At 04:48 16 August 2005, Gerhard Wesp wrote:
Ian wrote:
If you are in a situation (perhaps recovering from
a spin) with your nose
pointing 60 deg down below the horizontal and the
ASI reading 180 km/h and
accelerating rapidly. You could try:

[ leave A/B closed and pull 4G ...]

I have not worked out the maths of the two options
but I think that in
a clean glass ship, you would have a better chanced
completing the first
manoeuvre without exceeding VNE than the second.

I couldn't resist the temptation and did the maths.
I kind of lost the
habit, so it took me 20 minutes. The result is: My
intuition was
right: Do *not* use the airbrakes.

Even in an ideal ship (zero drag) and with the nose
pointing vertically
down initially, the peak speed is only 240km/h under
your assumptions
(4g pull-up and 180km/h initially). In a real ship
and with only 60
degrees down, the peak speed would of course be lower.

Here's the script with the phugoid equation (Mathematica).
Feel free to
modify the initial conditions and parameters and play
around. The
unknowns are v1, v2, the horizontal and vertical component
of the speed
vector.

kmh = 1 / 3.6
Ng = 4
g = 9.81
v0 = 180 kmh
tmax = 8
dt = .1

v =
NDSolve[
{
v1'[ t ] == Ng g * v2[ t ] / Sqrt[ v1[ t ]^2 +
v2[ t ]^2 ] ,
v2'[ t ] == Ng g * -v1[ t ] / Sqrt[ v1[ t ]^2 +
v2[ t ]^2 ] - g ,
v1[ 0 ] == 0 ,
v2[ 0 ] == -v0
} ,
{ v1 , v2 } ,
{ t , 0 , tmax }
][[ 1 ]]

Table[ ( Sqrt[ v1[ t ]^2 + v2[ t ]^2 ] /. v ) / kmh
, { t , 0 , tmax , dt } ]

Regards
-Gerhard

I think the ground might get in the way before I have
done the sums :-)