Cruise horsepower

This will be a short one. I cited a web site a couple of posts back that has some very interesting articles on automobile physics. The author uses coefficient of drag, estimates of tire rolling friction, etc. to determine that his Corvette needs about 26 horsepower to cruise the highway at 60 miles per hour.



I can get at this problem from a different point of view. I get about 31.5 miles per gallon at 55 miles per hour. This is using fuel at the rate of 55/31.5 or 1.75 gallons per hour. Those 1.75 gallons contain about 1.75*125,000,000=218,000,000 joules of heat energy in the chemical bonds I release by burning them in my cylinders. About 25% or 54,600,000 joules goes to maintaining my 55 miles per hour, the rest is wasted as heat expelled to the environment (an inevitable consequence of the second law of thermodynamics, i.e., you can't break even).



So I'm using 54,600,000 joules per hour to maintain motion, or 54,600,000/3600=15,200 joules per second, otherwise known as watts. Now a horsepower is 746 watts, so I'm using 15,200/746=20.4 horsepower. Pretty darn close to the web site author's number, especially considering I'm looking at a speed 5 miles per hour lower. I really love it when different approaches to a problem confirm each others' results.



To carry the analysis a little further (at the risk of causing any remaining reader to throw up his or her hands in despair), force X speed = power, thus power/speed=force. So: 55 miles per hour is 24.6 meters per second; 15,200 watts/24.6 meters/second = 618 Newtons (the metric unit of force). 618 Newtons is 139 pounds of force. That's all it takes, applied continuously, to move me down the highway at 55 miles per hour in my Jeep Grand Cherokee Limited. I'm going to take an informal survey. I bet most people think it's a whole lot more.