They state that “time is cash,” which might undoubtedly hold true. However if that’s the case, how do you finest optimize your expenses? Let’s consider your Most vehicles still run on gasoline. It’s not excellent for the environment, however it’s pretty tough to beat the energy density in fuel. The quantity of gas that a car utilizes, nevertheless, depends on the driving speed. If a car simply sits at rest, it utilizes gasoline to run the engine however it doesn’t go anywhere– this is an extremely low fuel performance state. As the car increases speed, it takes less time to travel one mile such that it improves fuel efficiency (in miles per gallon). As the automobile continues to increase speed, there is an air drag force that triggers the engine to work harder and burn more fuel, so that the effectiveness decreases.But how do you get a model for the fuel efficiency of a cars and truck as a function of speed? You might construct something based upon the approximated air drag on the vehicle, or you could simply get a design experimentally. I’m choosing the second method. You can gather data with some kind of gadget that plugs into your OBD( on-board diagnostic) port. These things are pretty remarkable. I have one that provides a lot of great data. Here is a plot of the fuel performance for different speeds for my car together with the average of all users with the very same car.But wait! I can get back at much better information.

Here is the exact same plot for ALL automobiles(that utilize the same OBD) in my region. In this case, I caught the information and packed into plot.ly so that I could fit a function to the data.It’s not ideal, however it looks like I can fit a parabolic function to this information. This provides the following relationship in between effectiveness and speed. Yes, I am using royal units because that’s what the OBD uses.Also, I know– it’s OK, I know. You just gloss over these formulas when I put them in here. Honestly, it’s great. You don’t need to know the values of the fitting specifications. By including them in this post you can see that they in fact exist. As a benefit, if you need to reproduce my design these numbers are going to help.OK, however how does this function work? Based upon this model (this is simply a model), I can discover the fuel performance for any cars and truck speed. Let’s state I have a vehicle taking a trip at 10 mph, according to this it would get 10.22 MPG. At 100 miles per hour, it would get 13.5 MPG– warning: don’t drive at a speed of 100 mph.Finally, there is one more part to this gas cost. If I understand the number of miles(let’s call this d)and the fuel efficiency (F )as well

as the rate of gas(P) per gallon, then I can calculate the expense of driving.Paying for gasoline is just part of the commuting price.Time is Money Let’s state you make 15 dollars per hour. If your commute takes one hour, that is like losing 15

dollars since that’s time you might have been working.

### Yes, I stated”like”losing 15 dollars. You aren’t really losing loan, however just remain with me for now.Oh, maybe you do not earn money by the hour? If you are a salaried employee (or especially if you are self used), that travelling time is still time– it’s still like lost money.

Wait. What if your job is to drive a car? What if you are an Uber driver? I guess this design doesn’t work for that case.Anyway, let’s say that your pay rate is R( in dollars per hour). The amount of money lost depends upon the travelling time– which likewise depends on the range. That puts the overall cost( lost salaries plus fuel)

at: That’s it. We are prepared to look at travelling costs.Optimizing the Speed You are going to have to make some choices here. In particular, you require identify how far you are going to commute and how much you make per hour. You need to understand the price of gas too. As soon as you have those two price quotes, you can enter them in the following

### calculation. When you click the”play “button, it needs to produce a great plot of cost as a function of driving speed. If you want, you can just use my default values so that you do not have to alter the code.Boom. There you have it. Notice that the code likewise prints out the optimum speed and overall cost. Warning: if the ideal speed is greater than the published speed limit, just go the speed limit.If you change the travelling distance, the overall expense modifications. The optimum speed does not change. Why?Create an algebraic expression for commuting expense as a function

of driving speed. Take the derivative of expense with regard to speed to discover the minimum cost. Yes, this is the timeless max-min issue in calculus.

- Do you get the exact same outcome as in the program? If you do not, somebody made a mistake.How high does the price of gas need to get so that somebody making 15 dollars an hour would have an optimal travelling speed of 60 miles per hour? You can resolve this with brute force or you could produce another program.The fuel efficiency function I use has a max efficiency of around 25 MPG. What if you eliminate all the effective cars and simply have trucks and SUVs? Produce a
- new efficiency function and find the brand-new optimal speed.Use a model for the air drag force(I would state it is proportional to the speed squared )and approximate the decline in efficiency when going from 65 miles per hour to 75 miles per hour.
- Does this sort of concur with my performance function?Suppose you make 15 dollars an hour. How does the ideal commuting speed modification with the price of fuel? Make a plot of optimal speed vs. gasoline price.OK, that should be enough homework
- to keep you hectic during your daily commute.