Draw an arc knowing radius and length but not chord

Hi,

I need to draw an arc of 1220mm length and with a radius of 720mm. Is

the only way to do this by calculating the chord, (...er, calculator

anyone?), or is there a SU way that I just don't know?

Thanks in advance.

nikkko:

Check users manual, select the two end points then enter 720mm r.

Another appraoch provided you have the intersect of the two line segs you are drawing an arc for.

Use the Bezier, order 2 ( 3 control points) by selecting the two end points then the intersect point

mac1,

Please re-read the question and see how your answer does not

relate to it. There is a given arc length.

For now I can only think of two 'solutions'

1) by calculation.

2) by narrowing it down to the right value, i.e. cutting off part of

the arc, measure it, cutting off, measure ...... till it is within the

tolerance that you accept. Start with the right radius and adjust

the number of segments while approaching the value 1220mm

(=tryal and error)

Wo3Dan

Trial and error won't do it - I'm building a model of an existing design, (curved sliding door), and the length has to be exactly 1220mm - so I'm going to have to calculate the chord for the time being. I'm new to SU and this design has a lot of curves so the problem is almost certainly going to come up again.

There isn't a way of drawing a shorter arc, measuring it and then adding the appropriate length? I can't find any way of extending an arc by a given amount either.

I drew the thing out using a circle of 720 mm raius and 36 segments, then measured a segment length and ended up using 9 segments and most of the tenth one to get total segment lengths of 1220 mm, which gives

a subtended angle of 87.2 degrees.

Lemastre,

Like Robc in the other thread about arcs, (started by nikkko) you talk about adding up segment lengths. Their sum is NOT the same as the arcs length. You must know that.

To see what I mean just pick an arc. Calculate the total segment length and compare it with the value

in the 'Entity Info'. Now change the number of segments and repeat the calculation. It will be different from what you had calculated before. And also check the 'Entity Info' This ARC LENGTH did not change. It is the highest value of the three, representing the arc length. And the most precise notation you will get by using the 'Text' tool after selecting a higher precision. As described before.

nikkko,

With tryal and error you can achieve fast results within 1mm or

even better. Just a matter of adjusting.

Wo3Dan

NIKKO,WODAN:

You are correct I misread the post. Try this to get close:

1) Layout out your 1200 mm line and divide it by 4;

2) Draw your 720mm circle tangent to this line end;

3) Draw circle at the above 1/4 center with radius equal to the 3/4 value;

4) Where the two intersect is the desired arc on the 720 mm circle;

5) This gave me 1229.170250mm

BTW I used 64 segs

nikkko exactly is 1220 + - .05 or 1220.000000000000000?

Don't think you will get that even if you calculate??. Not with SU's

approximations

nikkko,

For multiple different instances tryal and error is no option.

You may want to use a spreadsheed to set up the calculation.

Radius input is named R

Arc length input is named A

Chord length output is named C

Use this formula in the spreadsheed to get the right chord:

C = 2*(sin(A/(2*R) ) ) *R

So input R and A result in output C

Back to SU you can use C and R while applying the 'Arc' tool to get a most accurate result for practical purposes. (at least 6 decimal figures correct on screen / I did input 8 figures after entering decimal point, which was accepted correctly, checked by scaling *100 later)

-Select the 'Arc' tool.

-Click first point and dragg.

-Type value C from spreadsheet and hit [Enter].

-Dragg to see bulge in right plane and direction.

-type value R followed by r and hit [Enter]

Wo3Dan

p.s. When using a calculator be sure to set angles to Rad, not

Deg(rees)

FYI additional info:

1) Spread sheet is not required(?), the subtended angle is just 1220/720 in rads, the angle is just 1220/720 x 360/(2 xPI). If one sets this angle and the radius, uses these end points and arc tool the accuracy is ~.003 mm;

2) My layout technique above for projecting an arc length unto a circle is drafting 101, the accuracy is proportional to the fourth power of the substened angle and should be a short estimator. At 60 degs it should be 1/400 short and 30 1/14400. At 1220/2( 48 degs) SU gives +.247534 long and ~97 it is +9.170329 long!. I think this error is caused by the intersect points occurring on the straight line portion of the segment causing a short radius and the substended angle thus too large by about + .8 degs

Thanks for the input.

So today I drew the arc by calculating the chord. I used the equation, arc / circum x 360 to get the angle, and then found a handy web site calculator which gave me the chord based on the angle and the length of two sides of the isosceles triangle, i.e. the radius. Not too painful.

I can't remember the accuracy off the top of my head, (subsequently consumed by an urgent need to draw curved, tubular handles), but it was within my tolerance of .25mm.

I wonder why in the entity details for the arc the only element not editable is length of arc?

And I just found this site which does all the calcs based on radius and arc length. I haven't checked this for accuracy yet, (I'm done for the day), but it looks ok.

I haven't had the time to look at scripts yet, but is this the kind of thing, (trivial maths), that a script is good for? Or is this something to add to the SU wish list? I can imagine being able to place the first end of an arc, pull out in the direction I want the chord to go and then enter in the vcb something like "720r, 1220l" to indicate radius and length, hit return and let SU do the maths.

"And I just found this site ..."

oops:

http://www.handymath.com/cgi-bin/arc18.cgi [dead link]

aaargh...

http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry

Hi Nikkko, hi folks.

Thanks for the address of this site.

By entering the two known values (radius and arc length) it is easy to

get the values required by SU like chord and bulge (width and heigth

on the web page).

See also this SU file for ideas:

http://groups.google.com/group/SketchUp/web/Arc%20with%20known%20length%20and%20radius.skp [dead link]

Jean (Johnny) Lemire from Richelieu, Quebec, Canada.

mac1,

Thanks for the input. A few things though. I just tried to keep things simple and easy for repetition. So I used three cells in Excel. There must be dozens of little mathematical programs on the web doing the same. You do use a calculator, don’t you? Mine happens to be the spreadsheet to quickly repeat the ‘input+input=>output’

operation. (and save the program with others for next time) With that output I can use the ‘Arc’ tool in its most basic form to achieve the result desired.

I converted the arc length to the proper chord length. (could be done with the calculator, as also mentioned and as you wish) You convert the arc length to the proper angle, thereby forcing you to go on constructing the arc but also using other SU tools. Well, if you insist. But then I will have to disagree with you about bringing in the use of the ‘Circle’ tool. You can construct vérrrry! accurate without this tool. -Calculate the angle (use spreadsheet or calculator) -Draw a line with length of desired radius -Copy/Rotate the line using the calculated angle for input (SU will accept at least 8 decimal figures) (*)

-Use the ‘Arc’ tool from open endpoint to open endpoint

-after the second click just input the radius value +r and hit [Enter]

This way the number of segments can still be changed afterwards.

If you are unsure about the accuracy just scale up the model *100 and once more *100 (so *10000). I got 12200000.000496mm when scaled up

(*) an angle value can be shown with 3 decimal figures. As an example to check rounded (or not) input:

Copy/rotate an edge 2.12345678 degrees and type *160 and hit [Enter]. Measure the angle between first and last edge and compare with the calculated total angle to check accuracy.

Wo3Dan

p.s. I will check out the links from nikkko, thanks

nikkko,

Thanks for the handy site.

(behind the third cell there must be something like

2*R*sin(A/(2*R))

;-)

Wo3Dan

Hello All,

Interesting discussion and replies, thanks to everyone since I will keep these tricks in mind if I am ever faced with a similar problem. I have a curiosity question for Nikkkko. Why is your design constraint the length of the curve? You said you were modeling a curved sliding door. Couldn't the curve be created with a radius and an angle between start and stop? In that case the arc length itself becomes irrelevant to the creation of the object. Also, you wouldn't have the posted problem to begin with...

-LP

wo3Dan;

1) I think you, Gully,Taff and a host of others on this site need a standing ovation because you continually push, with your tips and suggestions, the limits of Su beyond what the designers originally had in mind;

2) I was not trying to cast dispersions on your approach but to raise the question of what is required. I come from the old school of better is the determent of good enough?

3) nikkko answered my previous question about the tolerance, he says 0.25mm;

4) Based on that and all the collective inputs I have the conclusions ; a) using drafting techniques to layout the arc length on the ref circle is very inaccurate for substented andgles >= 60 degs and the use of SU with this technique is not recommended; b) for errors around 3/1000 mm range using the SU built in protractor to layout out the substended angle combined with the radius can be used; c) for more accuracy then your approach must be used. As aside, using SU to issue a drawing package for this type of use would require your approach since they are normally with xxx.xxx and 10 mil accuracy so you would want to report at least L= 1220.000xxxx and cannot be done with other approaches(?)

my 2 cents worth

G day

Wo3Dan

Forgot to answer some of your other questions, yes I do use a calculator, first propragm I wrote was for a IBM card reader type ( 1120?) , have generate Excel spread sheets pages long including many fuctions etc, still have HP 41 and 11c, designed and built my own computer I am using now with a P4 3.2 Ghz processor and hyper threading and a 865 PERL Intel motherboard and 4 GB of memory, have things I helped designed and built now sitting in the Air and Space museum at the Smithsonian. Any more cheap shots??

mac1,

I take it that ‘cheap shot’ means my question about using a calculator is ‘below the belt’. Well, it wasn’t intended to be. It was an honest, although rhetorical question. Meaning that one needs to use at least something besides SU to tackle the conversion. And for repetitive need I just ‘grabbed’ Excel which most of us have on the computer anyway. There was no offence intended, not at all!

b.t.w. Impressive curriculum vitae you got! (no sarcasm!!!!!)

Wo3Dan

wo3Dan

Sorry this old dog misinterpreted your intent!

I forgot to tell you I still have my Pickett dual base log log vector hyperbolic slide rule. Does that classify as a computer? Accuracy sucks. Excel may get sick on hyperbolic functions? Some reading this probably don't know what this( slide rule ) is.

G day

wo3Dan

Your tip to use the rotate tool to set precise angles is great! Never entered my mind and don't remeber seeing any tips etc about that! . This should be up in red. This makes the answer to this question almost trival. Using angle= length/ radius =>converting to degrees=> using the rotate tool to copy the radius and set the angle and the arc tool gives at least a five place accuracy!

Please don't tell me to read the manual!

mac1,

Never mind the misinterpretation.

Log / Slide rule….???? What.s that?

..

..

Well, I used to use the basic ones at school and later on, even when also using my first TI.

(was it to check the TI-answers or the other way around?) My first TI-calculator I bought for (don’t laugh) fl 675,- (over $300.-) back in 1972/73. It had some extra functions (like factional and (more) statistic functions) that are not on the TI30 shown on this WIKI-page:

The equivalent would now cost about $5.-

I’m certainly not going to tell you to look things up in the manual. I know it’s there. And yes, if necessary I like to see if SU can tell me more about (for instance) accepting input. The N times rotation of a small angle => measuring the difference between first edge and end result at least tells me something about rounding off input. N=160 was just a small number, keeping the result <360 degrees.

I know that when building a house a length of 7085,009256mm is completely ridiculous.

In fact, for practical reasons I designed my house with a roof pitch of H=10/V=13. No angle mentioned. Now the funny thing is some people helping me wanted to know the angle in degrees. Simple question. When asked why I got some answer like: "to be able to lay out the steel-truss-plan on the floor for construction". Huh???

I’ve never regretted doing so.

See you again somewhere on the forums, regards,

Wo3Dan

Mine was a HP43 , company even got a special deal. Mine is still around here some where, had LED screen!!

Thanks, see ya

GDay

Hello again and thanks for all the input.

-LP

I need to input a specific arc length because the door is already being manufactured to that length! Also, the door is constructed from a rectangular section tube frame with a galvanized sheet metal covering. The galvanized sheet comes in specific sizes so if I can tailor the door to a size of my choosing then I can reduce waste cut.

Wodan

I very much like your technique of calculating the angle and rotating a line using the copy/rotate tool. I hadn't thought of that. This also solves another problem of mine because there are many other

elements which I need to draw and which are centered on the same point - the rail the door hangs on, the curved walls, the cladding on the walls, the tubular frame of the door and so on. I've pretty much completed the first drawing but have to attack a second one this week. What I'll do is draw out a line with various points which represent radii of each of the elements named above then rotate to the left and to the right to give me their appropriate start and finish points. This should save me a lot of time.

I've only been using SU for a couple of weeks so have lots to learn, but from my limited experience I still think arc drawing and particularly editing, (lengthening, shortening), could be easier. For me it's the least intuitive of tools. For now though, thanks again for the really useful help and if anyone wants to see the finished product, here it is: http://kazuba.eu/index.php?option=com_content&task=view&id=53&Itemid=72 [dead link]

nikkko,

Thanks for sharing information about the endproduct. Always nice to hear you could apply our suggestions to help in the modeling process in SU.

I see that you are in a satisfactoty branch of busines. It's about something we need / have to use on a daily base, ;-) I've read most of the info, interesting.

One not so unimportant thing I liked about France (amongst many other things), also this summer, is that these "publical objects" seem to be around whenever you "need" one.

Glad to be of help,

Wo3Dan