Re: How do you figure out the HORESPOWER of a car?

Hi there, Vincent! I’m sorry that I’m a little slow to respond. I’ll try to make my answer as good as I can to try to make it up to you.

The first thing you should know is exactly what horsepower is. There is a great article on howstuffworks.com about horsepower. You can find it at http://auto.howstuffworks.com/horsepower.htm. I would suggest reading that article first, then come back here and continue reading this explanation. Here are a few important things you should remember:

1. Power is the rate at which you do work. When accelerating a car, the “work” is increasing the vehicle’s speed. The rate is just how fast you do it.
2. The horsepower an engine can produce varies with the engine speed. Most often when you hear a number quoted for an engine’s horsepower, it is the maximum horsepower (and they usually give the speed at which that occurs as well; i.e. 300 hp at 5500 rpm).
3. Engine horsepower is just that: power measured at the engine. By the time it gets to the wheels, some losses have occurred, and the total power will be lower. This is often referred to as rear wheel horsepower.

Okay, but you probably don’t have a dynamometer, so you want to try to figure this out on your own using your program. To be really accurate can be very tricky. Let me start with a rough estimate:

If you know how much the vehicle weighs, and how fast it accelerates, then you can get a rough estimate of horsepower. Newton’s Second Law of Motion says that force = mass * acceleration. And power = force * speed. So then power = mass * acceleration * speed. If you’ve ever seen a G-TECH, that is basically what they do. A G-TECH is basically an accelerometer. It can measure acceleration and speed. So if you tell it how much your car weighs, it can estimate horsepower!

Let’s try a real example: let’s say you have a 3500lb car that accelerates from 0-60mph in 6 seconds. First, I have to change some units. Pounds are actually a unit of weight, not mass, so I must divide by gravity to get mass (the English unit of mass is the slug):

1 slug = 32.2 lbs
3500 lbs = 108.7 slugs

1 mph = 1.47 ft/sec
60mph = 88 ft/sec

Power = 108.7 slugs * (88 ft/s) / 6 sec * 88 ft/sec
= 140300 ft-lb / sec
= 255 hp (1 hp = 550 ft-lb/sec)

The next problem is the vehicle mass. The weight of the car alone is not an accurate representation of the total mass that needs to be accelerated. There are many rotating components (tires, driveline, engine, flywheel, transmission, etc.) that all have their own rotational inertia which will affect the acceleration performance. It would take me a long time to explain each of those components. It would also take a lot of work to determine each of their inertia’s. Although, many of them can be estimated. The book “Fundamentals of Vehicle Dynamics” by Thomas Gillespie is a great book for this type of information. Chapter 2 is all about acceleration performance and it gives some good estimates for the masses of the components involved. This is another reason dynamometers are preferred for measuring horsepower: since a dynamometer can measure power without acceleration, there is no need to know the mass of all of the components involved.

The last problem is rear-wheel vs. engine horsepower. There are losses in the driveline due to mechanical and viscous friction. For vehicles with automatic transmissions, there are some significant losses due to the transmission pump and the efficiency of the torque converter. A general rule of thumb is 10-20% loss in the driveline. So whatever you determine for a rear-wheel horsepower, add 10-20% to estimate power at the engine.

I hope this information gets you off to a good start. If you really want to write a good program, I would really suggest getting the book I mentioned above. It’s a common book used at colleges for introductory vehicle dynamics courses, so you may be able to find it at a college library or bookstore. It’s also sold by the Society of Automotive Engineers, so you could buy it at their website if you want. Good luck.