Re: Aircraft design question

Date:         21 Mar 2001 18:33:22 
From:         "Matthew Willshee" <matthew@amber-matt.freeserve.co.uk>
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Dafydd ab Hugh <dafyddNO@SPAMsff.net> wrote in message
news:airliners.2001.3@ditka.Chicago.COM...
> Dear aerospace engineers;
>
> My wife is an aerospace engineering student at Cal Poly Pomona, and
> for her senior thesis, she is supposed to design a passenger window
> for a future single-stage-to-orbit (SSTO) vehicle.  This vehicle would
> take some number of passengers from a vertical takeoff into orbit or a
> suborbital arc and back down to a horizontal landing on a commercial
> airport runway.  Think of Reagan's 1980s proposal of an "Orient
> Express."

> But she's been unable to find any publications that discuss designing
> passenger windows on commercial jets, hypersonic aircraft, spacecraft,
> or anything else.

> There must be something out there; engineers build airplanes with
> passenger windows, so somebody knows how to design them!

The windows will probably be glass, which is a ceramic.  I have tried to
give a summary of the strength issues below.  The source is "Engineering
Materials 2" by M.F.Ashby and D.R.H.Jones.  I would recommend this book - it
is very readable.  There is a good explanation of the issues involved in
designing with ceramics and even a case study on pressure window design in
there.

You cannot think of ceramics of having a failure strength as such - they
have a probability of failure at a given stress.  The variation depends on
both stress and volume and can be described by a Weibull distribution:

loge (Probability of survival) =  - (V/V0) * (sigma/sigma0)^m

loge is logarithm to the base e
m = Weibull exponent (about 10 for glass).
Sigma0 and m are experimental constants found by testing batches of samples
of volume V0 (there are some example values in the book and I guess any
materials text would have something similar).  Sigma0 is the stress at which
a batch of samples of volume V0 would have a probability of survival of 1/e.

Why do we have to use probability?  The failure strength is set by the size
of flaws or cracks in the material.  how large the cracks in a given piece
are is purely down to chance.  This also explains why volume has an effect.
A larger piece of material has a greater chance of having a given size of
crack.

That is not the whole story - cracks grow over time under stress so any
window will break eventually under any stress.  The book gives

  ( sigma / sigma test )^n = (t test) / t

n = slow crack growth exponent - about 10 for glass.

Armed with this we can make an attempt at sizing the glass.  Pick a design
lifetime (1000's of hours) and an acceptable probability of failure (a very
small number such as 1/1 000 000 000).  Get some materials data which will
have some sort of failure stress.  Use the time equation to factor the
stress based on the experimental test time for the materials data and your
design life time. Factor again using the Weibull equation and your design
probability of survival (1- acceptable failure probability) to get an
acceptable stress in your window.  Consider a stress safety factor, which
will further reduce your maximum allowable stress.

Finally pick a geometry so that you can relate the pressure load on the
window to stress.  Stresses for simple geometries like plane circles and
hemispheres should be available in tables.  The thickness of window for a
given size should then come out of the equation.

It will probably be necessary to make assumptions and there won't be any one
right answer.  This is what engineering design is about.

Regards,
Matthew Willshee