Suppose an unpowered, rigid, mechanical, lightweight aircraft (e.g. sport glider) is descending at a steady glide in a constant trim (hands off) configuration in a standard atmosphere. The pilot applies a quick elevator input and then goes hands off again, causing the nose to pitch up and the glider to gain altitude momentarily before eventually returning to a steady glide.
Suppose we measure the maximum angle of attack reached, (or max pitch angle, if that's easier), the maximum altitude gain, and the time it took to reach those maximums after the control input.
How would those values (max altitude gain, max angle, and times to get there) differ if the same control input occurred at 5,000 feet vs 10,000 feet above sea level? Support your answer using physics/ aviation formulas or reputable references.
My thoughts so far
Since the "effective" air speed of the glider in a particular trim configuration is expected to remain the same across altitudes, then I would assume the lift and drag force changes generated by the control input would be the same at any altitude.
However, the "true" airspeed of the glider is from what I could find about 10% higher at 10k, which results in greater momentum to resist changes in motion and greater kinetic energy that can translate into height.
However, I'm not sure if those two (momentum vs kinetic energy) would cancel each other out.
If kinetic energy alone is considered, I'd expect the altitude gain to be greater at higher altitudes, and I'm not sure about max angles or the times to get there.