Car's Max. Fuel-Efficient Speed

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A car's maximum fuel efficiency occurs at speeds of 55-60 mph due to the interplay of various forces affecting performance. Air drag, which increases with the square of velocity, significantly impacts fuel consumption, with power requirements scaling cubically. The engine operates most efficiently at approximately 80% of maximum torque and 35% of redline, aligning well with these speeds. Additionally, tire rolling resistance and other losses contribute to overall efficiency, with automatic transmissions further reducing mpg by about 15%. Understanding these factors helps optimize driving speed for better fuel economy.
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What is the thermodynamical reason that a car's maximum fuel efficiency is for speeds 55-60 mph? (See http://www.mpgforspeed.com/ )
 
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In your link, the maximum fuel efficiency curve shows a nearly flat region between 35 and 55 miles per hour. There are many contributions to the curve.
1) Air drag force is proportional to velocity squared. the power scales as velocity cubed.
Air drag depends on the frontal area of the vehicle, the drag coefficient, and the air temperature (and elevation).
2) The engine is most efficient at about 80% of max torque, and 35% of redline.
3) all other major losses (e.g., tire rolling friction coefficient) are linearly proportional to velocity.
4) For automatic transmissions, subtract 15% from your mpg.
5) If you have an automatic w/ torque converter lockup, use it.
So, derive the equation for air drag.
 

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