Energy needed by a vehicle (Part 2)

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How much energy does a vehicle need – Part two.

Well. If you tuned into part one, you will know there are basically three things that determine the amount of energy a vehicle needs. The mass (or weight) of the vehicle, (which is only important when it is changing speed or direction), friction drag from the drivetrain - predominantly the tires, and aerodynamic drag – how much the air “pushes back”.

We also learned that it does not matter how quickly the vehicle accelerates, at the end of that acceleration it will have used the same amount of energy to get there, and it will contain the same amount of kinetic energy (momentum). We learned the only thing that effects this is the mass of the vehicle.

I want to make a note right here that the above statement is not entirely true. Remember that aerodynamic drag increases at the square of the speed. While at low speeds this is negligible, as the terminal speed goes up we will have to consume an extra amount of energy in order to overcome this drag. I am going to ignore this for now as the math would only get more complex. That  is simply not necessary to understand the concepts, at least for an automobile at highway speeds. A racing vehicle, on the other hand, is another story…

Also, before we begin, I want to define a few terms.

• Energy is the ability to do work. A Unit of energy is defined by a few different terms. For our purposes they can be used interchangeably.


• BTU (British thermal unit) is a unit of energy. 1 BTU is approximately the amount of energy in a kitchen match. BTU is commonly used to describe the energy content of a fuel.
• KWh (Kilowatt-Hour) is likewise a unit of energy. 1 KWh equals 3,414 BTUs.
• Joule – The metric (SI) form. There are 1055 Joules in a BTU, or 3,601,770 Joules in a KWh.


• Work is the conversion of energy from one form to another (IE: Potential to kinetic). It is measured in ergs, foot-pounds, or, yes, the Joule.


• Power is rate at which work is done or energy is converted (More power=faster conversion) It is measured in watts (SI) or horsepower. It can also be measured in BTUs per hour (BTU/h) One horsepower is equal to 746 watts, or 2,546 BTU/h.


• Force is push. You apply force to cause acceleration. It is measured in Newton’s. 1 Newton = 225 lbs of “push”


• Mass – Mass is the amount of “stuff” something has. It is measured in Pounds or grams (Kilograms).


• Weight You might think this is the same as mass. It is NOT. Weight is the force that gravity exerts on a mass. This concept is important! For example, on the moon, your body will still have the same mass (amount of stuff), but your weight will be 1/6 of what it is here. In the absence of gravity, you will not have any weight, but you sill still have the same mass!

OK. Confused? It takes a while, and a bit of study, to understand the different units of measurement, and what the terms mean. Don’t worry. Just understanding the conversion factors is sufficient for this discussion.

Let me go back to the cereal box once more. The box is the “gas tank”. Inside it we have corn flakes. Those flakes are units of energy (Btu’s or KWh). We have a bowl that will be our Mass. We accelerate that mass by filling it with corn flakes (energy). In order to fill it, we do Work by pouring the flakes out of a hole in the box. The size of that hole – how quickly we can do our work, is called power. Each time a new flake goes into the bowl, we have applied a bit of force, in the form of energy. The more flakes we put in the bowl, the larger the result (speed). I hope that helps, but, now I am hungry.

We had previously determined that a 3000 pound vehicle needs approximately 540 BTUs of energy to accelerate to 65 MPH, on a level surface, and disregarding aerodynamic drag.

So, how much does it need to overcome drag? Well, that gets much, much, more complex. I also cannot write the formula in this blog (or, I don’t know how). The amount of aerodynamic drag on a particular vehicle depends on the shape of the vehicle, it’s frontal area, it’s coefficient of drag (how slippery it is), and, of course, the exact speed it is travelling at. The math gets rather complicated, and it is different for every single different design or shape of vehicle. Since we are talking concepts here, and not a specific vehicle, we simply cannot readily figure this one out. So.

Because of that, I will offer a generic number. At 65 MPH, the average car needs about 30 horsepower to overcome drag. Not very accurate, after all, what is average? But, hey, this is concepts.

Let’s apply that to a practical example calculation. 30 hp equals 76,380 BTUs per hour. A gallon of gasoline contains 124,000 BTUs. A modern car converts about 22% of that (or 27,280 BTUs) to useable power at the wheels. So, 89,100/27280 equals 2.7 gallons of gasoline in one hour, or  24 MPG.

Of course, in the real, practical, world, we are more concerned about things like MPG, and the energy needed to travel a mile (or 100 miles) in a real vehicle. I will wrap up this discussion by looking at some real world examples of energy consumption. And, again, the point I want you to take away is that these energy requirements are independent of the means or efficiency of propulsion.  The energy needs are the same.

So, I will diverge from the theoretical discussion, and discuss what these things mean as relates to our real world use of fuels. There is not room for a detailed examination, so I will just throw some numbers out there. Again, understand the concepts!

The actual amount of fuel that is needed will  depend entirely on the efficiency of the power source. A modern Internal Combustion automotive engine is approximately 28% efficient. That means only 28% of the BTUs in the gasoline are actually used to apply force to the vehicle. The rest are wasted as heat. Since that ICE vehicle needs a lot of gears – transmission, differential, there is also a significant loss of energy (due to friction) before the power gets to the wheels. Estimates of these losses are anywhere from 5% to 12%.  That means, even in the best case scenario, only 23% of the BTUs in the gasoline are available to actually power the car. Many estimate this number to be as low as 15% for real world vehicles.

Compare that to an electric vehicle. Electric motors are better than 90% efficient. Since most times the motors are more directly coupled to the wheels, the frictional losses are also less. That means that maybe 85-90% of the energy stored in the batteries is available to power the vehicle. Remember, the vehicle still has the same energy requirements, and we have to put that energy into the batteries in the form of electricity. Electricity that is simply generated elsewhere.

In the world of electric vehicles, since they are very sensitive to energy consumption, the amount of energy they consume is a readily available statistic. The Tesla roadster is a real world 2700 pound car, powered solely by electricity. According to Tesla it uses .217 KWh (740 BTUs) for each mile traveled. The Chevy Volt is a near real world Plug in hybrid that weighs 3500 lbs, and reportedly uses .250 KWh (853 BTUs) per mile.

For a conventional Gasoline powered vehicle, I use my own 2005 Chevy Malibu for an example. It weighs 3700 pounds, and has gotten 24 MPG over it’s life, mostly in-town. A gallon of gasoline contains 124,000 BTU’s. Applying an 18% total efficiency factor (middle of the range) we can calculate that each gallon is contributing 22,320 BTU’s to actually powering the vehicle. That would mean it is using 930 BTUs, or  .272 KWh. per mile.

What we can see here, is that as the weight goes up, the energy requirement also goes up, but not by much. Remember, the only time that weight itself comes into play is when we accelerate. We can also make the assumption (in fact true) that the Chevy Malibu has more aerodynamic and frictional drag than either the Tesla, or the Chevy Volt, which accounts for much of it’s increased need for energy.

I hope you understand from this discussion what affects the amount of energy a vehicle needs. These are basic rules of physics. It does not matter WHERE the vehicle gets it’s energy from, this is the energy it needs to operate. One more time, that is an important distinction. Whether it is a gasoline, diesel, biodiesel, electric, hybrid, hydrogen, or sled dogs, any particular size, shape and weight vehicle needs a certain amount of energy put into it in order to move you and your stuff to Grandma’s house. And, that, I guess, is my point.

Read part one of this article!

Comments

[car donation tax deduction]

Thanks for your informative post. Only problem I can see with electric cars is the lack of fill up stations, and the length of time it takes to juice up the batteries when you do find a station that provides for electric cars.

Thought provoking post,

Thanks

[Myrella]

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