Answers.Body: <p>After a bit of fiddling in LeoCAD, I can confirm that the mid radius (i.e. the distance from the center of the torus to the axis of an axle) is 3.5 studs plus 2 <a href="https://bricks.stackexchange.com/questions/691/what-are-ldus-and-how-do-they-relate-to-lego-bricks">LDU</a>s (equal to 3.6 studs, or 72 LDUs).</p>
  <p>Consequently, the inner radius is 2.6 studs (or 52 LDUs), and the outer radius is 4.6 studs (or 92 LDUs).</p>
  <p><a href="https://i.sstatic.net/rQ8eL.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/rQ8eL.png" alt="CAD drawing of a quarter-torus, annotated" /></a></p>
  <p>Note that the odd offset (2 LDUs / 0.1 studs) is half of the &quot;lip&quot; of a <a href="https://bricks.stackexchange.com/questions/9860/quality-of-brick-modified-1-x-1-with-headlight-over-time">headlight brick</a>, or half the height of a stud's cylinder. There are techniques to achieve a 2 LDU offset; see e.g. <a href="https://bricks.stackexchange.com/questions/673/how-to-make-a-1-ldu-offset">this question</a>. Here's a possible assembly, just to demonstrate:</p>
  <p><a href="https://i.sstatic.net/Eiicq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Eiicq.png" alt="torus-aligning assembly, perspective" /></a>
  <a href="https://i.sstatic.net/JkMS8.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/JkMS8.png" alt="torus-aligning assembly, front" /></a></p>
  <hr />
  <p>Edit: it has been noted that 72 LDUs is also the height of three bricks. This allows to, for example, align a 2x2 round tile using brackets like so:</p>
  <p><a href="https://i.sstatic.net/UrXNl.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/UrXNl.png" alt="torus aligned with a 2x2 tile at 3 bricks of height" /></a>
  <a href="https://i.sstatic.net/8YSRz.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8YSRz.png" alt="torus aligned with a 2x2 tile at 3 bricks of height" /></a></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-05-16T16:50:01.587Z
Answers.Text: 72 LDU is also 9 plates or 3 brick heights... makes a lot more sense now, thx
Answers.UserDisplayName: Michael Verschaeve
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-05-16T17:03:55.460Z
Answers.Text: However, I'm not that happy with your connection example. technic holes in bricks are 0.1 mm = 0.25 LDU offsetted to their bottom. Your connection example would likely be considered illegal (depends a bit on how you connect back...)
Answers.UserDisplayName: Michael Verschaeve
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-05-16T17:10:24.437Z
Answers.Text: It was a 10-minute hack in LeoCAD. Besides, I tend to forget about some of those really specific cases of illegal/stressed connections.
Answers.UserDisplayName: IvanSanchez
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-05-16T20:30:36.497Z
Answers.Text: It's 72 LDU not 72 studs (as the post says).
Answers.UserDisplayName: Henrik supports the community
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-05-16T20:41:07.493Z
Answers.Text: Sorry, butter fingers :-)
Answers.UserDisplayName: IvanSanchez
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-05-16T14:42:34.857Z
Answers.LastActivityDate: 2023-05-16T20:40:48.023Z
Answers.LastEditDate: 2023-05-16T20:40:48.023Z
Answers.UserDisplayName: IvanSanchez
Body: <p>What is the inner/outer or mid radius of the 45 degree arc the following element makes?</p>
  <p><a href="https://www.bricklink.com/v2/catalog/catalogitem.page?P=65473" rel="noreferrer">https://www.bricklink.com/v2/catalog/catalogitem.page?P=65473</a>
  <a href="https://i.sstatic.net/3DsCy.png" rel="noreferrer"><img src="https://i.sstatic.net/3DsCy.png" alt="enter image description here" /></a></p>
  <p>I tried to align several of the elements in 90 and 180 degree arcs in stud.io, the end of the arc never seems to align with any modules, so I'm inclined to think the radius is nonsensical. Is there any way two or more of these elements can be combined so the open ends align with in system modules?</p>
  
Tags: <size>
Title: Radius of the 45 degree elbow piece
UserDisplayName: Michael Verschaeve
ThreadText: # Radius of the 45 degree elbow piece
  
  (Asked by: username_0 on 2023-05-16)
  
  What is the inner/outer or mid radius of the 45 degree arc the following element makes?
  
  <https://www.bricklink.com/v2/catalog/catalogitem.page?P=65473>
  [![enter image description here](https://i.sstatic.net/3DsCy.png)](https://i.sstatic.net/3DsCy.png)
  
  I tried to align several of the elements in 90 and 180 degree arcs in stud.io, the end of the arc never seems to align with any modules, so I'm inclined to think the radius is nonsensical. Is there any way two or more of these elements can be combined so the open ends align with in system modules?
  
  **Tags:** size
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2023-05-16. Score: 7 | Accepted answer
  
  After a bit of fiddling in LeoCAD, I can confirm that the mid radius (i.e. the distance from the center of the torus to the axis of an axle) is 3.5 studs plus 2 [LDU](https://bricks.stackexchange.com/questions/691/what-are-ldus-and-how-do-they-relate-to-lego-bricks)s (equal to 3.6 studs, or 72 LDUs).
  
  Consequently, the inner radius is 2.6 studs (or 52 LDUs), and the outer radius is 4.6 studs (or 92 LDUs).
  
  [![CAD drawing of a quarter-torus, annotated](https://i.sstatic.net/rQ8eL.png)](https://i.sstatic.net/rQ8eL.png)
  
  Note that the odd offset (2 LDUs / 0.1 studs) is half of the "lip" of a [headlight brick](https://bricks.stackexchange.com/questions/9860/quality-of-brick-modified-1-x-1-with-headlight-over-time), or half the height of a stud's cylinder. There are techniques to achieve a 2 LDU offset; see e.g. [this question](https://bricks.stackexchange.com/questions/673/how-to-make-a-1-ldu-offset). Here's a possible assembly, just to demonstrate:
  
  [![torus-aligning assembly, perspective](https://i.sstatic.net/Eiicq.png)](https://i.sstatic.net/Eiicq.png)
  [![torus-aligning assembly, front](https://i.sstatic.net/JkMS8.png)](https://i.sstatic.net/JkMS8.png)
  
  ---
  
  Edit: it has been noted that 72 LDUs is also the height of three bricks. This allows to, for example, align a 2x2 round tile using brackets like so:
  
  [![torus aligned with a 2x2 tile at 3 bricks of height](https://i.sstatic.net/UrXNl.png)](https://i.sstatic.net/UrXNl.png)
  [![torus aligned with a 2x2 tile at 3 bricks of height](https://i.sstatic.net/8YSRz.png)](https://i.sstatic.net/8YSRz.png)
  
  > **Comments:**
  > **username_0**: 72 LDU is also 9 plates or 3 brick heights... makes a lot more sense now, thx  
  > **username_0**: However, I'm not that happy with your connection example. technic holes in bricks are 0.1 mm = 0.25 LDU offsetted to their bottom. Your connection example would likely be considered illegal (depends a bit on how you connect back...)  
  > **username_1**: It was a 10-minute hack in LeoCAD. Besides, I tend to forget about some of those really specific cases of illegal/stressed connections.  
  > **username_2**: It's 72 LDU not 72 studs (as the post says).  
  > **username_1**: Sorry, butter fingers :-)  
  
  ---
  
  