where , is the wertical welociry component, av/at is wertical acceleration,
g is the acceleration of graviry, G is the drag coefficfest, 5 is atmospheric
density, S is the drag reference area, V is tacal welccity aagnitude, W is
wehicle weight, and 3 is the angle SetCveen the wenicle longitudinal axis and
the horizontal plane.
For a rocket wehicle such as the one under considera-
tion which has adequate static stabiiiry, it is reasonable to assime that if
aerodynamic forces are large enough that the drag is significant, they are
also large enough to hold the wehicle at zero angle of attack.
be the only aerodynamic force acting.
Thus drag will
This implies than sin @ = v/v.
By
substituting this in the above equation, the relation becomes:
- = tw) (5) Gur +8
Note chat g and p are functicus of altitude, or Z, only;
(3) is constant
during coasting flight; G is a fiction of Mach mmber which is, in turn,
a ferction of ambient temperature (again a functica of 2} and velocity;
welocity is obviously a function of both the horizontal and wertical velocity
components.
Frou this, it appears thst vertical action fs coupled to hori-
zontal wotioa by G and Vv.
.
a
Boch theoretical and actual trajectories {ndicate that these motions
are approximately independent.
Obwiously the product (c,¥) is either con-
stant or a function of Z only.
A typical drag coefficient curve is shown
at the right.
In the region above Mach 1, the drag coefficient is propor-
tional to 1/M.
The Mach mmber is defined
by che following expression:
Ms
y
hg.0o/T
,
.
§
~~
where T is aubient temperature in degrees
=
Bankine and V is welocity in feet per sec-
$
ood.
.
we te
—s
This tce=perature is again a function
anf
we
anleoimua
wenn
Tec
the
—_—_—_——
dene
Toe
mem fF Fi.
freee
£
a
cient may be approxinated as the product
of a function of altitude and the reciprocal of the welocicy between Mach mobers
°o
t
2
3
4
Mach Niober
291
59