Yes but to understand why we first need to know the 3 factors I mentioned above...
Energy density (calorific value)
| Petrol | Ethanol | LPG |
| 45.8MJ/kg | 19.9MJ/kg | 50.3MJ/kg |
Mass density (litres per kilogram at 15degC)
| Petrol | Ethanol | LPG |
| 0.737 | 0.789 | 0.51propane > 0.57butane so 50/50mix 0.54 |
Now we know the energy density (calorfic value) of 1kg of each fuel and the actual density of each fuel we can work out how much energy is in a litre of each fuel, it's just calorific value x density.
| Petrol | Ethanol | LPG |
| 33.75 MJ/L | 15.70 MJ/L | 27.16 MJ/L |
But there are 2 reasons for the longer pulse on ethanol compared to petrol.
The first reason is that if we want the engine to make the same power, then due to the lower calorific value (per litre) of ethanol compared to petrol we need to inject more ethanol... The engine produces power by using heat energy to expand air in cylinders to create pressure to push on pistons so if we want the same push on pistons from ethanol as from petrol we need to use more ethanol. But the engine ECU meters air coming into the engine so if it were just a case of lower calorific value with same stoch ratio the driver would just put their foot down more to compensate for lower power and the ECU would self compensate for needing more fuel by increasing fuel to match the increased airflow when the driver put their foot down more.
The second reason is because of the difference in stochiometric ratio....
| Petrol | Ethanol | LPG |
| 14.7 | 9.0 | 15.4 |
From the above table we can see that for any given airflow the engine will need around 63% more mass of ethanol than it would need mass of petrol to keep mixture correct. But again we need to refer to actual density (KG/L) to compensate the 63% for litres instead of kg.
| Petrol | Ethanol | LPG |
| 1 (no compensation) | (14.7/9) x (0.737/0.789) = 1.526 (+52.6%) | (14.7/15.4) x (0.737 / 0.54) = 1.303 (+30.3%) |
The above table figures (if I quickly did my sums properly lol...) just show how much the pulse length of an ideal injector (that flows the same volume of any of the fuels) would need to be changed by to swap between fuels to keep mixture the same (lambda equivalence ratio = 1), they don't tell you how much fuel you'd need to burn to get the same power so don't necessarily reflect on mpg.
But we can work out how much longer or shorter the injector would need to pulse for the same engine power. I'll probably come back to this because I have to do some work now lol, but in gist we take the above injector percentage correction factors, go back to looking at our energy per litre table, and calculate how much longer or shorter the injector needs to pulse for to get the same calories of heat energy into the engine.
Idle could be a problem on ethanol even if we fit a system that corrects injector pulse length to correct mixture, because it's not just the mixture or calorific value that change. The engine will need a certain amount of heat energy just to idle but the amount of airflow to get that heat is very different on ethanol to on petrol, so the idle air control system needs to be able to adapt to flow the extra air. There's no extra IAV (idle air valve) on an E51 (there is on an E50 with 3.5 engine), on the E51 idle air is controlled by the fly by wire throttle... But whether or not it will throw any error codes for the unexpected extra air necessary to maintain idle is another matter besides the subject of mixture.
Wow
