Apparently I'm an Eco Driving Ace (First Tank MPG)

I think you guys forget that the exact same wind resistance and friction exists whether you are driving in flat terrain or hilly terrain, so you can safely remove that from the equation as it relates to these two scenarios.

1) If you had a car on top of a hill with all PE and no KE, which then travels down a hill and back up to its original height. You input energy to overcome air resistance and friction to reach your original height at no speed.

2) You have another car travelling on a flat surface, and KE equal to the PE of the first car. You input energy to overcome air resistance and friction to maintain speed.

3) You have a third car with the same KE as the first car travels up a hill (with input energy) and coasts back down to its original speed (same KE, same PE).

The only input energy of all scenarios then is to overcome friction and resistance, even in case #3) the energy to go up the hill is then taken away on the downhill leg by air resistance and friction

The only other differences are the different speeds they run at (will affect fuel economy by the square of the speed), and if we have to run the ICEs and/or batteries of each car differently which affects the thermal efficiency, or introduces conversion losses (i.e. running at 37% efficiency during cruising vs 32% efficiency during peak power demand).

If you can maintain the Prius' thermal efficiency throughout the entire time it needs to provide power, then it will not matter if hills are present or not.

PE to KE and KE to PE is 100%. It's not the same as say, Chemical Energy (Battery) to Electricity. Or KE -> Electricity -> Chemical Energy (Battery). This is why regenerative braking is lossy and climbing a hill is not. Climbing a hill is a perfect store of energy, if the desired conversion is to kinetic energy through falling.

 

Here is another take - Why does pulse and glide work? It works because you pulse at a higher engine efficiency than if you continued along at the same speed and you build up KE in the process, the you use that KE to overcome your usual frictions. Think of hill climbing and descending as a vertical Pulse and Glide

 

^^ P&G works because of two reasons:

1. Low speed steady state driving at ~ 35 mph does not place the ICE in an efficient Thermodynamic zone;

and 2, During the glide phase the IC engine is not spinning.

Oddly enough, the major reason is 2. You can verify this by noting the drop off in P&G fuel economy 1 mph over the ICE cut-off threshold

 

Ok, Guys. I'll try one more time, then I'll quit. There seems to be two arguments here about energy and hills. First, a few of you have claimed you get all your PE converted to KE when you coast down a hill. Sorry, that is flatly impossible. If you coast down a 1000 ft hill from rest and then immediately use your KE to coast up an adjacent 1000 ft hill, you will not reach the peak. One hundred percent conversion from PE to KE is impossible for an automobile in the real world. I recommend visiting the open courseware website at MIT and viewing Professor Walter Lewin's video with the wrecking ball; it illustrates this principle. I know first year physics classes often have such problems in the texts, but these are idealized models and do not conform to the real world. The second argument, if I understand it, is that they run the ICE in a more efficient mode while going uphill. I, admittedly, do not have any data on fuel efficiency curves, but it seems hard to believe the ICE going up a hill is running more efficiently than it is when cruising on a flat highway, where cars always get their best fuel efficiency. Regardless, it costs more energy to go up the hill than you can recover going down the hill. Any other conclusion means the Prius is a perpetual motion machine. I have highjacked the OP's thread too much already, so this is my last word. If anyone would like to discuss this further, please contact me offline. BTW, I mean no hard feelings to anyone who has contributed to this discussion. I have enjoyed the exchange.

 

2 thoughts in reply, Check the Gen 3 Prius BSFC curve and note that I specifically stated that one keep to a 20 Hp ICE output while hill climbing. Also P&G works better than a steady cruising on a flat road. Sure there are always conversion losses between energy states, the question asked in an early post was whether hills are detrimental to good fuel economy. I answered on the basis of experience that they are not, if one can climb at 20 Hp ( highest efficiency), and coast down ICEless at a speed less than 45 mph( otherwise the ICE starts up and spoils things) . I do it all the time and it works, getting better gas mileage than driving on a flat road. My Insight 1 would not do this but the Prius sure will. There is another thread from a few years ago where another Prius owner made the same observation based on his experience as well.

 

It's hard to say, but I would guess that a hill with a moderately steep incline and a longer, more gradual decline at traditional glide speeds would be best. The pulse would be short and the glide would be longer than usual. Also, the longer decline would make it easier to maintain a safe and consistent speed without hitting the brakes. Can it beat flat terrain? I don't know.