How do the accelerator pedal and rpm interact in an internal combustion engine?

[Sailor]

congratulations fellows..you have just entered the world of hot rodding. Since the first IC came off Henry Ford’s production line the first guy to tinker with it wanted to go faster than the other guy. You have asked the one big question- How to make the IC go faster.

As one old hot rodder told me when I was learning to trouble shoot the IC engine.
you need fuel, you need air and you need a spark...AND... the spark at the proper time.

Nothing happens until we enter a fuel/air mix into the engine. It must be ignited at the proper time to make power.
The stoichiometric air-fuel ratio (14.7:1) that is the ideal ratio for lowest emissions, but this isn't the best ratio for power. It used to be that 12.5:1 was considered the best power ratio, but with improved combustion chambers and hotter ignition systems, the ideal now is around 12.8:1 to 13.2:1. This is roughly 13 parts of air to one part fuel. It's what combustion engineers call an excess fuel ratio and is intended to ensure that all the air is used to support the combustion process. This is because air is the oxidizer in combustion. Too many racers think that adding additional fuel beyond the ideal to create a richer mixture will make more power. This doesn't work because you can only burn the fuel when you have enough air to support combustion. That's why engines make more power when you add a supercharger or nitrous--you're shoving more air in the cylinder so that you can burn more fuel. Regardless of the amount of air in the cylinder, it still requires a given ratio of fuel to burn. Add too much extra fuel, and power will decrease.

The intake manifold is a big pipe and you can only fit so much fuel/air thru it..period. Typical normally aspirated internal combustion engine. So we start using superchargers to cram in more mix.
regarding the ignition. Todays advanced CD ignitions actually provide multiple sparks at idle and low RPM and provide a long spark at high RPM ( long being in crankshaft degrees). It does this to make more efficient burning of the fuel air mix at idle and higher RPM. We went from 25000 volts at the spark plug and a small gap of .025” to 50,000 plus volts over a 0.060 to .080 gap to again, more completely burn the mix.

one huge aspect you have not addressed is that you need to remove the spent fuel / air mix form the combustion chamber efficiently. This directly impacts on the intake manifold side of the equation.

bottom line is compression ratio is a constant but all other factors will vary all over the place depending upon the RPM.

Wonderful post Ranger Mike

But do you have any precise numbers of what the fuel to air ratio is through the whole rang of rpm ?

I think that would pretty much nail the question

 

[PhysicoRaj]

But do you have any precise numbers of the the fuel to air ratio is through the whole rang of rpm ?

I think that would pretty much nail the question

UNDOUBTEDLY!

 

[Sailor]

Compression ratio decides pre-ignition and is RPM dependent. Power at low RPM requires lower CR to prevent pre-ignition. At high RPMs, a higher CR improves fuel economy, since there is insufficient time to pre-ignite. CR should not be held constant.
With direct fuel injection, the AFR needs to be varied over the whole range. It is only when high octane fuel and concern over NOx emission is concerned that AFR must be carefully adjusted to remain stoichiometric. That gross generalisation is a false assumption.

That's very interesting Baluncore, only thing needed now is some numbers to support your assumption

In the past I did thought that the compression ratio could be variable but couldn't find a single reference to aid this assumption

However, the only numbers I can remember for fuel to air ratio's were between 12:1 to 13:1 through the whole range, and this is not enough of space to deal with

So when a car manufacturer says their engine has a 10:1 CR you think this only happens near top rpm ?There was NO generalization in what I wrote, I simply said if the variation is NOT CONTROLLABLE then it should be omitted, otherwise it is OK

 

[Sailor]

As far as I know, that optimum ratio is used at or near top rpm. At the idle, I don't think all engines make use of the optimum ratio.. it is lower than that, i.e., lesser fuel than in the optimum ratio. In other words, a leaner mixture. A richer mixture than the optimum does not provide power, I agree. But a leaner mixture than the optimum obviously produces less power>>lower rpm!

at idle it is said to be 12:1 and at maximum it is about 13:1 so how do you think this could be translated into the accelerator pedal ?

 

[Sailor]

UNDOUBTEDLY!

Numbers say it all

 

[PhysicoRaj]

 

[Sailor]

Wow, what a graph ...
so from 3750rpm to 4250rpm the increase in rpm meant an increase in A/F
however, from about 4500 all the way down the the increase in rpm translated into a decrease in A/F


I think we've got two clues here :
1- the A/F has no influence on the rpm
2- this engine is a maniac

I don't think this is a normal engine it might be modified or something because of the wide A/F range, but I might be wrong, anyways, thanks PhysicoRaj for sharing

 

[xxChrisxx]

What a terribly meandering thread. Why don't you just ask the question you want the answer for.

The amount of fuel injected is determined by the ECU, or in the olden days the jets and geometry of the carbs.
ie. You can pick a value that you want via fuel mapping.The AFR will determine the torque produced, maximum torque will come at an AFR of 12.5:1ish. That will mean the engine will accelerate faster than more lean mixturesEDIT: The reason you get most power when slightly rich is two fold.

Real engine don't burn all the fuel at stoichiometric.
Excess fuel provides charge cooling.

 

[Sailor]

What a terrible, meandering thread. Why don't you just ask the question you want the answer for.

The amount of fuel injected is determined by the ECU, or in the olden days the jets and geometry of the carbs.
ie. You can pick a value that you want.The AFR will determine the torque produced, maximum brake torque will come at an AFR of 12.5:1. That will mean the engine will accelerate faster than more lean mixtures..EDIT: The reason you get most power when slightly rich is two fold.

Real engine don't burn all the fuel at stoichiometric.
Excess fuel provides charge cooling.

I'm sorry but I think this is the most irrelevant comment which answers a question nobody asks

 

[xxChrisxx]

You've not actually asked a clear question, that's the problem.

1- Compression ratio

Take this as constant.

Air fuel ratio

VARIABLE - Controlled by the fuel map, typically based on mass airflow and manifold vacuum.

Ignition Rate

VARIABLE - I assume you mean spark advance/ignition timing. Controlled by the spark advance map.

4- Air flow rate through intake manifold

Controlled by the throttle opening. So depends on what you are doing with the throttle.What do you actually want to know.

As currently it seems to be what affect does AFR have on the RPM. You've rightly come to the conclusion that it doesn't affect it. However the AFR will have an affect on how quickly RPM changes.

 

[PhysicoRaj]

The picture was actually a random one I got in a google search..
Yes,this thread is a meandering one, awful enough, because it has limited destiny. I currently know what we are after, but I don't know where we are going.

 

[Sailor]

You've not actually asked a clear question, that's the problem.

OK then, here is the question ... again ... sort of :
How does the action of the accelerator pedal changes the rpm of the internal combustion engine ?

right now the focus is on gasoline/Otto engines, but later on we can discuss diesels

hope now it makes more sense to you I have also added this to the first post and made some minor tweaks to it.

Take this as constant.

VARIABLE - Controlled by the fuel map, typically based on mass airflow and manifold vacuum.

VARIABLE - I assume you mean spark advance/ignition timing. Controlled by the spark advance map.

Controlled by the throttle opening. So depends on what you are doing with the throttle.What do you actually want to know.

As currently it seems to be what affect does AFR have on the RPM. You've rightly come to the conclusion that it doesn't affect it. However the AFR will have an affect on how quickly RPM changes.

So, when you say that fuel mapping is variable, is it utilized intentionally to accelerate the engine or you just mentioned it as a general information to state the variability of it ?

And again please note the following :

- *: In general I'm not referring to an absolute constant quantity, so if there would be any variation that is not controllable or not meant to regulate the engine speed (rpm) then this should not be considered in the explanation, such variations are the resultant of thermal deficiencies or mechanical friction.

And what do you think would happen if we hold the AFR constant at say 12.5:1 and utilized the accelerator pedal (air flow rate) for accelerating the engine, ain't it possible ?

 

[Sailor]

The picture was actually a random one I got in a google search..
Yes,this thread is a meandering one, awful enough, because it has limited destiny. I currently know what we are after, but I don't know where we are going.

please recheck the first post, I have modified it a bit ...

 

[xxChrisxx]

How does the action of the accelerator pedal changes the rpm of the internal combustion engine?

Engine torque accelerates the engine (increases the RPM). This torque comes from how much fuel you are burning in a given engine cycle. More fuel = more torque = more power = more go.

The throttle can be though of as a torque demand control, more throttle opening = more torque requested.
For this purpose we will assume a linear throttle pedal map.

This means:
Foot off = Zero torque demand
40% opening = 40% demand
WOT = full torque demand
etc

This means that we can assume that as the air flow through the manifold (load) is proportional to throttle travel.

So the more the butterfly valve opens, the more air gets let into the engine. This variable is volumetric efficiency. This act of opening the throttle drops the manifold vacuum, or gives a positive pressure if forced induction is used.

From this we can measure the manifold pressure, and knowing the geometry of the engine intake we know how much air is flowing into the engine.

For a given amount of air, we can actually tell the ECU to inject a differences amount of fuel depending on what we want to achieve. For power we want more fuel, for emission we want stoichiometric and for economy we want less fuel.


I've not fully read the link below but it shows a typical fuel map (for a bike, but the principle is the same). It shows two maps, a stock one from the factory and a new 'suggested' one. It's a map based on variables of load (throttle opening) and engine speed.

http://www.tuneboy.com.au/Tutorials/TuneEditTutorial2.html

As you can see from the stock map:
At idle (low load low speed), the ECU leans out the engine. Then at cruising (mid load, mid speed) it gets stoichiometric. Then at acceleration events (high to full load) it enriches the mixture for maximum power.
EDIT: Something specific to note from this map is how the AFR alters based on engine speed at full load. Starting at almost stoich at low RPM then getting more rich as more power is needed


The seconds map shows basically rich running everywhere this will give more power.
EDIT: Do not take these values as 'correct', but the principle that the values can be tuned based other measured variables and a desired outcome. I suspect the new map will actually cause poor running at low engine speeds.

Another good link with a couple of images of fuel maps:
http://www.formula1-dictionary.net/map_fuel.html

 

[PhysicoRaj]

please recheck the first post, I have modified it a bit ...

I have to thank you for that..

And a good post by Chris. What he gave is the exact answer to your 'latest' question. Hope you got your answer.

 

[Sailor]

Engine torque accelerates the engine (increases the RPM). This torque comes from how much fuel you are burning in a given engine cycle. More fuel = more torque = more power = more go.

http://www.tuneboy.com.au/Tutorials/TuneEditTutorial2.html

Nice links, thanks xxChrisxx

but here is one image from this link
http://www.tuneboy.com.au/TBImages/10111AF.gif
www.tuneboy.com.au/Tutorials/TuneEditTutorial2.html

for this bike engine example it shows that at a 49 load the AFR is CONSTANT at 14:1 from 900rpm to 7500rpm, and we both agree that the CR is held constant, so we can say that pressing the accelerator pedal doesn't mean an alteration of the AFR → therefore it doesn't translate into higher torque directly

Now to explain why would the torque be higher in some specific rpm ranges, I'm thinking that the values of valve timing/ valve lift/ ignition efficiency and engine breathing at a giving speed together with the overall design of the cylinder and the head must play the role here and produce the required torque, in other words: you do not give permission for higher torque and then the rpm increase, on contrary to that, you first release the pedal to get more rpm and as it climbs up you then receive the correspondent high torque that is associated with whichever that rpm value is.

awaiting for Baluncore to bring some figures that show a variation of the CR as a driving factor to increase rpm ...

 

[Sailor]

I have to thank you for that..

And a good post by Chris. What he gave is the exact answer to your 'latest' question. Hope you got your answer.

You're Welcome PhysicoRaj,

please check my reply ...

 

[xxChrisxx]

Your main driver for torque output (power at the specific rpm) is the amount of air you have available. Think of AFR values, and deviations from stoichiometric to be 'trim' rather than the main driver.

Infact you'll often hear AFR referred to as 'fuel trim'.

I'll flip your post around a bit.

Now to explain why would the torque be higher in some specific rpm ranges, I'm thinking that the values of valve timing/ valve lift/ ignition efficiency and engine breathing at a giving speed together with the overall design of the cylinder and the head must play the role here and produce the required torque

As engine with fixed inlet and outlet geometry and with a fixed valve overlap will breathe most efficiently at a single rpm. This will tail off the further you deviate from this single figure.

This is known as volumetric efficiency. Think of it as a 'cylinder filling %'. If we assume that you get the same measure of combustion at all RPM (i.e. it combusts with the same efficiency at all RPM). Then the torque curve will exactly follow the volumetric efficiency curve.

If the engine filled the cylinders with 100% of the air available at all rpm, then it would produce a flat torque curve. Ie At 7000rpm it'll be flowing 2x as much air as it would at 3500rpm for a given time.

It's important to note that PER CYCLE the engine is flowing the same amount.

So:
Lets say this bike has a 1000cc engine and it's most efficient breathing is at 7000rpm at WOT (100% load) with a VE of 100%. But at 6000rpm it only breathes at 80% volumetric efficiency.

Per Cycle:
6000rpm - 0.8L air is available for combustion
7000rpm - 1L of air is available for combustion

With 20% more air available at 7krpm than at 6k, you would expect 20% more torque to be produced.

for this bike engine example it shows that at a 49 load the AFR is CONSTANT at 14:1 from 900rpm to 7500rpm, and we both agree that the CR is held constant, so we can say that pressing the accelerator pedal doesn't mean an alteration of the AFR → therefore it doesn't translate into higher torque directly

The AFR values are not consequential to the throttle opening. They are a value we define. So the AFR is constant between those RPM and that load value, because we have told the ECU to try to make it constant.

Each of those boxes on the fuel map is telling the ECU:
At X RPM and Y load. Inject Z fuel to give the desired AFR.


So taking from above:
Although the AFR is constant over that rev range, a larger quantity of fuel is being injected PER CYCLE based on the volumetric efficiency.

What you should take from this is, the amount of air available is the primary driver for torque. From that we can add more or less fuel via the AFR fuel map to trim the power output.

You could set the map to 14.7 everywhere.
You could then set the map to 12.5 everywhere.

The rich map would give more power for a given quantity of air.

 

[xxChrisxx]

It's also worth posting this separately as it's important.

you do not give permission for higher torque and then the rpm increase, on contrary to that, you first release the pedal to get more rpm and as it climbs up you then receive the correspondent high torque that is associated with whichever that rpm value is.

It doesn't really make sense to split this up as cause and effect as you have. Though from a physical point of view the chain of events is:
open throttle -> more air -> more fuel -> more torque -> increase in RPM
repreat

It's convenient to just think of it that opening the throttle does both simultaneously. Thinking of the throttle as a 'torque request' is merely an abstraction to aid thought.

 

[Sailor]

Lets say this bike has a 1000cc engine and it's most efficient breathing is at 7000rpm at WOT (100% load) with a VE of 100%. But at 6000rpm it only breathes at 80% volumetric efficiency.

Per Cycle:
6000rpm - 0.8L air is available for combustion
7000rpm - 1L of air is available for combustion

That's nice, now we can say we have nailed one fact which is the AFR doesn't/ shouldn't contribute in the acceleration of the engine as we press the accelerator pedal contrary to what is said in other forums.

Now, what you are stating here implies a change in CR, that is when a cylinder that has a CR of 10:1 is filled with 80% of air but would still compress it to the same volume then we now got an 8:1 CR, is it what you are saying ?

 

[Sailor]

It's also worth posting this separately as it's important.
It doesn't really make sense to split this up as cause and effect as you have. Though from a physical point of view the chain of events is:
open throttle -> more air -> more fuel -> more torque -> increase in RPM
repreat

It's convenient to just think of it that opening the throttle does both simultaneously. Thinking of the throttle as a 'torque request' is merely an abstraction to aid thought.

again this implies the same concept which is a variation in CR value as the more fuel is associated with the more air that enters due to the increased flow rate while being at a constant AFR

So is there any figure for the minimum CR value at idle ?

 

[Averagesupernova]

All I can say is WOW! Talk about a thread that is getting nowhere.

 

[Sailor]

All I can say is WOW! Talk about a thread that is getting nowhere.

this topic might be a little complicated for some

Maybe that's why there is a lack of precise information about it on the internet ...

however, so far we have concluded that out of the four factors I have posted earlier, one of them is constant and that is the AFR, on the other hand the CR seems to be variable contrary to what we have thought, which then makes it three variables and one constant

and till now that defines the two primary factors for accelerating the gasoline engine by the accelerator pedal and these are :
- the air flow rate
- the compression ratio

as the third variable which is the firing rate has no direct effect in the process...

only thing missing now are some values of the variation of the CR, additionaly I would still want to ask about the possibility of having this value constant by say adding an electric supercharger ...

any thoughts what would happens then ?

 

[xxChrisxx]

Now, what you are stating here implies a change in CR, that is when a cylinder that has a CR of 10:1 is filled with 80% of air but would still compress it to the same volume then we now got an 8:1 CR, is it what you are saying ?

No! And it is very, very important that this next bit doesn't get glossed over.
The compression ratio is a RATIO. It doesn't matter how much stuff you have in the cylinder.

Compression ratio is determined by the geometry of the engine only! The volume at BDC and the Volume at TDC.
CR = V1/V2

V1 = Cylinder Volume at bottom of the stroke 10
V2 = Cylinder Volume at bottom of the stroke 1

CR = 10:1

This is a constant, it does not change.

If the cylinder is 200% filled, the compression ratio is 10:1
If the cylinder is 100% filled, the compression ratio is 10:1
If the cylinder is 80% filled, the compression ratio is 10:1
If the cylinder is 0.001% filled, the compression ratio is 10:1
You could fill it with the entire contents of the universe, or 1 molecule. The compression ratio would still be 10:1


I can't really stress how important this point is.

 

[xxChrisxx]

however, so far we have concluded that out of the four factors I have posted earlier, one of them is constant and that is the AFR, on the other hand the CR seems to be variable contrary to what we have thought, which then makes it three variables and one constant

Why you think the AFR is constant.
The previous posts have made it clear that it is a dependent variable

That's nice, now we can say we have nailed one fact which is the AFR doesn't/ shouldn't contribute in the acceleration of the engine as we press the accelerator pedal contrary to what is said in other forums.

We could say that, but we'd be very wrong.

What you should take from this is, the amount of air available is the primary driver for torque. From that we can add more or less fuel via the AFR fuel map to trim the power output.

You could set the map to 14.7 everywhere.
You could then set the map to 12.5 everywhere.

The rich map would give more power for a given quantity of air.

This clearly states that being richer WILL affect power output, and therefore the speed at which the engine will accelerate.

 

[jack action]

I might repeat stuff already said, but for clarity purposes, here I go:

To change the rpm you need to accelerate (or decelerate) the crankshaft assembly. To get an accelation, you rely on good old $F = ma$; or in rotation:

$$\tau_{in} - \tau_{out} = I\alpha$$ (reference)

$\tau_{out}$ is the torque needed to maintain the load put on the engine and $\tau_{in}$ is the torque due to the pressure exerted on the piston (minus the losses).

If they are both equal, then $\alpha = 0$. Otherwise, the rotational acceleration $\alpha$ becomes either negative or positive, leading to a reduction or an increase of the rpm.

What we can control and vary is $\tau_{in}$.

Here is a mathematical definition of $\tau_{in}$:

$$\tau_{in} = BMEP\frac{V_d}{\theta_c}$$ (reference)

$BMEP =$ Brake Mean Effective Pressure;
$V_d =$ Volume of air displaced for one cycle (displacement);
$\theta_c =$ crankshaft angular duration of one cycle.

Knowing that the Brake Specific Fuel Consumption ($BSFC$) can be defined by:

$$BSFC = \frac{\rho_{atm}VE}{AFR \times BMEP}$$ (reference)

$\rho_{atm} =$ atmospheric air density;
$VE =$ Volumetric Efficiency;
$AFR =$ Air-Fuel Ratio.

Replacing $BMEP$, we get for $\tau_{in}$:

$$\tau_{in} = \frac{\rho_{atm}}{BSFC}\frac{VE}{AFR}\frac{V_d}{\theta_c}$$

This equation gives us all the parameters that affect the torque of the engine:

$\rho_{atm}$: It is a given so it cannot be controlled by the operator;

$BSFC$: It depends on the design and construction of the engine (thermodynamic cycle, friction losses, combustion efficiency, etc) so it cannot be controlled by the operator;

That leaves us with 4 different ways to control the input torque of the engine (in other words, how to change its rpm):

$VE$: We can achieve that by restricting the airflow. Less air means less air-fuel mixture, hence less energy released during combustion. This is what happens in a gasoline engine when we control the throttle with the gas pedal while keeping the $AFR$ constant;

$AFR$: We can achieve that by controlling the fuel input, while keeping the air inlet (or $VE$) constant. This is what happens in a diesel engine when we control the fuel pump with the gas pedal.

$\theta_c$: We can achieve that by varying the length of a cycle. This is the control used in a hit-and-miss engine. The intake valve stays close as long as needed to prevent the air-fuel mixture to enter the cylinder, hence lengthening the cycle (in number of revolutions of the crankshaft).

$V_d$: We could achieved that method by varying the displacement of the engine. For example, by cancelling intake valve overture for certain cylinders when we want to decrease the torque. Although, I never heard of any engine working this way (Variable-displacement engine are close, but the objective is not to control the torque of the engine).

Other parameters can slightly vary (ignition advance, compression ratio, stoiechiometric AFR (in gasoline engine), etc.) but their purpose is not to control the torque input, but to achieve optimization of the combustion under a given circumstance.

For example, a rich AFR will give more power and a poor AFR will give better fuel economy, and this at any rpm. So it is typical to set a poor mixture at idle (who needs power at that rpm?) and to get the richest mixture at high rpm (why would you go all the way to the max rpm if you didn't want all the power you can get?). But all of this has nothing to do with controlling the torque input of your engine.

 

[Baluncore]

… however, so far we have concluded that out of the four factors I have posted earlier, one of them is constant and that is the AFR, …

That can not be concluded. You are assuming the engine has a simple carburettor.

Carburettors restrict variation of AFR, while direct fuel injection makes any AFR possible.

There is rarely an advantage in running on the rich side of the stoichiometric mix, but there can be significant advantages of running on the lean side. Many engines are designed to operate with excess air when idling cool.

 

[Sailor]

Compression ratio is determined by the geometry of the engine only! The volume at BDC and the Volume at TDC.
CR = V1/V2

V1 = Cylinder Volume at bottom of the stroke 10
V2 = Cylinder Volume at bottom of the stroke 1

CR = 10:1

Let's put terminology aside for a second ...

what you have stated here is that in a given condition a certain volume of air and let it be V1 will fill the cylinder and therefor is compressed into a new volume V2 as the cylinder reaches TDC, now this compressed amount WILL have different resultant properties (e.g temperature, pressure) than a volume V3 that equals 0.8V1 and enters the same cylinder to be compressed into V2 while keeping CONSTANT elementary pressure and equal densities

Now aside from the normal "compression ratio" you referred to which indicates the physical boundaries of the metal cylinder, let's make up a NEW terminology in this discussion and call it "air compression ratio"

Now it's clearly that V1/V2 is different than V3/V2, hence the variation in "air compression ratio" which in essence implies a variation in the volumetric efficiency
And that's exactly what I meant

So now the question is how much could V3 differ from V1 and still be combustible ?

 

[Sailor]

Why you think the AFR is constant.
The previous posts have made it clear that it is a dependent variable

No, we actually had an evident that an engine could (and I'm thinking this is the ideal case) accelerate with an absolute CONSTANT AFR

The variation of the AFR (in gasoline engines) should be meant to modify the consumption/economy of the vehicle rather than to accelerate it

And this is exactly what I have observed from other real world readings of the AFR value ...

This clearly states that being richer WILL affect power output, and therefore the speed at which the engine will accelerate.

in a gasoline engine the difference between a richer and a leaner state has a very narrow band that would makes the acceleration effect almost redundant

 

[Sailor]

I might repeat stuff already said, but for clarity purposes, here I go:

To change the rpm you need to accelerate (or decelerate) the crankshaft assembly. To get an accelation, you rely on good old $F = ma$; or in rotation:

$$\tau_{in} - \tau_{out} = I\alpha$$ (reference)

$\tau_{out}$ is the torque needed to maintain the load put on the engine and $\tau_{in}$ is the torque due to the pressure exerted on the piston (minus the losses).

If they are both equal, then $\alpha = 0$. Otherwise, the rotational acceleration $\alpha$ becomes either negative or positive, leading to a reduction or an increase of the rpm.

What we can control and vary is $\tau_{in}$.

Here is a mathematical definition of $\tau_{in}$:

$$\tau_{in} = BMEP\frac{V_d}{\theta_c}$$ (reference)

$BMEP =$ Brake Mean Effective Pressure;
$V_d =$ Volume of air displaced for one cycle (displacement);
$\theta_c =$ crankshaft angular duration of one cycle.

Knowing that the Brake Specific Fuel Consumption ($BSFC$) can be defined by:

$$BSFC = \frac{\rho_{atm}VE}{AFR \times BMEP}$$ (reference)

$\rho_{atm} =$ atmospheric air density;
$VE =$ Volumetric Efficiency;
$AFR =$ Air-Fuel Ratio.

Replacing $BMEP$, we get for $\tau_{in}$:

$$\tau_{in} = \frac{\rho_{atm}}{BSFC}\frac{VE}{AFR}\frac{V_d}{\theta_c}$$

This equation gives us all the parameters that affect the torque of the engine:

$\rho_{atm}$: It is a given so it cannot be controlled by the operator;

$BSFC$: It depends on the design and construction of the engine (thermodynamic cycle, friction losses, combustion efficiency, etc) so it cannot be controlled by the operator;

That leaves us with 4 different ways to control the input torque of the engine (in other words, how to change its rpm):

$VE$: We can achieve that by restricting the airflow. Less air means less air-fuel mixture, hence less energy released during combustion. This is what happens in a gasoline engine when we control the throttle with the gas pedal while keeping the $AFR$ constant;

$AFR$: We can achieve that by controlling the fuel input, while keeping the air inlet (or $VE$) constant. This is what happens in a diesel engine when we control the fuel pump with the gas pedal.

$\theta_c$: We can achieve that by varying the length of a cycle. This is the control used in a hit-and-miss engine. The intake valve stays close as long as needed to prevent the air-fuel mixture to enter the cylinder, hence lengthening the cycle (in number of revolutions of the crankshaft).

$V_d$: We could achieved that method by varying the displacement of the engine. For example, by cancelling intake valve overture for certain cylinders when we want to decrease the torque. Although, I never heard of any engine working this way (Variable-displacement engine are close, but the objective is not to control the torque of the engine).

Other parameters can slightly vary (ignition advance, compression ratio, stoiechiometric AFR (in gasoline engine), etc.) but their purpose is not to control the torque input, but to achieve optimization of the combustion under a given circumstance.

For example, a rich AFR will give more power and a poor AFR will give better fuel economy, and this at any rpm. So it is typical to set a poor mixture at idle (who needs power at that rpm?) and to get the richest mixture at high rpm (why would you go all the way to the max rpm if you didn't want all the power you can get?). But all of this has nothing to do with controlling the torque input of your engine.

:thumbs:

Excellent intricacy jack action, and thank you very much for the highly valuable input, that pretty much nailed almost all of the aspects about this subject

So again we can conform the following :
- the AFR is/ could/ should be CONSTANT, in other words we DO NOT require richer AFR to accelerate the engine.
- the VE here relates to both the change in the compressed volume of air (air compression ratio as I've called it) and the change in air flow rate, so it's clearly that these two factors are VARIABLES.
- Firing rate is totally obsolete, though it is still variable.

Now the definition of $\theta_c$ is very interesting because I think it describes BMW's Valvetronic system, and infact I did think about adding this technology to the discussion later on

varying $V_d$ in order to control the rpm is almost infeasible and doesn't make sense at all

So back to my question about keeping the air compression ratio constant while still being able to change the rpm, I thing this COULD be done by altering the value of $\theta_c$, although this may not be the case with Vaivetronic, nevertheless, I believe there would not be enough room to have a complete variation in speed which would then makes it similar to the variation of AFR in a gasoline engine

As for diesels, I think their concept is pretty much straightforward and easy to understand


Again thank you jack action very much,

 

[Sailor]

That can not be concluded. You are assuming the engine has a simple carburettor.

Carburettors restrict variation of AFR, while direct fuel injection makes any AFR possible.

There is rarely an advantage in running on the rich side of the stoichiometric mix, but there can be significant advantages of running on the lean side. Many engines are designed to operate with excess air when idling cool.

check post #51 it shows the outputs of a modern ECU controlled engine

This coincides with my findings before starting this thread, and again what you describe could be related to fuel economy and should not be confused with the pure acceleration action of the engine by the throttle pedal inputs

 

[PhysicoRaj]

This is still not getting anywhere. Sailor, clearly specify what other clarifications you need. I think except for A/F ratio, all other three have been seriously dealt with and you don't have any objections regarding that.
Regarding A/F ratio, it is both constant and variable, depending on the construction of the engine (carburettor? Injection? Special carburettors?).

 

[Sailor]

This is still not getting anywhere. Sailor, clearly specify what other clarifications you need. I think except for A/F ratio, all other three have been seriously dealt with and you don't have any objections regarding that.
Regarding A/F ratio, it is both constant and variable, depending on the construction of the engine (carburettor? Injection? Special carburettors?).

Actually I think this thread has progressed nicely and we've come to the conclusion in post #66

The only one question that remains is :

how much could V3 differ from V1 and still be combustible ?

regarding the variability of the AFR in a gasoline engine and by eliminating the deficiencies of carburetors and ECONOMY intentions, we are left with a very narrow range of values to play with, therefore IDEALLY it should be CONSTANT which means the accelerator pedal could (and is) function normally when we hold the AFR constant

 

[Baluncore]

This coincides with my findings before starting this thread, and again what you describe could be related to fuel economy and should not be confused with the pure acceleration action of the engine by the throttle pedal inputs

Many vehicles couple the accelerator pedal directly to the injection pump.
The air flow is kept proportional to RPM. The accelerator pedal causes a change of the AFR alone.
The title of this thread is “Accelerator pedal and rpm”.

 

[PhysicoRaj]

Actually I think this thread has progressed nicely and we've come to the conclusion in post #66

You mean this?

This coincides with my findings before starting this thread, and again what you describe could be related to fuel economy and should not be confused with the pure acceleration action of the engine by the throttle pedal inputs

This is not true for all engines.

Edit: As Baluncore said, it depends.