The analysis looks quite reasonable, though the drafting benenfit results from a decrease in density seems iffy. Air near room temperature below 200 mph is pretty much incompressible — there won’t be a density change. Though, I admit, I don’t know how to model drafting either other than the lower pressure cause by the wake of the lead vehicle means less pressure drag. Check out Anderson’s <i>Aerodynamics</i> if you get the chance.
I just skimmed through the article and it looks good. However, there are some inaccuracies. I believe the Engine Mass Airflow equation is missing both the gas constant and the engine displacement. Also, the power required curve is cubic, not expontential — as the equation above it shows. And the equation for drag force, while correct, looks as if area is squared, rather than velocity.
The drafting section is very wrong.
The density is constant. The effect of drafitng is a reduction in your air velocity. It’s crude simplification considering the turbulence of the wake behind the lead vehicle, but nevertheless a velocity reduction is far closer to the truth than the density dropping.
This doesn’t result in a penalty for the lead truck or car. You get something but they don’t lose anything that they wouldn’t have lost without you. The turbulent wake behind the truck is a region of low pressure which causes a light suction on the truck. This is where most of the drag comes from. If you drive further behind, the turbulent air settles and gets churned up again by you. You both lose.
I also feel you are slightly incorrect about your conclusion on acceleration. Slow acceleration is not the key. Low revolutions are. Accelerating with 1/4 throttle is slow acceleration. Close to full throttle but low revs shouldn’t be called slow acceleration. Many people interpret it wrongly and drive like fuckwits.
Your explanation for the fuel inefficiency of high revs isn’t quite right. More air being sucked in means more power which means less time accelerating. However, the high revs result in much more power lost to internal friction, a slightly richer mixture (depends on the car but this is common), and more breathing inefficiency in the engine.
While hard to find, graphs of power per flowrate of fuel vs rpm are available. These show that the efficiency drops with increasing revs. If this wasn’t the case, full throttle high rev acceleration would be as efficient as low rev acceleration and it would be quicker. The quicker acceleration would offset the large flow rate during acceleration. Unfortunately this constant efficiency engine doesn’t exsist.
However, there are some inaccuracies. I believe the Engine Mass Airflow equation is missing both the gas constant and the engine displacement. Also, the power required curve is cubic, not expontential — as the equation above it shows. And the equation for drag force, while correct, looks as if area is squared, rather than velocity.
There might definitely be some inaccuracies – other than knowing how an engine worked, prior to this, I really didn’t know anything about the details of it’s operation. On the other hand, I think the equation will still be accurate because the measurements are based on data at the MAP sensor prior to entering the engine – therefore, the fuel should be roughly equivalent to the air passing that sensor based on the stoichiometric ratio. Also, changing engine compressions will result in a change in drawn air (which will in turn change the fuel draw). You’re right the drag force equation is supposed to have velocity squared – somewhere in the transition from PowerPoint, the equation got skewed and the exponent slid to the left (it was a layered graphic).
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