When the basic equations of physics are questioned they should be tested by real experimental data.

Having recently worked on the compensation of the vario in my Ventus 2, I just happen to have such data. Several pull ups from 180 km/t to 95 km/t were recorded by the igc-logger (and on film).

Theory first (in SI units):

Potential energy: m * g * h
(m: mass, g: acceleration due to gravity - about 9.8 m/s^2, h: altitude)

Kinetic energy: ½ * m * v^2
(v: speed)

As a result, the theoretical lossless altitude gain by a pull up is:

dh_theory = ½ * (v_start^2-v_final^2) / g

This equation does not depend on the mass of the glider !

Experimental data:

24 pull ups from three different days in relatively calm air.
Average start speed: v_start = 49.8 m/s ± 0.4 m/s
Average final speed: v_final = 26.3 m/s ± 0.7 m/s
Average altitude gain: dh = 90 m ± 3 m

Using the equation above and the average start and final speeds, I find the theoretical altitude gain to be: dh_theory = 91 m ± 4 m

Actually, I was a little surprised to see such a close agreement.

No variation between days or direction of flight is seen (i.e. correct wind correction). The duration of the pull ups is 10 seconds. The quoted uncertainties are the statistical standard error of the average. Further analysis shows that the uncertainties on dH and dH_theory are highly correlated. I could think of several potential error sources but have not investigated their influence.

The mass of the Ventus 2? Well, it doesn’t matter…

Jan

PS! The mass-independent conversion from speed to altitude was actually given as an example in my school physics book when I was 14 years old. At that time I questioned the physics book due to the general (incorrect) understanding of this topic among glider pilots.