I've noticed an interesting thing with regards the fuel consumption of my E220 CDI (W211) Estate . I am a qualified engineer (BSc and MSC and Chartered) working in the aerospace industry and I've attempted to explain my findings using my Engineering knowledge. The purpose of this thread is to see if you guys and gals concur with my explanation and also to see if any of you have noticed the same with your driving. Its gonna be a long post! And having just read it, it would appear that I cant deny that I am a geek!
So, if I drive my car at 70 MPH (all numbers are indicated as on the dash, not actuals - but this shouldn’t matter) - I get 41 MPG. However, if I increase my steady speed to 80 MPH - I get better MPG 42.5-43. Why is this I thought? So here comes the VERY SIMPLISTIC Engineering Theory...
Drag - drag increases with the square of the speed - therefore drag from 70 to 80 does not go up by 1-7/8ths (approx 12%) but more like 1-(70sq/80sq) - more like 23%. This is one of the reasons why driving faster uses more fuel. However, drag is really measured by frontal area divided by length – known as drag co-efficient or CDa. Think of it this way, I have to punch a hole in the air directly in front of me to move forwards. But once I've made that hole, i can pass as much of the body of the car through it for free (ie I don’t have to make a new hole in the air once the top of the windscreen is through). This is why most trains have a flat front end. There is very little reason putting a pointy nose on a train as after it has punched a hole in the air - the whole of the length of the long train doesn’t have to do any more work in pushing the air aside to get past that point - hence long trains have some of the lowest drag coefficient (CDa - remember Audi made a big thing of them in the 80s) of any transport system. Also, this is one of the benefits of putting BIG front spoilers/airdams on cars - the idea being to force the air over the car, pushing the car onto the ground and therefore lowering its frontal area. So, here we have a drag curve which increases with speed. But my Merc is the Estate version, so its probably has a lower CDa than the equivalent saloon as once we are past the top of the windscreen, the airflow doesn’t get disturbed again until the end of the car...ie - its a very short train!
Engine - All thermal engines are (a) a compromise and (b) have a sweet spot where they are 'right sized'. What do I mean by these statements? Well, the engine is a compromise in the sense that at low speeds it is clearly too big for the job in hand (a 5.0L V8 doing 30 mph!) and at high speed it is too small (that’s why we stop accelerating) . And like the drag, we have a nice curve against rpm where we can see peak power and torque. And this isn’t at the max allowable revs for the engine as at very high revs, we have to overcome a lot of internal mechanical work (ie stopping the cylinder at the top dead center and the stopping it again at bottom dead center 7000 times per minute!!), and also we want the engine to last a few 100’000s of miles! . But that’s not all, all thermal engines give us their best thermal efficiency when they are worked hard. Here we are looking for the biggest differences (and again this is simplified) in both inlet and outlet temperatures and pressures and we get this when we work the engine hard (but not too hard – see above!, jet engines are better at being worked hard as their limiting factor is often the turbine blades melting – but in general you can keep revving a jet harder for better efficiency, so you build the smallest engine you can get away with based on your max power needs and rev the bollocks off of it!).
So what does this all mean for getting the best MPG on a cruise? Well, as we drive faster, the engine becomes more thermally efficient as we are working it harder, also our speed increase so we do more miles for a given time/amount of fuel used (hence MPG increases) but on the down side the work needed to be done to push against the static air also increases (quite alarmingly – it’s a speed squared rule!). So if we plot all of these curves we can find the speed that gives us our best MPG and sweet spot where the engine is ‘right sized’ – ie exactly the right size – for the job it is doing.
Now the E220CDi has the smallest diesel engine, being worked hard by a big turbo (the turbo basically recovers energy from the exhaust stream), and at 70 mph we still haven’t reached the peak of our efficiency curve – which I suspect is quite flat by now. By increasing our speed by 10 mph we do indeed increase our fuel flow, but we are now travelling 12.5% faster – so the net effect is to decrease the amount of fuel needed to cover a single mile – hence the increase in MPG. Also, I suspect that the estate in avantgarde form (ie lowered suspension, so a bit less frontal area, and a long flat roofline, and skinnyish tyres on the 220) is quite slippery and this offsets a bit of the drag increase. I also suspect that the 220CDI engine will show better gains than the bigger diesel s as it really is the smallest engine for the job in hand (which is what aeroplane makers do, see above).
Anyway, I hope this is of interest. Please feel free to contradict me and point out the errors in my assumptions. And, has anyone else experienced this increase in fuel economy by driving faster?
So, if I drive my car at 70 MPH (all numbers are indicated as on the dash, not actuals - but this shouldn’t matter) - I get 41 MPG. However, if I increase my steady speed to 80 MPH - I get better MPG 42.5-43. Why is this I thought? So here comes the VERY SIMPLISTIC Engineering Theory...
Drag - drag increases with the square of the speed - therefore drag from 70 to 80 does not go up by 1-7/8ths (approx 12%) but more like 1-(70sq/80sq) - more like 23%. This is one of the reasons why driving faster uses more fuel. However, drag is really measured by frontal area divided by length – known as drag co-efficient or CDa. Think of it this way, I have to punch a hole in the air directly in front of me to move forwards. But once I've made that hole, i can pass as much of the body of the car through it for free (ie I don’t have to make a new hole in the air once the top of the windscreen is through). This is why most trains have a flat front end. There is very little reason putting a pointy nose on a train as after it has punched a hole in the air - the whole of the length of the long train doesn’t have to do any more work in pushing the air aside to get past that point - hence long trains have some of the lowest drag coefficient (CDa - remember Audi made a big thing of them in the 80s) of any transport system. Also, this is one of the benefits of putting BIG front spoilers/airdams on cars - the idea being to force the air over the car, pushing the car onto the ground and therefore lowering its frontal area. So, here we have a drag curve which increases with speed. But my Merc is the Estate version, so its probably has a lower CDa than the equivalent saloon as once we are past the top of the windscreen, the airflow doesn’t get disturbed again until the end of the car...ie - its a very short train!
Engine - All thermal engines are (a) a compromise and (b) have a sweet spot where they are 'right sized'. What do I mean by these statements? Well, the engine is a compromise in the sense that at low speeds it is clearly too big for the job in hand (a 5.0L V8 doing 30 mph!) and at high speed it is too small (that’s why we stop accelerating) . And like the drag, we have a nice curve against rpm where we can see peak power and torque. And this isn’t at the max allowable revs for the engine as at very high revs, we have to overcome a lot of internal mechanical work (ie stopping the cylinder at the top dead center and the stopping it again at bottom dead center 7000 times per minute!!), and also we want the engine to last a few 100’000s of miles! . But that’s not all, all thermal engines give us their best thermal efficiency when they are worked hard. Here we are looking for the biggest differences (and again this is simplified) in both inlet and outlet temperatures and pressures and we get this when we work the engine hard (but not too hard – see above!, jet engines are better at being worked hard as their limiting factor is often the turbine blades melting – but in general you can keep revving a jet harder for better efficiency, so you build the smallest engine you can get away with based on your max power needs and rev the bollocks off of it!).
So what does this all mean for getting the best MPG on a cruise? Well, as we drive faster, the engine becomes more thermally efficient as we are working it harder, also our speed increase so we do more miles for a given time/amount of fuel used (hence MPG increases) but on the down side the work needed to be done to push against the static air also increases (quite alarmingly – it’s a speed squared rule!). So if we plot all of these curves we can find the speed that gives us our best MPG and sweet spot where the engine is ‘right sized’ – ie exactly the right size – for the job it is doing.
Now the E220CDi has the smallest diesel engine, being worked hard by a big turbo (the turbo basically recovers energy from the exhaust stream), and at 70 mph we still haven’t reached the peak of our efficiency curve – which I suspect is quite flat by now. By increasing our speed by 10 mph we do indeed increase our fuel flow, but we are now travelling 12.5% faster – so the net effect is to decrease the amount of fuel needed to cover a single mile – hence the increase in MPG. Also, I suspect that the estate in avantgarde form (ie lowered suspension, so a bit less frontal area, and a long flat roofline, and skinnyish tyres on the 220) is quite slippery and this offsets a bit of the drag increase. I also suspect that the 220CDI engine will show better gains than the bigger diesel s as it really is the smallest engine for the job in hand (which is what aeroplane makers do, see above).
Anyway, I hope this is of interest. Please feel free to contradict me and point out the errors in my assumptions. And, has anyone else experienced this increase in fuel economy by driving faster?
