Application Results

Hello World!

So quick update: I have officially graduated UC Davis, and am going to Purdue in the fall! However I'm not going to talk about that, I'm going to do something very different this blog. Instead of life updates... I am going to do some MATH!!!!!

The problem

I am the proud owner of a Backfire electric skateboard. Don't be fooled by UC Davis, which claims that bikes are the premier mode of transportation around this campus. Skateboards are better for many reasons. Firstly, they are harder to turn sharply in compared to a bike, which ensures that you plot out the most efficient path to your class beforehand, saving you from wasting time frivolously meandering around campus admiring the scenery. Secondly, it has no shock absorbers, which means that you get bounced up and down on the way to class, ensuring that your hair is superbly floofed upon arrival. It is battery powered which means you don't need to engage in any sort of physical activity, which would be unbecoming of an engineer, and finally, it goes much faster than a regular bicycle which allows you to go to class faster, with only the minor downside of massively increasing risk of a serious injury upon collision.

However this board has one serious downside: sometimes, the battery gets low. In that case, I must make an important decision as to how long I will charge it. Charge to long, I miss being late to the event I'm trying to skate to because I leave too late. Charge to little and my board isn't charged enough to make it causing to to slow down, and eventually stop, forcing me to carry a heavy board the rest of the way. There is a simple solution to this: carry the charger where ever I go and if I have an important meeting, charge the board during class. However there lies a much better solution which makes my engineering heart happy: create a convoluted and impractical mathematical system to determine how long to charge my board!!!

The Math/h1>

The Backfire G2 Black with Super Power Hobbywing Motors and 96mm Wheels has a maximum velocity of 38 kilometers per hour, or 10.5556 meters per second. It has a 42 volt, 5.2 amp hour, 187 watt hour, Changhong Sunpower Cell battery. Changhong Sunpower Cell batteries are lithium batteries, meaning that their charge efficiency, which represents how much of the actual amperage that is input translates into actual usable energy, is nearly 100%. So the time that it takes to charge can be estimated by the amp hours divided by current coming out of the wall socket. In the US, most wall sockets emit 15 amps, but the charger that comes with the skateboard can only output 1.5 amps. So the time to charge should be about 3.46 hours. According to both an electric skateboard review site and empirical data, this roughly correct. I am going to go with 3.46 as the final value seeing as the 3.5 figure in the review site was likely rounded. Finding the speed at which the battery discharges is tricky because that depends on my weight, the hill slope, and the speed at which I am riding it. So a better way to look at is would be the range of the skateboard, which is about 18 km. A full charge of 3.46 hours, or 12480 seconds, will yield you 18 km or 18000 meters. So the range you get per charge time is 1.442 m/s. I'm going to change up the units a bit to make this easier, because when I write 1.442m/s it looks like I'm talking about the velocity, so I'm going to use my own unit of 'charge seconds' which refer to seconds the board spends charging. So the final answer is 1.442m/cs. The average human walks 1.4 m/s. However I have short legs and am also carrying a very heavy electric skateboard. So in order to find my walking speed while encumbered by a 7.4 kg board, I timed myself. Lucky for me there are a multitude of walking speed apps on the apple store, and it was easy to determine that while carrying the board I can walk 128 meters in 103 seconds, with a rate of 1.24 meter per second, which seems reasonable. So lets say I have to be somewhere 6000 meters away, but my battery is only 30% full. A 30% full battery can go 5400 meters. So the 5400 meters will take 511.57 seconds. Then, there are 600 meters which I have to walk, which will take 483.87 seconds. So the whole process will take 995.44 seconds. Then lets say instead, I spend 120 seconds charging the battery. That will add 120 x 1.442 = 173.04 meters to the amount the board can go. So, the 5573.04 meters will take 527.96 seconds and the remaining 426.96 meters will take 344.32 seconds. So transportation will take 872.28 seconds, and an extra 120 for charging makes 992.28 seconds. So evidently, the optimal solution for this is, charge until the board is full, it will ultimately save time.

May you be ever victorious in your endeavors.
M.E.W