Formula, BMEP from time area

[StepVino]

Hi, I was just given some formulas to get a BMEP value
from port time areas. These are just a couple:

Intake (tranfer, boost):
BMEP(BAR) = 2400 x Time area - 9.66 (upper range)

Exhaust:
BMEP(BAR) = 1050 x Time area - 5.975

They seem to assume a lot. Would anyone know the
origin of these formulas, or maybe be able to explain
a bit how they were determined?

tx

 

[Big B NRG]

Isn't this explained in the Bell book Walter?

 

[StepVino]

Hi Bram, in Bell's book he says he never found the time area
concept useful. Jennings just shows how to use TA, and gives
an example, but doesn't make a connection between TA and
BMEP.

 

[EGT]

The connection between BMEP and the different time area's is imperical determined bij Blair using regresion formulas.

 

[StepVino]

Thanks egt. That will make it easier to earch for more
info, short of getting his book for now.

 

[Browni]

Hi Bram, in Bell's book he says he never found the time area
concept useful. Jennings just shows how to use TA, and gives
an example, but doesn't make a connection between TA and
BMEP.

We have had a discussion about this I think.

TA explanation in Jennings book is very very poor, so it's all useless.

The time-area in real world (for engine designing) is very important, doesn't matter if we talk about 4-stroke valves or 2-stroke ports!

Because not only the port cross section, port duration is important, but the port width from time to time.

For the demostration I've made a diagram (from my Excel algorithm):

http://mbk.tar.hu/time-area.pdf

You can see that the port openings, the port durations and the cross sections are the same, just the (fictious) blue port is inverted (yellow port). Because of this the blue port has more time area.


The time area calculation is a quite simple integral:

Where:

I = time area
n = operating RPM
φ1 = port opening
φ2 = port closing
A = sum cross sections (not equal to the port cross section)

 

[StepVino]

Thanks Browni. I get something slightly different for the time area
equation. The only part I remember having to assume was the
expression for mean area:

 

[StepVino]

Here's something else I find confusing.

Do I have these Blair formulas correct?
Transfer plus boost:
BMEP = 2400xTA -9.66 Upper
BMEP = 587xTA + 0.128 Lower

Can't find the reference, but 'upper' and 'lower'
stand for higher, or lower primary compression ratio?
Does anyone know the compressions that would be
considered low. or high? This is second question
though.

My first question comes from solving these for
any BMEP, eg say 10 BAR, and solving for TA

TA=0.008192 Upper
TA=0.01682 Lower

Assuming I have the correct equations, and labeled
them correctly as upper and lower, I don't undertand
why a higher primary compression would need less
time area than a lower primary compression.

In a way it makes sense (on writing this down the clouds are
clearing ). Higher primary compression would mean
faster flow out of the ports, so they don't need to be
as big to flow the same amount in the same time, and
same flow = same power = same BMEP?

Amazing how the case compression effects tranfer ports
TA, doubling needed TA. I can see why the Jennings TA
can be useless numbers... unless, Jennings always assumed
primary compression fixed at 1.5 (common number seen in lit.),
and this corresponds to Blair upper or lower compression?

I tried to match up TA between Jenning and Blair. Nothing
conclusive yet (assuming there's something to be found).
I did notice that at high BMEP:
Blair exhaust mean area (not TA) is close to Jennings max exhaust area,
Blair tranfer mean area (upper) is close to Jennings min tranfer area.

This has a familiar ring: for racing engine use max exh area, min
intake area. Could this mean that Blair 'upper' primay compression
is ~1.5?