# Automotive Formulas For Engine Cylinder Perssure

1. Mar 10, 2017

### Jason Louison

Hi! I am a new member to this great Forum! I am so excited to be a part of this wonderful community. Anyway, as the title suggests, I am looking for a way to calculate the pressure in each cylinder of any Four Stroke Engine at any given crank angle of Cylinder One. I have been trying creating a spreadsheet based on a very interesting PDF document I found a couple of weeks ago. One cylinder is fine, but trying to make the formulas for cylinder pressure for each cylinder flexible to change/adapt to the change in degrees per cylinder is getting to be really frustrating. Does anyone know a whole, single function out there for cylinder pressure?

Thanks ~ Jason Louison.

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• ###### ProjectIII.pdf
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2. Mar 10, 2017

### Work Hard Play Hard

Based on the crank angle alone, no, there is not an equation for pressure. There are many more variables involved beginning with if there is a piston offset or not.

3. Mar 10, 2017

### Jason Louison

Thanks, Removed Unnecessary Data Tables, But I think The Turning Moment Diagram is off.

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• ###### Computer Simulated Engine Performance.numbers.zip
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4. Mar 10, 2017

### xxChrisxx

Assume the forcing profile is the same then just phase each cylinder according to firing order.

I'm on my phone, so cant see the zip properly.

5. Mar 11, 2017

### Work Hard Play Hard

My first thoughts also but I don't think that's what he is asking. I think the question is; When cylinder 1 is calculated for pressure at a given crank angle is there an equation that will concurrently give the pressure at the remaining cylinders at that same moment. It's why I brought up offset pistons because then the stroke timing is an additional variable to factor in. Typically offset results in a longer power stroke in terms of time but the velocity of the piston is not linear so it's different at every cylinder at any given single moment. Equations for time are not the same as those for angle. The equation would need to include conversions of variables. From there cylinder head valve timing and air flow and air pressures have to be factored in at every crank angle in relation to the number 1 cylinder in the OP's example. How precise is the equation going to be depends on how far the inclusion of variables is going to go. If there is a single equation for this that covers all engines it's one I've never seen or heard of. I'm not even sure if this is possible to determine from mapping performance through the typical ECU. Not that it wasn't possible. It was a matter of decisions about what needed to be recorded for the family car. Tuner chips even recorded at predetermined crank angles for specific engines and not continuously for the entire 720 degrees of a complete cycle.

6. Mar 11, 2017

### xxChrisxx

How the hell do you view the data? What is the fundamental approach to modelling this? As I can't really make sense of what you've just said. I can't tell if I'm just not getting context.

Fundamentally in every multi cylinder engine; what one piston does (whatever that may be) they all do. If he has a working model for one cylinder, as stated , it's just a case of applying the same thing at a different time.

Last edited: Mar 11, 2017
7. Mar 11, 2017

### Jason Louison

Solved (sort of)! I just had to add some conditional statements that change the value depending on the crank angle for ALL cylinders.

"0°-180°" Argument:
IF(AND(\$A2<180),0.9×Atmospheric Pressure(psi)

"180°-360°" Argument:
IF(AND(Crank Angle≥180,Crank Angle<360),(Atmospheric Pressure(psi)×((Cylinder Clearance Volume+Cylinder Displacement Volume)÷Total Immediate Cylinder Volume)^Expansion Coefficient)

"360°-540°" Argument:
IF(AND(Crank Angle≥360,Crank Angle<540),(Maximum Pressure(atmospheres)×(Cylinder Clearance Volume÷Total Immediate Cylinder Volume)^Expansion Coefficient),

"540°-720°" Argument:
IF(AND(CrankAngle≥540,Crank Angle<720),1.1×Atmospheric Pressure (psi)

And then a 720°-900°argument, a 900°-1080°, and so on. Combined, these formulas ensures that cylinder pressure is accuratley calculated for all cylinders, no matter what angle they start at or end with!
I would share the spreadsheet, but the file is too large to upload here, unfortunately.

8. Mar 11, 2017

### Jason Louison

Some of the graphs I have made so far!

9. Mar 11, 2017

### Work Hard Play Hard

I understand but as I said he's asked for an equation to do it all at once. He's also asked for a an existing equation which the equation would need to be universal for every engine. You can't assume the valve timing which effects pressure for every engine is the same. Can't assume combustion time measured in degrees of crank angle is the same for every engine. How many variables in the end are there going to be for a universal equation? If you are aware of an function that does this please let me know.

Getting the pressure at 8 different crank angles and then adding them up is not one equation. Or as the OP put it, one function.

Edit, Jason's last 2 posts weren't here when I started but I stand by what I wrote. Programming a series of arguments for graphing is not the same as a single function for any engine in spreadsheet form.

Last edited: Mar 11, 2017
10. Mar 11, 2017

### xxChrisxx

I think you misinterpreted what he wanted to do. It's pretty clear that he had a single cylinder model he was happy with and just wanted to phase the calculation. This is what he has done by the conditional statements. By universal engine he meant 1,2,4,6,8,12 cylinder etc.

OP your model is effectively turning the PV diagram of the cycle into a torque vs crank angle. Are you going to consider inertia effects and friction?

EDIT: Or have you, I can't tell if inertia is already in there from the graphs. : /

Last edited: Mar 11, 2017
11. Mar 11, 2017

### Jason Louison

Yes, there are Inertia Contribution columns in the data tables for each cylinder. The Pressure-Volume diagrams have not been implemented yet, but will be soon :)

12. Mar 11, 2017

### xxChrisxx

Is this a run moving 'quasi-statically' then? As that torque profile looks like it's only based on cylinder pressure.

13. Mar 11, 2017

### Jason Louison

What do you mean by that?

14. Mar 11, 2017

### xxChrisxx

That is for a four cylinder model. Sum up those four cylinder torque values to get torque @ the crank, and looks at the profile.
Try doing this with the model running with different engine speeds.

15. Mar 11, 2017

### Jason Louison

:D I'm so stoked! This is going so well right now!

Last edited: Mar 11, 2017
16. Mar 11, 2017

### Jason Louison

The question now is how do I distort that p-V diagram given peak torque rpm's and current rpm's....

17. Mar 11, 2017

### Jason Louison

May need to start a new thread. : /

18. Mar 11, 2017

### xxChrisxx

It makes sense to keep it in this thread, as it's a natural progression. Distorting the p-V diagram is where things get 'wooly', and this is where Work Hard Play Hard's comment about not having a single formula is oh so true. There isn't really any way to calculate it by hand.

However, there are some broad assumptions we can make that moves the model closer to reality. For each stage of the process we can introduce assumptions that cause losses. You may want to start by reading the finalpaper.pdf again with the assumptions they make.

eg. Ideal otto assumes isochoric combustion (ie instant prssure raise). - We know this isn't true in reality, the burn begins bTDC and peaks aTDC.

19. Mar 11, 2017

### Work Hard Play Hard

Obviously you're right but I'm not sure it's necessarily so clear.

1. I am looking for a way to calculate the pressure in each cylinder of any Four Stroke Engine at any given crank angle of Cylinder One.
2. I have been trying creating a spreadsheet
3. One cylinder is fine, but trying to make the formulas for cylinder pressure for each cylinder flexible to change/adapt to the change in degrees per cylinder is getting to be really frustrating.
4. Does anyone know a whole, single function out there for cylinder pressure?

As I said in my first comment, my first thoughts were the same as yours but #3 suggests otherwise with the other statements.

Have you seen this Jason? It gets referenced and cited often.

http://r.search.yahoo.com/_ylt=AwrBTzvmncRYBIUAczxXNyoA;_ylu=X3oDMTByNXM5bzY5BGNvbG8DYmYxBHBvcwMzBHZ0aWQDBHNlYwNzcg--/RV=2/RE=1489309286/RO=10/RU=https%3a%2f%2fwww.hcs.harvard.edu%2f~jus%2f0303%2fkuo.pdf/RK=0/RS=UrH3DzAaKtGEVFDzfmDAgHUV9CA- [Broken]

Last edited by a moderator: May 8, 2017
20. Mar 11, 2017

### Jason Louison

No, I haven't, but it seems like a good resource. Right now im trying to think of ways to incorporate "losses" in my spreadsheet, so I can get a realistic p-V relationship like this:

Last edited by a moderator: May 8, 2017