Relative energy consumption on incline?

Question

If a vehicle travels in a straight line to a point 10km distant which has an elevation of 1000m.Will the enrgy expended/fuel consumption be the same if the rate of climb is a constant 100m per 1km.compared to 9km flat,followed by a climb of 1000m in the final 1km.

Answer 1

from a physicist's point of view, the energy consumption would be only slightly higher in the second case,

but from an engineer's point of view, the 2nd case is a lot more power hungry.

let me explain : for a physicist, the 1st case, your wheels will have to fare sqrt(101) km while in the 2nd case, they will have to fare 9+sqrt(2). The 1st case is a slightly shorter trip. so your wheels will have to turn a few times more in the 2nd case than in the 1st case, and therefore, you'll have to consume more energy. (the difference of height is the same in both cases, so a physicist wouldn't care about it)

However, an engineer will also consider the strain put on the engine !!! and an engine doesn't work as efficently when put under a lot of strain, like in case 2... so the difference of power consumption will be a lot higher for an engineer.

Answer 2

Since the asker said nothing about the speed at any point in either journey, no one's comments about power are relevant. (power = energy/unit time). He also said nothing about type of vehicle, so one must not assume it has to be what many consider to be a conventional road vehicle powered by an internal combustion engine riding on rubber tires.

This entirely theoretical ? has an easy theoretical answer: The energy requirement depends ONLY on the height of elevation. Fuel consumption would, of course, involve how efficiently the fuel was employed to produce the energy required, but since no details were given on this, no anwers can be rationally rendered.

Answer 3

If you ignore everything that makes such a problem interesting, such as air resistance, speed profile, engine efficiency change at different power outputs, etc, and accept that you are in a vehicle that can climb vertically as stated for the second case, it's the same climb, same energy.
Actually, contrary to answer 1, an automotive engine does work more efficiently when heavily loaded, especially at low rpm. Lighter loading means part throttle which results in more pumping losses relative to energy obtained.

Answer 4

The minimum possible energy consumption is the same but in practice it depends on the mechanism used to do it.
The answer depends on the efficiency of the vehicle at a 1/10 gradient compared with the efficiency at 1/infinity and 10/1. Without knowing these the question is impossible to answer.

Answer 5

In real life they are not same. The weight it carries is different at any given time. So it will spend different energy.

Answer 6

ask him