Calculation of the maximum possible knee wall height

Hello :)

we are about to purchase a plot of land and are dealing with the associated development plan. We would have wished for the possibility of a second full floor, which is not possible/seems not to be possible. As a compromise, an attic with a very high knee wall and a correspondingly flat roof would be conceivable. My information is as follows: maximum building height 9m, pitch angle 30 - 52° possible. Here is the wording regarding the attic:

"According to § 16 and § 20 of the Federal Land Utilization Ordinance, construction with one full floor (Z I) and a floor area ratio (floor area ratio) of up to a maximum of 0.35 is permitted. Above the permitted full floor, extensions with at least one sloped roof as well as extensions that are set back from at least one exterior wall of the building are only permitted if they cover at most 3/4 of the gross floor area of the underlying floor at a height of ≥ 2.3 m"

Can anyone recommend a program/calculator or similar with which a calculation of the roof pitch and knee wall is possible? I think our absolute minimum requirement for the knee wall is 1.50m, rather 1.80m; otherwise the purchase would not be an option. A conversation with the responsible authority has not been possible so far due to Covid-19.

Best regards

Can anyone recommend a program/calculator or similar with which a calculation of the roof pitch and the knee wall is possible?

The program is called calculator. At 30° pitch you reach 1.73 m and at 52° after 78 cm distance a height difference of 1.00 m.

I think our absolute minimum requirement for the knee wall is 1.50 m, preferably 1.80 m;

I think differently: a sensible knee wall starts at 1.0 m, a reasonable one is between 1.2 and 1.4 m, and with 1.8 m knee wall it is already borderline (not only for the full storey limit). With the knee wall, the window head height effectively also rises.

You can also arm yourself with a set square and draw sections on a grid block. The building authority is a poor contact for calculations; that would be the responsibility of an architect, who also sometimes knows routes that a layperson or a planner from a construction company does not know. 30 degrees for a roof is quite simple with the grid planning... But 30 degrees is not flat!

Gable roof 30°
House width 10m
This results in a knee wall height of approximately 1.40m

Sketch

Thanks to everyone for the timely responses and especially for the explanation with the drawing! :)