Area under the curve explained
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From: Universe.Milkyway.Solarsystem.Earth.NorthAmerica.USA.FL.Tampa
Area under the curve explained
Not certain if I am the only guy still having trouble with following the dyno results. I have seen this mentioned a lot on the mrev v2 threads.
http://www.sportcompactcarweb.com/ed..._technobabble/
an excerpt from the article:
http://www.sportcompactcarweb.com/ed..._technobabble/
an excerpt from the article:
Let's take a step back to see why this is. If you plot anything out on a standard x/y graph (that's Cartesian coordinates, for those of you who like old, stuffy, European sounding names for your graphs), the area under that plot will be the sum of whatever your x-axis is times whatever your y-axis is. That doesn't make any sense at all, does it?
It will, if you look at an example. Say you plot speed on the y-axis and time on the x-axis for a car that is going a constant 1 mile per minute (that's 60 mph) for 5 minutes. Even without a graph, it's pretty simple to figure out how far the car traveled. Speed times time equals distance, so the car traveled five miles. Great.
But guess what? The area under that curve (which happens to be a line, in this case) is exactly the same thing. Since the area under this curve is a rectangle, area simply equals length times width, or speed times time. Amazing. This parity remains even when the curve is a strange shape, so if that same car wandered through traffic making an erratic speed vs. time curve, the area under that curve would still be the distance traveled.
OK, so what? Let's look at something a little more exciting than wandering through traffic. How about accelerating? Acceleration multiplied by time gives you speed, so on a chart of acceleration vs. time, the area under the curve will tell you the final speed. Now here's something we can brag about. All this rambling about charts and graphs starts getting relevant when you remember that acceleration is directly proportional to force, and force is simply what torque becomes when your drive wheels hit the road. So, torque vs. time, along with a few constants like gear ratio, tire size and vehicle weight, will give you speed. Ah, ha! Now you see why the area under the torque curve is the most important of all.
This explains why the 150 hp from Volkswagen's turbocharged, five-valve 1.8T seems so much more powerful than the 150 hp from a Neon. The torque curve of the Volkswagen is tall, wide and of bountiful area.
Of course, it should be noted that torque vs. rpm, as you would get off a dyno chart, is not the same as torque vs. time. Because the car will be going faster at high rpm, the engine will spend less time around 7000 rpm than it did, say, around 3000 rpm. And, of course, to get any truly useful data, you need to look at the force at the contact patch after the engine's torque has been multiplied by the various gear ratios and divided by the radius of the wheel and tire. The area under the curve argument is still good for general comparisons, however, and is most often useful when comparing various modifications to the same car, in which case all the questions about rpm vs. time, gearing and tire size become pretty much irrelevant.
It will, if you look at an example. Say you plot speed on the y-axis and time on the x-axis for a car that is going a constant 1 mile per minute (that's 60 mph) for 5 minutes. Even without a graph, it's pretty simple to figure out how far the car traveled. Speed times time equals distance, so the car traveled five miles. Great.
But guess what? The area under that curve (which happens to be a line, in this case) is exactly the same thing. Since the area under this curve is a rectangle, area simply equals length times width, or speed times time. Amazing. This parity remains even when the curve is a strange shape, so if that same car wandered through traffic making an erratic speed vs. time curve, the area under that curve would still be the distance traveled.
OK, so what? Let's look at something a little more exciting than wandering through traffic. How about accelerating? Acceleration multiplied by time gives you speed, so on a chart of acceleration vs. time, the area under the curve will tell you the final speed. Now here's something we can brag about. All this rambling about charts and graphs starts getting relevant when you remember that acceleration is directly proportional to force, and force is simply what torque becomes when your drive wheels hit the road. So, torque vs. time, along with a few constants like gear ratio, tire size and vehicle weight, will give you speed. Ah, ha! Now you see why the area under the torque curve is the most important of all.
This explains why the 150 hp from Volkswagen's turbocharged, five-valve 1.8T seems so much more powerful than the 150 hp from a Neon. The torque curve of the Volkswagen is tall, wide and of bountiful area.
Of course, it should be noted that torque vs. rpm, as you would get off a dyno chart, is not the same as torque vs. time. Because the car will be going faster at high rpm, the engine will spend less time around 7000 rpm than it did, say, around 3000 rpm. And, of course, to get any truly useful data, you need to look at the force at the contact patch after the engine's torque has been multiplied by the various gear ratios and divided by the radius of the wheel and tire. The area under the curve argument is still good for general comparisons, however, and is most often useful when comparing various modifications to the same car, in which case all the questions about rpm vs. time, gearing and tire size become pretty much irrelevant.
Last edited by Foo_G; May 12, 2006 at 11:35 AM.
Yep, area under the curve is really what dictates how a car is going to perform, especially in a 1/4 mile race. Area under the curve is also why the 260-280hp G35/350Z 6MTs post identical ET/MPH as the 298-300hp G35/350Z 6MTs.
People need to realize that peak numbers are bascially meaningless. It's the shape of the curve that counts. People get so excited to see a mod making an additional 10whp, but in reality the gain only occurs for 300-500rpms over the upper spectrum of the rpm band. Sorry guys, the car will be no quicker in 0-60 or the 1/4 mile. More power is there, but it's really not useful. Now if the entire powerband was elevated 10whp, then yes the car will be quicker.
People love to say torque wins races. This is somewhat true because HP is simply derived from torque. However, what really wins races is a fat and long powerband.
A 700whp single-turbo Supra's have tiny little powerbands. They operate like a light switch, power is either on or off. A 500whp twin turbo Supra has a much fatter and more useable powerband and when you calculate the average power for the powerband, it would shock you to see the lower-powered Supra actually has more power under the curve therefore will often out ET/MPH far more powerful Supras. Like the saying goes, what does an 800whp Supra and a 400whp Supra have in common? They both run 12s.
People need to realize that peak numbers are bascially meaningless. It's the shape of the curve that counts. People get so excited to see a mod making an additional 10whp, but in reality the gain only occurs for 300-500rpms over the upper spectrum of the rpm band. Sorry guys, the car will be no quicker in 0-60 or the 1/4 mile. More power is there, but it's really not useful. Now if the entire powerband was elevated 10whp, then yes the car will be quicker.
People love to say torque wins races. This is somewhat true because HP is simply derived from torque. However, what really wins races is a fat and long powerband.
A 700whp single-turbo Supra's have tiny little powerbands. They operate like a light switch, power is either on or off. A 500whp twin turbo Supra has a much fatter and more useable powerband and when you calculate the average power for the powerband, it would shock you to see the lower-powered Supra actually has more power under the curve therefore will often out ET/MPH far more powerful Supras. Like the saying goes, what does an 800whp Supra and a 400whp Supra have in common? They both run 12s.
Joined: Aug 2005
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From: Universe.Milkyway.Solarsystem.Earth.NorthAmerica.USA.FL.Tampa
Fun you mention supras my neighbor has one and is building to 1000HP and has been a bit puzzld why his numbes are really improving. I think he is in the 800 to 850 HP range now and his time slips have not improved that much over time.
I understood the area under the curve but I really need to see the comparo to peak. I had a little trouble departing from the gavity of peak HP.
Thanks for the follow up to the article I think I am in a safe orbit now.
I understood the area under the curve but I really need to see the comparo to peak. I had a little trouble departing from the gavity of peak HP.
Thanks for the follow up to the article I think I am in a safe orbit now.
Originally Posted by DaveB
Yep, area under the curve is really what dictates how a car is going to perform, especially in a 1/4 mile race. Area under the curve is also why the 260-280hp G35/350Z 6MTs post identical ET/MPH as the 298-300hp G35/350Z 6MTs.
People need to realize that peak numbers are bascially meaningless. It's the shape of the curve that counts. People get so excited to see a mod making an additional 10whp, but in reality the gain only occurs for 300-500rpms over the upper spectrum of the rpm band. Sorry guys, the car will be no quicker in 0-60 or the 1/4 mile. More power is there, but it's really not useful. Now if the entire powerband was elevated 10whp, then yes the car will be quicker.
People love to say torque wins races. This is somewhat true because HP is simply derived from torque. However, what really wins races is a fat and long powerband.
A 700whp single-turbo Supra's have tiny little powerbands. They operate like a light switch, power is either on or off. A 500whp twin turbo Supra has a much fatter and more useable powerband and when you calculate the average power for the powerband, it would shock you to see the lower-powered Supra actually has more power under the curve therefore will often out ET/MPH far more powerful Supras. Like the saying goes, what does an 800whp Supra and a 400whp Supra have in common? They both run 12s.
People need to realize that peak numbers are bascially meaningless. It's the shape of the curve that counts. People get so excited to see a mod making an additional 10whp, but in reality the gain only occurs for 300-500rpms over the upper spectrum of the rpm band. Sorry guys, the car will be no quicker in 0-60 or the 1/4 mile. More power is there, but it's really not useful. Now if the entire powerband was elevated 10whp, then yes the car will be quicker.
People love to say torque wins races. This is somewhat true because HP is simply derived from torque. However, what really wins races is a fat and long powerband.
A 700whp single-turbo Supra's have tiny little powerbands. They operate like a light switch, power is either on or off. A 500whp twin turbo Supra has a much fatter and more useable powerband and when you calculate the average power for the powerband, it would shock you to see the lower-powered Supra actually has more power under the curve therefore will often out ET/MPH far more powerful Supras. Like the saying goes, what does an 800whp Supra and a 400whp Supra have in common? They both run 12s.
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From: Marietta, Georgia
Just as a dyno uses the drum acceleration over 1/100 of a second intervals to calculate the tire to drum torque by measuring the tiny increases in drum speed over the 1/100 of a second.
Obviously this is not real world since the lack of wind resistance and the drum not equalling the cars weight allow the engine to accelerate much much faster but it works to give an approximation of the torque with large correction factors.
Obviously this is not real world since the lack of wind resistance and the drum not equalling the cars weight allow the engine to accelerate much much faster but it works to give an approximation of the torque with large correction factors.
Last edited by Q45tech; May 13, 2006 at 07:11 AM.
I don't like how the SCC article can be confusing for someone who is not familar with basic physics and calculus (integration). There's a lot that can be said on a topic like this to clarify/better explain the physics of car stuffs, but i'll focus on the most basic of it, force/acceleration.
Distance (or displacement), Speed (or velocity), and Acceleration are all inter-related. they measure how far a car goes, the speed that it is going at a given moment, and how fast it can change speeds.
Distance or displacement is governed by speed and a duration of time (i.e. 60mph for 1 hour = 60 miles)
Speed is governed by acceleration and a duration of time (i.e. accelerate at some rate for 10 seconds and you will be at X mph)
Acceleration is governed by the amount of force put out or applied, measured as torque in ft-lbs.
You measure an engine's output of force, measured in torque.
On a dyno, you measure a car's output and plot it on a graph with Torque(ft-lb) on the Y axis, and engine speed (rpm) on the X axis.
-------
So, from this torque graph, you can calculate a horsepower graph, but the horsepower graph can be misleading if improperly interpreted. What is most important is the amount of force/torque put out by the engine, in the engine range YOU NEED it to operate in (i.e. 2000-4000rpm daily driver, or 4000-6000rpm spirited driver, or 5000-7000rpm race only, are all examples). To simplify things, lets stick to only a torque curve.
The higher your line graph of torque output, the more it is putting out, and thus the larger area you will have under the curve on the graph. Since your engine is always moving along the torque curve as the engine speed (rpm) changes (as you speed up or shift to a higher gear), one should be concerned with the power output over the a certain range of the rpm band you are analyzing, giving you a start and end point to analyze... which gives you 4 boundaries to calculate the area of the figure made (its not a pretty rectangle though). This area under the curve can be used to simplify and allow visual comparisons between two different situations (say pre/post applying a mod), for the boundaries you set off to analyze.
It isnt enough to simply say "mod X made 10 more ft-lb (at its peak)" because you car will only sit at that peak torque rpm speed for a brief moment. It is also important to look at the graph and examine all the changes a mod does, by looking at how the area under the torque curve changed (either up, or down, and in what engine rpm speeds that it changed up/down).
--------
*side note*
One of the most common misconceptions that I have seen with horsepower is that people seem to believe a higher horsepower point on a dyno graph automatically means higher acceleration. This is almost always NOT true. Acceleration will follow the torque curve almost exact (minus losses to friction/air resistance/etc). If the torque dips at some point, which typically is towards the top end for most cars, acceleration will also dip. Horsepower may continue to rise slightly, but the car will accelerate slower than it was at an earlier point of the engine speed, especially compared to the peak torque range.
Example on the G, from many dynos posted, it looks like torque drops off dramatically after 5000-something rpm... but the horsepower figure is still pretty high (mid-200s at the wheels)... but it will not accelerate as fast when you are at 6000rpm vs if you were at 4000something rpm where peak torque hits... despite the horsepower figure being much lower than the mid-200something amount at 6000rpm.
Distance (or displacement), Speed (or velocity), and Acceleration are all inter-related. they measure how far a car goes, the speed that it is going at a given moment, and how fast it can change speeds.
Distance or displacement is governed by speed and a duration of time (i.e. 60mph for 1 hour = 60 miles)
Speed is governed by acceleration and a duration of time (i.e. accelerate at some rate for 10 seconds and you will be at X mph)
Acceleration is governed by the amount of force put out or applied, measured as torque in ft-lbs.
You measure an engine's output of force, measured in torque.
On a dyno, you measure a car's output and plot it on a graph with Torque(ft-lb) on the Y axis, and engine speed (rpm) on the X axis.
-------
So, from this torque graph, you can calculate a horsepower graph, but the horsepower graph can be misleading if improperly interpreted. What is most important is the amount of force/torque put out by the engine, in the engine range YOU NEED it to operate in (i.e. 2000-4000rpm daily driver, or 4000-6000rpm spirited driver, or 5000-7000rpm race only, are all examples). To simplify things, lets stick to only a torque curve.
The higher your line graph of torque output, the more it is putting out, and thus the larger area you will have under the curve on the graph. Since your engine is always moving along the torque curve as the engine speed (rpm) changes (as you speed up or shift to a higher gear), one should be concerned with the power output over the a certain range of the rpm band you are analyzing, giving you a start and end point to analyze... which gives you 4 boundaries to calculate the area of the figure made (its not a pretty rectangle though). This area under the curve can be used to simplify and allow visual comparisons between two different situations (say pre/post applying a mod), for the boundaries you set off to analyze.
It isnt enough to simply say "mod X made 10 more ft-lb (at its peak)" because you car will only sit at that peak torque rpm speed for a brief moment. It is also important to look at the graph and examine all the changes a mod does, by looking at how the area under the torque curve changed (either up, or down, and in what engine rpm speeds that it changed up/down).
--------
*side note*
One of the most common misconceptions that I have seen with horsepower is that people seem to believe a higher horsepower point on a dyno graph automatically means higher acceleration. This is almost always NOT true. Acceleration will follow the torque curve almost exact (minus losses to friction/air resistance/etc). If the torque dips at some point, which typically is towards the top end for most cars, acceleration will also dip. Horsepower may continue to rise slightly, but the car will accelerate slower than it was at an earlier point of the engine speed, especially compared to the peak torque range.
Example on the G, from many dynos posted, it looks like torque drops off dramatically after 5000-something rpm... but the horsepower figure is still pretty high (mid-200s at the wheels)... but it will not accelerate as fast when you are at 6000rpm vs if you were at 4000something rpm where peak torque hits... despite the horsepower figure being much lower than the mid-200something amount at 6000rpm.
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From: Universe.Milkyway.Solarsystem.Earth.NorthAmerica.USA.FL.Tampa
Originally Posted by Q45tech
Just as a dyno uses the drum acceleration over 1/100 of a second intervals to calculate the tire to drum torque by measuring the tiny increases in drum speed over the 1/100 of a second.
Obviously this is not real world since the lack of wind resistance and the drum not equalling the cars weight allow the engine to accelerate much much faster but it works to give an approximation of the torque with large correction factors.
Obviously this is not real world since the lack of wind resistance and the drum not equalling the cars weight allow the engine to accelerate much much faster but it works to give an approximation of the torque with large correction factors.
what is your opinion of road dyno software which access the car via the odbII port. I have the www.autoenginuity.com scantool and it has an application called speed tracer that comes with it.
I would appreciate a third person review of the application if you have the time.
regards,
Noah
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From: Universe.Milkyway.Solarsystem.Earth.NorthAmerica.USA.FL.Tampa
Originally Posted by Bobalude
I don't like how the SCC article can be confusing for someone who is not familar with basic physics and calculus (integration). There's a lot that can be said on a topic like this to clarify/better explain the physics of car stuffs, but i'll focus on the most basic of it, force/acceleration.
Distance (or displacement), Speed (or velocity), and Acceleration are all inter-related. they measure how far a car goes, the speed that it is going at a given moment, and how fast it can change speeds.
Distance or displacement is governed by speed and a duration of time (i.e. 60mph for 1 hour = 60 miles)
Speed is governed by acceleration and a duration of time (i.e. accelerate at some rate for 10 seconds and you will be at X mph)
Acceleration is governed by the amount of force put out or applied, measured as torque in ft-lbs.
You measure an engine's output of force, measured in torque.
On a dyno, you measure a car's output and plot it on a graph with Torque(ft-lb) on the Y axis, and engine speed (rpm) on the X axis.
-------
So, from this torque graph, you can calculate a horsepower graph, but the horsepower graph can be misleading if improperly interpreted. What is most important is the amount of force/torque put out by the engine, in the engine range YOU NEED it to operate in (i.e. 2000-4000rpm daily driver, or 4000-6000rpm spirited driver, or 5000-7000rpm race only, are all examples). To simplify things, lets stick to only a torque curve.
The higher your line graph of torque output, the more it is putting out, and thus the larger area you will have under the curve on the graph. Since your engine is always moving along the torque curve as the engine speed (rpm) changes (as you speed up or shift to a higher gear), one should be concerned with the power output over the a certain range of the rpm band you are analyzing, giving you a start and end point to analyze... which gives you 4 boundaries to calculate the area of the figure made (its not a pretty rectangle though). This area under the curve can be used to simplify and allow visual comparisons between two different situations (say pre/post applying a mod), for the boundaries you set off to analyze.
It isnt enough to simply say "mod X made 10 more ft-lb (at its peak)" because you car will only sit at that peak torque rpm speed for a brief moment. It is also important to look at the graph and examine all the changes a mod does, by looking at how the area under the torque curve changed (either up, or down, and in what engine rpm speeds that it changed up/down).
--------
*side note*
One of the most common misconceptions that I have seen with horsepower is that people seem to believe a higher horsepower point on a dyno graph automatically means higher acceleration. This is almost always NOT true. Acceleration will follow the torque curve almost exact (minus losses to friction/air resistance/etc). If the torque dips at some point, which typically is towards the top end for most cars, acceleration will also dip. Horsepower may continue to rise slightly, but the car will accelerate slower than it was at an earlier point of the engine speed, especially compared to the peak torque range.
Example on the G, from many dynos posted, it looks like torque drops off dramatically after 5000-something rpm... but the horsepower figure is still pretty high (mid-200s at the wheels)... but it will not accelerate as fast when you are at 6000rpm vs if you were at 4000something rpm where peak torque hits... despite the horsepower figure being much lower than the mid-200something amount at 6000rpm.
Distance (or displacement), Speed (or velocity), and Acceleration are all inter-related. they measure how far a car goes, the speed that it is going at a given moment, and how fast it can change speeds.
Distance or displacement is governed by speed and a duration of time (i.e. 60mph for 1 hour = 60 miles)
Speed is governed by acceleration and a duration of time (i.e. accelerate at some rate for 10 seconds and you will be at X mph)
Acceleration is governed by the amount of force put out or applied, measured as torque in ft-lbs.
You measure an engine's output of force, measured in torque.
On a dyno, you measure a car's output and plot it on a graph with Torque(ft-lb) on the Y axis, and engine speed (rpm) on the X axis.
-------
So, from this torque graph, you can calculate a horsepower graph, but the horsepower graph can be misleading if improperly interpreted. What is most important is the amount of force/torque put out by the engine, in the engine range YOU NEED it to operate in (i.e. 2000-4000rpm daily driver, or 4000-6000rpm spirited driver, or 5000-7000rpm race only, are all examples). To simplify things, lets stick to only a torque curve.
The higher your line graph of torque output, the more it is putting out, and thus the larger area you will have under the curve on the graph. Since your engine is always moving along the torque curve as the engine speed (rpm) changes (as you speed up or shift to a higher gear), one should be concerned with the power output over the a certain range of the rpm band you are analyzing, giving you a start and end point to analyze... which gives you 4 boundaries to calculate the area of the figure made (its not a pretty rectangle though). This area under the curve can be used to simplify and allow visual comparisons between two different situations (say pre/post applying a mod), for the boundaries you set off to analyze.
It isnt enough to simply say "mod X made 10 more ft-lb (at its peak)" because you car will only sit at that peak torque rpm speed for a brief moment. It is also important to look at the graph and examine all the changes a mod does, by looking at how the area under the torque curve changed (either up, or down, and in what engine rpm speeds that it changed up/down).
--------
*side note*
One of the most common misconceptions that I have seen with horsepower is that people seem to believe a higher horsepower point on a dyno graph automatically means higher acceleration. This is almost always NOT true. Acceleration will follow the torque curve almost exact (minus losses to friction/air resistance/etc). If the torque dips at some point, which typically is towards the top end for most cars, acceleration will also dip. Horsepower may continue to rise slightly, but the car will accelerate slower than it was at an earlier point of the engine speed, especially compared to the peak torque range.
Example on the G, from many dynos posted, it looks like torque drops off dramatically after 5000-something rpm... but the horsepower figure is still pretty high (mid-200s at the wheels)... but it will not accelerate as fast when you are at 6000rpm vs if you were at 4000something rpm where peak torque hits... despite the horsepower figure being much lower than the mid-200something amount at 6000rpm.
Great info thanks. This stuff is starting to make sense.
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From: Universe.Milkyway.Solarsystem.Earth.NorthAmerica.USA.FL.Tampa
Originally Posted by escobar929
didnt you guys ever take calculus and learn bout the area under the curve 
Got that in algebra I&II and yes I took calc. I do not know how it applies to the cars over all performance. Calculating area is one thing but understand what this means for the car is something completely new to me.
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While doing calculations on torque and HP for physics class one year, I came up with a spreadsheet that calculated 0-60 and 1/4 mile times from dyno charts. I realized that once you factor in shift points, only the top end of the torque/hp curves make a difference. Think of it this way: You are drag racing, and you're in a car that has a peak torque around 5500rpm. So you drive up to say 6500rpm so when you shift, you are around 5000rpm, or pretty close to your peak. You shift like this all the way to 6th. Now, if you have the same car that has the same exact area under the curve, but peaks at say 4k. While in 1st you will be ahead of the other car, but you have to shift earlier to stay in your peak, which means you'll be slower because of your shifts, and because you have to shift more often. If you run up to 6000rpm and shift like the other car, you'll have let the other car catch up in 1st and it will take you in the rest of the gears because you're now out of your powerband for the rest of your gears. While a flat power band would be better than the peak at 4k rpm, it still will have lower power at high rpms, hence losing to the car that has peak at high rpms. This explains why high revving motors high peak motors are still very potent.
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