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Sarah Forst posted on December 12, 2011 23:50 
Hi Sarah,
I have a question that's been bugging me for years. It's a two-fold question relating to the same scenario. Say I would like to accelerate to a specific speed while going up a hill with a moderately steep grade. I either continue in the higher gear I'm already in but that's not in the ideal powerband, and let the engine build speed slowly; or I drop into a lower gear that's in the right powerband range, get to my desired speed and hold the throttle at a constant RPM once I'm there. My first question is: which is better for fuel economy? My second question is: which is better for the longevity of the engine? I have my own theories on the matter, but I'd much prefer your expert opinion.
Cheers!
Sean
Great question Sean- I can use my mad Excel skills! If math and graphs weren't your thing in school, you can skip to the end for the answer without all the boring details. We really have to look at the components that contribute to fuel consumption in controlled environments to understand what their individual impact is.
One factor affecting fuel economy is the force of drag- not the RuPaul kind! Air resistance can be calculated by 1/2 of the car's coefficient of drag (Cd) x the surface area of the front of the car (A) x the density of air * (r) times the speed of the car (v) squared.
Air resistance = 0.5 (Cd x A)(r x v^2)
Holding the coefficient of drag and the surface area of the front of the car constant (assuming you're talking about driving the same car), drag force increases exponentially as vehicle speed increases. So if you accelerate more quickly to get up to that higher speed, you'll need more power and consume more fuel to overcome the greater drag force at that speed for the longer period of time, versus getting up to speed slowly. Simply put, lower speeds = lower fuel consumption. Chalk one point for accelerating to your speed more slowly.
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| This is a comparison of two vehicles- Car A has a 0.27 coefficient of drag and Car B has a 0.32 coefficient of drag. Both assume constants for other variables, such as 68 degrees ambient temperature, sea level, and 26ft squared front surface area. Notice how the drag force increases exponentially as speed increases and especially how much greater the force is for the car with the larger coefficient of drag. This variance between the two cars also increases with speed. |
Air density is one variable that is needed in order to calculate drag force. Air density is impacted by altitude, ambient temperature, and humidity. Air density increases with increased air pressures but air density decreases with higher temperatures, higher altitudes, and to a lesser extent, increased humidity. A lower air density reduces drag and aerodynamic lift but can lead to lower engine horsepower since it reduces the amount of oxygen available for combustion.
Air/Fuel ratio also plays into fuel consumption. For gasoline engines, the stoichiometric air/fuel ratio is 14.7:1. Stoichiometric refers to the ideal ratio of fuel and oxygen from the air that leads to complete combustion. This is also where a 3-way catalyst runs the most efficient at keeping emission output low. At light throttle cruising conditions, most engines are tuned close to a stoichiometric 14.7:1 air/fuel ratio. A leaner air/fuel ratio (ie. 16.5:1) will consume less fuel than a richer a/f (12.5:1); less parts fuel per unit of air.
You can calculate an assumption of fuel consumption (not including the impact from increased drag forces) at various speeds if you know mass air flow of the engine, an equation involving air density, engine displacement, rpm, and volumetric efficiency.
Fuel consumption (fuel mass) = Engine mass air flow / A/F ratio
We can use adequate assumptions for some of these variables in order to map fuel consumption for illustrative purposes. Without turning this answer into a book going through all the calculations and unit conversions, I'm leaving units out of this graph just to show the relationship. FYI, I used a naturally aspirated SR20DE engine since I've used these variables for similar calculations in the past so I have the data on hand.
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| This is a fuel consumption graph that shows fuel mass used between 20 and 80mph in 10 mph increments, in both 3rd and 4th gears for this example. You can see by this graph how using 3rd gear will consume more fuel than 4th gear. |
This graph shows how speed affects fuel consumption during closed loop operation when the ECU uses input from the oxygen sensor to maintain close to a 14.7:1 ratio for all conditions. However, there are open loop situations such as cold engine operation or heavy loads or wide open throttle where the engine ignores the O2 sensor inputs and adjusts the mixture to be leaner or richer than the ideal ratio. At wide open throttle for instance, the mixture runs closer to a richer 11.5-12.7:1 air/fuel ratio, which helps to keep the engine cool and less prone to detonation. Many factory turbocharged cars are programmed even richer at wide open throttle. Since the engine is usually tuned for a richer air/fuel mixture when accelerating or under heavier loads or at wide open throttle, that's another point for slower acceleration.
Tuesday, December 13, 2011 4:04 AM
I hope I am not off track with this. Pertaining to modern ECUs and AFR in closed loop, where you would expect the greatest fuel economy because of a stoichiometric ratio. You may be able to build MPG strategies based on the ECU logic for closed to open loop switching. For example, when learning to tune fueling related things on my Subaru in closed loop, slow and minimal changes to throttle plate position was one key. What do you think Sarah? Would the gains be too minimal to bother? You also mention keeping your tires inflated to the proper PSI. Is there a formula that can be charted so see what "possible" MPG improvement could be made when increasing PSI over factory?
Tuesday, December 13, 2011 10:26 AM
Modern ECUs already have fuel economy savings strategies in place. Many will not even allow fuel enrichment unless you are at WOT. Also, BSFC plays a big part in this equation. You would want to stay in the engine rpm range with the best BSFC. In some instances, it may be 3000 rpm at 45% load, instead of 2000 rpm with 30% load. Very complicated indeed.
Tuesday, December 13, 2011 1:18 PM
Neither blanket statement is all of it. BSFC might be where the engine is most efficient but not where the car is.
Tuesday, December 13, 2011 5:13 PM
Too much tech.... brain is melting... On to look at pictures and drool...
Tuesday, December 13, 2011 6:58 PM
As far as the tire pressure, your best bet for better fuel economy is to decrease rolling resistance, which I assumed as a constant in the equation. Besides things like tire material, wheel size, and temperature, rolling resistance that is affected by tire pressure would be due to contact area and sidewall flex. Lower tire pressures would usually lead to more sidewall flex and a greater contact patch, increasing the rolling resistance. That is why you get crappy mpg if you let your tires get down to something like 20-25psi. But over-inflating the tires could lead to a loss of traction or you may skip over the imperfections in the road which also doesn't help with fuel economy. So I'd say just use the recommended psi- I don't think any improvement would be significant enough for the implosion of your brain figuring it out ;).
Tuesday, December 13, 2011 8:09 PM
Does MotoIQ have a gas powered project sipster? I can only fantasize having my D17 WPC-coated (can't afford it)
Tuesday, December 13, 2011 8:53 PM
Project Honda Ruckus
Tuesday, December 13, 2011 8:57 PM
doesn't count ;-P
Tuesday, December 13, 2011 9:18 PM
I read in Popular Science or Popular Mechanics that they found minimal gains by bumping up pressure (single digit percent with a 5psi bump). However by having the pressure 5psi lower than recommended, mpg dropped much more (I think around 15%). Sorry about the guesses at numbers, I can't find the article now.
Tuesday, December 13, 2011 10:00 PM
What about the role of pumping losses? I was under the impression that one of the biggest efficiency gains you get from driving at low RPM and high load was that the engine doesn't have to suck against the throttle body.
Wednesday, December 14, 2011 8:53 AM
Sarah, you did a good job of covering the basics of how to improve or effect your fuel economy but as Mike poked at with BSFC, you should have said that answer depends on exacts of engine speed, grade, gear ratios and the specific engine. As it's a fixed scenario of speed A to speed B, drag has little effect but the engine performance map (like this: http://expha.com/articles/images/10_graph_2.gif) is what is really needed to answer the 'specific question'. It's what is actually used in the industry for finding fuel economy gains. The other major factor being is the rate of acceleration!! Basically the question was WAY to vague to give a defined answer but I think he got the idea with what you said :)
Wednesday, December 14, 2011 2:12 PM
^ She DID indicate the assumptions made etc.... Of COURSE she HAS to make assumptions to even offer an answer to such a broad question. Hell her answer was over my head but I understad the variables based ont he text as well as the assumptions one MUST make. As A writer myself I would be frustrated by those coming in after the fact to nitpick or point out alternatives that could have been given. No offense to you but reading this in many different articles (not by you specifically) does offer some frustration for those of us that put this stuff out there. You even said yourself that the person asking got their question answered, which IMHO is the most important thing! Just venting a bit, but food for thought. wd
Thursday, December 15, 2011 12:21 PM
didn't mean for it to sound like knit picking. I was trying to expand upon what Sarah said and expand on how one gets a real answer for such a problem. Anyone with an logger and wideband could actually get a 'ballpark' idea/answer for this if they wanted. This is where rate of acceleration dictates engine load for said gear and thus fuel consumed while sweeping across that load (see graph from previous post) for the two gears with the same rate of acceleration. Then you get your actual answer. The fixed rate of accelerational also allows you to neglect drag and rolling resistance as both scenarios would have identical values...in that perfect test environment that we engineers dream of too :)
Wednesday, August 08, 2012 1:55 AM
So on the subject of too low of RPM... Im about to undertake the 6 speed swap into my NX2000. Using the 04+ Spec-v gearing with a 4.133 final drive, should put 60mph @ 2273 rpms... is that too low for proper oiling inside the engine?
Wednesday, August 08, 2012 9:01 PM
Oiling volume is 'linear' with engine speed on a 'Gerotor' (generating rotor) oil pump, which I believe you have. Most OEM pumps are that but some are changing now for variable flow for efficiency reasons. Regardless, RPM won't effect whether or not you have sufficient oil. Nissan designed that engine to operate in that RPM, so you should have no issues :)
 
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