How to calculate BMEP from P-V Graphs?

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Discussion Overview

The discussion focuses on the calculation of Brake Mean Effective Pressure (BMEP) from pressure-volume (P-V) graphs, particularly in the context of engine performance analysis. Participants explore various methods and considerations for deriving BMEP from given P-V data, including integration techniques and numerical methods.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant inquires about the feasibility of calculating BMEP from P-V traces for wide open throttle and part load conditions.
  • Another participant provides a formula for BMEP based on horsepower, displacement, and RPM, but this is challenged due to the lack of direct values from the P-V data.
  • A suggestion is made to integrate the pressure-volume data (PdV) to determine work done, which can then be used to calculate power over a cycle.
  • It is proposed that integrating the area under the P-V curve yields the Indicated Mean Effective Pressure (IMEP), which is related to BMEP.
  • Participants discuss practical methods for integration, including using software for numerical integration or manual methods such as a planimeter.
  • One participant expresses regret for not considering numerical integration in Excel, acknowledging it as a straightforward approach.

Areas of Agreement / Disagreement

Participants generally agree on the need to integrate P-V data to derive BMEP, but there is no consensus on the best method to achieve this or the specific calculations involved. Multiple approaches and tools are suggested, reflecting differing opinions on practicality and effectiveness.

Contextual Notes

Participants mention various assumptions regarding the integration process, such as the need for average pressure values and the specific cycle duration for different engine types. The discussion does not resolve the complexities involved in accurately calculating BMEP from P-V graphs.

Who May Find This Useful

This discussion may be useful for individuals interested in engine performance analysis, particularly those looking to understand the relationship between P-V data and BMEP calculations, as well as those seeking practical integration techniques for engineering applications.

nb89
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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?
 
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see Horsepower - Please help - Confused! posted on Feb 14 2009

BMEP = ( Hp x 13000) / ( liter displacement x RPM)
 
that doesn't really help considering all i am given are values of different pressures and volumes
 
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.
 
Sure, integrate to find the area enclosed by the PV curve; this gives you the IMEP.
 
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.
 
xxChrisxx said:
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 :)
 
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. :(
 
xxChrisxx said:
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! :)
 

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