Vertical penetration
Vertical penetration is a scalar measurement, of distance, of the maximum altitude an object, most often an aircraft, can gain at any particular moment in time, thereby converting all of its energy from kinetic, to gravitational potential.
Calculation
Assume an aircraft has the same mechanical energy at two separate points in its flight - one when the aircraft is straight and level, holding a constant airspeed, and negligible altitude and the other, following a sudden 90 degree pitch increase in attitude, when the aircraft has noticeable altitude, and negligible airspeed. Assuming the aircraft can 100% efficiently convert all of its kinetic energy to potential (theoretically have a radius of 0 in the turn, refer to centripetal force), the aircraft has the same mechanical energy in both points, the sum of the kinetic and potential energy of the first point, equaling the potential energy of the second:
$\,mgh_2 = \frac{1}{2}mv_1^2$
where m is the mass, v is the speed, h is the height of the body, and g is the is standard gravity. In SI units (used for most modern scientific work), mass is measured in kilograms, speed in metres per second, height is in metres, standard gravity in Metre per second squared, and the resulting energy is in joules.
Notice that neither mass nor standard gravity were given subscripts indicating which point they correspond to. This is because both are assumed constant. It is worth noting that this is very mildly incorrect for both. As an aircraft operates, it consumes fuel, oil, etc., which slightly decreases mass. And since the standard gravity is inversely proportional to the distance between the body and Earth, and the aircraft is gaining altitude (increasing said distance), slightly decreasing standard gravity.
By dividing by standard gravity and mass, and rewriting h2 as Δh, as h1 = 0 shows that
$\Delta h = \frac{\frac{1}{2}mv_1^2}{mg}$
by canceling out mass, and rewriting v1 as simply v as point two has no velocity, and moving the $\frac{1}{2}$ to the denominator, the formula for vertical penetration has yielded:
$\Delta h = \frac{v^2}{2g}$