These are my calculations for the lifecycle emissions of the Tesla Roadster, and a few diesel cars for comparison, using data from Tesla Motors (for car efficiency), The U.S. Energy Information Administration, the International Energy Agency, and the U.S. National Renewable Energy Laboratory.

I’ve used the same reference numbers as in my other thread to prevent confusion. Read the spoilers to access calculations and related information.

I provide the low-end and high-end emissions CO2/kWh in order to give an understanding of the possible range and what emission reductions are possible using the current mix of energy sources. I also provide the emissions according to the U.S. Energy Information Administration as they actually are so people know what is actually emitted per kWh.

Quick trivia question: How much of all the emissions in the U.S. come from the production of electricity? SPOILER

So now we know electricity is related to significant GHG emissions, the question arises, “how much GHGs are emitted per kWh and how many kWhs does the Tesla Roadster use per km?”

Starting with Tesla Roaster numbers (**ref6**, **ref7**, Link from Lensman: **ref23**):

80% efficiency battery-to-wheels

70% efficiency plug-to-battery (52.8kWh in ESS / ~75kWh at plug)

110Wh/km/1000 = 0.110kWh/km Roadster (Advert efficiency)

Alternatively, 31kWh/100mi = 0.193kWh/km at the plug for the Roadster (typical EV usage) SPOILER

Or 28kWh/100mi = 0.174kWh/km (Roadster EPA combined-cycle at the plug – this was originally on the front page of Tesla Motors’ website but now has been removed.) SPOILER

0.53km/MJ = 1.89MJ/km Jetta

93.5% efficiency power plant-to-plug in the U.S. (according to the U.S. Energy Information Administration (EIA): **ref4**)

(0.80)*(0.70)*(0.935) = (0.5236)

Or 52% efficiency plant-to-wheels

(0.110kWh/km)/(0.5236) = 0.21008kWh/km plant-to-wheels for the Roadster (advert efficiency)

Alternatively, (0.193kWh/km)/(0.935) = 0.20602kWh/km plant-to-wheels for the Roadster (typical EV usage)

Or, (0.174kWh/km)/(0.935) = 0.186kWh/km plant-to-wheels (Roadster EPA combined-cycle)

Electric generation in the U.S. (EIA: **ref1**)

Coal | 231,857,000kWh |

Petroleum | 30,657,000kWh |

Natural Gas | 173,106,000kWh |

Nuclear (+other) | 54,376,000 + 39,000 = 54,415,000kWh |

Hydro (+pumped) | 72,142,000 + 18,664,000 = 90,806,000kWh |

Other Renewables | 4,066,000kWh |

Total | 584,907,000kWh |

Electricity Lifecycle CO2 Emissions in grams per kWh (International Energy Agency (IEA): **ref20**)

Explanation: SPOILER

Knowing and more accurately accounting for the emissions profiles of the “other,” “other renewables,” and pumped hydro categories would tend to increase the emissions created in producing electricity for the Tesla Roadster off the U.S. grid in terms of these high and low estimations.

Coal | 790 – 1,182 grams CO2 / kWh |

Petroleum | 790 – 1,182 grams CO2 / kWh |

Natural Gas | 389 – 511 grams CO2 / kWh |

Nuclear (+other) | 2 - 59 grams CO2 / kWh |

Hydro (+pumped) | 2 – 48 grams CO2 / kWh |

Other Renewables | 7 – 731 grams CO2 / kWh |

Electricity Lifecycle CO2 Emissions in the U.S. are in the range of:

Calculations: SPOILER

Low-end lifecycle emissions = 470g CO2/kWh

Calculations: SPOILER

High-end lifecycle emissions = 700g CO2/kWh

According to the EIA the U.S. average is 1.35lb. CO2 emissions/kWh (**ref22**):

(1.35lb/kWh)*(453.6g/lb.) = 612.36gCO2/kWh Emissions

If you are tempted to argue with the Energy Information Administration’s calculation of emissions you might be comforted to understand they are well within the range of emissions calculated by the International Energy Agency and about 32 grams different from what we find using the emissions the Fusion Institute of Technology Wisconsin measured in doing a case study of a few specific electric plants.

A 2009 Audi A4 2.0 TDI e diesel gets 51.13 mpg U.S. and puts out 119g CO2/km (**ref16**)

The Jetta gets 50mpg according to Tesla Motors and 122gCO2/km (Link from Lensman: **ref23**, Link from Technopete: **ref24**).

The BMW 320d gets 57.36mpg U.S. and puts out 109gCO2/km (Alerted to this by Trick: **ref25**)

The Volvo S40/V50 DRIVe Start/Stop - 72.4mpg (British and I believe on the EU combined-cycle) diesel people carrier puts out 104gCO2/km (**ref26**).

Lifecycle emissions for diesel were obtained from the U.S. National Renewable Energy Laboratory (**ref19**). The U.S. imports 57% of its oil according to the EIA (**ref27**)

Using 1.0628kg oil to obtain 1kg diesel (calculated by adding the emissions from 1kg refined diesel back minus the oxygen) we obtain the following numbers for 1kg diesel lifecycle CO2 emissions (in grams CO2) SPOILER

:Extraction | 1.0628*((46.6327*0.43)+(79.1874*0.57)) = 69.28 grams CO2 / kg |

Oil transport | 1.0628*((17.8928*0.43)+(76.6231*0.57)) = 54.59 grams CO2 / kg |

Diesel refining | 360.42 grams CO2 / kg |

Diesel transport | 218.26 grams CO2 / kg |

Total | 702.55 grams CO2 / kg |

As we have 38.6 MJ/liter diesel and 0.833kg/liter diesel we can find

(38.6 MJ/L)/(0.833kg/L) = 46.33MJ/kg ***originally I accidentally multiplied instead of dividing; correcting my mistake means diesels produce fewer emissions than I had thought***

(702.55/kg)/(46.33MJ/kg) = 15.16g/MJ

Calculations: SPOILER

1mpg diesel = 0.011017304km/MJ

Calculations: SPOILER

**146gCO2/km lifecycle emissions for the A4 (U.S. EPA combined cycle I think)**

Calculations: SPOILER

**151gCO2/km lifecycle emissions for the Jetta (I think on the EPA combined-cycle, as it was in Tesla’s U.S. Advert)**

Calculations: SPOILER

**133gCO2/km lifecycle emissions for the 320d (on the EU combined-cycle)**

Calculations: SPOILER

**127gCO2/km lifecycle emissions for the Volvo (I think on the EU combined cycle)**

For the Tesla Roadster:

Calculations: SPOILER

= 129gCO2/km EIA Tesla Roadster (Advert) Lifecycle Emissions

Calculations: SPOILER

= 126gCO2/km EIA Tesla Roadster (typical EV) Lifecycle Emissions

Calculations: SPOILER

= 114gCO2/km EIA Tesla Roadster (EPA combined-cycle) Lifecycle Emissions

**Some might argue the EPA numbers should be used. But things change if you listen to ex-Tesla Motors employees. Darryl Siry, Tesla Motor’s former Chief Marketing Officer (CMO) had this to say in May 2009, “ the problem is that the EPA driving cycle numbers systematically overstate what the typical driver is going to see in their daily driving…I would say that as a general rule of thumb, if a company quotes an EPA range, you should apply a factor of 70% to that to get a realistic average range for a full charge”** (

**ref30**).

Taking this into consideration, the EPA emissions for the roadster need to be adjusted as they vary inversely with the energy efficiency (measured in range for EVs or km/MJ).

Doing so, we find:

(88gCO2/km)/(0.7) = 125g CO2/km Low-end Tesla Roadster (adjusted EPA combined-cycle) Lifecycle Emissions

(130gCO2/km)/(0.7) = 186g CO2/km High-end Tesla Roadster (adjusted EPA combined-cycle) Lifecycle Emissions

(114gCO2/km)/(0.7) =

**163g CO2/km EIA Tesla Roadster (adjusted EPA combined-cycle) Lifecycle Emissions**

**That’s right. Using the EPA quoted efficiency the way a former C-level executive from Tesla Motors advises us to, the Tesla Roadster emits 163g CO2/km lifecycle emissions using electricity off the U.S. grid.**

Some would argue the same rule applies to ICEVs like the diesels we used in the above example. But doing some research on that as well we find it is not so. John Voelcker from greencarreports.com says one of VW’s Jettas got 24% higher city mileage and 10% higher highway mileage than reported by the EPA. “*Last July, Volkswagen hired independent tester AMCI to test the Jetta TDI's "real world" mileage on the road. They came back with 38 city / 44 highway--or 24 percent and 10 percent higher respectively*” (**ref31**).

Many diesel and other ICEV drivers also find their mileage to be higher than the EPA numbers. I know before I sold my Honda Accord I usually got between 32 and 38 mpg while the official EPA number was only 28 (I mostly drive in the city). And I use the gas pedal.

Now, did anyone notice what the Tesla Roadster emits compared to the diesels?

............................................................

**Plug-And-Play Numbers**

Unless cited, the data in this section has already been referenced and cited above.

Tesla Roadster efficiencies | |

Advert at wheels efficiency (b) | 110Wh/km/1000 = 0.110kWh/km |

Typical EV* at-plug usage (c) | 31kWh/100mi = 0.193kWh/km |

EPA at-plug usage (d) | 28kWh/100mi = 0.174kWh/km |

Roadster Batter-to-wheels efficiency (e) | 0.80 |

Roadster Plug-to-battery efficiency (f) | 0.70 |

U.S. grid efficiency (g) | 0.935 |

EPA EV error adjustment factor (h) | 0.7 |

*It should be noted “Typical EV,” as used in the above table, refers to Tesla kWh/km using the typical EV plug-to-battery efficiency of 70% and the typical EV battery-to-wheels efficiency of 80% as measured by Tesla Motors itself and resulting in a kWh at-the-plug number measured by Tesla Motors itself. An EV’s kWh/km at-the-wheels may be different than the Roadster’s and, in such a situation, would result in a different kWh at-the-plug usage even if it has the same plug-to-wheels efficiency.

Emissions from the production of electricity | |

U.S. EIA Average grams CO2/kWh (i) | (1.35lb/kWh)*(453.6g/lb.) = 612.36gCO2/kWh |

U.S. kWh from Coal (i_{kCoal}) | 231,857,000kWh |

U.S. kWh from Petroleum (i_{kPetro}) | 30,657,000kWh |

U.S. kWh from Natural Gas (i_{kNG}) | 173,106,000kWh |

U.S. kWh from Nuclear (+other) (i_{kNuke}) | 54,376,000 + 39,000 = 54,415,000kWh |

U.S. kWh from Hydro (+pumped) (i_{kHydro}) | 72,142,000 + 18,664,000 = 90,806,000kWh |

U.S. kWh from Other Renewables (i_{kRen}) | 4,066,000kWh |

IEA Coal avg grams CO2/kWh Low (i_{CoalEmL}) | 790 grams CO2 / kWh |

IEA Coal avg grams CO2/kWh High (i_{CoalEmH}) | 1,182 grams CO2 / kWh |

IEA Petroleum avg grams CO2/kWh Low (i_{PetroEmL}) | 790 grams CO2 / kWh |

IEA Petroleum avg grams CO2/kWh High(i_{PetroEmH}) | 1,182 grams CO2 / kWh |

IEA Natural Gas avg grams CO2/kWh Low (i_{NGEmL}) | 389 grams CO2 / kWh |

IEA Natural Gas avg grams CO2/kWh High (i_{NGEmH}) | 511 grams CO2 / kWh |

IEA Nuclear avg grams CO2/kWh Low (i_{NukeEmL}) | 2 grams CO2 / kWh |

IEA Nuclear avg grams CO2/kWh High (i_{NukeEmH}) | 59 grams CO2 / kWh |

IEA Hydro avg grams CO2/kWh Low (i_{HydroEmL}) | 2 grams CO2 / kWh |

IEA Hydro avg grams CO2/kWh High (i_{HydroEmH}) | 48 grams CO2 / kWh |

IEA Other Renewables avg grams CO2/kWh Low (i_{RenEmL}) | 7 grams CO2 / kWh |

IEA Other Renewables avg grams CO2/kWh High (i_{RenEmH}) | 731 grams CO2 / kWh |

**Derived Variables**

j = i_{kCoal} + i_{kPetro} + i_{kNG} + i_{kNuke} + i_{kHydro} + i_{kRen}

k = either i, k_{L}, or k_{H}

One would use “k_{L}” to determine the lowest possible emissions per kWh electricity using the current mix of sources.

One would use “k_{H}” to determine the highest possible emissions per kWh electricity using the current mix of sources.

One would use “i” to determine the actual emissions per kWh electricity using the current mix of sources.

k_{L} = (i_{kCoal} * i_{CoalEmL}) / j + (i_{kPetro} * i_{PetroEmL}) / j + (i_{kNG} * i_{NGEmL}) / j + (i_{kNuke} * i_{NukeEmL}) / j + (i_{kHydro} * i_{HydroEmL}) / j + (i_{kRen} * i_{RenEmL}) / j

k_{H} = (i_{kCoal} * i_{CoalEmH}) / j + (i_{kPetro} * i_{PetroEmH}) / j + (i_{kNG} * i_{NGEmH}) / j + (i_{kNuke} * i_{NukeEmH}) / j + (i_{kHydro} * i_{HydroEmH}) / j + (i_{kRen} * i_{RenEmH}) / j

Knowing and more accurately accounting for the emissions profiles of the “other,” “other renewables,” and pumped hydro categories would tend to increase the emissions created in producing electricity for the Tesla Roadster off the U.S. grid in terms of these high and low estimations.

a = (either (b /e / f), c, or d)/ g

It should be noted some dispute Tesla’s quoted efficiencies, claiming the Roadster attains higher efficiencies than stated by the Tesla Motors website. Those asserting this ridiculous argument will find a = d/g mutes their ability to complain as the EPA (a third party) is quoting at-the-plug kWhs which makes battery-to-wheels efficiencies unneeded.

For the record, 70% plug-to-battery and 80% battery-to-wheels efficiencies are fairly typical of EVs – meaning the Roadster is a decent representative of what one could expect in plug-to-wheels efficiency (but not necessarily in kWh at-the-wheels/km).

Derived variables | |

U.S. total kWh produced (j) | 584,907,000kWh |

Emissions avg/kWh (k) | either i, k_{L}, or k_{H} |

Lowest IEA Emissions avg/kWh (k_{L}) | 470g CO2/kWh |

Highest IEA Emissions avg/kWh (k_{H}) | 700g CO2/kWh |

Roadster kWh/km at the plant (a) | (either (b / e / f), c, or d)/ g |

In the general case;

a * k = grams CO2/km lifecycle emissions

Adjusting for blown-up EPA or advertised range;

a * k / h = grams CO2/km lifecycle emissions

**Results:**

Advert Emissions EIA average =

((b / e / f) / g) * i = 129gCO2/km

Advert Emissions IEA Low =

((b / e / f) / g) * k_{L} = 99gCO2/km

Advert Emissions IEA High =

((b / e / f) / g) * k_{H} = 147gCO2/km

Typical EV Emission EIA average =

(c / g) * i = 126gCO2/km

Typical EV Emissions IEA Low =

(c / g) * k_{L} = 97gCO2/km

Typical EV Emission IEA High =

(c / g) * k_{H} = 144gCO2/km

EPA combined-cycle Emissions EIA avg =

(d / g) * i = 114gCO2/km
**((d / g) * i) / h = 163g CO2/km**

EPA combined-cycle Emissions IEA Low =

(d / g) * k_{L} = 88gCO2/km

((d / g) * k_{L}) / h = 125g CO2/km

EPA combined-cycle Emissions IEA High =

(d / g) * k_{H} = 130gCO2/km

((d / g) * k_{H}) / h = 186g CO2/km

**For Diesels**

Diesels burn diesel fuel. According to the EPA (**ref34**);

CO2 emissions from a U.S. gallon of diesel being burned = 2,778 grams x 0.99 x (44/12) = 10,084 grams/gallon

Apparently this varies according to undefined parameters. Around 1% of the carbon burned in a diesel vehicle engine does not bond with oxygen, thus the 0.99 factor.

~9,800 grams of CO2 emissions/gallon were used in calculating emissions for the A4 and Jetta. VW may have some sort of process that prevents some of the carbon from bonding with oxygen. This results in around a 2-3g CO2/km reduction in emissions for the A4 and Jetta compared to the norm.

There are also emissions related to the extraction of oil, transportation of oil, refining of oil into diesel, and transportation of diesel.

Adding the emissions (minus oxygen) from refining oil into diesel gives us 1.0628kg oil needed to produce 1kg of diesel.

57% of U.S. oil consumed is imported.

43% thus is domestically produced.

One can then properly interpret the following table:

Extraction | 1.0628*((46.6327*0.43)+(79.1874*0.57)) = 69.28 grams CO2 / kg |

Oil transport | 1.0628*((17.8928*0.43)+(76.6231*0.57)) = 54.59 grams CO2 / kg |

Diesel refining | 360.42 grams CO2 / kg |

Diesel transport | 218.26 grams CO2 / kg |

Total | 702.55 grams CO2 / kg |

There are 3.1529736kg for each gallon of diesel.

3.1529736kg/gallon * 702.55 grams CO2/kg = 2215.12 grams CO2/gallon

So we have 2215.12 grams CO2/ gallon emitted from oil extraction, oil transportation, oil-to-diesel refining, and diesel transportation.

Combining the CO2 emitted in burning diesel in vehicles, 10,084 grams CO2/gallon, with the CO2 emitted from oil extraction, oil transportation, oil-to-diesel refining, and diesel transportation, 2215.12 grams CO2/gallon, and we get 12,299 total grams CO2/gallon of diesel:

10,084 grams CO2/gallon + 2215.12 grams CO2/gallon = 12,299 grams CO2/gallon lifecycle emissions

Knowing there are 1.60934km/mile, we can directly convert miles per U.S. gallon of diesel to grams CO2/km emitted as follows:

(12,299 grams CO2 / U.S. gallon of diesel) / (Miles/ U.S. gallon of diesel) / (1.60934km / mile) = grams CO2/km lifecycle emissions

Alternatively, we can use this formula using 2,215 instead of 12,299 and adding the result to quoted vehicle CO2/km emissions.

For the Volvo we find;

(12,299 grams CO2 / U.S. gallon of diesel) / (60.29 Miles/ U.S. gallon of diesel) / (1.60934km / mile) = 127 grams CO2/km lifecycle emissions

The A4 and Jetta emit 2-3g less per km than the general rule would dictate.

A4 gets 51.13 mpg U.S. and puts out 146g CO2/km lifecycle emissions (ordinary diesel would put out 149).

The Jetta gets 50 mpg U.S. and puts out 151g CO2/km lifecycle emissions (ordinary diesel would put out 153).

The 320D gets 57.36 mpg U.S. and puts out 133g CO2/km lifecycle emissions.

**If we work the formula backwards we find the Tesla Roadster’s 163g CO2/km is the same amount of emissions a diesel getting 46.89 mpg U.S. would emit. So if you average 47 mpg U.S. or more in your diesel vehicle, then your vehicle emits fewer grams of CO2 / km than the Roadster does using electricity off the U.S. grid.**

Last edited Wed, 22 Sep 2010, 1:51am by student

Bill Nye says limits for a dielectric are simply what have been demonstrated to date.

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