Are Electric Vehicles Worth It?

Year after year we feel our wallets tightening as we need to fuel the means to move about freely in our highway centric society. Car companies continue to develop vehicles with better gas mileage, hybrids are more common place, and if you happen to live in certain cities, perhaps you have seen vehicles that don't require gas at all. They are still a novelty to many and in parts of the country are still non-existent. In this post I will endeavor to answer the question to myself and my readers "are electric vehicles worth it?"

Before I begin I would like to establish a couple of parameters:

1) Put aside your biases about gas vs. electric cars. In order for this writing to be effective, math and science must be allowed to speak above politics and cause. As an engineer myself, this principle is fundamental to the success of my work. One can be passionate about a given subject, but the science behind your work must drive it. As such, I will put the equations I use in this post and will draw conclusions as I go. The only structure will be the order in which I address specific issues. I do not consider myself to be "environmentally" savvy or even aware, but I do have a respect for challenging the status quo, competition within a genuinely free market, and finding innovative solutions to complex problems.

2) This is not an advertisement - however, I will focus on Tesla Motors' Model S as I am more familiar with it. If you want to read about the Model S, go to www.teslamotors.com. I will also allude to the Nissan Leaf and the BMW i3.

3) As you read, keep in mind a few simple rules about economics (my dad's rules actually):

• Everything we do is a cost vs. benefit situation - Is it worth buying a new gadget? What would we do with it? Pros and cons, etc. So, when reading the information contained here, bear in mind that the costs and benefits of a transportation solution for you may not be worth it to somebody else - and that is perfectly OK.

• Nothing is free - it isn't free to extract oil from the ground, refine it, then transport it to market any more than it isn't free for us consumers to buy it. Newer technologies obviously aren't free, or even cheap. Though EV's don't use gas, you still have to pay for the electricity to power it, which isn't free to produce either.

• Profit is good - I may be stepping on a few toes here, but consider this: a new and innovative technology cannot continue to expand, reach more people, or meet market demand unless the producer is making enough money to justify that expansion. Even Elon Musk himself (Tesla's CEO) has said that he can't mass produce the car he wants everybody to have until he has enough capital to do so. Proof is in the link at the bottom of this page.

• Everything is finite - there is no such thing as unlimited resources. Whether oil lasts 10 years, 100, or 1000 it is still a finite number. What happens when a river can no longer supply the means to power a dam? Even the Sun will fade!

• Politicizing will not impact any of the above - if a company builds an innovative, marketable (in demand), and affordable product, people will buy it. How does a company project itself? The market is what makes our economy tick. Putting on the screws politically won't change what the market is willing to do for a company or a product that people want or performs in a way that grabs people's attention. 

The first question that should be answered is defining "worth." Worth is a largely subjective term, but for a vehicle owner I would surmise the biggest points considered when buying a car are:

• Efficiency - can it do what you want it to (work) and take you where you want to go using resources you deem adequate. (Energy (fuel) and time).
• Cost to buy and use the vehicle in question

Efficiency:

Efficiency can be defined as how much energy is expended to do a piece of work when compared to another process doing the same task. If a Process A uses less energy moving an object from Point A to Point B than Process B in the same amount of time, Process A is deemed to be more efficient. The unit used to define energy mathematically is the Joule (J).

Physics 101: Energy and matter cannot be created or destroyed, only converted from one form to another. The net energy between two processes working on the same system always equals zero. This is called "conservation of energy."

Energy is stored in gasoline as chemical energy. When you add oxygen and a spark, the chemical energy is released as thermal energy, as hot expanding gasses from combustion does work on the pistons, crankshaft, and wheels, thermal energy is transformed into mechanical energy. Some of this energy is lost due to waste heat in the engine and drag as the vehicle overcomes its own mass, friction, and air resistance. The mechanical energy is transformed into kinetic energy as the car starts moving.

Electric vehicles are not exempt. Energy is stored electrically in the batteries, is drawn by the motor
as demand requires, is transformed into mechanical energy on the wheels, and kinetic energy as the car begins to move. Some electric vehicles allow some of the kinetic energy to be recaptured in the form of "regenerative braking" - ergo, the vehicle's motion turns the motor into a generator when the driver takes their foot off of the accelerator (almost called a gas pedal), recharging the batteries as the vehicle slows. Some call this a "one pedal" system as the regenerative braking mechanism slows the vehicle down and you only need to tap the brakes to bring the vehicle to a halt.

With that out of the way, time for some math:

How much energy is in a gallon of gasoline? According to Google: 132x10^6 Joules or 132 Mega Joules (MJ).

MJ = J/1,000,000

For comparison, my vehicle holds 21 gallons of gas which equals 2,772 MJ of available energy.

Many vehicles hold from 9 gal - 25 gal of gas, which translates to 1,188 MJ - 3,300 MJ

Ok - what about electric vehicles? The Tesla Model S holds either 60 or 85 Kilowatt Hours (kWh) of electrical charge. Converting kWh to Joules, you get:

60 kWH = 216 MJ and 85 kWH = 306 MJ

The equation for the conversion of units where E = Energy is: E(J) = 3,600,000 * E(kWH)

Raw energy isn't the whole story, what about range? You need to be able to go the same distance as something else using less energy to claim more efficiency. Lets do a little more math:

My vehicle gets an average 20 miles per gallon. If I use every drop of gas (21 gal), I get a total range of 420 miles. If I assume no loss of energy (not possible) I would use 2772 MJ of energy as described above. So, how much energy does a Tesla Model S use over distance?

Using the range estimator on Tesla's website, I achieved an average of 250 miles per charge on the 85 kWh battery. To travel 420 miles, I need the following:

(((420 miles - 250 miles) / 250 miles per charge) * 85 kWh) + 85 kWh = 143 kWh

(((total distance - expected range per charge) / expected range per charge) * energy available) + energy in one charge

143 kWh = 514.8 MJ used over 420 miles

In conclusion 515 MJ < 2772 MJ - so energy efficiency is a definite yes. (Assuming ideal conditions
and no waste; climbing hills, driving at a higher speed, even using too much heat or A/C can considerably increase the amount of energy used by a Tesla, but even if I needed a 2nd or 3rd charge, I would still be well below the optimum energy consumed by my current vehicle).

Another component in the efficiency equation is time. The full story is: can you go the same distance, using less stuff, in less time. Things get a little fuzzier and more subjective as I'll explain.

Change in distance / change in time is what we call velocity or speed. Ideally we would like to get to our destination as quickly as possible. That doesn't just mean how fast you are going on the road, but how much time is spent refueling.

In the case of electric cars, if you are merely driving around town within the vehicle's range, the vehicle can be recharged when not in use at home or at a charging station like any electronic device can. The caveat being you need a circuit with adequate capability to charge the car. Think of an electrical circuit like a faucet (Tesla uses this analogy) -  you need:

• Voltage (a differential - or capacity to hold charge/energy - size of the pipe) 
• Amperage (a measure of the 'flow of stuff' through the pipe). 

The larger your voltage, the more Amps you can support on the circuit. The more amperage you have, the faster the vehicle can be charged.

Your charge (kW) is how much stuff you have. A standard 110 volt outlet doesn't have the capacity to charge the car in an adequate amount of time (though you could use a standard outlet if you really wanted to), it is recommended to have a 240 Volt circuit capable of handling 40 Amps.


The equations are set up like this: Power (W) = Voltage (V) * Current (A)
Energy (kWh) = (Power (W) * time (hr)) / 1000

Doing the Math: 240V * 40A = 9600W, then 85 kWh = (9600W * 8.85 hr) / 1000
(you are solving for the time variable in this case)

So you can fully charge an 85 kWh battery overnight. Most people won't use that much charge in a day so 8.85 hours is the max time required. Tesla also has a "dual charging" system that allows the battery to be charged at 80 amps if the circuit can handle that much current. (The charger converts the Alternating Current (AC) from the wall to Direct Current (DC) the battery uses.) If you do the math, the time required to charge the car to full drops to 4.43 hours. The Nissan Leaf uses a 24 kWh battery and the BMW i3 uses a 22 kWh battery on the same type of circuit.

In summary, light to moderate driving on a day to day basis without driving beyond the vehicle's range can result in the car being charged from home without the need to visit any gas stations, thereby saving time. You could also conceivably charge at work or at other locations that support charging if the infrastructure is in place.

On the other side is extended road trips. The maximum range of Tesla's best car is 250-300 miles. The circuit I described above dramatically increases the time required to get from point A to B if your charge is depleted, which really becomes a problem for cars like the Nissan Leaf which have a
maximum range of 85 miles.

A common road trip I take is 580 miles in length one way. Maximizing my vehicle's range, I require one complete tank of gas (21 gal) plus 8 extra gallons.

Refresh: max range: 420 miles, average mpg: 20
580 (total distance) - 420 (expected range) = 160 miles; 160 miles left / 20 mpg = 8 gal

Along the way I usually stop for one 30 minute meal and one 10 minute fill up. Adding driving time (~9 hrs @ posted speed limits), it is about 9.5 - 9.75 hrs to my destination.

In Tesla's best vehicle, I require 2 complete charges to get to my destination. Using the model above in a dual charge setting (assuming such circuits are available), it would take 8.85 hours in charge time alone to cover that much distance. It isn't efficient, but neither is it the whole story.

Tesla is developing what are called "Superchargers" along major interstates in areas with shopping, lodging, and food to quickly charge vehicles with Supercharging enabled. According to Tesla's website, a Supercharger can deliver 170 miles of range per 30 minutes of charge time. (Roughly 45 minutes for a full 85 kWh charge). This system bypasses the AC chargers and drops Direct Current directly into the battery pack.

charge time = number of charges * time per charge
charge time = (580 miles traveled / 250 miles expected range) * (250 miles range / 340 miles of range per hour)

charge time = 1.7 hours
total time = 1.7 + 9 hours

Added difficulty is incurred if you are driving off of major interstates. I can reach most areas I would frequent in my region on one charge or less, but another of my favorite spots would require a 9 hr charging stop because there are no Superchargers in range.

In conclusion efficiency based on time is dependent on what you do with your vehicle, where you are, and how much you value your time. A lot of electric vehicle infrastructure exists on the west coast and other major metropolitan areas and Tesla is planning to place Superchargers such that the entire continental US has range coverage. Tesla will also introduce a "battery swap" which exchanges your depleted battery for a full one and takes half the time to replace as filling a 21 gallon gas vehicle. This service to my knowledge is not in place yet, nor do I know if it will cost anything.

If you mainly drive in the city and have an adequate circuit, you can recharge overnight and never waste any time "filling your tank." Much of the central US does not currently have a lot of EV infrastructure  and travel over distance is difficult with current economy model electric vehicles like the Leaf. While you can drive through many parts of the US, Canada, and Europe on the Supercharger network, you may have to get creative when driving off the beaten path. I think this will improve as more infrastructure is introduced, but as it stands, I give efficiency over time a rating of: "it depends."

Cost:

The other major variable in determining a car's worth is how much it costs. I am going to divide cost into two parts: cost to own, and cost to operate. At the end of this analysis, I am going to project these two cost brackets over time to see how much a person pays for their vehicle. 

Cost to own includes: 

• Total amount paid to purchase the vehicle
• down payments
• taxes
• fees
• monthly loan payments, including interest
• In home charging infrastructure if applicable

Cost to operate includes:

• Cost of fuel
• Maintenance costs
• Yearly tab/registration fees
• Insurance payments

The Tesla Model S has a price tag that is comparable to luxury sedans. Their 60 kWh vehicle starts at ~$70,000 and the 85 kWh version is around $80,000. The short range Nissan Leaf (~80 miles of range) has a price tag comparable to many new compact vehicles.

Tesla intends to develop an economy car that costs ~$35,000 called the Model 3, but the vehicle won't be on the market for several years at least. The 3 is rumored to have a range similar to the Model S. If that is indeed the case, many middle class urban consumers will probably jump at the opportunity.

I spend anywhere from $70 - $82 for a full tank of gas (gas prices fluctuate from $3.30 - $3.90 a gallon) and drive about 12k - 15k miles per year. Assuming my overall driving pattern is average and no upward trend in gas prices, I will spend ~$2430 in gas per year.

(21 gal tank * $3.60 per gallon (avg)) * (13,500 miles driven per year / 420 miles of range) =  $2430

The cost to operate an electric vehicle is incorporated into your power bill. In my area, electricity is dirt cheap, around 9 cents per kWh.

To rehash what was stated above, the Model S has: 200 - 250 miles of range and a 60 kWh or 85 kWh charge. My estimations assume total mileage over the course of a year and an an empty to full charge. Other EV vehicles like the BMW i3 and Nissan Leaf have 22 - 24 kWh batteries.

The cost per full charge = 85 kWh * $.09 = $7.65 per charge
The 60 kWh battery would cost -  60 kWh * $.09 = $5.40 per charge

Over the course of the year, assuming averages are the same, the cost to drive is as follows:

(13,500 miles driven / 250 miles per charge) * $7.65 per charge = $413 per year
(13,500 miles driven / 200 miles per charge) * $5.40 per charge = $364 per year

These figures do not factor in possible uses of the Supercharger network (free for Tesla owners), costs incurred from using public charging stations, or other sites with compatible charging equipment.

The savings in fueling an electric vehicle vs. gas is pretty obvious. But adding insurance, car tabs, and vehicle payments easily doubles what I pay for all of the above plus maintenance on my current vehicle. In fact, driving my current vehicle for 15+ years would only match what I expect to pay for a Model S (85 kWh battery) over the same time period. A graph showing this trend in 6 month intervals is below.



Bear in mind, the comparison is for my vehicle and my driving habits. If you drive a luxury sedan, the cost savings could be much more significant.

I still have many questions about how much value an electric vehicle really has:

• If electric vehicles become more mainstream, governments will not be thrilled over the loss of gas tax revenue. Government always wants a piece of the pie so over time, cost of electricity could go up, as could gas taxes, car tabs, or even a "per mile road use tax" could be introduced. I was told that a "road use fee" is required when paying for tabs in my home state.

• How stable are lithium ion battery systems? There have been instances of high energy lithium ion batteries catching fire. The most well known examples are the Boeing 787 battery and the Tesla Model S. I was told that in the Model S' case, fires only occurred after a crash with debris puncturing the battery pack. I was told by a Tesla employee that Elon Musk himself (Tesla's CEO) tested their fix by driving the car over cinder blocks. I understand that to mean that he stands by the quality of the system he is producing. (The guy means business, just an FYI).

• How would you target drivers that live in condos or apartments? In bigger cities, condo and apartment complexes will probably start to introduce charging stations, but in the suburbs, I imagine development will be slow. An EV driver will have to devise a clever means of keeping their vehicles charged. Some may be able to charge at work, others at public charging stations, or even using Superchargers on a regular basis if their area has them. The trick is finding ways to charge the vehicle while not wasting your own time.

• Are electric vehicles really good for the environment? Batteries use highly reactive compounds and many parts of the US still generate power by way of coal or other fossil fuels. The number of coal fired power plants continues to drop, but that power has to come from somewhere. Some individuals use solar systems to charge their vehicles, but such systems are expensive and would take a very long time to match the amount of money spent using the regular power grid. The math above has already shown that the best EVs use far less energy over distance than many gasoline vehicles so I would conclude that they use far less physical material in generating the power they need. In fact, doing some very simple math from above:

One gallon of gasoline = 132 MJ 

1 85 kWh charge = 306 MJ

Energy over 420 miles = 514.8 MJ

So, one 85 kWh charge on the Model S is equivalent to about 2.5 gallons of gasoline and energy expended over the range of my current vehicle equals 3.9 gallons. So, yes you still have to burn physical material to generate the energy needed (the law of conservation of energy requires it), the math clearly shows that you are using much, much less on Tesla's battery pack then on my 4.0L V6 engine.

 

To answer my original question - are electric vehicles worth it? For my own needs, there are a couple of big questions. Namely the cost of the car and where I can keep it reliably charged. A Model S has range that is acceptable, excellent charging capability on the go, and is a very comfortable way to travel. Other vehicles currently on the market require a driver to stay within 40-50 miles of their home charging station, which for me wouldn't work particularly well. Each person's requirements and expectations are different, but whatever you decide, don't let myth and urban legend drive your decision. (like Tesla cars spontaneously combusting due to bad batteries).

That is not to say I don't enjoy working on my current vehicle - a Tacoma pickup. It is reliable, acceptable gas mileage for a truck in its class, maintenance isn't a hassle, and gets me off the beaten path. However, the idea of driving cross country without paying a penny for fuel in a very comfortable, fast, eye candy type vehicle is quite attractive. 

In my next entry, I will go into more technical detail about the Model S and other electric vehicles I have had the opportunity to test drive. (A quick preview: it was a LOT of fun!)

If you want to read more about Elon Musk's plan, go here: Master Plan