X-Virus-Scanned: clean according to Sophos on Logan.com Return-Path: Received: from mail16.syd.optusnet.com.au ([211.29.132.197] verified) by logan.com (CommuniGate Pro SMTP 5.1.12) with ESMTPS id 2346528 for flyrotary@lancaironline.net; Sat, 22 Sep 2007 21:40:00 -0400 Received-SPF: none receiver=logan.com; client-ip=211.29.132.197; envelope-from=lendich@optusnet.com.au Received: from george (d220-237-243-228.dsl.nsw.optusnet.com.au [220.237.243.228]) by mail16.syd.optusnet.com.au (8.13.1/8.13.1) with SMTP id l8N1dFFa012672 for ; Sun, 23 Sep 2007 11:39:17 +1000 Message-ID: <003a01c7fd82$93cab660$e4f3eddc@george> From: "George Lendich" To: "Rotary motors in aircraft" References: Subject: Re: [FlyRotary] Re: Area of a circle Date: Sun, 23 Sep 2007 11:39:24 +1000 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0037_01C7FDD6.63A847F0" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Antivirus: avast! (VPS 0657-0, 12/12/2006), Outbound message X-Antivirus-Status: Clean This is a multi-part message in MIME format. ------=_NextPart_000_0037_01C7FDD6.63A847F0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable 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,=20 3.draw a triangle to center of one circle,=20 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) =20 I agree with Al, George. =20 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. http://med.ee.nd.edu/MED5/PAPERS/S5_3/S5_3.PDF 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 -----=20 From: Al Gietzen=20 To: Rotary motors in aircraft=20 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 Chaps,=20 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!? George (down under) -------------------------------------------------------------------------= ----- -- 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.=20 Version: 7.5.488 / Virus Database: 269.13.28/1021 - Release Date: = 21/09/2007 2:02 PM ------=_NextPart_000_0037_01C7FDD6.63A847F0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ed,
Don't struggle - I have worked it = out.
1.The easy way is to first find the = area of the=20 total circle,
2.Then find the chord of the overlapped = section,=20
3.draw a triangle to center of one = circle,=20
4.find the angle of this = triangle,
5.use it as a fraction of 360=20 degrees,
6. find the value of this fraction of = the whole=20 area of the circle
7. find the area of the triangle, = that each=20 end of chord to centre make
8 take the area of the triangle from = the fraction=20 of the circle
9. this gives the ellipse or one = side of the=20 overlap.
10. multiply by 2 for total overlap = - if the=20 circles are the same size.
 
Now to work on the slices - which are = really only=20 half of the overlap, I think!
 
Now having said all that I through I = could short=20 cut the process by looking at the calculations for area of an Oval (L x = B x .8)=20 or area of an ellipse (1/2 L x 1/2B x Pi) which have similar outcomes, = but don't=20 appear at first glance to be similar ( enough) to the abovementioned = method -=20 although I haven't checked my calculations yet.
As I only need the trend of variance = and not the=20 exact figures the shorter versions may be quicker, but the lass ( = neighbour)=20 will show mw how to use Excell which is probably quicker and more=20 accurate.
Thanks again!
George ( down under)
 
I agree with Al, George. 
 
However, if you wish to enjoy the thrill of = calculating=20 that area (which is not a trivial task), here is a document that has = all the=20 information (formulas) you need.
 
http://med.ee.nd.= edu/MED5/PAPERS/S5_3/S5_3.PDF
 
     Now if you are = willing to=20 assume that the throttle plate  thickness and its rod are not a = factor=20 (maybe not a bad real-world assumption just to get the = area of=20 the opening - but different story regarding its effect on air flow = which is=20 why Al's suggestion is a good one), I have attached a spreadsheet with = this=20 simplification of the math.
 
Ed
 
----- Original Message -----
From:=20 Al = Gietzen=20
To: Rotary motors in = aircraft=20
Sent: Saturday, September 22, = 2007=20 12:06 PM
Subject: [FlyRotary] Re: Area = of a=20 circle

George;

 

Determining the=20 area of the opening of a circular butterfly with position is = certainly=20 complex enough; but the flow is likely not directly proportional = because of=20 the complexities of the flow characteristics and pressure changes. =  I=20 would think measuring it is really the only way.  Do you have = access to=20 a flow bench?

 

Sorry; = probably=20 not very helpful,

 

Al=20 G

 

-----Original=20 Message-----
From: Rotary=20 motors in aircraft [mailto:flyrotary@lancaironline.net] On Behalf Of George = Lendich
Sent: Friday, September 21, = 2007 9:21=20 PM
To: Rotary = motors in=20 aircraft
Subject: = [FlyRotary] Area of a circle

 

Chaps, 

I am trying to work = out the area=20 of carb inlet as it is opened incrementally.

 

This involves the = overlapped=20 portion of two circles, as well as, a circle cut into slices ( = straight=20 cuts).

 

This should give me an = indication of the linier or otherwise, volume of air as it sweeps = through=20 the carb.

 

This then should = indicate the=20 shape of the grind of the needle in maintaining continuity of = the=20 mixture ratio of fuel to air.

 

Any helpers with this=20 one!?

George (down=20 under)

--
Homepage:  http://www.flyrotary.com/
Archive and=20 UnSub:  =20 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:=20 21/09/2007 2:02 PM
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