Taking Insight Lean Burn from 45 to 55 MPH-Impossible?

[jime57]

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?

[3-Wheeler]

Hi Jim,

I think you are close, but over calculating just how much power is required.

If you look at the post here...

http://ecomodder.com/forum/268030-post22.html

... you'll see that rolling drag is not proportional to speed. Therefore, the hp requirement does not go up as quickly as the cube of the velocity, but is close.

It also means that you should be able to get a reduction in Cd easier than the classic V^3 equation would lead one to believe.

Hope this helps, Jim.

[jime57]

Originally Posted by 3-Wheeler

Hi Jim,

I think you are close, but over calculating just how much power is required.

If you look at the post here...

http://ecomodder.com/forum/268030-post22.html

... you'll see that rolling drag is not proportional to speed. Therefore, the hp requirement does not go up as quickly as the cube of the velocity, but is close.

It also means that you should be able to get a reduction in Cd easier than the classic V^3 equation would lead one to believe.

Hope this helps, Jim.

Actually, the equation from Phil that I worked with only considers the drag or hp needed to overcome wind resistance. Click his link in my post. I did click through to your link on rolling resistance and looked at your data. From extrapolation of your average curve, it looks like the rolling deacceleration at around 50 MPH would be around .2 M/s^2, and rising with speed. So the power to support that rolling resistance would make matters worse by that amount, I think Maybe I have the direction wrong, but doesn't seem so.

In any case, it is a daunting task to raise the lean burn threshold by Cd reduction alone, since changing frontal area(A) is mostly unavailable. I don't see us ever getting to a CdA of 2.74ft^2 from a stock value of 5ft^2.

All very interesting to contemplate. Thanks for your post

[jime57]

Oh -- now I see what you mean about rolling resistance going up more slowly with the increase from 45 to 55 MPH. It isn't a cube relationship. Looks almost linear. Still that factor is small compared to wind resistance and so the picture is still pretty glum.

BTW, at what tire pressure are you making the roll-down measurements? You can PM me if you like.

[some_other_dave]

I believe that Basjoos has gotten his Civic to where it will stay in lean burn up over 90 MPH; his estimate was that it might stay there even at 100 MPH!

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-soD

[jime57]

Originally Posted by some_other_dave

I believe that Basjoos has gotten his Civic to where it will stay in lean burn up over 90 MPH; his estimate was that it might stay there even at 100 MPH!

Aerocivic - Honda Civic modifications for maximum gas mileage - aerocivic.com

-soD

Though we much admire his work, the Aero Civic is a much different animal than the Insight 1. Larger, more powerful engine for one thing. Do you see a problem with my math? Lets stick to substance on the Insight. Cross car comparisons are of limited value.

[aerohead]

Originally Posted by jimepting

Though we much admire his work, the Aero Civic is a much different animal than the Insight 1. Larger, more powerful engine for one thing. Do you see a problem with my math? Lets stick to substance on the Insight. Cross car comparisons are of limited value.

Jim,I think the premise of the math is okay.
The power absorption of the tires isn't going to very much so the rolling force will remain a constant,however at the higher speed,the power necessary to overcome R-R will increase.
If we knew the original R-R power at lean-burn,and working with ft/sec velocity,then :

Power(RR)=[ initial lean-burn velocity/550( lb-ft/hp)x ( R-R drag force [weight X coefficient RR] )]
--------------------------------------------------------------------------

New Power(RR)=[ new velocity/550 X ( R-R drag force )]
--------------------------------------------------------------------------
Once you're cruising at the new lean-burn velocity,the only variable you changed was the Cd.
Acceleration affects(Polar moment of inertia) have disappeared.
If the BSFC characteristics of the engine are 'flat',as the power curve suggests,then projecting the required Cd seems reasonable.

[jime57]

One reason I kept the math fairly simple was that I figured I wouldn't be able to really sort out the RR contribution, and I assumed it would be nearly constant between 45 and 55 MPH. It rises a bit of course, but I think that the assumptions get us close to the answer. As 3-Wheeler pointed out, the required Cd reduction is a bit overstated because the RR component isn't a cubic relationship to speed.

Having done the math, one could come to a quicker intuitive feel for the problem of getting the lean burn threshold moved up. The MAJOR drag at these speeds is wind and since it goes up with the cube of speed, then getting Cd down enough to make a major threshold difference is going be very hard. Of course, this is all Insight specific. Other cars with other engines may perform differently.