Given an annulus with known dimensions how would I find the length of a line connecting the inner and outer edges at an arbitrary angle?

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite












Given an annulus with origin A and radii R1 & R2, a point on the inner radius B, and an angle theta to an unknown point on the outer radius C I need to find the length of line segment BC.



I'm working in OpenSCAD so I must solve this problem mathematically but I have diagrammed it in FreeCAD below.



enter image description here



  • knowns: A, B, R1, R2, theta

  • unknowns: C





geometry







share|cite|improve this question



















  • 1




    in triangle $ABC$ we know side $AB$, side $AC$, and angle $ABC$. We want to find the third side $BC$
    – Lozenges
    Sep 1 at 7:05










  • Lozenges... thank you. I made this way too hard in my head /facepalm
    – rennat
    Sep 1 at 7:07










  • For anyone else who stumbles onto this page, here is the solution directly from my openscad file: theta = 180 - vaneAngle; chordLength = innerRadius * cos(theta) + sqrt(pow(outerRadius, 2) - pow(innerRadius, 2) * pow(sin(theta), 2)); and yes it is for a centrifugal blower :)
    – rennat
    Sep 1 at 7:38















up vote
0
down vote

favorite












Given an annulus with origin A and radii R1 & R2, a point on the inner radius B, and an angle theta to an unknown point on the outer radius C I need to find the length of line segment BC.



I'm working in OpenSCAD so I must solve this problem mathematically but I have diagrammed it in FreeCAD below.



enter image description here



  • knowns: A, B, R1, R2, theta

  • unknowns: C





geometry







share|cite|improve this question



















  • 1




    in triangle $ABC$ we know side $AB$, side $AC$, and angle $ABC$. We want to find the third side $BC$
    – Lozenges
    Sep 1 at 7:05










  • Lozenges... thank you. I made this way too hard in my head /facepalm
    – rennat
    Sep 1 at 7:07










  • For anyone else who stumbles onto this page, here is the solution directly from my openscad file: theta = 180 - vaneAngle; chordLength = innerRadius * cos(theta) + sqrt(pow(outerRadius, 2) - pow(innerRadius, 2) * pow(sin(theta), 2)); and yes it is for a centrifugal blower :)
    – rennat
    Sep 1 at 7:38













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Given an annulus with origin A and radii R1 & R2, a point on the inner radius B, and an angle theta to an unknown point on the outer radius C I need to find the length of line segment BC.



I'm working in OpenSCAD so I must solve this problem mathematically but I have diagrammed it in FreeCAD below.



enter image description here



  • knowns: A, B, R1, R2, theta

  • unknowns: C





geometry







share|cite|improve this question















Given an annulus with origin A and radii R1 & R2, a point on the inner radius B, and an angle theta to an unknown point on the outer radius C I need to find the length of line segment BC.



I'm working in OpenSCAD so I must solve this problem mathematically but I have diagrammed it in FreeCAD below.



enter image description here



  • knowns: A, B, R1, R2, theta

  • unknowns: C





geometry




geometry






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 1 at 6:38

























asked Sep 1 at 6:11









rennat

1013




1013







  • 1




    in triangle $ABC$ we know side $AB$, side $AC$, and angle $ABC$. We want to find the third side $BC$
    – Lozenges
    Sep 1 at 7:05










  • Lozenges... thank you. I made this way too hard in my head /facepalm
    – rennat
    Sep 1 at 7:07










  • For anyone else who stumbles onto this page, here is the solution directly from my openscad file: theta = 180 - vaneAngle; chordLength = innerRadius * cos(theta) + sqrt(pow(outerRadius, 2) - pow(innerRadius, 2) * pow(sin(theta), 2)); and yes it is for a centrifugal blower :)
    – rennat
    Sep 1 at 7:38













  • 1




    in triangle $ABC$ we know side $AB$, side $AC$, and angle $ABC$. We want to find the third side $BC$
    – Lozenges
    Sep 1 at 7:05










  • Lozenges... thank you. I made this way too hard in my head /facepalm
    – rennat
    Sep 1 at 7:07










  • For anyone else who stumbles onto this page, here is the solution directly from my openscad file: theta = 180 - vaneAngle; chordLength = innerRadius * cos(theta) + sqrt(pow(outerRadius, 2) - pow(innerRadius, 2) * pow(sin(theta), 2)); and yes it is for a centrifugal blower :)
    – rennat
    Sep 1 at 7:38








1




1




in triangle $ABC$ we know side $AB$, side $AC$, and angle $ABC$. We want to find the third side $BC$
– Lozenges
Sep 1 at 7:05




in triangle $ABC$ we know side $AB$, side $AC$, and angle $ABC$. We want to find the third side $BC$
– Lozenges
Sep 1 at 7:05












Lozenges... thank you. I made this way too hard in my head /facepalm
– rennat
Sep 1 at 7:07




Lozenges... thank you. I made this way too hard in my head /facepalm
– rennat
Sep 1 at 7:07












For anyone else who stumbles onto this page, here is the solution directly from my openscad file: theta = 180 - vaneAngle; chordLength = innerRadius * cos(theta) + sqrt(pow(outerRadius, 2) - pow(innerRadius, 2) * pow(sin(theta), 2)); and yes it is for a centrifugal blower :)
– rennat
Sep 1 at 7:38





For anyone else who stumbles onto this page, here is the solution directly from my openscad file: theta = 180 - vaneAngle; chordLength = innerRadius * cos(theta) + sqrt(pow(outerRadius, 2) - pow(innerRadius, 2) * pow(sin(theta), 2)); and yes it is for a centrifugal blower :)
– rennat
Sep 1 at 7:38
















active

oldest

votes











Your Answer




StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2901417%2fgiven-an-annulus-with-known-dimensions-how-would-i-find-the-length-of-a-line-con%23new-answer', 'question_page');

);

Post as a guest






















active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes















 

draft saved


draft discarded















































 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2901417%2fgiven-an-annulus-with-known-dimensions-how-would-i-find-the-length-of-a-line-con%23new-answer', 'question_page');

);

Post as a guest
































































-

這個網誌中的熱門文章

How to combine Bézier curves to a surface?

圖片
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of Bézier curves of different orders. But this algorithm is defined in a two dimensional space for now. To shift it into the third dimension I need to somehow combine the Bézier curves. Given two curves in each two dimensions, how can I combine them to build a surface? I thought about something like a curve of a curve. Or maybe I could multiply them somehow. How can I combine them to cause the wanted behavior? Is there a common approach? In the image you can see the input, on the left, and the output, on the right, of the algorithm that works in a two dimensional space. For the real application there is a three dimensional input. The algorithm relays only on the adjacent tiles. Given these it will define the control points of the mentioned Bézier cur...
閱讀完整內容

Mutual Information Always Non-negative

圖片
Clash Royale CLAN TAG #URR8PPP up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 '12 at 15:38 Cameron Buie 83.6k 7 71 154 asked Jun 17 '12 at 15:30 Omri 359 3 13 3 Convexity of the function $tmapsto tlog t$. – Did Jun 17 '12 at 15:33 In addition, the convexity properties require the coefficients in the linear combination sum 1. Then, as p(x,y) is a probability distribution, it fullfits such condition. – Francisco Javier Delgado Ceped Aug 10 at 18:44 add a comment  |  up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 ...
閱讀完整內容

Why am i infinitely getting the same tweet with the Twitter Search API?

圖片
up vote 0 down vote favorite My code workes perfectly for other queries, but for one query I am infinitely getting the same tweet. I can't understand what the problem is. API call: query='Allergic asthma OR Nonallergic asthma OR Occupational asthma OR EIB OR Exercise-induced bronchoconstriction OR Nocturnal asthma OR Cough-variant asthma' new_tweets = api.search(q=searchQuery, count=100, since_id=since_id, lang='en',tweet_mode='extended') if not new_tweets: print("No more tweets found") break for tweet in new_tweets: if True: print(jsonpickle.encode(tweet._json, unpicklable=False)) my_file = open('searchTweets.txt','a') my_file.write(jsonpickle.encode(tweet._json, unpicklable=False)+'n') my_file.close() else: continue Output in file: https://pastebin.com/JmRCsTeE These are the JSONs of the same Tweet. Other queries that work: Breast cancer OR Prostate cancer OR Colon cancer OR Lung cancer Type 2 dia...
閱讀完整內容