> E-3C is -10 degrees "Up" (towards the tail).  X-Axis is nose to tail (+X is
> aft, nose Xo is 236 Inches & Tail Xo is 1702 inches, i.e. about 1466 Inches
> long).  Y-Axis is left to right (right is +Y, looking forward).  Z is Top
> to bottom, top being +Z. Top of payload bay is 500 Inches, Lowest point of
> belly of ship is about 260 Inches.
> 
> The center of the ET & SRB is about 55 inches in the Z direction.  The ET
> is 153.8 feet long, and has a diameter of 27.6 feet.
> 
> Assuming the External Tank nose cap is at X 0 Inches, the SRB cap is X
> 420.5 Inches & the Orbiter nose is about X 654.5 Inches.
> 
> Given the above, I believe that some smart physics or engineering student
> should be able to figure out the moment of inertia with respect to
> different actuator positions and thrusts.  Show me your brilliance, be
> brave & post it to the world.  Yes, I realize that the X, Y & Z "zero"
> points are not at a particular point on the hardware, but that is where
> NASA defines them.  If I am missing any important piece of information,
> 
> 
>                               Ken Hollis

Ok, you talked me into it.

First from the numbers given:

Total Stack Mass (Weight) = 4.443 M lb
Total Thrust Less 1 SRB   = 4.08  M lb

for a 
Thrust to Mass Ratio      = 0.93  

So even if you can control it, it's going to hit the ground. :~(
Of course there is no good reason to keep the dead SRB, so lets dump it.  
Now we have

New Stack Mass (Weight)   = 3.12  M lb   
Total Thrust Less 1 SRB   = 4.08  M lb 
 
for a 
New Thrust to Mass Ratio  = 1.3
 
So now it has a chance to fly.  :~)

Now assuming the center of mass for the SRB, Ext. Tank, and Shuttle are 
at the center of the demisions Ken gave and that the Payload C.M. is 
at the Suttle C.M. the total C.M. moves from 

NormCM = 1173 x + 0 y + 52.5 z  inches

to 

NewCM = 1124 x + 101.9 y + 76.5 z  inches

when the dead SRB is droped.

The thrust from the remaining SRB is applyed at

Thrust = 2211 x + 246 y + 55 z inches.

For the SRB to push through the new CM it needs to gimbal 7.6 deg., which 
is just inside the 8 deg. limit above.

Well I've had enough fun with this.  Will someone else work this out 
for the SSME?  Stay tuned for the next episode of As The Suttle Fails to 
find out!

John Childers 
ee00jc@unccvax.uncc.edu