In: Advanced Math
analyze the performance of a gasoline engine at various loads based on data given and to determine the torque curve, power curve and performance parameters of BMEP, volumetric efficiency, and Air/fuel ratio, plotting the data vs RPM. Making three graphs: one graphing Torque and Power.
Also address t
a. How do the torque curve and power curve compare (max values @ same RPM)?
b. Is volumetric efficiency constant, or varying with RPM..what is trend?
c. Is BMEP a constant? Does it compare more with torque or power output?
Board Time | Absorber RPM-C | Torque | Barometer | Air Temp. | Air Flow | Air Flow |
sec | RPM | lb-ft | PSI | F | Data | CFM |
0.015 | 2172 | 53.876 | 14.21 | 64 | 345.86 | 34.59 |
0.030 | 2177 | 53.896 | 14.21 | 64 | 347.65 | 34.77 |
0.050 | 2180 | 54.011 | 14.21 | 64 | 342.63 | 34.26 |
0.070 | 2174 | 53.744 | 14.21 | 64 | 343.56 | 34.36 |
0.090 | 2182 | 53.595 | 14.21 | 64 | 349.31 | 34.93 |
0.110 | 2170 | 53.879 | 14.21 | 64 | 342.84 | 34.28 |
0.131 | 2174 | 53.754 | 14.21 | 64 | 344.96 | 34.50 |
0.151 | 2192 | 53.859 | 14.21 | 64 | 349.31 | 34.93 |
0.171 | 2178 | 53.808 | 14.21 | 64 | 344.01 | 34.40 |
0.188 | 2183 | 53.785 | 14.21 | 64 | 346.86 | 34.69 |
0.206 | 2182 | 53.872 | 14.21 | 64 | 344.62 | 34.46 |
0.226 | 2167 | 53.781 | 14.21 | 64 | 342.23 | 34.22 |
0.246 | 2174 | 53.714 | 14.21 | 64 | 347.26 | 34.73 |
0.266 | 2166 | 53.933 | 14.21 | 64 | 341.47 | 34.15 |
0.286 | 2160 | 53.659 | 14.21 | 64 | 343.18 | 34.32 |
0.306 | 2168 | 53.771 | 14.21 | 64 | 348.12 | 34.81 |
0.326 | 2165 | 54.028 | 14.21 | 64 | 342.30 | 34.23 |
0.340 | 2169 | 53.568 | 14.21 | 64 | 345.69 | 34.57 |
0.356 | 2175 | 53.612 | 14.21 | 64 | 346.64 | 34.66 |
0.376 | 2162 | 53.832 | 14.21 | 64 | 340.82 | 34.08 |
0.396 | 2166 | 53.487 | 14.21 | 64 | 345.96 | 34.60 |
0.416 | 2179 | 53.561 | 14.21 | 64 | 347.77 | 34.78 |
0.436 | 2166 | 53.490 | 14.21 | 64 | 342.03 | 34.20 |
0.456 | 2173 | 53.315 | 14.21 | 64 | 348.22 | 34.82 |
0.476 | 2171 | 53.440 | 14.21 | 64 | 342.23 | 34.22 |
0.492 | 2164 | 53.291 | 14.21 | 64 | 344.51 | 34.45 |
0.511 | 2171 | 53.183 | 14.21 | 64 | 346.14 | 34.61 |
0.531 | 2171 | 53.287 | 14.21 | 64 | 341.15 | 34.11 |
0.551 | 2165 | 52.919 | 14.21 | 64 | 343.62 | 34.36 |
0.571 | 2173 | 53.017 | 14.21 | 64 | 348.34 | 34.83 |
a)You are probably thinking of the formula relating power torque
and rotational speed, P = T?, which would imply a linear
relationship between power and torque. However the relationship is
not linear because both power and torque also depend directly on
the rotational speed.
For example the torque of a permanent magnet D.C. electric motor
depends linearly on the rotational speed:
T = b – a?
(where b is the torque at zero rotational speed and
‘a’ is also a constant).
This is a straight line. We can now substitute this into P =
T? and obtain the formula for power:
P = b? – a?^2
Which is quadratic and clearly not the same “shape” as the torque
formula. It does not depend explicitly on the torque value
itself.
For an internal combustion engine, the relationship between torque
and r.p.m. is more complex, but the same applies. If you could
somehow devise an engine with a constant torque output the power
would indeed depend linearly on r.p.m. Many engines have a near
constant torque output in the middle of their rev range which
approximates this condition.
b)Volumetric efficiency is the ratio of actual amount of air and fuel mixture inducted into the cylinder to the swept volume of the cylinder.
For any engine the volumetric efficiency is not constant throughout the operating range.(considering it is designed to operate in a range and not at a constant speed like gen-sets)
The volumetric efficiency is maximum in a particular range of engine speed which depends on whole lot of engine design factors which are not a part of the question.
Volumetric efficiency thus varies with engine speed and other factors. Mass of air increases because there are more number of cycles at higher speeds. Usually the volumetric efficiency of the engine is highest where it produces maximum torque.
c)BMEP:The average (mean) pressure which, if imposed on the pistons uniformly from the top to the bottom of each power stroke, would produce the measured (brake) power output.
Please note that BMEP is purely theoretical and has NOTHING to do with ACTUAL CYLINDER PRESSURES. It is simply a tool to evaluate the efficiency of a given engine at producing torque from a given displacement
BMEP=150.8*TORQUE/DISPLACMENT(FOR 4 STOKE ENGINE)
BMEP=75.4*TORQUE/DISPLACMENT(FOR 4 STOKE ENGINE)
ANOTHER FORMULA TO CALCULATE BMEP
BMEP = n * T * 2 * pi / D
where
n = no. of revs per power stroke (2 for 4 stroke)
P = Power (watts)
D = displacement (m^3)
N = revs / sec
T = torque (Nm)