Fuel Efficiency: Car #1 vs Car #2 | Ask an Expert

[PookAir]

The qwustion is:
2 identical cars with their engine rev 2000rpm. The only difference is that car num #1 is in 4th gear and car num #2 is in 3rd.
Which car will use more fuel per minute?
Considering they are driving on leveled ground.
And does it Make a difference if they are going uphill or downhill instead?

Was arguing with a friend and I would be glad if you could help out

Thanks a lot

 

[mender]

We need to know the speeds of the two cars before we can answer that properly. For example, are they both going the same speed or is one going 30 mph in 3rd and the other at 40 mph on 4th?

 

[Averagesupernova]

I don't agree that we need to know the speed since the question is how much fuel per minute and not fuel per distance. There should be more vacuum on the vehicle in the lower gear since it is more lightly loaded. Engine vacuum is just about ALWAYS a relative indicator of fuel economy. So maybe I have given you enough clues to figure it out yourself?

 

[jack action]

The car in 4th gear will most likely take more fuel per minute than the one in 3rd gear.

First, if the cars are identical, the one in 4th gear will necessarily go faster at the same rpm. More speed means more power required. If we assume that the 3rd gear ratio is 1.26:1 and the 4th gear ratio is 1:1, the speed will be 1.26 times faster in the 4th gear and it will require 2 times the power to fight the aerodynamic drag (= 1.26³).

The fuel consumption rate (r) per power produced (P) by an engine is the BSFC. So:

r = P * BSFC

In a typical engine - at 2000 rpm - the BSFC will probably be lower in 4th gear, around 15% less than in 3rd gear. So the fuel consumption rate should be around 1,70 times greater in 4th gear than in 3rd gear (= 2 times the power * 0.85 times the BSFC).

This is assuming no acceleration and neglecting rolling resistance, which should lower the difference between the two because it is not related to speed and mostly constant. If the speeds are small, it might leads to a lower fuel consumption rate in 4th gear because the power needed will be nearly the same in both gears (0.85 ~ 1 times the power * 0.85 times the BSFC).

Going uphill or downhill will simulate a constant acceleration or deceleration. Going uphill will further lower the difference between the two - just like rolling resistance - because the power needed is also independent of speed. Going downhill should have the reverse effect.

I had this nice discussion in another thread that might interest you.

 

[mender]

So the assumption is that the speeds are different; reasonable assumption but I wasn't going to make that. Better to have a clear description of what the proposed scenario is before answering, but maybe that's just me.

 

[Averagesupernova]

2 identical cars each in different gears and both engines spinning 2000 RPM, how could you assume anything BUT they are traveling at different speeds?

 

[mender]

Easily, given the way people ask questions. Seen it quite a lot, have stopped assuming that what they type is what they mean.

"Oh, I meant identical other than the final drive gear ratio! My buddy and me were wondering whether having a numerically higher differential gear with the transmission in direct drive would be more efficient than a lower diff gear and the transmission in 3rd (same car speed for 2000 rpm). In other words, how much difference is there between the efficiency of bevel gears and hypoid gears."

 

[The Chase]

The answer has been given here already, but as a little addition it is worth noting that VERY low loads can cause poorer specific fuel consumption due to immense pumping losses experienced due to an almost completely closed butterfly valve on the throttle. Though in this example I'm sure this doesn't need to be taken into account as traveling along at 2000RPM in either 3rd or 4th gear should provide ample butterfly valve opening for this phenomena to be irreverent. I have attached a little JPEG of an experiment I performed recently demonstrating this effect.

 

[mylarcapsrock]

The answer has been given here already, but as a little addition it is worth noting that VERY low loads can cause poorer specific fuel consumption due to immense pumping losses experienced due to an almost completely closed butterfly valve on the throttle. Though in this example I'm sure this doesn't need to be taken into account as traveling along at 2000RPM in either 3rd or 4th gear should provide ample butterfly valve opening for this phenomena to be irreverent. I have attached a little JPEG of an experiment I performed recently demonstrating this effect.

Actually, the pumping loss is most extreme at this engine speed in a lightly loaded cruise mode- it's ALL about throttle angle- so if both were at WOT up hill the loss would be insignificant. If you were to take a vacuum gauge and run it at idle then at 2,000, I think you will see what I mean.

At 2k only the load will be different for this test- they will both use very nearly the same amount of fuel, with the 4th gear engine using slightly more.

 

[Ranger Mike]

You are almost there...but...I suspect hanging a vacuum gage on an engine in the dyno room is not telling the whole story.Leaving aside air resistance for the moment, the answer is the lowest RPM in the highest gear.

As for the specific question you posed, air resistance also comes into play Big time. For any vehicle, the higher the speed, the greater the air resistance. But some vehicles have far less drag than others, and so the effect of air resistance for those vehicles is less than it is for others.
Waddel Wilson ( famous Nascar Crew chief) one said “ ifin you're moving , you're moving air” or something like that
Basic mathematical formula for the amount of power it takes to move your car at certain speeds.

Driving load = av + bv2 + cv3

The "av + bv2" part has to do with how much power it takes to overcome the resistance due parasitic drag, internal friction of the engine, like ring drag, bearing rotating friction etc.. plus tire

resistance, disc brake drag, drive shaft friction, transaxle gear friction etc..all to get the car rolling at a given speed.

The "cv3" part has to do mostly with power required to overcome wind resistance (or "drag") while driving.

When doing this formula, your replace a, b, and c with the speed you're driving at. Let's assume this speed is in miles per hour (mph).

The biggie is the "power of 3" aspect of this formula..It means that wind drag will be the largest force your car will have to fight. And believe me..it is HUGE.

Ifin we are going 60 mph:

Driving load = 60 +3600 + 216,000 = 219660 units

These "units" could be anything - horsepower, Newtons, Joules ,cans of beer??

Based on this formula, the amount of power required to drive at 60 mph is 219660 units. Based on the same formula, the amount of power required to drive at 65 mph is 278915 units. The difference is 59255! This is an increase of about 27% more effort your car has to make just to drive 5 mph faster

not being a degreed professional engineer...i can not explain it more but recommend you check out this link which is very in detail reagrding the formula...
http://autopedia.com/stuttgart-west/Physics/StuttPhysics06.html

 

[The Chase]

Actually, the pumping loss is most extreme at this engine speed in a lightly loaded cruise mode- it's ALL about throttle angle- so if both were at WOT up hill the loss would be insignificant. If you were to take a vacuum gauge and run it at idle then at 2,000, I think you will see what I mean.

At 2k only the load will be different for this test- they will both use very nearly the same amount of fuel, with the 4th gear engine using slightly more.

/

Did you check the picture I posted? Clearly, pumping losses are NOT at the most extreme at mid-cruising load, throttle angle is further reduced at zero load under tickover situations, therefore pumping losses are the most extreme here.

 

[mylarcapsrock]

/

Did you check the picture I posted? Clearly, pumping losses are NOT at the most extreme at mid-cruising load, throttle angle is further reduced at zero load under tickover situations, therefore pumping losses are the most extreme here.

I don't care what your graph shows, really, anyone can make a graph to represent anything. Use a vacuum gauge- or even a scanner, on a properly running engine and get back to me.

There is a reason EGR valves were introduced on vehicle engines besides the blending of a neutral gas. The introduction of the EGR necessitates the increase of the throttle angle to maintain the same power level- reducing the pumping loss.

 

[Ranger Mike]

mylar..not cool...no need to get personal...no one is going to dummie up a graph to thwart you..



.the Exhaust Gas Reg valve is on the engine for one reason..so cars can pass the smog test ..i.e. stupid regulations for car emissions...makes engines run super lean and super hot...

 

[The Chase]

The tests were conducted within an enclosed engine test cell, which includes vast amounts of digital measurement equipment (yes, including digital measurement of intake manifold pressure). I'm not here to get into conflict, only share knowledge with like minded people, if you have data to prove your stance on this issue then please, I'd love to hear it. But currently all you have is your opinion - and that doesn't really account for much.

 

[mylarcapsrock]

Chase, my deepest apologies if you thought I was assaulting you in any way, shape, or form. I am too new here and didn't know your credentials, my apologies. But after 35+ years of working on cars, I still have to disagree with your tests in a real world platform. Oh my, I just looked again at your picture and noted that it's based on DIESEL performance- NO WONDER I disagree! Diesels don't have a throttle plate to induce pumping loss.

Ranger, that is a very popular misconception about Exhaust Gas Recirculation- it was ORIGINALLY used in that way, but was found years later to have the added benefit of reduction in pumping losses. As EGR flow is introduced into the cylinder, a wider angle of throttle opening is required to maintain the desired power level- thus the reduction in pumping losses. Believe me, it took a while for me to wrap my head around it as well. There are many things we, as technicians, were taught incorrectly and have been forced to "unlearn"!

 

[Ranger Mike]

thank you mylar..i will look into this..maybe you ca n teach old dog new tricks??

 

[The Chase]

Traditionally no they don't, modern designs are trending to do so however in order to achieve suitable intake manifold vacuum for EGR operation and to avoid excessive lean out and therefore NO and NOx production at higher loads.

Now please, let this lie here and allow the thread to die like it should have done several posts ago.

 

[mylarcapsrock]

Ok, consider it done, I'll not discuss anything diesel with someone who thinks they can run "lean". Have a nice weekend.

BTW, EGR TPs are gone already.

 

[The Chase]

*Sigh*

Yet another test on an older diesel engine with direct injection and no throttle valve. Note how NO and NOx production increases as air to fuel ratio becomes more LEAN.

Really, all I have heard so far is how your experience as a technician for 35 years is a far more valid proof than any actual data collected in the real world with scientific tests.

 

[brewnog]

Hmm, your graph shows NO2 to NO ratio; not NOx production. Just saying...

 

[The Chase]

Appologies, that was poorly written. I was trying to demonstrate how NO2 production is increased in comparisson to NO production at higher loads due to the more abundant amount of oxygen present when the engine is leaning further. I have a BMEP vs NOx specific results but these are more likely explained due to higher combustion temperatures (I have included them anyway). The main point, however, is compression ignition engines do run lean.

 

[brewnog]

Saying CI engines run lean is a generalisation and just doesn't apply to all conditions. I would be very interested to see your data purportedly showing increased nitrogen oxides formation with increasing air fuel ratio under load, and the operating conditions this was observed under.

 

[The Chase]

If a generalisation, would you not agree it is at least usually true in most situations? Would you also agree it's more accurate than suggesting compression ignition engines cannot run lean at all? I'm unsure what data you would like to see, perhaps you could tell me what data you would like to see plotted against each other and I could do so, I'd be glad to do so.

 

[brewnog]

Sure, I agree with your general comments, but not the generalisation.

I would like to see your plot of exhaust NOx concentration against AFR for a constant BMEP. I would be surprised to see NOx increasing with increasing AFR; and if this is the case, I would be keen to understand the circumstances around this.

 

[mylarcapsrock]

OK, as my experience isn't good enough for you, perhaps this paper is:

www.uiweb.uidaho.edu/bioenergy/BiodieselEd/publication/03.pdf

The use of the term "lean" in discussing diesels is almost a misnomer, as diesels do not have a true stoichiometric point as their little cousins, the gassers. Leanness would almost be more exact in this instance. This paper also gives a good explanation of biofuel chemistry and the resulting emissions problems.

Feel better now?

And NO, they don't run LEAN! They run clean of soot or clean of NOx- pick one as you are picking nits here. It's all about combustion chamber temps on the flame front and the pressure. THIS is the reason for DEF and SCA application on new diesels and the elimination of EGR.

 

[The Chase]

@ Mylarcapsrock

Great paper! I've read that one recently, let me quote a few things from it for you;

"NOx emissions are associated with high gas temperatures and fuel lean
conditions and, in contrast to most other pollutants, are usually observed to increase when
biodiesel is used [4]."

"While the bound oxygen on the biodiesel molecule may play a role in leaning the air-fuel ratio in NOx formation regions, the dominant mechanism seems to be the effect of changes in the physical properties of biodiesel, such as the speed of sound and bulk modulus, on the fuel injection timing [5]."

Seems they mention 'lean' quite a few times in regard to compression ignition engines. So if that was your point, thanks for correcting yourself! Without balancing the chemical equation for a generic diesel fuel the stoichiometric point is (roughly) 20-25:1 and anything higher than that is lean, the fact fuel isn't pre-mixed in a manner akin to that of a spark ignition engine does NOT factor into this. Air to fuel ratio is very simply calculated from mass flow rate of air divided by the mass flow rate of fuel, hence compression ignition engines (generally) run lean.

Soot formation is associated with rich burn along with increased CO emission, NOx is associated with lean burn due to (as you correctly mention) higher combustion temperatures and flame propigation rates, these are two EFFECTS from running lean or rich.

@Brewnog

I don't have any data with a constant BMEP across the same fuel type as A/F was changed due to experiments being conducted under different loads therefore altering the BMEP. I can plot NO or NOx (or both) against a BMEP value that isn't constant and provide the A/F ratio of each point? I don't know if that is of any use to you. I think the increasing NOx values with a further leaning charge is caused by higher combustion temperature, I can provide data for exhaust gas temperatures bellow the exhaust manifold for all data, again if that's of any use to you.

 

[xxChrisxx]

The fact fuel isn't pre-mixed in a manner akin to that of a spark ignition engine does NOT factor into this. Air to fuel ratio is very simply calculated from mass flow rate of air divided by the mass flow rate of fuel, hence compression ignition engines (generally) run lean.

I've not done anything with engines and combustion for a long time, but ^this^ is how I seem to remember it.

I also see why the argument that 'lean' with respect to stoich is a bit of a moot point as you never really have a stoichiometric mixture and it depends on the goal. Stoichiometric point for diesel very similar to petrol engines (about 15:1). The longer the HC chain, the more it converges to 15:1 when you discount anything that isn't C or H.

For convenience, diesel AFRs are rich/lean with respect to some nominal ratio. De facto being 20-25ish:1.

As I remember it's the whole reason for the push to GDI petrols was allowing ultra lean burn at low load, thus saving little CO2s from flying out the exhaust. Local rich burn, and a secondary fuel injection phase to clean up the combustion giving an overall lean burn w.r.t mass of air and fuel.

 

[mylarcapsrock]

What happens when the engine is driven further than 25:1, like to 35:1? Does it quit running? Is this LEAN?

 

[xxChrisxx]

Your point?

Also define what you mean by lean.

 

[mylarcapsrock]

your point?

Also define what you mean by lean.

exactly