Academic essays aren't the place for surprises, we're afraid. They wouldn't do well in a haunted house.
At the beginning of the essay, tell the reader what you're going to do, and then do it in a systematic, organized way. It's okay being predictable. No one's going to take off any points because you didn't buck the system. The reader should know what to expect and the essay should deliver on those expectations without going off on any major tangents. No sines or cosines either. You should be able to justify every paragraph, every sentence, every word in your paper in terms of how it supports your thesis. If it doesn't obviously relate to your thesis, it probably doesn't belong in your paper. Sadly, it may just end up in a word orphanage, with other words that are still searching for their place in the world. Sympathy is no excuse to leave them in your essay, though. Nix those little buggers.
The important elements of keeping your essay organized include
Example: Say you've got an introduction that promises to explain the three reasons that all pet dogs should be named Dog. Your essay should then explain those three reasons, in the order they appeared in the thesis. If you have one paragraph that delves into the mummification process used by the ancient Egyptians, then you've probably gone off track.