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Copyright 1996, 2000, Denis Cousineau
 
Lego Brick measurements.
Height, width, and weight
In the following sections, torque of a Lego motor and strength of
pneumatics are all measured using Lego bricks as weight. It is therefore
necessary to know their dimension and their weight.
The standard 4 ´ 8Lego brick is constructed
as follow:
A 1 ´ 1 Lego bricks can also be measured in
terms of bump:
Width 
1 bump 
0.80 cm 
Height 
1.2 bump 
0.96 cm 
Height of a plate 
0.4 bump 
0.32 cm 
As seen, one brick and two plates on top of each other equal 1.2 + 2 ´
0.4, or 2 bumps (or equivalently in cm: 0.96 + 2 ´
0.32, or 1.60 cm). This represents exactly 2 bumps high, so that a beam on the
side can connect nicely with horizontal beams separated by two plates.
Its weight is 2.5 grams each standard Lego brick. With 400 of them, you
have exactly a kilogram (that is, approximately 2.2 lb).
Angles
The new beams are very convenient, but also composed of a weird angle. If
you place them on a wall, as shown below, we see that the 1angle beam is
adjusting perfectly over holes located at 3 bumps on the horizontal and 4
bumps on the vertical. This is a triangle with sides 345, as you certainly
remember from your trigonometry courses. What is less known is that this
triangle forms an angle of 36.87° (you can check this by noting that cosine
of 36.87 is 0.8, or 4 bumps for a radius of 5 bumps; similarly, sine of 36.87
is 3/5, or 0.6). The twoangle beams are simply composed of 45° angles,
easier to manage...
Method of measurement.
Of course, it is merely impossible to take one brick, and arrive to the
above precision. The most accurate technique to measure small things is to
measure a lot of them, and then divide by the number of measured objects. To
measure the length of a brick, I noted that in 1 meter (100 cm), exactly 125
bumps could be assembled side to side. This lead to the simple calculation
that 1 bump is 4 fifth of a cm, or 0.8 cm. Similarly, in a meter, I can put
104 bricks on top of each other, so that the height is 100/104 cm. For the
weight, I put together all my standard bricks (I have 440 of them), and went
to the grocery to weigh them. Result is 2.44 lb, or 1.1 Kg. Dividing 1100
grams by 440 bricks gives 2.5 g per brick.
