geometry expert required

[sunnybob]

Having quit my schooling at the earliest possible moment because it was far more secondary than it was modern, my maths /algebra / geometry can only be described as non existant.
So i need help for my project please.

I want to draw an arc onto graph paper (well, more exactly a curve).

I only have two measurements, and I have had to look up even the name of the measurement, but the chord length is 1 metre, and the height between the chord and arc length is 20 mm.
Is it possible using only those two measurements to guide me to drawing that curve?

For example, i know the height at the centre of the chord, what would be the height at each 10th of the distance (100 mm) along the chord?

grateful thanks to any who can help.

 

[MikeG.]

What are you trying to achieve?

It sounds to my that this would be a doddle with a spline (thin bendy stick with straight grain), some clamps, and some offcuts:

 

[NazNomad]

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


You need a piece of string 20½ feet long. :-D

 

[transatlantic]

I guess you could also do this - where F1 and F2 (1000mm) would be offset by your 20mm?

 

[NazNomad]

That's an ellipse though, not the arc of a circle.

 

[Brandlin]

an 'arc' is a section of a circle.
a 'curve' is any kind of line that isnt straight - and there are many types.

what mikeG suggests is a very simple practical method for drawing a curve, and assuming the stick bends uniformly you'll get a curve (in this case i think an approximation to a catenary?) but not an arc.

i think we need to know a little more of what you want to achieve.

For example an arc can be defined by the chord length and height at the centre, because you can construct the centre point and draw using a compass

If you need some other mathematical type of curve then the chord length and height wont be enough to define the curve.

 

[AndyT]

I agree with Mike. If it's not convenient to use clamps and blocks, just cut a slot in the end of the stick and use a piece of string, like this

 

[transatlantic]

That's an ellipse though, not the arc of a circle.

Well I was thinking the top half. But yeah, it is incorrect as it gives perpendicular sides, woops

 

[Brandlin]

naz while that calculator will do the maths, i think what the OP is asking is how to construct the arc/curve. So assuming it is an arc he wants, he still has to construct the centre from his available information.

i'm not sure what he really needs, hence my questions.

 

[MusicMan]

Here's the maths IF and ONLY IF the curve you want is a circle. (If it isn't a circle, it is not defined).

the formula you want is

r^2 = a^2 + (r-s)^2

r is the radius of the circle
a is the half-length of the chord, 0.5 m in your case
s is the distance from the chord to the outside of the circle at the mid point, 0.02 m in your case.

Keith

 

[MrTeroo]

Here you go:

 

[bugbear]

Sagitta!

This is the same maths you need for calculating blade cambers and the curve a plane with a given length and blade projection will cut.

BugBear

 

[sunnybob]

I've since looked up and found Sagitta, but it doesnt help because i dont know the radius.

the bendy stick is one method, but whos to say the stick bends evenly along its length?

I'm trying to make a more accurate wooden katana sword, known as a bokken, and the blade is a curve of the above dimensions. thats all.

 

[katellwood]

You need to make a Camber slip

slide the ply round the nails and the obtuse angle describes the required curve.

did it here

I mainly use it for setting out bay/bow windows where the radius is too large to be done with a trammel

 

[NazNomad]

I've since looked up and found Sagitta, but it doesnt help because i dont know the radius.

You do if you use my link... The radius is 25½ ish ft (I forget exactly)

 

[Brandlin]

I've since looked up and found Sagitta, but it doesnt help because i dont know the radius.

the bendy stick is one method, but whos to say the stick bends evenly along its length?

I'm trying to make a more accurate wooden katana sword, known as a bokken, and the blade is a curve of the above dimensions. thats all.

Hi sunnybob.

it sounds like you are not trying to draw an arc. So a lot of the maths above is going to be irrelevant.

Part of the problem is that you keep using the word 'curve' as though there is only one. You know the end points of the curve and you can plot one point in the middle.
Can you imagine that there are an infinite number of curves that run through those three points. Your curve is as i and others have said here... undefined.

In this instance your best way to draw such a curve would be the bent stick method.
As long as the stick has similar stiffness along its length then it should be precise and accurate. It draws an curve known as a catenary (the same shape overhead cables make draped between pylons) but given the very shallow nature of the curve you want i dont think anyone except you is going to notice.
I have had more luck using an aluminium ruler on edge as the 'stick' this removes problems of the wood variation and is better for shallow deflections like yours.

 

[MikeG.]

I've since looked up and found Sagitta, but it doesnt help because i dont know the radius.

You do now. It is 6260mm (if the curve you are after is an arc [ie part of a circle]).

the bendy stick is one method, but whos to say the stick bends evenly along its length?

You flip it over and repeat. If you only get one line, it bent perfectly. If you get two lines, you get to choose the upper ones or the lower ones.

 

[ColeyS1]

1/2 the span squared + rise squared

Divided by 2x rise

Sent from my SM-G900F using Tapatalk

 

[MikeG.]

........For example, i know the height at the centre of the chord, what would be the height at each 10th of the distance (100 mm) along the chord?

Working out from the middle in 100mm increments: 19.2mm, 16.8mm, 12.8mm, & 7.2mm (again, assuming it is an arc you are after).

 

[sunnybob]

mike... thats the answer i was hoping for, something simple enough for me to copy.
I can measure that out on graph paper and see if it looks right to me.
thank you.