# Checking Arc Tangencies

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Hi All

Was hoping to get some braintrust opinions on what is the best way to check if two joining arcs are actually tangent to each other?

i feel like i should perhaps know but its 7:30pm on a Friday and my brain is fried.....

thank you all anyway!

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I would start by drawing lines from the centres of the arcs to the endpoint of the arcs, and see if that made geometric sense.

Post an example drawing for folk to play with.

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In the first example, of the two red reverse curves - the green and cyan lines are constructed from the endpoint to the center of each arc.

If those lines are parallel, the arcs are tangent.

In the second example, of the two red concentric curves - the green line is drawn from the center of the larger arc to the endpoint. If the centerpoint of the smaller arc lies exactly on this line (The circle represents the endpoint of the short radius) - then they are tangent.

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what is the best way to check if two joining arcs are actually tangent to each other?

The Properties will tell you the angle of the arc at either end. If the angle at the end of one arc is the same as the beginning of the other, they're tangent. QED.

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Thank you all for your tips n tricks, I will check it out when I'm back in the office.

Eldon, I've never done this before (used google drive)

but hope it works...

Regards

United

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I see your LT but in CIV3d if you make an alignment an option is check tangents.

Re compare two line angles, the accuracy of your units settings also needs to be as far as you can push it I drew two lines moved top point a very small amount, with units set to say 0.0 accuracy, the angle is 0.0 for both increasing reveals 0.0 v's 0.00309 so in practice is not tangential. It comes down to how close to 0.0000000 is acceptable.

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Well thanks to you peeps ive luckily confirmed I do seem to have tangecies. Its bloody 3 arcs joining end to end! And luckily theyre all ok according to both the angles and centre line checkes mentioned above.

BIGAL, that sounds nifty, I actually use 12d for design however. Never used civil3d unfortunately. I see what your saying regarding angles, but I suppose for me (civil design) the construction tolerances are probably not capable of achieving that perfection anyway?

I am guilty now and then of accepting lesser standards though...trying to change that

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Thank you for successfully posting a sample drawing.

I found some non-tangential points at the nosings of the traffic island. Otherwise all seemed fine.

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For any one, drawing traffic islands is one of those things that have a few variables and it can take a couple of goes to get them right, there not locked in to exact dimensions rather a overall goal of length and taper lengths a few mm does not matter, when using fillet you often find that the island shortens so you have another go. The tolerance on true tangential is pretty good as the guy pouring the kerb uses his experience to take out the tiny blip. What is not obvious in image is there is another radius at the taper joint point hence the couple of goes to get it right.

The shape above should have true tangents, draw a center line add the two circles at correct total length, draw 2 parallel lines from big circle, draw line using tan from small circle to the intersection point of horizontal line, then fillet this intersection, this is where variability creeps in selecting that intersection point getting the shape right.

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Thanks again guys, unfortunately the layout for my job was done by some one else, and hence I do have some funny curve radiuses and things like the traffic island.

I'm a bit inexperienced myself so its been a lot of work for me and challenges, but ive enjoyed learning along the way. As a Civil Engineer, who works in design, curves, arcs and the works has been a huge weakness of mine, which this job had plenty of. I'm glad ive invested some time to get my head around the geometry side of things etc and whilst the theories are a little bit over my head, I can apply the principles now at least and make sure I run a few checks for tangency etc.

I know what you mean BIGAL, the shape you see there is the lip, I believe one must think about the what the radius will be at the back of kerb right? I think I went with the notion minimum 0.3m radiuses for back of kerb. What say you? I should look into redrawing that one I think. Its juts a bit awkward to get the orientation right as the intersecting roads are at angles not perpendicular too.

Cheers again all.

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I've actually got one more question if that's ok yall!

[/img]

As per the image above, if you wanted to fillet an arc between the cyan and magenta lines, the cyan being an arc and the magenta being a straight, is it possible to get an arc in there that will have its end point at the end of the magenta line? I would like that point to be the tangent point for the arc. Ive tried guessing radiuses, and I tried a circle TTR which worked I think, but I couldn't trim the circle as I was getting the "does not intersect at 2 points' message.

Thanks everyone!

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Btw I hope that's clear enough which lines I'm referring to....I've highlted them and their end points are showing.

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I would construct the arc. There may be an automatic way of doing things.

First of all, draw a line from the centre of the arc to its end point. Then draw the tangent to intersect with the magenta line (it is very easy to draw lines at 90° when Polar tracking is in action). Now draw the angle bisector between these two lines (blue line). Now project your first line to intersect this angle bisector line. Where they cross is the centre of the arc.

Kerb nosings are sometimes precast in 90° sections, so the actual junctions with the straights can be a bit of a bodge.

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The way I construct an angle bisector is to draw a circle centred at the intersection point. Then trim this circle with the tangents. Then draw a line from the intersection point to the mid point of the arc. This is the angle bisector.

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Re kerb radius it can go as low as zero for back to back if your lip is 0.6m rad with a 0.3m kerb then radius is zero. Often the ped walk is cut at 90 so kerb goes around again rad is zero with a 45 mitre.

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Given the two point options Eldon your answer is correct for matching the arc end point draw a line from end to center point then the circle tangent length then a 90 line from the line point gives the new center.

To match a known point is a bit harder and may require an iteration to keep filleting till end point matches the point co-ords. There is a mathematical answer and its inside surveyors reverse curve formulas, the one required is for non parallel lines. Its something that is on my wish list to do as its a pain in Autocad to do reverse curves very quickly. Not at work else would post diagram.

For parallel then variables are R1 R2 offset and distance between ends or combinations of known solving the unknown. These are fairly simple mathematical formulas.

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I see that my solution only uses the end of the arc as a fixed point, but not the end of the straight. So the end of the straight is wherever the arc ends.

My feeling is that it is not possible geometrically to join your two fixed points with an arc being tangential at each fixed point. You need a transition curve of varying radius. Or you could draw a polyline and give it tangential directions at each end.

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Your correct Eldon it comes down to picking a radius, or which point to match to. The attached is the formula for reverse curves.

Reverse curves.pdf

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Thanks guys for sharing your thoughts, appreciate it. I never gave arcs and curves much thought, ran away from them, but understanding them is so important for horizontal geometry!

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so i'm back playing with arcs again, and noticed that when i was trying to fit an arc between a straight and an arc, the fillet command would produce an error of "cannot fillet between these two entitites".

It is an arc and a polyline in question, with z values at 0, and i have set a radius i wish to achieve for the fillet command.

Then i tried the Circle, Tangent command and it does seem to produce a circle that fits at the desired radius.

Why would the fillet command not work yet the circle command seems to achieve what i am after? Or is the arc from the Circle command not going to be quiet right?

Thanks again everyone!