Dave,

As a Prius marathon man and an HCH hypermiler with some 38,000 miles in my HCH, I can attest that a harder acceleration is better for FE in the P&G mode in the HCH. As to the rest of your post, I barely passed 9th grade algebra, and never took Alg II, and I don't even know what Trig or Calc are.

The problem I have with a hard acceleration pulse mode, is that the IMA is in assist mode draining the battery pack. In glide mode, the battery is not getting recharged. It does not take long before the battery pack is empty.

Further, it seems to me (a history major, not a physicist), that much of the increased ICE efficiency would come from using the energy stored in the battery pack without replacing it.

In my mind, the only sustainable P&G in the HCH is to ensure that during pulse you are also charging the battery pack. This means a very gradual acceleration with a whole lot of gas pedal control, watching the IMA display to make sure you have green lights, not none or blue. I have found P&G in this manner in my HCH is good for FE of 113 mpg over a closed course and the battery back pack stays charged. That's good enough for me.

Bob