Let's say I am driving in a BMW 318 TDS (gasoil) :
on flat terrain, at 70km/h, with only one passenger, at 2000rpm
on a climbing terrain, at 70km/h, with 4 passengers and a loaded car at 2000rpm
How does that affect what is actually happening in the engine ? Does the engine "know" that there is more work do to, and inject more gasoil ? If so, approximately, up to how many times more than on flat terrain ?
As you are traveling on flat land and transition to an uphill slope, whether you (the driver) realizes it or not, you must press the accelerator down further in order to maintain speed (or engine RPM). The vehicle control systems recognizes this and pushes more fuel into the system to compensate. This gives you more power to make it up the hill. If the grade is too steep and the load too heavy, the transmission (if automatic) will downshift to allow the engine to remain within it's peak power band and to get a better torque advantage. The powertrain control module (PCM) calculates engine load and output so as to apply the appropriate fuel mapping.
It is hard to actually calculate how much more fuel is injected or "how many times more" as you say, because there are too many factors involved. These factors are: grade of slope traversing, engine size, fuel mapping, how well tuned the vehicle is, and load size (including weight of vehicle and cargo). Just know that the further you press the "go" pedal, the more fuel you are using. With more load, even more fuel is being used to maintain the same speed and rpm.
EDIT: As noted from moderator Bob Cross, you as the vehicle operator (or a good mechanic) can attach a device to your OBDII port (if applicable) and devise this information. What I was saying is there is no way we can devise this information for you over the internet without a LOT more information.
