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## 5.4 Assignment - Lecture 5: Regen Braking

### 5.4.1 Problem

For this assignment, you will be computing the distance travelled on energy that was generated through regenerative braking.

For any given vehicle, a certain amount of time driving the vehicle is spent braking (which may include cruising down-hill and decelerating). It has been found that the portion of time used for these actions is not negligible, especially in a short-distance (e.g. city) environment. When braking, kinetic energy is converted to heat on the brake pads, which essentially counts as lost energy. Regenerative Braking attempts to regain that energy by activating a small generator during times of braking, which would generate energy and store it in the batteries.

In the in-class exercise, we have computed the total amount of energy in the Segway batteries, given a certain distance travelled. We will assume that during parts of that distance travelled, regenerative braking was used to generate energy. We will further assume that about 20% of the time travelled in a city environment, the generator is activated due to braking. We now want to find out what additional distance travelled was due to regenerative braking.

Just as there are inefficiencies for converting energy to mechanical power, a quantity that we assumed was about 50%, there are inefficiencies in converting mechanical power to electrical energy. We will assume that these inefficiencies are also 50%. This means, for example, that only 50 of 100 units of mechanical power are actually converted to electrical energy.

You will be reusing the variables from the in-class exercise. To do this, you merely need to call exercise_batterypower from your assignment file, e.g. assignment4.m. See Figure 5.26.

Here's a summary of variables required for this assignment:
• disttotal = 16 km = 16000 m (total distance travelled)
• ηoverall = 50% = .5 (overall efficiency eff_overall; variable from in-class exercise)
• fractionregen = 20% = .2 (fraction of travel during which regenerative braking is used)

While you may approach this exercise anyway you like, you are required to include one function written by yourself.

Here are some more explanations and suggestions for solving the problem.

Consider the following: For any distance travelled, 20% of the time is used for regenerative braking. Whatever amount of energy is recovered from this 20% is stored in the batteries. Now, the rider can travel some additional distance on the recovered energy. 20% of this additional distance, regenerative braking is used again to recover energy, which is again stored in the batteries. The rider can now travel some additional distance on the 20% of energy recovered from the 20% of recovered energy from before. Et cetera ad infinitum.

Figure 5.27 describes exactly this relationship, from which you should be able to derive a formula.

 Figure 5.27
The derived formula will include a geometric series, which you should formulate in a separate function.

As for the overall efficiency, consider the following: For a given distance over which energy is regenerated through regenerative braking, only 50% is actually stored in the battery - the remaining 50% is lost due to inefficiencies. Similarly, when using the stored energy, 50% is again lost due to inefficiencies. Make sure that you consider these inefficiencies in your computation.