Quote:
Originally Posted by wungun
Since power is the rate of doing work, four times the work done in half the time requires eight times the power.
Again, this does not add up go me.

Hi wungun,
There are 3 engineering properties to consider.
Force is pushing on something. If you weigh 150 lbs you exert a force against the earth of that many pounds.
If you want to move an object, like a car, you can push on it with a force, say 90 lbs. If you push and jog along at 5 mph you are using 1.2 hp, that's
power. Horsepower is just a conventional way of saying lb*mph (with a conversion factor).
Now to go anywhere you need energy. Burning gasoline releases
energy, in units of horsepower hours. A gallon has about 45 hp hr of energy. Energy and work have the same units.
Imagine a car that only has wind resistance. (OK  that's an airplane.)
At 60 mph the wind resistance force on my imaginary car is about 90 lbs.
If my imaginary car had an engine that was 33% efficient at 15 hp, and it takes 15 hp to go 60 mph Then I could go for an hour on 1 gallon of gas and that would move me 60 miles. That's 60 mpg.
Now if I went 120 mph the
force needed to overcome wind resistance is four times more than at 60 mph. The
power rquired to overcome wind resistance is 8 times higher. The
energy in a gallon of gas is not changed.
So in my imaginary car I also have an engine that can produce 120 hp at 33% efficiency. With that engine I can go 120 mph. With 1 gallon of gas delivering 15 hp hr through the engine, I can go for 7.5 minutes. That's 15 miles. Thats 15 mpg.
So at twice the speed I can travel for 1/8 as much time, and go 1/4th the distance on the same amount of fuel. I've done the same amount of
work, but the engine needed to be 8 times more
powerful. If I wanted to go faster, say 240 mph it would take 960 hp. I'd have just less than a minute of fuel, and I'd move 3.75 miles. (3.75 mpg)
mort