# How to calculate power required by vehicles

1. Jan 27, 2010

### likephysics

I am trying to compare electric power vs gas power.
How do you calculate the power required by gas vehicles, say to go 50miles at constant speed.

2. Jan 27, 2010

### physixlover

insufficient data.

3. Jan 27, 2010

### quantumdoodle

yes. we need the mass of the car. the friction index, fuel efficiency and all that other stuff and may be the cost of the two type of fuels? r u trying to do some sort of reserch project?

4. Jan 28, 2010

### Lsos

Speed is the most important part you missed here. Any discussion of power needs a mention of speed.

For example, depending on how fast it's going, a car might need 25 watts or it might need 10,000 horsepower.

5. Jan 28, 2010

### likephysics

Quantum, not for a project. Just curiosity.
Lets say the car is Honda civic. Lets assume its a 2000lbs, fuel efficiency is 30MPG.
Can we ignore the friction index?
How much power would be required to go 100miles?

6. Jan 28, 2010

### conway

At some point air resistance dominates rolling friction. That's because it is quadratic with velocity. A quick measure of air resistance is given by the Bernoulli pressure 1/2*(rho)*(v^2). For 40 m/sec this gives approx 1000 N/m^2. Take this over the cross section of the vehicle (approx 1 sq meter) at the velocity in question and you get a power of 40 kW or about 50 horsepower.

Streamlining helps only up to a point. That's because the friction of sliding sideways through the air eventually equals the amount of friction of butting headlong into the air. This point occurs for a cylinder approx 40 times its diameter in length. In the above example, then for a cylindrical car 40 meters long and 1 meter in diameter, you would have 100 horsepower consisting of 50 horsepower butt-end friction and 50 horsepower irreducible sliding friction.

7. Jan 28, 2010

### Lsos

You can't ignore friction, becase that's the main reason a car burns gas in the first place. If there was no friction, you can just get it up to speed, turn off the engine, and coast forever or until you get to your destination. Power required = 0.

And again, for a proper discussion of power, you need to know the speed. conway even had to make one up to attempt to solve the problem. But it can vary anywhere between 0 to millions of horsepower.

Perhaps what you're asking about is energy required. If that's the case, you almost answered your own question when you said "fuel efficiency is 30mpg."
Simple math tells us that at 30mpg, we would consume 1.66 gallons of fuel in 50 miles.
That's 219MJ of energy.
Assuming a car is 25% efficient, it actually uses 55MJ of that energy.
I'll assume an electric motor would be 80% efficient, which means a battery would probably need about 69MJ to go 50 miles under the same conditions.

8. Jan 29, 2010

### likephysics

Thanks everyone.
Can you tell me how you arrived at 219MJ?

9. Jan 29, 2010

### Bob S

Gasoline contains about 44,000 joules per gram, or about 120 MJ per gallon, so 1.66 gallons represents about 200 MJ of energy.

The two biggest kinetic energy power losses are due to air drag and tire rolling friction.

Air drag power loss is See http://en.wikipedia.org/wiki/Drag_(physics)

Pdrag= ½ρ·A·Cp·v3

Where A = frontal area of vehicle, ρ = air density, Cp = drag coefficient, v = velocity.

The other kinetic power loss is due to tire rolling friction see http://en.wikipedia.org/wiki/Rolling_resistance

Ptire = RRC·m·g·v ≈0.01 m·g·v

where RRC= tire rolling resistance coefficient, m= vehicle mass and g = 9.81 m/s2

Bob S

10. Jan 30, 2010

### likephysics

Bob, thanks for the explanation.

11. Jan 30, 2010

### Lsos

I just looked up "gasoline" on wikipedia. It said "132MJ/gallon". I multiplied it by 1.66

12. Jan 30, 2010

### Bob S

This Wiki table shows automotive regular gasoline to be 114,000 BTU per gallon, or 120.3 MJ per gallon, using 1055 MJ per BTU.
http://wapedia.mobi/en/Gasoline_gallon_equivalent [Broken]

This table from Oak Ridge national Laboratory in USA

http://bioenergy.ornl.gov/papers/misc/energy_conv.html [Broken]

under Fossil Fuels states Gasoline: US gallon = 115,000 Btu = 121 MJ = 32 MJ/liter (LHV). HHV = 125,000 Btu/gallon = 132 MJ/gallon = 35 MJ/liter

HHV (higher heat value) is with all energy used, including condensing water vapor after combustion.

LHV (lower heat value) is with steam (water vapor) exhausted after combustion.

Bob S

Last edited by a moderator: May 4, 2017
13. Jan 30, 2010

### Phrak

As you have asked, the numbers favor electic over gasoline. But this is misleading. Electric power, for the most part comes from coal, fuel oil, hydroelectric and other sources.

Conversion of coal, fuel oil, hydroelectric and other sources to charge electric car batteries involves significant energy loss.

There are losses in conversion to electricity. There are power transmission losses. There are losses in converting the voltage of the power mains to the voltage required to charge the batteries. There are incured charging losses in the batteries; it takes more energy to charge the batteries then they acquire.

And in the end, the bottom line is not BTU comparison but cost.

Last edited: Jan 31, 2010
14. Jan 31, 2010

### likephysics

Phrak, I am keeping all this in mind.
Also, extracting gasoline involves loss. I am not sure if its comparable with the electric power conversion loss. Probably would be.
This whole thing started bcoz I got excited about supercapacitors. I saw 120F and got excited. But the energy stored is much less than NiMh battery. Only advantage is instant charging.

15. Jan 31, 2010

### Phrak

Like you I'm very keen on electric vehicles. I'm not sure how this will develop.

The extraction of gasoline from crude costs about 15% energy, if memory serves me. I don't know what pumping and other energy costs are. But, really, what will drive us as the human beings that we are, is the incured cost--our labours, not energy units.

Isn't the energy density of Lithium polymere better than NiMH?

16. Jan 31, 2010

### OmCheeto

If you are comparing gas to electric, it is good to know that gas cars get really bad gas mileage at low speeds.
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Graph of a typical ICE

The graph of a typical electric vehicle would start out at extremely high equivalent mpg's at zero mph and drop according to the graph described by the two equations in Bob_S's post #9.

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Last edited by a moderator: May 4, 2017
17. Jan 31, 2010

### sophiecentaur

To make a fair comparison between the two systems, you would need to introduce regenerative braking. It would be applicable to electric cars or to hybrids. The hybrid could be an optimal solution, so that would make the answer to the original question more complex, in as far as there wouldn't, ideally, be an either / or but a bits of both answer.

18. Jan 31, 2010

### likephysics

The Li-poly battery in your cell phone(3.7V, 1000mAH) has comparable energy as a NiMh used in digital camera(1.2v, 2500mAH).
Li-Po has 13.3KJ
NiMh has 10.8KJ

I remember reading that LiPo cannot be charged at a fast rate(1C). That may not be true.

19. Jan 31, 2010

### uart

Hi likephysics. You dont compare energy density by comparing the total energy of two random batteries. Energy density can refer to either volume energy density (kJ/L) or mass energy density (kJ/kg). For electric vehicles the latter (mass) is usually the most important consideration.

The mass energy density of NiMH is about 250 kJ/kg compared with up to 700 kJ/kg for Li Ion. So Li Ion is quite a long way ahead in this regard. NiMH's main advantage in the past has been that it's more tried and tested, with proven long term reliability in both early EV prototypes and production vehicles alike. LiIon (and it's derivates like Li polymer and Li Iron Phosphate etc) were later comers and so are a bit less tried and tested in this area, though their adoption and reliability in EV application is rapidly progressing.

20. Jan 31, 2010

### OmCheeto

Someone here at the forum pointed out to me that there is development on fast charging LiPo batteries:

Though I'm not sure how they come up with the "six minutes". The battery in my laptop takes hours to charge:

http://www.apple.com/batteries/" [Broken]

I'd pursue your super capacitor idea for now, lest fast charge LiPo's are just vaporware.

Last edited by a moderator: May 4, 2017