While I read the thread on bumper shape this morning, I discovered the elegant equation here:
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for the hp required to overcome wind resistance. It is from some stuff that Phil posted. I guess I'd seen it before, but just gave it casual thought. As the coffee kicked in I began to see a more profound and sinister implication of the equation.
Insight 1 owners have a powerful interest in getting the lean burn limit up to a higher speed - mostly to avoid being run over by 18 wheelers
In studying the equation, I realized it could answer a basic question in regard to raising the lean burn limit.
Question: How much improvement must we make in the Cd or frontal area to substantially improve the lean burn limit?
I finally realized that with very few assumptions, we could arrive at a calculated answer for a very real example, say going from a reliable lean burn at 45 MPH to a reliable lean burn at 55 MPH. The primary assumption needed is that the horsepower of the little 3 lunger is fairly constant across that RPM range. The assumption isn’t strictly true of course, but it is close enough for “back of the envelop” thinking.
By a very simple set of algebraic manipulations, eliminating constants, given the above assumption, we can arrive at the equation:
(V1)^3/(V2)^3= (CdA)2/(CdA)1
(Don't know how to keep site from changing my subscripts to regular font but the savy should be able to see where the subs are.)
If one carefully analyzes the rearranged equation, it is clear that 3 of the 4 quantities in the equation are know, so only the last quantity, (CdA)2 remains to be calculated
Setting V1=45MPH, V2=55MPH, (CdA)1=5
(In other words, how much would the CdA of the car have to change to extend a fairly reliable lean burn from 45MPH to 55MPH)
Just simply plugging in the numbers, one arrives at a (CdA)2 value of:
2.7 !
Or, in other words the CdA must be reduced by almost half! Since the "A" factor is virtually impossible to change in a significant sense, the entire load must go to Cd reduction. To me, it seems like a Cd reduction of 40-45% is certainly “a bridge too far” and that this goal never works out. Perhaps extending lean burn by 2-3 MPG is achievable?
Comments, Corrections, Flames?