At 17:23 05 January 2011, Derek C wrote:
On Jan 5, 10:33=A0am, Doug Greenwell wrote:
At 09:25 05 January 2011, Derek C wrote:



On Jan 5, 12:00=3DA0am, "
wrote:
So, in between level flight and vertical flight, there must be a
region
where the wing lift is less than in level flight, right? I'm
saying
there is a continuous reduction in the lift the wing must provide
as
th=3D
e
climb angle increases.

Only two months till March flying starts...gotta solve this
problem
while we still have time!

--
Eric Greenwell - Washington State, USA (change ".netto" to
".us"
to
email me)

Yeah....you got it......the lift is the cosine of the climb angle
times the weight.........

level.....0 degrees climb.. =3DA0Cosine 0 =3D3D 1 =3DA0 =3DA0so
lift
=
=3D3D100%
glid=3D
er
weight

5 degree climb (reasonable tow climb angle) =3DA0 Cosine 5 =3D3D
996
=
=3DA0
=3DA0=3D
so
lift =3D3D 99.6% of glider's weight

45 degree climb (unlikely but just for demonstration) =3DA0 cosine
45
=3D3D
.
707 =3DA0so lift would be only 71% of glider's weight

90 degree climb =3DA0 Cosine 90 =3D3D o =3DA0 so lift would be
zero.

If we keep the airspeed constant, the drag shoud be constant....so
the
only variables are lift and thrust. =3DA0 as the thrust vector gets
bigger, the direction of flgith gets steeper climb, and the lift
vector gets smaller.

Cookie

So according to you, pulling a load up a 10 degree slope should
require less energy than pulling it on the flat! Anybody who has ever
ridden a bicycle can tell you that is not the case!

For a glider on tow, the combined vector of Lift and Thrust (provided
by the tug) has to equal the combined vector of weight plus drag. As
the glider is not rigidly connected to the tug, the extra lift has to
come from its wings (at least at moderate climb angles). For a given
airspeed this can only be done by increasing the angle of attack.
Hence you are closer to the stalling angle.

I am not sure that this is the correct explanation, but it seems to
fit the observed facts.

Derek C

There are two components to the energy required in this case - (1) the
energy required to overcome friction (which will indeed be slightly
less,
because of the reduced reaction force perpendicular to the slope), (2)
th=
e
energy required to lift the load up a given height

(NB this assumes that you are pulling the load at a constant speed -
otherwise we would have to take kinetic energy into account as well)

(1) can be reduced to (near) zero by reducing friction - using rollers
fo=
r
example, or in your alternative example of a bicycle - the equivalent
effect in a glider on tow is reducing drag by careful streamlining or
increased aspect ratio.

(2) is fixed, and independent of speed or slope angle - raising any
objec=
t
a given height requires a fixed amount of energy (=3D
mass*acceleration
d=
ue
to gravity*height change). =A0

Both components of the energy input are provided by you pulling the
load
up the slope.

A glider on tow is exactly the same. =A0The wing lift corresponds to
the
reaction force between the surface and the load. =A0The drag
corresponds
=
to
the friction force between the surface and the load. =A0The tug
correspon=
ds
to you pulling the load - and is doing all the work against friction
and
gravity. =A0The lift/reaction force does no work - all it does is stop
th=
e
load sinking into the ground or the glider falling further and further
below the tug.

Imagine a perfect glider with no drag* on tow (=3D pulling a load up
the
slope with no friction, or a perfect bicycle) ... what happens if you
release the rope (or stop pedalling)? =A0If the wing lift were
responsibl=
e
for the climb rate then you would carry on climbing until you ran out
of
atmosphere (or hill)

* fortunately not currently available in the shops, since it would
ruin
the sport! =A0- Hide quoted text -

- Show quoted text -

To take your points above in order:

1) Gliders, at least decent ones, are pretty low drag anyway.

2) Kinetic energy from the tug is being used to raise the mass of the
glider up against gravity, so that it gains potential energy. Once
that source of kinetic energy is removed (i.e. you pull off tow), the
mass will stop going up and will start to descend due to the force of
gravity acting downwards. To maintain forward momentum gliders have to
continually descend through the air in which they are flying.

Gliders appear to get near to the stall during slow aerotows at much
greater than their normal free flight stalling airspeeds. I would
suggest that aerotowing must increase the wing loading in some way.

Derek C


2) that's exactly the point! The energy from the tug (not its kinetic
energy, but the work done in pulling the tow rope) is being used to
increase the potential energy of the glider ... the glider wing lift is
not contributing to the increase in potential energy because it is
perpendicular to the direction of motion and hence does no work.