The Brick Bakery:Diagonal bracing.

Did you ever have a situation where you needed to brace a Lego Technics structure with a beam placed diagonally?

It's hard to find a set of horizontal and vertical spacings that produce a good fit. You can use Pythagoras' theorem to compute this exactly - but it's painful to search through all the possibilities looking for a good fit.

In many situations, you can tolerate a small error in the exact dimensions - and this makes it possible to find many horizontal and vertical combinations that come close enough to an exact fit to be useful.

I have only listed combinations that result in a diagonal beam length less than 15 studs because the longest Technic beams are 16 studs - which have only 15 holes.

Exact fits:

There are only four combinations that produce exact fits for reasonable sizes of beam:

Perfect Fit


  3 studs x 10 plates =  5 studs exactly
  6 studs x 20 plates = 10 studs exactly
  8 studs x 15 plates = 10 studs exactly
  9 studs x 30 plates = 15 studs exactly

Loose fits:

In these cases, the diagonal brace will be a little longer than you ideally would like - so it will tend to force apart the layers of plates in the vertical direction. Sometimes this is acceptable (especially if the error is small).

This table lists all the combinations that are too loose ...these are sorted with the best fit first:

Good Fit - Errors less than 1/100th of a stud


 13 studs x 13 plates = 14.001 studs
 11 studs x 12 plates = 12.002 studs
  3 studs x 13 plates =  6.003 studs
 15 studs x  1 plates = 15.005 studs
 13 studs x  1 plates = 13.006 studs
 14 studs x  1 plates = 14.006 studs
  6 studs x 26 plates = 12.007 studs
 11 studs x  1 plates = 11.007 studs
 12 studs x  1 plates = 12.007 studs
 10 studs x  1 plates = 10.008 studs
  9 studs x  1 plates =  9.009 studs

Reasonable Fit - Errors less than 1/50th of a stud


  8 studs x  1 plates =  8.010 studs
  7 studs x  1 plates =  7.011 studs
  6 studs x  1 plates =  6.013 studs
 10 studs x 28 plates = 15.015 studs
  5 studs x  1 plates =  5.016 studs
  9 studs x 11 plates = 10.018 studs

Poor Fit - Errors less than 1/20th of a stud


  4 studs x  1 plates =  4.020 studs
 15 studs x  2 plates = 15.021 studs
 14 studs x  2 plates = 14.023 studs
  2 studs x 22 plates =  9.024 studs
 13 studs x  2 plates = 13.025 studs
  3 studs x  1 plates =  3.027 studs
 12 studs x  2 plates = 12.027 studs
 11 studs x  2 plates = 11.029 studs
  4 studs x 23 plates = 10.032 studs
 10 studs x  2 plates = 10.032 studs
  8 studs x 19 plates = 11.034 studs
  9 studs x  2 plates =  9.035 studs
  2 studs x  1 plates =  2.040 studs
  8 studs x  2 plates =  8.040 studs
  7 studs x 18 plates = 10.042 studs
  9 studs x 20 plates = 12.042 studs
  9 studs x 16 plates = 11.044 studs
  7 studs x  2 plates =  7.046 studs
 15 studs x  3 plates = 15.048 studs

Very Poor Fit - Errors less than 1/10th of a stud


  1 studs x 25 plates = 10.050 studs
 14 studs x  3 plates = 14.051 studs
  6 studs x  2 plates =  6.053 studs
 13 studs x  3 plates = 13.055 studs
  3 studs x 24 plates = 10.058 studs
  9 studs x 27 plates = 14.058 studs
 13 studs x 19 plates = 15.059 studs
  6 studs x 29 plates = 13.060 studs
 10 studs x 21 plates = 13.060 studs
 12 studs x  3 plates = 12.060 studs
  1 studs x 20 plates =  8.062 studs
  7 studs x 10 plates =  8.062 studs
  5 studs x  2 plates =  5.064 studs
 11 studs x  3 plates = 11.065 studs
  3 studs x 16 plates =  7.068 studs
  6 studs x 17 plates =  9.069 studs
 10 studs x  3 plates = 10.072 studs
 12 studs x 13 plates = 13.078 studs
 14 studs x 14 plates = 15.078 studs
  4 studs x  2 plates =  4.079 studs
  9 studs x  3 plates =  9.080 studs
  1 studs x 15 plates =  6.083 studs
 15 studs x  4 plates = 15.085 studs
 11 studs x 22 plates = 14.087 studs
  2 studs x 17 plates =  7.088 studs
  8 studs x  3 plates =  8.089 studs
  8 studs x 29 plates = 14.091 studs
 14 studs x  4 plates = 14.091 studs
 10 studs x 12 plates = 11.092 studs
 10 studs x 17 plates = 12.093 studs
  5 studs x 19 plates =  9.097 studs
 13 studs x  4 plates = 13.098 studs

Tight fits:

Lego doesn't like being put under too much tension - but here are all of the combinations that are too tight by less than one tenth of a stud.

These are ranked with the most accurate fit first. Entries towards the bottom of the table are probably unusable:


  6 studs x  9 plates =  6.997 studs
 12 studs x 18 plates = 13.994 studs
  2 studs x 27 plates = 10.984 studs
  6 studs x 23 plates = 10.984 studs
  3 studs x 29 plates = 11.982 studs
  1 studs x  7 plates =  2.973 studs
  7 studs x 14 plates =  8.964 studs
  2 studs x 14 plates =  5.946 studs
  4 studs x 11 plates =  5.946 studs
  4 studs x 20 plates =  8.944 studs
  8 studs x 10 plates =  8.944 studs
  6 studs x 13 plates =  7.940 studs
  5 studs x  8 plates =  5.936 studs
 14 studs x 13 plates = 14.935 studs
  7 studs x 21 plates = 10.934 studs
 11 studs x 17 plates = 12.932 studs
  5 studs x 12 plates =  6.931 studs
 10 studs x 11 plates = 10.925 studs
 12 studs x 12 plates = 12.924 studs
  3 studs x 21 plates =  8.920 studs
  1 studs x 12 plates =  4.903 studs
  5 studs x 27 plates = 11.901 studs

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Steve Baker <steve@sjbaker.org>