312 GD&T: Application and Interpretation Copyright Goodheart-Willcox Co., Inc. may also be plotted on grid paper to determine the amount of positional variation. This method is explained later in this chapter. Position Calculations from Coordinate Measurements Coordinate measurements may be used to cal- culate the diameter of position tolerance consumed by a measured hole. The position tolerance used, or consumed, by the produced hole location must be equal to or less than the allowable position tolerance for the hole. To determine if a hole position is acceptable, it is necessary to obtain the measured coordinates for the produced hole location. Coordinate measurements to each of the produced hole positions are made relative to the datum reference frame. Refer to Figure 8-20. The given fi gure shows the measured coordinate data entered in a table. The difference between the measured coordinate data and the required basic dimensions is calculated to determine the X and Y location variation for each hole. The X and Y varia- tions (delta coordinate values) are used to calculate the required diameter of circle to enclose the delta coordinates. The given fi gure shows a drawing and a pro- duced part. It also includes a table that shows the measured diameter of each hole, the measured X and Y coordinates, the basic dimensions for the true position coordinates, and the calculated X and Y coordinate variations for each hole. The diameter of position variation result- ing from the coordinate variations, in this case the X and Y coordinate variations, may be calculated using the formula in Figure 8-21. The formula for diameter position variation can also be expressed as Pv = 2[(x2 + y2)1/2]. After obtaining information shown for hole #1 in the previous fi gure, we see that the X coordinate variation is .006″ and the Y coordinate variation is –.001″. The calculations of the diameter position variation require squaring the two coordi- nate variation values (.000036″ and .000001″ respec- tively), then fi nding the square root of the sum of the two squares (.00608″). This value is the hypotenuse of the coordinate errors, and therefore is the radius of a circle centered on the true position. To determine the diameter, the radius is multiplied by 2. The posi- tion variation for the example hole is .0122″ diameter. Because this value was determined from mea- sured data, it may be labeled as the measured position variation diameter or position tolerance consumed. For the hole position to be acceptable, the measured position variation diameter must be less than or equal to the allowable position tolerance. As previously explained, the allowable position tolerance is equal to the specifi ed tolerance plus any applicable additional tolerance. An additional toler- ance is applicable where the tolerance value includes the MMC modifi er and the controlled feature has departed from MMC. An additional tolerance is also possible where the tolerance includes the LMC mod- ifi er and the feature departs from LMC. The information provided in Figure 8-20 shows that hole #1 was produced at .191″ diameter. The specifi ed MMC is .188″ diameter. The difference between the produced hole size and the specifi ed MMC size permits an additional tolerance of .003″. The allowable position tolerance for hole #1 is determined by adding the specifi ed tolerance of .012″ and the additional tolerance of .003″. The max- imum allowable position tolerance for hole #1 at its produced size is .015″ diameter. Because the .0122″ = 2 X + Y 2 2 + = Coordinate variation .006 -.001 = 2 .000036 + .000001 = 2 .000037 = 2 (.00608) Additional tolerance .003 Allowable tolerance .015 X Y .506 -.500 .374 -.375 = .0122 Diameter position variation Measured location Specified location Diameter position variation = 2 .0062 + (-.0012) Allowable tolerance Specified tolerance Any applicable additional tolerance Produced hole size MMC size .191 -.188 Specified tolerance Additional tolerance .012 +.003 Diameter position variation must be less than or equal to allowable tolerance Diameter position variation Allowable position tolerance .0122 ≤ .0150 ≤ Goodheart-Willcox Publisher Figure 8-21. Allowable tolerance and actual position variation may be calculated and compared to determine if a produced part is acceptable.