Learn Russian: Согласно здравой логике, проект нужно сдать к вечеру. - According to sound logic, the project needs to be handed in by evening.

The preposition согласно (according to) requires the Dative case. Therefore, the feminine phrase здравая логика changes its endings to become здравой логике.

The word здравой looks related to health. How does it mean sound in this sentence?

You have a good eye! Здравый shares a root with words like здоровье (health) and здравствуйте (hello). In contexts like здравая логика or здравый смысл (common sense), it means healthy in a figurative way, translating nicely to sound or rational in English.

Is проект the subject of this sentence?

No, it is actually the direct object of the verb сдать (to hand in) and is in the Accusative case. Because проект is a masculine inanimate noun, its Accusative form looks exactly like the Nominative. The structure is an impersonal one that literally translates as: it is necessary to hand in the project.

Why use the perfective verb сдать instead of the imperfective сдавать?

The sentence focuses on the result and successful completion of the action by a specific deadline (к вечеру). Because it is a single, finalized action rather than an ongoing process or a repeated habit, the perfective aspect is required.