Obviously, it takes more gas to accelerate a car than it does to simply maintain a steady speed. And, in my experience, hard acceleration uses up quite a bit more gas than gentle acceleration.
What I’m looking for is mathematical proof of which is better.
Let’s just say that I’m stopped at a red light, and the road ahead of me has a speed limit of 90 kilometers per hour (25 meters per second). I want to accelerate to that speed, and then hold the car steady at that speed for as long as possible.
Suppose I accelerate at a rate of 2.5 m/s². That would put me at cruising speed in 10 seconds (and I would have traveled 125 meters, if I calculate it right).
But if I only accelerate at a rate of 1.25 m/s², it will take me 20 seconds to reach cruising speed, but I will also have traveled twice the distance (250 meters) before I reach cruising speed.
Since I have forgotten a lot of the formulæ that I learned in Physics 101, I thought I’d ask here. Which would require the least amount of energy?
The engine operates less efficiently with excess gas. There’s going to be an optimal rate of acceleration for each car that includes all the conditions such as total weight of the car, the slope of the road, temperature and humidity, and many more things. The optimal rate won’t come from stomping on the gas pedal. The fuel won’t be used very efficiently when you do that.
There energy required to accelerate to a given speed is just the kinetic energy of the car at that speed. It doesn’t depend on how quickly you accelerate.
In the real world, the most efficient way is to accelerate at a rate (& gear choice) that allows the engine to run at its most efficient rpm & power output.
Without stomping on the gas pedal you want to get to the highest gear as quickly as possible. The highest gear is going to be the most fuel efficient. So smoothly accelerate to the highest gear without flooding the engine with fuel. Sorry, I didn’t do well in high school math or physics.
I once took part in a fuel efficiency competition. This was on a track so no traffic.
The optimum method of getting the consumption down was to accelerate as gently as possible and change up as soon as possible. This is bad for the engine and transmission, but it demonstrates how you can get amazing mpg from a car.
Not necessarily. Brake specific fuel consumption plots often show peak engine efficiency at almost full open throttle, at an RPM close to where the torque peaks.
But there are a lot of factors other than engine efficiency that go into overall vehicle fuel consumption.
Engines are most efficient at WOT. So WOT til your target speed would be most efficient but…
Modern cars tend to richen up the mixture at WOT so you lose some efficiency. ECUs will go open loop past a certain throttle position, you want to stay in closed loop. Closed loop is where the ECU looks to the O2 sensor for tuning and keeps the mixture leaner. So maybe a bit after half throttle.
Of course, the most important thing is to look at the traffic and dont speed up so much that you have to hit the brakes.
All’s I know is when I drove a Prius it put fuel consumption/efficiency on the readout panel. When I gunned it from an intersection the MPG went down to, like 8mpg. When I accelerated slowly and steadily - honestly fine for someone watching a gauge in fascination, and not fine for those with “normal” engines behind me - the lowest mpg was more like 30. Cruising in 4th gear at about 45mph, it said I was getting 90mpg then. It was fun to drive in a totally geeky way.
When you put your foot down you use more fuel but you spend less time accelerating and more time in fuel efficient cruise so you can’t just look at instantaneous fuel figures.
Years ago I was told the most fuel efficient way was to accelerate at WOT in high gear and then coast in gear (so the injectors are shut off) until the speed drops enough to go WOT again. I guess that would be OK on an empty highway. Not very practical in most cases though.
Or at the very least, don’t accelerate in order to get to the next red light faster than everyone else…
which is what about 90% of drivers do. Most people drive pretty stupidly–almost nothing they do gets them to their destination appreciably faster, or saves them any fuel.
8 Mile road in Detroit is well known for this; if you hit the first green and just steadily go slightly over the speed limit you’ll hit every green light from Grosse Pointe to Farmington Hills/Livonia.