Hungry eyes

According to a recent article, there's an interesting wrinkle in the world of driverless cars: Apparently all the computing required to run one uses 2-4kW. As an additional quirk, this usage needs to happen more or less all the time, no matter how slow a car is going. In a typical gas-operated scenario, mileage is largely independent of speed (up to a point where air resistance starts going up a lot), but is heavily affected by starts and stops. Electrics improve upon this by sitting in pure standby while idle and recapturing some of the energy used for acceleration during braking.

The dynamic of a constantly operating energy sink alters mileage computations significantly, especially if it's using 2-4kW (about 3-5hp). I'll use the Nissan Leaf as an example (30 kW-hr battery, 100 mile range). Other electrics fare similarly enough for this analysis in consumption per mile.

We can calculate the loss of range off a full charge due to the computing. I'll use the following shorthand in computations:
S: average speed of travel (in mph)
D: distance traveled (in mi)
U: power utilized by computing (in kW)
C: battery capacity (in kW-hr)
T: time traveled (in hr)
R: maximum range


Full charge = energy used for miles + energy used over time
C = CD/R + UT

And the time spent traveling is:
T = D/S

C = CD/R + UD/S
C = D(C/R + U/S)
D = C / (C/R + U/S)

A semi-urban commute might happen at an average of 20-35mph. This seems counterintuitive because most speed limits are 35 or higher, but consider how often you have to stop at a light, or traffic is backed up. I'll use what I consider common examples, but your mileage may vary.

at 35mph, range is reduced to 72-84 miles.
at 20mph, range is reduced to 60-75 miles.
at 10mph, range is reduced to 43-60 miles.

Here's a table showing what fraction of nominal range is maintained at different speeds and power utilizations:

	U1	U2	U3	U4	U5	U6	U7
Speed	4	3	2	1	0.5	0.3	0.1
75	0.840	0.875	0.913	0.955	0.977	0.986	0.995
70	0.831	0.867	0.908	0.952	0.975	0.985	0.995
65	0.820	0.859	0.901	0.948	0.973	0.984	0.995
60	0.808	0.849	0.894	0.944	0.971	0.982	0.994
55	0.794	0.837	0.885	0.939	0.969	0.981	0.994
50	0.778	0.824	0.875	0.933	0.966	0.979	0.993
45	0.759	0.808	0.863	0.927	0.962	0.977	0.992
40	0.737	0.789	0.849	0.918	0.957	0.974	0.991
35	0.710	0.766	0.831	0.908	0.952	0.970	0.990
30	0.678	0.737	0.808	0.894	0.944	0.966	0.988
25	0.637	0.700	0.778	0.875	0.933	0.959	0.986
20	0.584	0.651	0.737	0.849	0.918	0.949	0.982
15	0.513	0.584	0.678	0.808	0.894	0.933	0.977
10	0.412	0.483	0.584	0.737	0.849	0.903	0.966
5	0.260	0.318	0.412	0.584	0.737	0.824	0.933

Depending on the speed of a commute, the computer can realistically impose a 20% or even higher overhead on range. I've highlighted the chart to show classes of ranges. I've somewhat arbitrarily decided that more than a 20% loss is red, 10-20% loss is orange, 5-10% is yellow, etc. The green category I chose at 2% or less loss because that amounts to less than a mile per gallon at the mileage achieved by current hybrid cars, though full electrics are generally rated around double that (~100mpg equivalent).

Clearly with the current tech this would be a major hit, especially for commuter situations (where the vast majority of driving, especially of shorter range electrics). I've focused on electrics for the moment because it's easier to do the math without converting between gas and electric consumptions. That said, if we use the baseline that current EVs are rated at 100mpg equivalent, it means they are about 2-3 times as efficient at producing miles per unit energy. Perhaps ironically, this means gasoline engines take a proportionally smaller hit from the self-driving computers since the energy used to power the computers is proportionally less than that used by the engine itself. Here's a similar table of a typical hybrid (assume 50mpg):

	U1	U2	U3	U4	U5	U6	U7
Speed	4	3	2	1	0.5	0.3	0.1
75	0.918	0.938	0.957	0.978	0.989	0.993	0.998
70	0.913	0.933	0.955	0.977	0.988	0.993	0.998
65	0.907	0.929	0.951	0.975	0.987	0.992	0.997
60	0.900	0.923	0.947	0.973	0.986	0.992	0.997
55	0.892	0.917	0.943	0.971	0.985	0.991	0.997
50	0.882	0.909	0.938	0.968	0.984	0.990	0.997
45	0.871	0.900	0.931	0.964	0.982	0.989	0.996
40	0.857	0.889	0.923	0.960	0.980	0.988	0.996
35	0.840	0.875	0.913	0.955	0.977	0.986	0.995
30	0.818	0.857	0.900	0.947	0.973	0.984	0.994
25	0.789	0.833	0.882	0.938	0.968	0.980	0.993
20	0.750	0.800	0.857	0.923	0.960	0.976	0.992
15	0.692	0.750	0.818	0.900	0.947	0.968	0.989
10	0.600	0.667	0.750	0.857	0.923	0.952	0.984
5	0.429	0.500	0.600	0.750	0.857	0.909	0.968

Also, ironically, as locomotive efficiency rises, the proportional drag of an always-on system rises. The same table for a 200mpg takes some pretty big hits even for a 100W system:

	U1	U2	U3	U4	U5	U6	U7
Speed	4	3	2	1	0.5	0.3	0.1
75	0.738	0.789	0.849	0.918	0.957	0.974	0.991
70	0.724	0.778	0.840	0.913	0.955	0.972	0.991
65	0.709	0.765	0.830	0.907	0.951	0.970	0.990
60	0.692	0.750	0.818	0.900	0.947	0.968	0.989
55	0.673	0.733	0.805	0.892	0.943	0.965	0.988
50	0.652	0.714	0.789	0.882	0.938	0.962	0.987
45	0.628	0.692	0.771	0.871	0.931	0.957	0.985
40	0.600	0.667	0.750	0.857	0.923	0.952	0.984
35	0.568	0.636	0.724	0.840	0.913	0.946	0.981
30	0.529	0.600	0.692	0.818	0.900	0.938	0.978
25	0.484	0.556	0.652	0.789	0.882	0.926	0.974
20	0.429	0.500	0.600	0.750	0.857	0.909	0.968
15	0.360	0.429	0.529	0.692	0.818	0.882	0.957
10	0.273	0.333	0.429	0.600	0.750	0.833	0.938
5	0.158	0.200	0.273	0.429	0.600	0.714	0.882

However, it's likely that by the time cars are twice as efficient much will have changed about our traffic. It might coincide with entire fleets of driverless cars that can coordinate in real-time and completely avoid traffic jams. Slow speeds may completely disappear.


In the nearer term, the question is whether this 2-4kW consumption is likely to drop significantly. The current systems are, as far as I know, running as software on relatively commodity compute devices. This is necessary because the technology is nascent. Over time, many routines can move to FPGAs or ASICs, which tend to come with gigantic power savings. This white paper suggests an FPGA has nearly an order of magnitude savings over GPUs. There will also be fabrication improvements that drive efficiency per operation downwards; it's not unrealistic to combine those two factors along with other efficiencies and get down to the 100W range in the next 5-10 years. At 100W, it's no worse than a stereo, and its highly optimized driving can probably save that much power compared to a human-operated gas pedal.