|
Ed,
Don't struggle - I have worked it out.
1.The easy way is to first find the area of the
total circle,
2.Then find the chord of the overlapped section,
3.draw a triangle to center of one circle,
4.find the angle of this triangle,
5.use it as a fraction of 360
degrees,
6. find the value of this fraction of the whole
area of the circle
7. find the area of the triangle, that each
end of chord to centre make
8 take the area of the triangle from the fraction
of the circle
9. this gives the ellipse or one side of the
overlap.
10. multiply by 2 for total overlap - if the
circles are the same size.
Now to work on the slices - which are really only
half of the overlap, I think!
Now having said all that I through I could short
cut the process by looking at the calculations for area of an Oval (L x B x .8)
or area of an ellipse (1/2 L x 1/2B x Pi) which have similar outcomes, but don't
appear at first glance to be similar ( enough) to the abovementioned method -
although I haven't checked my calculations yet.
As I only need the trend of variance and not the
exact figures the shorter versions may be quicker, but the lass ( neighbour)
will show mw how to use Excell which is probably quicker and more
accurate.
Thanks again!
George ( down under)
I agree with Al, George.
However, if you wish to enjoy the thrill of calculating
that area (which is not a trivial task), here is a document that has all the
information (formulas) you need.
Now if you are willing to
assume that the throttle plate thickness and its rod are not a factor
(maybe not a bad real-world assumption just to get the area of
the opening - but different story regarding its effect on air flow which is
why Al's suggestion is a good one), I have attached a spreadsheet with this
simplification of the math.
Ed
----- Original Message -----
Sent: Saturday, September 22, 2007
12:06 PM
Subject: [FlyRotary] Re: Area of a
circle
George;
Determining the
area of the opening of a circular butterfly with position is certainly
complex enough; but the flow is likely not directly proportional because of
the complexities of the flow characteristics and pressure changes. I
would think measuring it is really the only way. Do you have access to
a flow bench?
Sorry; probably
not very helpful,
Al
G
-----Original
Message-----
From: Rotary
motors in aircraft [mailto:flyrotary@lancaironline.net] On Behalf Of George Lendich
Sent: Friday, September 21, 2007 9:21
PM
To: Rotary motors in
aircraft
Subject:
[FlyRotary] Area of a circle
I am trying to work out the area
of carb inlet as it is opened incrementally.
This involves the overlapped
portion of two circles, as well as, a circle cut into slices ( straight
cuts).
This should give me an
indication of the linier or otherwise, volume of air as it sweeps through
the carb.
This then should indicate the
shape of the grind of the needle in maintaining continuity of the
mixture ratio of fuel to air.
Any helpers with this
one!?
--
Homepage: http://www.flyrotary.com/
Archive and
UnSub:
http://mail.lancaironline.net:81/lists/flyrotary/List.html
No virus found in this incoming message.
Checked by AVG Free
Edition.
Version: 7.5.488 / Virus Database: 269.13.28/1021 - Release Date:
21/09/2007 2:02 PM
|