How can I figure out total area under the curve of a cam lobe?
02-23-2003, 01:29 AM
#1
How can I figure out total area under the curve of a cam lobe? If you can find .006, .050, .200 duration and peak lift, and assuming the lobe follows a shape similair to an easily graphable curve, how can I find the total area under the curve?
Id like to be able to eventually figure out toal area, then break it down into how much area spent from seat to .100, .100-.200 etc
Id like to be able to eventually figure out toal area, then break it down into how much area spent from seat to .100, .100-.200 etc
02-23-2003, 07:14 AM
#2
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Re: How can I figure out total area under the curve of a cam lobe? This is what Cam Doctor does for you, call company who has rights to profile and they should be able to send you this info, or you could send your cam to Thunder Racing and Jason can measure it for you.
02-23-2003, 03:27 PM
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Re: How can I figure out total area under the curve of a cam lobe? Graph it and use trapezoidal estimation to get area under the curve. A cam doctor sheet will give you more data points for a more accurate estimation, and I'd assume it uses trapezoidal estimation as well to come up with the number, just on a much finer scale than your case where you only have 4 datapoints.
02-23-2003, 04:10 PM
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Re: How can I figure out total area under the curve of a cam lobe? </font><blockquote><font size="1" face="Verdana, Helvetica, sans-serif">quote:</font><hr /><font size="2" face="Verdana, Helvetica, sans-serif">Originally posted by jmX:
<strong> Graph it and use trapezoidal estimation to get area under the curve. A cam doctor sheet will give you more data points for a more accurate estimation, and I'd assume it uses trapezoidal estimation as well to come up with the number, just on a much finer scale than your case where you only have 4 datapoints. </strong></font><hr /></blockquote><font size="2" face="Verdana, Helvetica, sans-serif">I think the cam doctor goes in increments of a fraction of a degree, so jmX is right. I would definately not trust a 4 datapoint approximation.
<strong> Graph it and use trapezoidal estimation to get area under the curve. A cam doctor sheet will give you more data points for a more accurate estimation, and I'd assume it uses trapezoidal estimation as well to come up with the number, just on a much finer scale than your case where you only have 4 datapoints. </strong></font><hr /></blockquote><font size="2" face="Verdana, Helvetica, sans-serif">I think the cam doctor goes in increments of a fraction of a degree, so jmX is right. I would definately not trust a 4 datapoint approximation.
02-23-2003, 09:32 PM
#6
Re: How can I figure out total area under the curve of a cam lobe? Just if I wanted to play around with it, are there any porgrams that i could put a trapezoidal estimation formula into? Anything that would be easy for me to use besides pencil and paper? I dont know that formula very well. its in degrees not a real distance anyway does that matter?
02-24-2003, 12:37 AM
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Re: How can I figure out total area under the curve of a cam lobe? </font><blockquote><font size="1" face="Verdana, Helvetica, sans-serif">quote:</font><hr /><font size="2" face="Verdana, Helvetica, sans-serif">Originally posted by GrannySShifting:
<strong> Just if I wanted to play around with it, are there any porgrams that i could put a trapezoidal estimation formula into? Anything that would be easy for me to use besides pencil and paper? I dont know that formula very well. its in degrees not a real distance anyway does that matter? </strong></font><hr /></blockquote><font size="2" face="Verdana, Helvetica, sans-serif">Time to brush the dust off the old Calculus textbook. The trapezoidal rule is a pretty good way to approximate the integral (area under the curve) of a mathmatical formula. In cases where the exact mathematical formula is not or cannot be determined. Numerical integration can be performed using several methods, the trapezoidal rule being one of the easiest. Basically if you know the value of a function at certian points (lift at certain degree of rotation) you can calculate the area under the curve - it is the sum of all the areas of the trapezoids defined by drawing a line from zero lift to the lift at all known points. The more points you have, the more accurate the approximation will be. You could easily just use Excel to calculate this if you have decent data. If the data you have is limited - you only know the lift at a few specific points, you could probably fit a cubic spline throught the points and sample that at a higher frequency to get enough points to do a fairly accurate integration.
And no, the fact that the data is in lift versus degrees does not matter. The "area" will be defined in degrees * inches, not square inches. More "area" will be better in general.
<strong> Just if I wanted to play around with it, are there any porgrams that i could put a trapezoidal estimation formula into? Anything that would be easy for me to use besides pencil and paper? I dont know that formula very well. its in degrees not a real distance anyway does that matter? </strong></font><hr /></blockquote><font size="2" face="Verdana, Helvetica, sans-serif">Time to brush the dust off the old Calculus textbook. The trapezoidal rule is a pretty good way to approximate the integral (area under the curve) of a mathmatical formula. In cases where the exact mathematical formula is not or cannot be determined. Numerical integration can be performed using several methods, the trapezoidal rule being one of the easiest. Basically if you know the value of a function at certian points (lift at certain degree of rotation) you can calculate the area under the curve - it is the sum of all the areas of the trapezoids defined by drawing a line from zero lift to the lift at all known points. The more points you have, the more accurate the approximation will be. You could easily just use Excel to calculate this if you have decent data. If the data you have is limited - you only know the lift at a few specific points, you could probably fit a cubic spline throught the points and sample that at a higher frequency to get enough points to do a fairly accurate integration.
And no, the fact that the data is in lift versus degrees does not matter. The "area" will be defined in degrees * inches, not square inches. More "area" will be better in general.
