[RedDevil]

Originally Posted by IamIan

...The smaller the fluctuation the less of a penalty ... but there is always a aerodynamic joule penalty for the air to vehicle speed fluctuation.

We can crunch the equations if you like ... but ... it does not balance out.

We more or less agree on a lot of stuff, finaly
With 'pretty much' I meant 'almost'. But yeah, lets crunch numbers.

Air resistance has a quadratic correlation with speed. Higher speed also means longer distance travelled so we can represent it as a function of speed: R = C * V * V (where R is resistance, V the speed and C a constant representing the aerodynamic efficiency).
The energy required to overcome the resistance is the product of that resistance and the distance traveled; the distance is linear to the speed.
The equasion for the energy would be the same, just multiply both sides with the speed; ergo R * V = C * V^3 (^ designates power)

So now we compare that to a situation where the speed is slightly higher half of the time and the same amount lower for the other half. Let's call the difference D.
The required energy over that would be R * V = C * ((V + D)^3 / 2 + C * (V - D) ^3 / 2)
Simplifying the equasion it becomes R = C * (V^2 + 3D^2).
So the increase is just 3D^2

In words the total resistance increases by 3 times the square of the difference.

If the speed variance is say 10% of the average speed (like doing 60 mph and 50 mph alternatingly instead of a constant 55 mph) the increase in resistance is 3 times the square of 10%, which is just 3% for a 10 mph difference between high and low speed.
That's not nothing, but it is much less than you'd expect. It seems to contradict common sense. But the math adds up.

We can check the formula by making D equal to V. Doing half of the time double speed and half of the time at a standstill should see 4 times the power needed as the resistance while moving is 4 times higher, and all of the distance was covered at high speed. And sure enough the formula yields a 300% increase, so a total of 4 times higher.

Do the formula on a small variance (like 2% for +/- 1 mph at 50) then the formula yields just an 0.12 % energy increase. That's less than a mile on a full tank even if the only force in play is air resistance.

So there you have it. Yes, varying the speed does increase the total amount of energy you need to overcome air resistance, but the increment has a quadratic relation to the variance so if that is kept within a reasonable range, the extra energy required is not a major factor.

Today it was cold: just 8 Celsius coming home vs. 25 yesterday and it hurt FE. But I did get to practice P&G technique on a country road (being held up by some slow movers), alternating gentle acceleration to 40 mph while keeping the revs at minimum with coasting 'zero load' style to 30.
As I have a l/100 km indication on the MID it is not very accurate, but it had 4.0 l/100 km @30 km in the trip when I started P&G and 3.8 @35 km when I got home.
The fuel consumption on that stretch was 2.6 l/100 km (give or take half a l/100km). I did not draw from nor add to the battery doing that.

Give me lots of time and an empty road and I can easily get my Insight over 80 mpg by P&Ging like this . Make it a windless 30C day, then maybe 100 mpg is attainable.