Saturday, February 26, 2011

Spain Lowers Speed Limit


The Spanish government has announced plans to reduce the speed limit on motorways from 120 kilometers per hour to 110 kilometers per hour. The reduced speed is being implemented not for safety reasons but to reduce fuel consumption in this nation that imports all of its oil. The Green Machine applauds the Spanish government for their understanding of physics. The power needed to break through air resistance is proportional to the cube of the velocity at which the vehicle travels. The power to overcome rolling resistance is proportional to the velocity. On the freeway air resistance is the dominant consumer of a vehicle’s engine power. Performing the tedious math one can concur with the Spanish government’s analysis that by invoking the new speed limit on the motorways owners of gasoline powered cars will save 15% and owners of diesel powered cars will save 10% of their historic fuel consumption. The reason why the savings are larger at this reduced speed for gasoline powered cars than diesel cars is that gasoline cars at the lower speed will operate at a more optimum point in their efficiency versus power curve. Diesel engines have almost a constant efficiency rating at most points in their power curve.

Now that the Spaniards have realized the velocity of vehicle affects the fuel consumption perhaps we will deal with the three other major variables that also affect fuel efficiency. The first variable is the mass of the vehicle, the second the frontal area of the vehicle and the third is the coefficient of drag of the vehicle. Most cars and trucks now all look the same as companies have been able to wind tunnel test their vehicles to develop shapes that minimize the coefficient of drag. The Hummer was a design that simply did not even attempt to lessen the coefficient of drag and resembled the shape of a brick. The Toyota Prius and the Honda Insight can easily be mistaken as the other as these two vehicles have striven to minimize their coefficient of drag. Also smaller vehicles will have smaller frontal area and therefore have improved fuel efficiency. Auto companies are striving to minimize the mass of their vehicles. Alas a Prius still is quite heavy and weighs in at over 3,100 pounds. The Toyota Corolla is perhaps 400 pounds lighter than a Prius but as it is not hybrid powered it is not as fuel efficient as the Prius. The small hybrid system on the Prius allows the engine to operate most of the time at close to its peak efficiency on the power curve.

I have opined many times that lithium ion batteries are best suited in transportation for electric bicycles. The reason this is the case is that the bike has a low frontal area, a very low mass, and a low average velocity. The battery therefore only has to provide 200 watts of peak power and 60 watts of average power to keep a cyclist moving with a velocity of 10 miles an hour on a road that is flat. The electric cycle needs about 6 watt hours of energy per mile. By comparison a Tesla Roadster needs about 360 watt hours per mile on a flat road at velocity of 50 miles per hour. On the surface this sounds good. The Tesla only needs 60 times the energy of an electric cycle to travel a mile. The problem is not with the number of watt hours per mile, but with the power in watts needed to accelerate the vehicle. The Tesla needs a battery capable of providing 185,000 watts of peak power. This is 9,000 times as much instantaneous power as the 200 watts of peak power needed for the electric bike. The cost of a battery depends on both the energy stored (watt hours) and the instantaneous power delivered (watts). This is why the Tesla battery costs $55,000 and the bicycle battery only costs $150. If Spain can only get their speed limit down to 16 kilometers per hour (10 miles per hour) we will see a bunch of Spaniards on electric bikes.

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  1. Adding in some super capacitors to the system would reduce the strain on the batteries at acceleration.....

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