motorgliders as towplanes

Todd,


Nice! You must be the only guy out there who understands this stuff, the
forces acting on a glider in flight. (Other than me!)

Yes, analysis shows that in CLIMBING flight, lift must just be LESS that
it is in level flight. Same for descending (gliding flight) Lift is less
than it would be in level flight.

The difference between descending flight, level flight and climbing
flights is POWER.

In the case of a glider on towplane, the power (energy) comes from the
fuel powering the engine which in turn produces thrust at the propeller
which in turn produces a pulling force throught the rope to the glider.
We could call this "Thrust"

Excess power makes an aircraft climb!

If Thrust is greater than drag, the aircraft will climb. If Thrust is
equal to drag the aircraft will fly level. If thrust is less than drag,
(or nonexistant as in a glider in free flight), the aircraft will
descend.

As you said, lift does vary, but very little if climb or descent angles
are kept reasonable.

Drag and Thrust are the important variables. Gravity MUST remain
constant, and lift hardly varies worth considering.

Note that power, we should say energy, can be imparted to a glider in
several ways that will result in climbing flight. Of course by a tow
plane as mentioned above, but it could be energy from a THERMAL, RIDGE,
WAVE etc. These will all make a glider climb!

To beter understand how the lift gets less as the climb angle gets
greater, let's look at teh "extreme". Consider a glider attached by a
nose hook to a huge construction crane. The crane operator applies POWER
to the lifting cable and the glider is slowly lifted, vertically into the
air.

The glider has only two forces acting on it now, THRUST from the lifting
cable, and gravity. Thrust acting vertically upward, and gravity acting
vertically downward. In fact, these forces woud be equal, but oppposite
to each other. LIFT would necessarily be ZERO!

Cookie (From blairstown)









At 01:03 14 March 2009, wrote:
On Mar 13, 8:45=A0pm, Z Goudie wrote:
At 21:55 13 March 2009, The Real Doctor wrote:

How much extra lift do you think is required to climb?

Without going into the math (euphemism for I'm not sure how to!).

If you are not sure how to do the math, how can you be sure that you
are correct ?

In fact, I am able to do the math ( practicing aero engineer) and you
are not correct. The difference between lift ( and thus angle of
attack ) in a STEADY descent and a STEADY climb is practically non
existent.

To do the math, you should draw out a diagram of the drag, lift,
weight and towline. The aircraft is climbing on a line that is an
angle "gamma". Draw the towline force on this line pulling the
aircraft forward and up. Draw the drag in the opposite direction.
Draw lift at a right angle to this line and finally draw weight
pulling straight down.

Total up these 4 forces and making them balance out in the up-down and
forward-back directions gives you the relationship that lift =3D cosine
( gamma ) * weight. The steeper you climb, then less the lift !!!

If you make different assumption of the direction of the towplane
force, then you would get a different result.


Todd Smith
3S

On 14 Mar, 13:15, Bob Cook wrote:

To beter understand how the lift gets less as the climb angle gets
greater, let's look at teh "extreme". Consider a glider attached by a
nose hook to a huge construction crane. *The crane operator *applies POWER
to the lifting cable and the glider is slowly lifted, vertically into the
air.

Bad example, since tow planes pull - give or take a wee bit -
horizontally, regardless of climb angle.

Ian

On Mar 14, 9:43*am, The Real Doctor wrote:

Bad example, since tow planes pull - give or take a wee bit -
horizontally, regardless of climb angle.

Ian

Well, if I re-draw my force diagram so that the tow force is
horizontal. I get a new equation for lift :-)


lift = weight / ( cos( gamma) - sin(gamma) / LOD )

For a 10 degree climb ( thats about a 10knot climb rate at 60 knots
airspeed) and a LOD ( lift over drag ) of 30.

I get lift = 1.021 * weight.

That would increase stall speed by 1%.

So, while I completely agree that on tow a glider can feel much closer
to stall at an airspeed that is much higher than it's nominal stall
speed. I do not believe this is because it need's "more lift to climb
than glide". The math seems to show this is a dead end of
investigation.

More likely causes have already been proposed.
Elevator force needed to balance the pitching moment from the tow
rope.
Disturbed air behind the towplane.

Todd
3S

On Mar 14, 9:15*am, Bob Cook wrote:
Todd,

Nice! *You must be *the only guy out there who understands this stuff, the
forces acting on a glider in flight. *(Other than me!)


Hey Cookie, I hope to see you more this summer than last. If I can
afford the gas and tow fees :-)

Todd

On 14 Mar, 11:24, The Real Doctor wrote:

So in a 40:1 gliding descent, lift is 1599/1600 of weight, and in a
15:1 climb, lift is 599/600 of weight.

Correction for the purists ... "lift is *supporting* 1599/1600 ...
lift is *supporting* 599/600 ..."

Ian

On 14 Mar, 14:49, wrote:

So, while I completely agree that on tow a glider can feel much closer
to stall at an airspeed that is much higher than it's nominal stall
speed. *I do not believe this is because it need's "more lift to climb
than glide". *The math seems to show this is a dead end of
investigation.

More likely causes have already been proposed.
* * Elevator force needed to balance the pitching moment from the tow
rope.
* * Disturbed air behind the towplane.

Agreed. My money is on the towplane wake.

Ian

Agreed. My money is on the towplane wake.


I put my monies on the elevator authority/AoA ratio. We fly above
the wing wake (USA...) in most cases, in relatively clean air, but
sometimes in the clean air below it. Box the wake, it will tell you
where it is and where it isn't...

But typically glider's noses, on tow, are unnaturally high (and thus
AoA is higher...) for a given airspeed, in addition to being more
forcefully held there, both effects of course due to the rope's
pull. The elevator is the same size whether on tow or free flight
though, so the authority it can exert against the countering forces is
proportionately lower than in free flight...

The fix is the same regardless of why though- more speed... please!
(wings rocking in vain...)

-Paul

On 14 Mar, 16:53, The Real Doctor wrote:
On 14 Mar, 11:24, The Real Doctor wrote:

So in a 40:1 gliding descent, lift is 1599/1600 of weight, and in a
15:1 climb, lift is 599/600 of weight.

Correction for the purists ... "lift is *supporting* 1599/1600 ...
lift is *supporting* 599/600 ..."

Further correction

Oops. I forgot that drag acts down when climbing. I can't be bothered
doing the maths again, but I think it will lead to L = 1599/1600 W
gliding, 601/600 W climbing.

Ian

On 14 Mar, 17:24, sisu1a wrote:
Agreed. My money is on the towplane wake.

I put my monies on the elevator authority/AoA ratio. * *We fly above
the wing wake (USA...) in most cases, in relatively clean air, but
sometimes in the clean air below it. *Box the wake, it will tell you
where it is and where it isn't...

That'll tell you where the expanding conical turbulent wake of the
prop is ... there's also the smooth effect of the vortex sheet shed
from the wing to consider. One useful interpretation of the induced
drag is the effect the vortex sheet (modelled as tow tip vortices) has
on the local angle of attack of the wing ... the same will apply to
anything behind the tug ... like a glider ...

Ian

Most (sensible) people fly either above the tug's slipstream or below it.
In the first case the tug may be pulling the glider's nose down and in
the second case up. It doesn't seem to make a lot of difference to the
way the glider flies. There is a theory, mostly believed in by the good
folks of Oz, that low tow is slightly more stable. I can't somehow
imagine that the downwash from the tug has that much effect on a glider on
the end of a 150ft rope!

Derek Copeland

At 20:23 14 March 2009, The Real Doctor wrote:
On 14 Mar, 17:24, sisu1a wrote:
Agreed. My money is on the towplane wake.

I put my monies on the elevator authority/AoA ratio. =A0 =A0We fly
above
the wing wake (USA...) in most cases, in relatively clean air, but
sometimes in the clean air below it. =A0Box the wake, it will tell you
where it is and where it isn't...

That'll tell you where the expanding conical turbulent wake of the
prop is ... there's also the smooth effect of the vortex sheet shed
from the wing to consider. One useful interpretation of the induced
drag is the effect the vortex sheet (modelled as tow tip vortices) has
on the local angle of attack of the wing ... the same will apply to
anything behind the tug ... like a glider ...

Ian