{"id":1300,"date":"2025-12-02T16:18:26","date_gmt":"2025-12-02T16:18:26","guid":{"rendered":"https:\/\/thetrigonon.com\/?p=1300"},"modified":"2026-02-13T17:55:04","modified_gmt":"2026-02-13T17:55:04","slug":"errors-in-ab-measurements","status":"publish","type":"post","link":"https:\/\/thetrigonon.com\/index.php\/2025\/12\/02\/errors-in-ab-measurements\/","title":{"rendered":"Errors in AB measurements"},"content":{"rendered":"

If you are measuring pool covers and liners with buckets and tape measurements, how often do you feel something isn\u2019t \u201cright\u201d when you go to install, even though you felt you took \u201creally good\u201d measurements?\u00a0 \u00a0 <\/span><\/p>\n

Based on our detailed analysis, we have discovered that your measurements could be off by as much as 30\u201d (2 \u00bd feet) if you have as little as a 2\u201d mistake in the AB bucket locations.\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

To understand why this can happen, let\u2019s start with how AB measurements work.\u00a0\u00a0<\/span><\/p>\n

AB measuring relies on simple geometry to determine a desired point\u2019s location in space based on \u201ctriangulating\u201d distances from two other \u201cknown\u201d points, namely the A and B locations.<\/span><\/p>\n<\/div>

<\/span><\/div>

If we consider the buckets to be located along the X axis in an X-Y coordinate system, with A centered at (0,0) and B centered at (0, X<\/span>AB<\/span>), then any point we measure in space can be determined by taking 2 measurements: M<\/span>A<\/span> and M<\/span>B<\/span> as shown above. \u00a0 Using the 3 \u201cknown\u201d lengths M<\/span>A<\/span>, M<\/span>B<\/span> and AB, we can easily calculate the (x, y) coordinates of the point and plot on a graph as shown.\u00a0\u00a0<\/span><\/p>\n

Doing this type of measurement at key points around a pool, you can easily generate an image like the one below, which can be used by manufacturers to create covers and liners for the pool with exceptional accuracy.<\/span><\/p>\n<\/div>

<\/span><\/div>

BUT, the accuracy of what is built relies on the accuracy of the points captured.\u00a0 The calculation is precise, so all errors are introduced by errors in any or all of the three measurements used (e.g., M<\/span>A<\/span>, M<\/span>B<\/span> and AB).\u00a0 In other words, the accuracy of any point\u2019s location will be determined by the accuracy in each of the three measurements used (e.g., M<\/span>A<\/span>, M<\/span>B<\/span> and AB).\u00a0\u00a0\u00a0<\/span><\/p>\n

Let\u2019s first consider errors in M<\/span>A<\/span> and M<\/span>B<\/span>.\u00a0 If M<\/span>A<\/span> and M<\/span>B<\/span> are slightly wrong, then the location of the point will be roughly off by the same magnitude, in any direction.\u00a0 This can be demonstrated by the \u201ccircle of uncertainty\u201d shown in the picture below.<\/span><\/p>\n<\/div>

<\/span><\/div>

As a concrete example, if M<\/span>A<\/span> and M<\/span>B<\/span> have errors of roughly \u00bd\u201d, the most you would expect any points\u2019 location to vary would be 1\u201d in any direction.\u00a0 While this is not ideal, it can be managed by taking more accurate measurements to A and B from each point.\u00a0 Also, the error introduced will be \u201caveraged out\u201d over the course of all the measurements, as each will be somewhere within that \u201ccircle of uncertainty\u201d, and the overall shape of the pool outline will still be roughly accurate, since over all the measurements, we would expect each to fall within a small range around each \u201cactual\u201d point, as shown below.<\/span><\/p>\n<\/div>

<\/span><\/div>

As we started with, we determine a point\u2019s location using triangulation with three \u201cknown\u201d values.\u00a0 We\u2019ve discussed the errors introduced in two of them (namely M<\/span>A<\/span> and M<\/span>B<\/span>), now let\u2019s think about the third, the AB distance.\u00a0 Assuming you can take accurate measurements at any distance to AB (which can be difficult for many other reasons using tape measurements and buckets), the real problem is introduced with inaccurate measurements of the AB locations, since those changes are systemic, and impact every point differently.\u00a0<\/span><\/p>\n

The other complexity with AB is that errors are introduced in 2 ways.\u00a0 The first is if the AB location is not measured accurately when the AB\u2019s are setup, or it\u2019s recorded inaccurately, so that it differs from \u201creality\u201d by some amount.\u00a0 The second is that the AB length changes by mistakenly moving whatever is used to determine either the A or B location.\u00a0 If using buckets with tapes attached, this could be caused by pulling on the bucket too hard trying to get the tape taught, forcing it to slide along the deck.\u00a0 Even if you noticed this happened, you may not return the bucket to the exact original location before taking new measurements, resulting in a small change in the AB length.<\/span><\/p>\n

Both of these issues result in using a value of AB in the calculation that is \u201cwrong\u201d, resulting in incorrect values of X and Y.\u00a0 What we will show is that small changes in AB can have really dramatic effects on the calculated values of X and Y for any and all points.\u00a0<\/span><\/p>\n

To understand this, let\u2019s consider M<\/span>A<\/span> and M<\/span>B<\/span> to be fixed (well known) and think about what happens with small errors in AB.\u00a0 This can be modeled by connecting two rigid sticks at one end (where we are measuring the point from), as shown in the following picture.<\/span><\/p>\n<\/div>

<\/span><\/div>

If we then \u201cpin\u201d the A location, and move the B location along the X-axis, you can see what happens to errors in the AB length.\u00a0\u00a0\u00a0<\/span><\/p>\n

Let\u2019s first consider the situation where we inaccurately measure the distance between the A and B locations, such that the value we measure is larger than \u201creality\u201d.\u00a0 This will result in a calculation of the X,Y coordinates of the point as shown here.<\/span><\/p>\n<\/div>

<\/span><\/div>

Using the actual AB length, the point should be placed at the (x, y) coordinates of (-2, 4).\u00a0 But, since we use a longer length for AB in the calculation (using the same M<\/span>A<\/span> and M<\/span>B<\/span>) values, we actually calculate (x, y) to be about (-1, 4.5), which is much different from \u201creality\u201d.\u00a0 You can see the calculated value is \u201cpulled\u201d to the right as the B location slides to the right.\u00a0\u00a0<\/span><\/p>\n

This is true if we go the other way as well, just the opposite. \u00a0 If we consider the case where we measure AB to be shorter than \u201creality\u201d, we get the following.<\/span><\/p>\n<\/div>

<\/span><\/div>

Here, since B is moved to the left, it pushes the pivot point left and down, and results in an inaccurate measurement as well.\u00a0\u00a0<\/span><\/p>\n

This effect is identical if we move the bucket after measuring its AB separation length, and we have the following two examples. The first shows the bucket moving to the right.<\/span><\/p>\n<\/div>

<\/span><\/div>

And the second shows the bucket moving to the left.<\/span><\/p>\n<\/div>

<\/span><\/div>

So all of these show that incorrect measurements of AB, just like M<\/span>A<\/span> and M<\/span>B<\/span>, result in incorrectly calculated point locations.\u00a0 What may not be obvious in these pictures is the magnitude of change.\u00a0 The change in total distance from the actual point to the calculated point can sometimes be much larger than the shift in B, and this varies depending on where the point is located relative to A and B.<\/span><\/p>\n

To determine the possible amount of changes, we started with a simple pool outline calculated \u201cprecisely\u201d for a 20\u2019 x 45\u2019 pool, using buckets separated by 15\u2019 feet centered on the pool at 3\u2019 from the edge.\u00a0 The original drawing looked as follows:<\/span><\/p>\n<\/div>

<\/span><\/div>

Then, we calculated what would happen if AB was wrong by different amounts using the precise values of M<\/span>A<\/span> and M<\/span>B<\/span>.\u00a0 The results of this analysis are as follows:<\/span><\/p>\n<\/div>

<\/span><\/div>

This shows that if AB is wrong by as little as \u00bc\u201d, you will see some points off by at least 2 \u00bd\u201d.\u00a0 Even what may seem like a small change of \u00bd\u201d will result in some points being about 5\u201d off.\u00a0 This may be OK for some situations, but for pool liners, this will definitely result in the liner not fitting properly, especially at the steps and seams. \u00a0 BUT, if you somehow have AB wrong by only 2\u201d, you will have at least one point 27\u201d away from its actual location which would result in a cover or liner that doesn\u2019t fit at all.<\/span><\/p>\n

We took this a step further and ran many more possibilities, resulting in the table below:<\/span><\/p>\n<\/div>

<\/span><\/div>

The columns represent different AB lengths (bucket separations), and the rows are the amount of error introduced in measuring AB length.\u00a0 You can easily see that small changes in error in AB result in large movements of the calculated point from the actual point.\u00a0\u00a0<\/span><\/p>\n

To see this visually, we applied the same method to two pool situations with steps.\u00a0 The blue dots represent the calculated value using an AB that is \u00bd\u201d too big, and the orange dots are using an AB that is \u00bd\u201d too small.<\/span><\/p>\n<\/div>

<\/span><\/div>
<\/span><\/div>

In each of these cases, for a 20\u2019 x 45\u2019 pool with a 4\u2019 x 8\u2019 step setback, you see some points in the step area off by 7 or more inches. \u00a0 This is a BIG deal if you want the liner to fit!<\/span><\/p>\n

So what does this all mean?<\/span><\/p>\n

First, you should do everything you can to reduce errors in measurements.\u00a0\u00a0<\/span><\/p>\n

Second, you need to measure the distance between A and B as closely as possible, and make sure it doesn\u2019t change.<\/span><\/p>\n<\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":1307,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-1300","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blogs"],"yoast_head":"\nErrors in AB measurements - Trigonon<\/title>\n<meta name=\"description\" content=\"Learn what causes the worst errors in AB Measuring a pool and how to fix them and become as accurate as possible!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/thetrigonon.com\/index.php\/2025\/12\/02\/errors-in-ab-measurements\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Errors in AB measurements - 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