And to answer your question, rapid acceleration will almost always burn more fuel. Driving the way I mentioned with the right type of vehicle will not result in rapid acceleration, it will only operate the engine in a way that is efficient. All I did was step on the accelerator a little more gently. I had no problem keeping up with traffic.
I like your answer, but it's not what's born on my Land Cruiser with me driving. So I thought about things and I could be completely wrong. Twenty years have passed since I studied physics. It seems that fuel economy and specific brake power, as considered here, are taken in steady state.
Under acceleration, the degree of acceleration largely determines the efficiency with which the engine can work. Accelerate faster and throw more additional fuel to generate more power and generate more heat, and the process is more irreversible. Therefore, even if it reaches a more fuel-efficient state faster, it does so less efficiently. If you throw less additional fuel, you'll accelerate more slowly, but you'll waste less and develop less power, but you'll do the same amount of work.
Even if you are operating in a less efficient rpm range. It seems to me that the degree of acceleration plays an important part of the engine's efficiency, not just the RPM. In general, driving slower reduces friction due to air resistance, which means it requires less energy to maintain speed and, therefore, save fuel. The small problem with this is that the fuel consumption of the engine is not linear.
Therefore, reducing the speed does not save as much gas as you would expect if you only calculated the air resistance. In fact, if you end up in the wrong gear and the engine runs too slow or too fast, you may need more fuel than driving faster. However, this is only in certain special cases. So, in general, you save gas by driving slower.
It's actually more efficient to accelerate quickly to cruising speed. It's not WOT to score in every gear, but wasting time means you have to spend more time accelerating instead of maintaining a speed that consumes much less fuel. It's not about accelerating quickly per se, but about climbing quickly to a high speed, which saves more fuel because your RPM is lower. This is especially true for automatic ones, since you can't directly control when you prepare.
When I started driving, I drove slowly because I thought it would save gas, then I started driving faster when a friend told me that you use the same amount of gasoline, whether you drive slow or fast (as long as it's the same distance), you would only drive fast for a shorter time and drive slow for a longer time, but in the end the same amount of gas burns. In my experience with the two cars I have had so far with fuel economy indicators, there was an optimal point that could be reached for optimal acceleration efficiency. If you push hard enough on the accelerator, most cars with automatic transmissions will slow down and increase RPM to help you accelerate faster. I tried both ways for 4 weeks each of the daily trips and got 11% more fuel savings thanks to the fast acceleration method (and by fast I mean going around 4500 RPM before switching, below the 4800 cam phase switch, since the TL-S has a noticeable transition from VTEC).
So you switch to second (or the automatic transmission does it for you) and you can accelerate even more. Therefore, the most efficient way to drive is to minimize the times you need to accelerate (don't slow down if you don't have to, drive at a slower average speed and avoid hills). Maintain cornering speed so you don't have to accelerate so much at the start, wasting fuel. To accelerate quickly when the wheels turn very slowly (as if you were still), you need to be able to reach a certain number of RPM at which the torque is adequate.
For example, your car will most likely consume less gasoline with its engine running at 1800 RPM compared to 2300 RPM, and it's possible to drive at a handful of road speeds other than those RPM. One of the disadvantages of accelerating a little fast is that you can run into a red light at the speed limit, whereas another person wouldn't waste fuel getting to that speed if they accelerated slowly. In fact, I get noticeably better fuel economy on trips involving motorways by accelerating at a decent pace to get to highway speed, and then absolutely minimizing any additional throttle input. But when you need to accelerate, do it quickly, using the throttle near maximum and shifting just after maximum torque, to get the most out of the fuel you burn.
This seems contradictory and confusing, but that apparent contradiction is only because acceleration consumes more fuel than the cruise ship, no matter how you approach it. . .