How to calculate BMEP from P-V Graphs?

[nb89]

Main Question or Discussion Point

I have a P-V trace for a wide open throttle and a part load. Is it possible to calculate the BMEP from these graphs?

 

[Ranger Mike]

see Horsepower - Please help - Confused! posted on Feb 14 2009

BMEP = ( Hp x 13000) / ( liter displacement x RPM)

 

[nb89]

that doesnt really help considering all i am given are values of different pressures and volumes

 

[Q_Goest]

If you have pressure and volume you may integrate PdV to determine work, then divide by time to determine power.

For example, if you have a table of values that give pressure and volume, you should be able to take average pressure (gage pressure, not absolute) and change in volume, multiply to obtain work, then sum all work done over a single cycle (360 degrees of crankshaft rotation for a 2 stroke, 720 degrees for a 4 stroke) and divide by time it takes for that cycle to get power.

 

[brewnog]

Sure, integrate to find the area enclosed by the PV curve; this gives you the IMEP.

 

[xxChrisxx]

Q_Goest is bang on the money with this one, I used a similar type of thing in my masters disseration. Designing a vintage V8 racing engine using simulation techniques. huzzah.

Integrating real curves is a *****, either find a program that can make approximate curves from a set of data points or break out the graph paper.

 

[timmay]

Integrating real curves is a *****, either find a program that can make approximate curves from a set of data points or break out the graph paper.

If you have no better software than Excel, you can use a trapezoidal numerical integration approach reasonably well so long as the x-interval is pretty small compared to the sample length.

But when it comes to a manual method, use a planimeter! I've mentioned before with PV diagrams, they're absolutely fantastic and much better than counting squares :)

 

[xxChrisxx]

Those are two marvellous suggestions. I feel especially silly about the numerical integration in excel as that is probably the easiest way to do it, I should have known that but never even thought to use the trapezoid rule. :(

 

[Q_Goest]

Those are two marvellous suggestions. I feel especially silly about the numerical integration in excel as that is probably the easiest way to do it, I should have known that but never even thought to use the trapezoid rule. :(

Actually, if you used the average pressure between two datapoints then you used the trapezoid rule! :)