Trades Math - Bolt Circle Chord Length

hi welcome to my channel math made easy with laurel i'm laurel and in this video we're going to talk about the cord length in a bold circle in the previous video we talked about how we calculate the coordinates for the holes on a bolt circle this video we're going to talk about how we calculate the straight line center to center distance between two adjacent holes and we're going to use right triangles to do that so just a bit of terminology first the cord length is different from the arc length and i did talk about how to calculate arc length in a previous video but in this example because these are five equally spaced holes if i wanted to find this arc length it's the length along the circumference so if it's a fifth of the whole circle we would simply find one fifth of the total circumference and that would be arc length on the other hand the center to center distance between those two holes is called chord length and in order to calculate that we need to use right triangles we don't have any triangles at all in this diagram and we certainly don't have any right triangles but i'm going to start off with a triangle to the center of our circle so if we were to draw from this the center of this hole to the center of the circle center of this hole to the center of the circle we have formed a triangle it's an isosceles triangle because this length will be the same as this length and this length will be the radius so will this this is not a right triangle this is an isosceles triangle but what we can do is bisect this angle here because it's an isosceles triangle when i bisect that angle it will form a right angle with the cord length and this length will be equivalent to this length that's only going to be true for isosceles or equilateral triangles and this is an isosceles triangle so that will work so now we have a right triangle we will know the radius of the circle we can find this length here which i'm going to call x and once we find x we can double it to get the distance but we also need to know the angle and the angle can be found by knowing how many divisions you have on your circle i think i can illustrate this best with an example so let's take a look in our example we have five equally spaced holes on this circle whose diameter is eight inches i want to find the center to center distance between two adjacent holes and it doesn't matter which two i choose so i'm going to start by drawing a line from the center of each of those holes to the center of the circle and that will form an isosceles triangle i know these lengths because they will be equal to the radius if the diameter is eight inches the radius will be four inches so each of these lengths will be four inches now i'm going to bisect this isosceles triangle and when i do that i'm going to actually form two right triangles because this will form a right angle with this side we can work with the top or the bottom one it doesn't matter i'll just redraw the bottom one what i'm going to do is find this distance right here but in order to do that i need an angle well what i'm going to do is find this total angle and then i'll divide by 2 to get this angle the way i find this total angle is i take a complete rotation of 360 degrees divide by the number of holes so i have five equally spaced holes so the angle between two adjacent holes has to be 72 degrees so this angle here is 72 degrees therefore half of that in this triangle would be 36 degrees now that i have an angle on this side i can find this side let's label the sides this side is across from my right angle so this is the hypotenuse this side i'm going to call this x is the opposite side it's opposite the angle so my trig function that uses opposite and hypotenuse is the sine function so the sine of 36 degrees will equal the opposite side over the hypotenuse in order to solve for x i need to multiply by four whatever i do to one side of the equation i have to do the other side so the fours will cancel and i'll get x by itself and it will equal 4 times the sine of 36 degrees which is 2.351 inches so remember i've just found this length i want to find this total length here so i'm going to need to double that value so to get the total distance between two adjacent holes i'm gonna take two times two point three five one inches to get four point seven zero two inches and we're done so it's a matter of finding the angle between the two adjacent holes drawing from each of those holes to the center of the circle to create an isosceles triangle bisect that isosceles triangle and work with the one right triangle find this length double it to get the whole distance you

Channel: MATH MADE EASY WITH LAUREL

Views: 1,410

Keywords: chord length, bolt circle, math for machinists, math for trades, trig for machinists

Id: cJ8U_9r8yj8

Length: 6min 8sec (368 seconds)

Published: Wed May 05 2021