"Koopas Ly" wrote in message
om...
Happy Thanksgiving to ya'll,

This is related to my previous "overweight" post. I want to know if
you agree with the following reasoning:

Context: you take off over your maximum gross weight, and wonder how
your climb speeds and performance are affected.

Vy: The AOA corresponding to the best rate of climb remains the same.
However, the airspeed at which the best rate of climb speed increases
by the square root of the ratio of the current weight and maximum
gross weight. The pilot then pitches to obtain that new, higher Vy
airspeed.

OK so far. As you add weight, the "power required curve" (Power Req'd vs.
AS) for the a/c moves up and to the right -- more power required and it
occurs at a higher AS. Power available doesn't change much -- the engine is
the same, prop efficiency does impart some variation with AS, but it's small
over the variations we're discussing here.

Vy occurs at the point where there is the greatest excess power. (The power
req'd curve addresses level flight, excess power is what causes the climb.)
Since the power required moved up and right and the power avail is approx
the same, Vy increases and the amount of excess power decreases so rate of
climb decreases.

Net affect is higher AS (speed along flight path), lower climb angle, higher
ground speed (cotangent climb angle) and lower rate of climb (tangent climb
angle).


Vx: Again, the AOA corresponding to the best angle of climb for
obstacle clearance remains the same. However, the airspeed to now
achieve the best angle of climb at the current weight increases by the
same square root of the ratio of the current weight and maximum gross
weight. The pilot then pitches to obtain that new, higher Vx speed.

Same as above, except that we replace power with thrust. Curves look the
same, but the key points occur at slightly lower airspeeds.

With added weight; Vx goes up, climb angle goes down, ground speed goes up,
and rate of climb goes down.


Best Glide Speed (best range): From a simple FBD with no thrust
vector, one can find that the best angle of glide is only dependent
upon the inverse tangent of the reciprocal of the lift to drag ratio
or:

Tan(glide angle) = 1 / (L/D), assuming small angles, glide angle ~
(L/D)^(-1)

L/D is purely angle of attack driven. Therefore, the glide angle does
not change with respect to weight.

You are correct. L/D is purely aerodynamic and doesn't change with weight.
But when weight goes up you need more lift to get the same glide angle.
Since you're gliding, the only way to generate more lift is to fly faster.
So your AS for best glide increases as weight goes up. Since you're going
faster, the sink rate also increases; but since the angle is the same, you
still glide the same distance -- you just get there sooner.

That last reason is why some gliders have water ballast tanks. Since they
almost always fly at best L/D when trying to cover ground, the added weight
lets them fly faster. Which is important when racing.

Gerry