Size of the terrace covering for shade

Currently planning a single-family house.

I am uncertain about the size of the terrace roof.

The terrace faces SE.

The width of the roof should be about 4 m. How far do I need to go in depth so that the roof provides shade on the terrace?

Shade is actually almost always provided by the roof. The question is, how much should be shaded. Our terrace is also oriented to the southeast and we have about 2.50m covered (lean-to roof). That is enough for us. A little sun is allowed to enter the room during the low-light seasons.

We tried to simulate the whole thing with the position of the sun and sun rays back then. In summer, actually one representation should point upwards and another downwards. At that time, it was about whether to make a 50 cm or 80 cm roof overhang and, with the recessed building part, either 2.1 m or 2.4 m. We ultimately decided on the smaller roof overhang so that we have a bit more sun at the dining table in winter and spring. In summer, both overhangs are sufficient for full shading.