# Selection of batteries and cars for a thermodynamics problem

awais1985

## Homework Statement

1) You are responsible for selecting automobiles that will be used in your company’s fleet. The vehicle that you select has the following combined wind drag and rolling friction force during average operation conditions. The relationship for this force is
Ff = (0.0214m + 7.83)
where, m=vehicle mass and Ff is the combined wind and rolling friction forces in N.
The automobile is either an all-wheel drive hybrid vehicle or a similar non hybrid vehicle. The Hybrid vehicle has a mass of 1200 Kg and is powered by a storage battery- motor combination that provides electricity to four wheel mounted motors. The batteries in the hybrid configuration are charged using an internal combustion engine-electrical generator combination or regenerative braking. The hybrid regeneration braking system can operate down to a velocity of 10 Km/hr when the standard friction brakes are applied. The efficiency of the regenerative braking mechanism is 69% and is defined as the energy added to the battery divided by the braking energy needed to reduce the speed of the automobile. Neglect internal energy of the vehicle and its systems in these calculations.
The non-hybrid vehicle is similar, but has a mass of 930 Kg and uses the same drive system an internal combustion engine-generator to directly supply the electrical power to the motors. The engine in both vehicle configurations is the same and has the same efficiency. The cost differential between the non-hybrid vehicle and the hybrid vehicle is \$7,700.

The different driving cycles are composed of the following individual activities.
a) The vehicle accelerates from a stop to a speed of 35 km/hr. This acceleration takes place in 18 seconds at a constant accelerate rate of 0.54 m/s2.
b) The vehicle stops from a velocity of 35 km/hr at a constant decceleration rate of 0.59 m/s2 during regenerative braking and of 0.65 m/s2 during frictional braking.
c) A hill climb with an elevation change of 75 m at an angle of 15 degrees and a constant velocity of 35 km/hr.
d) A hill descent with an elevation change of 75 m at an angle of 10 degrees and a constant velocity of 35 km/hr.
e) A level driving distance to be stated in the driving cycle.

1b) Determine the battery energy used and the thermal energy added to the environment (heat flow) for the each of the above components of the driving cycle.

1c) Using the above results consider two driving cycles that your company uses. The first is composed of 31 start and stops, 5 hill climbs and descents and a level, constant velocity component of 21 km.

1d) The second driving cycle is composed of two start stops, one hill climb and descent and 210 km of level, constant velocity driving.
Based on your calculations, write a recommendation for the vehicles to purchase. The company plans to purchase three vehicles, two will be used for the first driving cycle and the third for the second driving cycle. The recommendation is to the Chief Financial Officer of the company who has a MBA and a public relations background.

## Homework Equations

Ff = (0.0214m + 7.83)

Sum of energies in = sum of of energy properties + sum of energies out

## The Attempt at a Solution

To be fair, i am confused as to how to approach this question. what i have started off with is calculate the frictional force for both hybrid and non hybrid vehicles. Then as per my understanding what part b refers to is to write energy balance equations for all the four cycles? i was trying to write the Energy Balance equation for the first cycle and it came out looking something like this

for cycle A: 0 (no flow in) = change in chemical energy + change in kinetic energy + 0 (no flow out)

Please guide me as to how to proceed with this problem.

Homework Helper
Gold Member
As I see it each of the driving cycles (a-e) will consume energy and/or recover energy. I would work through each one in turn calculating how energy is expended or recovered. Quite a bit of work I think...

Some hints...

The total frictional force Ff appears to be independent of velocity (in this problem) which should make things easier (Remember Work = force * distance). Are you familiar with the standard equations of motion for constant acceleration (SUVAT)?

Some of the driving cycles involve changes in PE and KE as well as overcoming ff. Some trigonometry might be needed to work out height gained?

In one case (b) where it's decelerating note that the regenerative braking works down to 10km/h but below that the brakes are used. So not all the KE at the start of cycle b is recovered into the battery by the time it comes to a stop.

In short you will need to do some careful analysis of what happen in each driving cycle. Then add up the energy expended and recovered to give the total energy expended over all the cycles.

Do this twice, once for each vehicle.

Keep your working for later parts of the question.