Your calculations show that the energy losses are just as big in an electric car as in a ICE car, when they are not. The ICE car only turn 20 % of the energy in the fuel into power for transmission, AC etc. An electric car turns 75 % of the energy charged into the battery into power for transmission, AC etc.
This means that an electric car will use only 27 % (0,2/0,75) as much energy as a ICE car at the point of use. In reality the numbers will be a lot more even, as it takes about three times as much primary energy to make electricity in a steam plant. Hence an electric car will use 27 %*3= 81 % of the energy an ICE car uses do to the same work.
Let me do an example, without nuclear power to make it really simple.
Let's say you need 100 units of energy to power your ICE cars transmission. The efficiency of the ICE is 20 % and hence you need 500 units of oil (gasoline really, but let's ignore that for now) to to get your 100 units of energy to move your car. 400 units of energy are lost in the process, becoming heat radiating from the engine and doing no good.
The relevant equation is 100=X*0,20, where X is the amount of energy required to get the 100 units output and 0,20 being the efficiency of the car.
100=X*0,20
100/0,20=X*0,20/0,20
100/0,20=X
X=500
Ok, then we have the electric car. It also needs 100 units of energy to be propelled. The efficiency of the electric motor is about 90 % and the efficiency of the battery is about 80 %. Together they have an efficiency of roughly 75 % (0,9*0,8=0,72).
This means that to get 100 units of energy of output you need more than 100 units of input, just like in the ICE case. The relevant equation is:
100=X*0,75
100/0,75=X*0,75/0,75
100/0,75=X
X=133
Here we see the incredible efficiency of the electric motor and the battery compared to the wastefulness of the ICE. But one mustn't look at the electric car in an isolated way but as a part of a system. The power must be made somewhere, and there will be losses in that process.
Ok, to propel the car with 100 units of energy we need 133 units of electricity, but how much primary energy do we need to make the electricity? To make this really simple, let's say we use an oil plant to make the power. The plant has an efficiency of 33 %, that is, only 33 % of the energy content of the oil is turned into electricity while the remaining 67 % are turned into useless heat emitted to the atmosphere.
The relevant equation is:
133=X*0,33
133/0,33=X*0,33/0,33
133/0,33=X
X=404
Where 133 is the amount of electricity needed, 0,33 is the efficency of the power plant and X is the amount primary energy (oil in this case) needed to make the required power.
We can see that the electric car needs 404 units of energy (oil in this case) compared to the 500 units of primary energy (in the form of oil) required by the ICE car.
This means that the electric car only need roughly 80 % of the primary energy of the ICE car (404/500=(81 %)
So what would happen if we stopped using oil for combustion in ICE's and instead used oil for combustion in oil power plants to propel electric cars?
The answer is that the amount of oil needed to propel our cars would fall about 20 % (100 %-81 %= 19 %).
If we look at the graph we see that the amount of petoleum and NGPL today used in transportation is 26,5 quads. 80 % of this is 21,4 quads (26,5*0,80=21,4). This is the amount of primary energy needed to propel the fleet of electric cars. In the example above we used oil power plants to create the power needed, and this consumed 21,4 quads of oil. But obviuosly other sources of electric power could also be used: coal, nuclear, natural gas, biofuels, you name it (if you use anything other than steam plants the calculation will change somewhat).
Today the electric power sector consume 38,2 quads of primary energy to make electricity, as you can see in the graph. Switching to an electric car fleet would increase this number with 21,4 quads to 59,6 quads (38,2+21,4=59,6), or with 56 % ((38,2+21,4)/38,2=+56 %).
Now that was a relly, really pedagogic explanation, wasn't it?
