Need to calculate length of an arch can arise when performing the most various project works. It is development of arch overlappings, construction of bridges and tunnels, laying of automobile and railway tracks and many other things. Initial conditions for the solution of this task can be very different. In order that in the most optimum way to calculate arch length, it is necessary to know the radius of a circle and the central corner.
It is required to you
- - sheet of paper;
- - compasses;
- - ruler;
- - protractor;
- - computer with the AutoCAD program;
- - calculator.
Instruction
1. Construct a circle with the set radius. The principles its construction in the same AutoCAD, as on the sheet of paper. Having mastered ways of creation of different geometrical figures in the classical way, you very quickly will understand how it becomes on the computer. The difference is that at usual construction by means of compasses you find the center of a circle for a point where the needle is put. In AutoCAD find in the top menu the button "arc" or "Arch". Choose construction on the center, the initial point and a corner and enter the necessary parameters. Designate the center of a circle as the Lake.
2. By means of a pencil and a ruler or a computer mouse carry out radius. If you draw on a leaf, then by means of a protractor postpone the given size of a corner. For this purpose combine a zero mark of a protractor with a point Oh, note the necessary corner and carry out the second radius through the received point. Designate a corner as α. It is possible to call it and AOV if the corresponding letters to note points of intersection of radiuses with a circle. You need to find AV arch length.
3. If the size of a corner is set in degrees, then length of an arch is equal to the doubled work of radius of a circle on coefficient π and on a corner ratio α to the full size of the central corner a circle. It makes 360 °. That is it can be found on formula L=2πRα/360 ° where L – the required length of an arch, R-circle radius, and α – the corner size in degrees. The corner can be set also in radians. Then length of an arch is equal to the work of radius on a corner, that is L=Rα. In this case the rest of a formula was already reduced when translating degrees in a radian.
4. Designers quite often should count arch length, mean only the presumable height of the bridge or overlapping and length of flight. In this case make the drawing. Flight will be a chord, and height — a part of radius. Carry out it from the topmost point of future arch perpendicularly to a chord and continue further, to the estimated center of a circle. Height halves a chord. Connect the center to the ends of a chord, having received thus 2 more radiuses. Calculate radius on Pythagorean theorem, that is R= √ a2+(R-h)2.
5. Knowing the radius and a difference between it and height, according to the theorem of sine find the size of a half of a corner of the sector. The sine is the relation of an opposite leg to a hypotenuse, that is sinα=a/R. According to the table of sine find the size of a corner and set up him in a formula.