How do you explain why the A/S increases on thermal entry?

Fred wrote:
Just got asked this question, didn't have a quick and easy answer.
How do you explain it?


Although this thread is now pretty old, I would like to add my
contribution, for 2 reasons. The first one is that nobody among the
contributors made a clear distinction between two effects involved in
this process. The second one is to try to share with all the readers
of this newsgroup a quantitative estimate of one of these two effects.

The two effects among which I want to make a distiction a
1) the pitch stability of the glider tend to keep it at the same
angle relatively to the air airstream, as long as the pilot doesn't
move any control that would change that. The thermal make a change
in the direction of the airstream, the stability of the glider make
it follow this change by pitching down. This is a cause of long term
airspeed increase.
2) even in the absence of the first effect, e.g. if the pilot reacts
to the pitch down tendancy (that's what I teach to my students: don't
let the thermal accelerate your glider, otherwise it will throw you
outside by increasing your turn radius), there is a change in the
aerodynamic force (vector sum of lift + drag) which causes an
immediate acceleration.

Now let's have a closer look on the 2nd effect. In order to make a
rough estimate of this effect, I want to do some first order
approximations. i.e. neglecting what I consider as second order
quantities. More precisely I will consider some quantities as "small"
compared to others, and second order quantities are those which are
"small" compared to some one which is already "small". As primary
small things I will consider that drag is small compared to lift,
and the vertical speed of the thermal (increase) is small compared
to the airspeed.

The first thing caused by the thermal is to change the relative wind
in force and direction. As the thermal velocity is almost perpendicular
to the initial velocity, the change in force is a second order change,
so I will only consider the change in direction.

The change in direction causes an identical change in angle of attack.
This change causes a change in the aerodynamic force. As before the
thermal the aerodynamic force was exactly opposite to the weight, so
that the sum of all forces was zero, after the change, the net resulting
force causing an acceleration is just the (vector) difference beteween
the new aerodynamic force and the previous one. For a quantitative
estimate, as we usually count (and feel) acceleration in "g" rather
than in m/s² (or ft/s² for metrically challenged people), what is
interesting is the relative change in this force, this gives directly
the accelaration in g.

There is a change both in direction and in intensity. Both changes are
small, so the new direction is close to the previous one. So the change
in direction provides mainly an horizontal component of the differential
force an the change in intensity mainly a vertical componemt, mainly
being understood as: the difference with the real change is a second
order quantity and may be neglected.

I assume that the glider was near its best L/D speed. In this case the
change of L/D when there is a small change of angle of attack is a
second order change. So we neglect it, i.e. we consider that the
angle between the aerodynamic force and the direction of the relative
wind doesn't change. So the change in direction of the aerodynamic force
is the same as the change in the direction of the relative wind. This
change in radians is the ratio Vz/V of the thermal velocity to the
airspeed, so this is equal to the first order to the horizontal
relative change in force dFh/F and to the horizontal accelaration in
"g".

Now what is the vertical accelaration? To the first order the relative
change dFv/F is equal to the relative change of the lift coefficient
dCl/Cl. The lift coefficient Cl is near 1 at best L/D, so we may focus
on the absolute change dCl. The aerodynamic litterature says that for
a thin plate the theorical value of dCl/da (da being the change of angle
of attack) is 2pi, and "The result, that CL changes by 2pi per radian
change of angle of attack (.1096/deg) is not far from the measured slope
for many airfoils"
(http://www.desktopaero.com/appliedae...atresults.html). This
is for an infinite aspect ratio, there is a correction factor of
AR/(AR+2) for finite aspect ratio AR which is so close to 1 for the
usual aspect ratio of most gliders that we can assumme it is 1,
especially if we approximate 2pi by 6.

So the vertical acceleration is roughly 6 times Vz/V and 6 times
the horizontal acceleration. This explains (if such an explanation was
needed :-) that we mainly feel the vertical acceleration. A glider
flying at 50 knots and encoutering a 1 knot thermal (again for
metrically challenged people) will roughly accelarate by .02 g
horizontally and .12 g vertically.