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Comment by lucaspiller | Hacker News Reader

I did some tests on a long drive last week, for the Smart Forfour I had this was the fuel consumption. It was all along flat, straight parts of the highway. Reports were based upon the cars own fuel efficiency monitor.

- 135 km/h 7.8l/100km (30 mpg)

- 125 km/h 6.5l/100km (36 mpg)

- 115 km/h 5.4l/100km (43 mpg)

I never realised speed made such a difference!

(Mpg is US gallons)

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The reason why it matters is that air resistance is proportional to the square of your velocity. At high speeds that term dominates.

Due to some physics things that I don't understand, it actually ends up proportional to the cube of your velocity.

source: presentation by Dr. Rizzoni at Center for Automotive Research at OSU

It's actually neither square nor cubed, but you can use those approximations with varying success for different car shapes and Reynolds numbers. There are several different physical effects that together create drag: you have form drag, skin drag, interference drag, and even lift-induced drag (the last one essentially only on sports cars).

Power consumption is proportional to the cube.

Aerodynamic drag i.e. force opposite the direction of travel is proportional to the square of your velocity. Power consumption for steady cruising is equal to drag multiplied by speed. Thus power consumption is proportional to the cube of speed.

Right. And if you're measuring miles per gallon, you're interested in energy consumed per mile traveled, not energy consumed per second. And aerodynamic drag tells you energy consumed per mile traveled thanks to the relationship that energy is force times distance.

A dramatic demonstration of this is the Bugatti Veyron. Between the original version (1,001 hp) and the SuperSport version (1,184 hp) - the top speed only increased from 408 kmh to 431 kmh. So a 183 hp increase in power yields only a 23 kmh increase in top speed - bearing in mind that 183 hp is more than most passenger vehicles have in total.

It gets exponentially harder to push air out of the way the higher the speed gets.

That's

- 84.0 mph

- 77.5 mph

- 71.5 mph

For us in the states.

No, for you in the states it's 70mph ;-)

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