Originally Posted by footie
I was not totally doubt what you had written as I know you know more about this stuff than I do, as swamp keeps reminding me maths isn't my strong suit.
What I was explaining to mixja is that from experience in previous cars and in my most recent car (Audi S5) was that shifting at peak power proved to be as quick if not a little quicker, and this observation was based on trap speeds as you call it, finding that I was recording a quicker speed by shifting before redline.
I know all cars are different and what worked for the S5 may not work for something else.
The physics work regardless. If your car worked better when short-shifted, it wasn't producing power according to Audi's published curve.
The MazdaSpeed 3 is a good example of this phenomenon. It's very quick, but forget about redline or anything close. The published specs don't meet the actual torque and power curves in that car.