Angle of climb at Vx and glide angle when "overweight": five questions

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.

Even though you're flying at the Vy corresponding to your new weight,

Q1: Is it correct to say that that your climb rate is now LOWER than
your max. gross weight Vy, due to the increase in power required at
the higher load factor? If so, you'd agree that you're flying at a
"higher speed" but yet climbing slower? Is that "higher speed" the
speed along the flight path line or the horizontal velocity that's
parallel to the ground? Would clarifying this last question open
another can of worms? The rate of climb is the vertical velocity with
respect to the ground, that I am sure. I think I am confusing
aircraft airspeed with velocity along the flight path vector or
horizontal velocity with respect to the the inertial frame.

Q2: Further, is it correct to write that the thrust required to
counter the drag is higher at that moment? As such, is the angle of
climb at Vy is also lessened?


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.

Q3: Is it correct to infer that your thrust required to counter the
drag is higher at that moment? Hence, is the maximum climb angle less
that what it would be at max. gross weight?

Q4: Further, is it correct to write that your power required at that
moment is higher than at max. gross weight and as such, the rate of
climb at the maximum climb angle is reduced?


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.

Here's question 5: I would make the risky proposition of stating that
drag and power required ALWAYS increase with increasing weight. To
me, when you have neither thrust nor power available during gliding
flight, increasing weight/load factor STILL increases your drag and
therefore results in a higher descent / glide angle. Likewise, the
increase in weight/load factor under no power STILL triggers an
increase in power required and therefore higher sink rate.

Right now, I am seeing a contradiction between the 1/(L/D) equation
and what I've described above. I can't seem to figure out why.

Referring back to the best angle of climb question above, it appears
that increasing your weight decreases your max. climb angle. I just
don't see a difference between climb and descent angle insofar as both
being excess thrust or drag phenomena. Why would increasing your
weight decrease your max. climb angle but not affect your glide angle?
In both cases, I see an increase in drag with higher load factor
resulting in a decrease in max. climb angle and an increase in glide
angle. Max. climb angle is very much defined by best L/D (i.e. min.
drag) and excess thrust while min. glide angle (best glide angle) is
defined by best L/D alone. That best L/D is still analogous to its
"powered counterpart", as it still represents the point of minimum
drag. However, that drag has increased with the higher weight,
lessening the L/D ratio. As a result, without an engine, I expect
that the glide angle to increase (reducing range). Perhaps the fact
that there's no thrust vector has something to do with this fiasco.

Ok, I'll stop rambling. I hope I conveyed my thoughts clearly enough.

Happy Thanksgiving,
Alex