P&G Optimum Mass Model

[trebuchet03]

This has been on my mind for awhile now...

So I just started to develop a model to look at how mass plays a role in P&G and see if there's any optimum for mass.

I started to tinker in excel a few minutes ago, and quickly realized that it will require some numerical methods to accommodate for aero resistance (as it's a function of time). For coarse resolution (like 5mph increments) - it shouldn't be too difficult when done in excel

So, other than RR and Aero Resistance - what other factors should I include in this model?

[omgwtfbyobbq]

Over what kinda route? I don't think there's gonna be an optimum mass assuming a flat road w/ perfect weather and no stops unless you include catalytic converter light off time, and alla that stuff. The change in BSFC from idle to near WOT in a manual transmission should result in some difference, w/ a vehicle that has a smaller appropriate engine having an advantage. But, going back to my guess, it seems like the lower the Crr and CdA, the less energy is expended overall, but realistically, if the P&G interval is too short, and having a vehicle with very small mass would exacerbate this, the driver could end up running through the enriched cycle way too often. I mean, it really depends... What is the model looking at? Manual, auto, flat ground, nice weather, piecewise approximation of P&G or actually looking at the BSFC curve, emissions enrichment, etc...

[2TonJellyBean]

I personally think that any vehicle that can pulse and glide on a flat road to advantage has a suboptimal drivetrain for its mass and drag (although mass isn't as much of a factor on the flats -- in fact it should approach zero).

Boats don't P&G, nor transport trucks, nor trains, nor jet fighters limping home to base on fumes. I personally think that with a different powerband and/or different gearing to optimize the torque to the load P&G can only lower fuel efficiency. In the hills, it's more DWL than P&G, although at an extreme that is almost what it becomes.

[trebuchet03]

So mass is directly related to your glide time (and force/torque necessary for a pulse). I've got the glide modeled for flat terrain (a slope is easy to add in) - and I've been thinking of ways I can model the pulse such that I can verify with data.

But given that ideally we're running to optimize BSFC - the power generated shouldn't vary too much as the goal is to run only at optimum BSFC engine power. So, for a moment, consider power output constant.

Given a constant power output - the only variable inputs for one solution of the model should be mass and start/end velocity.

So, the difference between 2000kg and 1000kg gliding from 50mph to 40mph. The 2000kg body will glide for just shy of 40 seconds while the 1000kg body glides for 20 seconds. Which makes sense, if you double the mass, you double the momentum which means it should take total resistive forces almost twice as long to act on the body as those forces. I did include RR, but the difference is very low (10.6N v 21.2N).

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Mythbusters did a bit on a Helium filled football - does it get more hang time/distance. The answer is no, as helium has less mass making aero forces much more significant.

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Okay, so double the mass will nearly double the glide time - but also doubles the time necessary to accelerate. The thinking here is, stable acceleration through the pulse will yield better FE.....

Hrmmm, I may have just thought myself out of the idea.... Or just thought my way out of the method that the idea needs to be examined I'm just going to derive some system equations on paper (what I should have done from the start) and see where that takes me - I'll probably just find that mass cancels out completely for an ideal scenario

[omgwtfbyobbq]

Yeah, ya got it I think. I view it as average power over a distance given some speed. If you increase the mass, you will also increase the power required at some speed proportionally. While a heavier car may be better at glides IRL given different routes and our ability to figure what's best, if you're looking at steady state I think you'll find that assuming some ideal/constant engine efficiency via P&G, more mass just takes a little more energy overall, even if it does increase the glide distance over some range of speeds. But, like I said, in the real world, accounting for emissions controls is a valid consideration, so a vehicle that weighs twice as much may not spend nearly as much time in the enriched cycle and see higher overall engine efficiency.

Some people got together and did a P&G marathon with an Insight and saw something like 165mpg@18mph, but if ya look at the high end estimate of what the car needs to go all those miles at that speed and compare it to how much gas they used, the thing was only operating at most around 30% BTE, even though ~35% peak BTE was common almost two decades ago, and ~40% is near what the Insight is capable of IIRC. So, it was imo likely the emissions system that was responsible, and a heavier car (or one with a enclosed cat ) would have fewer enriched cycles to go through and get better mileage using the Pee and Gee at the same average speed. So, yeah... I think real world mass does play a part, but ya have to look at the FI programming to figure out the details imo. Otoh, in an ideal state, w/o any gas going to warm the engine and emissions system up after a glide, I don't think mass matters.