The amount of horsepower an engine makes is directly related to the mass air flow of the engine. Mass air flow is determined by volumetric efficiency VE, and the density (pressure-and-temperature) of the air. In turn, if you know the actual efficiency of the engine, and energy content of the fuel used, you can predict horsepower. Assume a 97.5% VE at 5400. At standard temperature and air pressure (77 degrees Fahrenheit, and 14.53 psi) this equals 22.56 lbs/hour air. Assuming 19000 BTUs per gallon of gas and a 0.33 (mechanical x thermal) efficiency this should produce 228 hp. Converting the mass flow to CFM = 309CFM. Now, add a K&N cone air filter into the picture. It may positively impact VE due to a lower air pressure drop at 309 CFM than the stock filter. Let’s say VE goes to 98%. Mini Cooper Cold Air Intake System
Based on the same calculation, the mass airflow is now 22.68 lbs/hr or230 HP. However, consider the temperature of the air. Under the hood, without any type of insulation, the temperature is probably not far from the temp of the thermostat. To be conservative, let’s say the new cone filter is breathing in 160 degree under hood air instead of 77 degree air. Using the previous formula, but adjusting the air temperature what is the mass flow rate? 19.64 lbs/hour. That amounts to 199 horsepower. Here are calcs for a couple other temps at 98% VE:
|
Temp |
Mass Air Flow |
Predicted HP |
|
40 |
24.36 |
247 |
|
77 |
22.68 |
230 |
|
100 |
21.75 |
220 |
|
120 |
21.0 |
213 |
|
140 |
20.3 |
206 |
|
160 |
19.64 |
199 |
|
180 |
19.03 |
193 |
Which means that for every 60 degree C the density changes by 10%. Assuming the engines volumetric efficiency stays the same, then we get 10% more power out of an engine, if we can reduce the inlet air temperature by 60 degree C.
MINI Coopers 