Area Under The Curve

I found a few pretty good write-ups that discuss the "area under the curve". I have added a paragraph at the bottom to show how it relates to the SHARP Mini Late Models however most of it is directly from the articles.

"One of the most common misconceptions about a vehicle is that the car with the higher horsepower will be the faster car. In my early days as an automotive enthusiast (high school), I too, was very guilty of perpetuating this stereotype. As I grew up and started fine tuning my direction in life, I found myself diving deeper and deeper into the world of performance automobiles. As I have spent a lot of time listening and learning from people who are far smarter than I, the one biggest thing that I notice is how little most people still understand about dynamometers. Bench racing still continues in parking lots and Facebook pages everywhere, based on peak numbers that someone claims rather than an understanding of the whole power curve.

When you see the horsepower numbers on an engine, you need to remember that number is just from one point on the power curve of an engine. When you are talking an engine that operates over a broad RPM range, you need to look at the area under the curve.

What do I mean by the area under the curve? It means when you look at the power curve of an engine, it is the area between the horsepower line and the 0 mark of the graph. You could also look at the torque line instead, but if one goes up for a certain point, so does the other. This is because horsepower is torque x RPM/5252.

What got me thinking about all of this was an article I saw about a 400HP 318. That got me to thinking about how the power curve would be different with a 360 vs a 318 at the same power level.

I plugged the specs into an old dyno program I have on my PC, and ended up with 416HP at 6,000 RPM for the 318. Not quite what they got in the article, but close enough for my purposes. And I am sure the numbers are probably off from what I put in, but as long as the program is consistent, that is what matters.

While I did look at the 318 vs 360, I decided to make the differences bigger to make it more obvious and easier to see on a graph.

So first, here is a 416HP 318:

So, not too bad of a power curve, but it definitely likes to rev. The peak numbers are 416HP at 6000 RPM and 389 ft-lbs at 5000.

The next engine was all the same specs, but the displacement increased to 440 cubic inches. The same heads, came intake etc.

Notice the difference. In this case, it made 419HP and 5000 RPM, and 476 lb-ft at 4000 RPM. So the horsepower numbers didn’t change much, just the RPM they were made at. But the torque numbers really jumped. 87 more lb-ft of torque, and 1000 less RPM.

To really make the point, lets look at even more cubic inches.

This time, 528 CI.

A big difference this time. 401HP at 4500 RPM and 533 lb-ft of torque at 3000 RPM.

If you don’t want to think about the area under the curve, look at what the numbers are at street RPMs. Just to make the numbers more obvious, lets look at the torque and HP numbers at 2000 RPM. The 318 is making 281 lb-ft and 107 HP at 2000 RPM. The 440 is making 416 lb-ft and 158 HP. The 528 is making 514 lb-ft and 196 HP at 2000 RPM.

From a racing perspective, there wouldn’t be that much difference between the engines at the track. That is of course assuming all other things were equal. All cars had the same traction, ideal gearing, weighed the same etc. The 528 would have some advantages, because of the greater spread between peak torque and horsepower, but the results would be close between the other two.

However, if you drive them on the street, were they are not operating at peak horsepower, you would see a big difference. The 528 is making more torque from 2000 – 5000 RPM than the 318 makes at its peak. Is it fair to compare two engines that are so different in displacement? Probably not, but it makes it easier to illustrate a point.

In a race engine, you are looking at the power produced in the range the engine will operate in, usually between the torque and horsepower peaks. But the more you can spread those two numbers, the easier the car will be to get the correct gearing, and the more forgiving it will be, it will be less peaky.

On the street, were an engine is often outside the peak numbers, having more power in the power band is a good thing. If you nail the throttle at 2000 RPM on each of the engines, which one will push you back in the seat harder?

I like seeing on Top Gear Jeremy commenting on how a European engineer would get more power out of a large American engine than the Americans do. But then again, he will take a similar power/displacement engine, jam it into a high gear, then go something like 30 – 150 MPH in one gear. That is due to the area under the curve. The ability to push you back in the seat no matter where in the RPM range the engine is.

Sure, a smaller engine that makes the same power is more efficient, but we are talking about fun here, not efficiency. If we wanted efficient, we would be drive a Prius, that doesn’t sound like fun to me.

So to recap, the more power an engine makes over the operating RPM range, the better. That is area under the curve. More power added to the bottom of the RPM range, even if the peak doesn’t change will make a car accelerate faster. Just remember, you need to know the power an engine makes everywhere, not just the peak numbers. An engine with less power and the peak, but more everywhere else will be faster. Just look at the 318 above, versus the 528. Sure, the 528 makes 15 less horsepower at the peak, but how often are you driving at exactly the peak horsepower RPM? And on the street, were you may need power right off idle, there is absolutely no contest."

How does this article relate to the SHARP Mini Late Models? We have recently acquired a dyno and started dyno testing the cars. Notice I said testing not tuning. All cars still operate under one tune. We have been collecting date to look at the “area under the curve”. For us in the circle track world that means looking at the data between lets say 11,000rmp-14900 for us. What you should have deciphered from this article is that HP numbers don't mean anything. When it comes to flat-out performance, the entire area under the curve isn't all that important. And in our situation, you might care more about the area under the curve from 11k to 14k RPMs. What matters most is the area under the curve within the RPM range that you care about, or our race range.

Still, curves and integrals give you a much better idea of the potential. So why don't they use them in discussion? Because the average joe who never took calculus doesn't give a shit. Peak numbers are easier to understand and more enticing.

Another way to express this concept is to talk about average horsepower over a given rev range, say between 2500-3500, which is typically the daily driving range. This is why torque feels fast, and this is what the phrase “power under the curve” means; More time at a higher average HP means more time accelerating at a greater rate.

Power under the curve could be compared to eating well all meals in the week but never really feasting, as opposed to peak power which is feast or famine.

In short we are using our dyno to better understand the various year models and how they perform on the racing surface. Our cars are super competitive and we have done a very good job thus far at balancing the year ranges. Hopefully in the off season we can further investigate the data collected for the betterment of the class. We are not and will not allowing our drivers to part swap looking for any gains. Our cars are built on equality.

One has to notice that we are one of the few classes in the country that is constantly researching and developing ways to level the playing field.

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