Sunday, 29 March 2009

Stud Formulae

Hey there, guys. I've just perfected some formulae to work out how many tubes and tube spaces there are on each brick. Look, I'll explain.

Sometimes when you want to work out how many tubes are on a Lego brick, simply counting them isn't enough. Firstly, I'll explain what tubes are.

Take an ordinary Lego plate, say a 4x4 square one. The studs (all 16) should be on top. Now turn the brick over. You should see an interesting pattern of what looks like studs, but are hollow. These are tubes. Studs from another brick will fit in between them.

So here's an easy way of finding out how many tubes there are on a brick which has so-and-so studs. To calculate this, you need two values: the number of horizontal studs and the number of vertical studs on a brick, if seen from above.

So, you can see that our brick has a vertical stud number (Sv) of 6 and a horizontal stud number (Sh) of 4. These can easily be swapped, you don't have to worry about which is vertical and which is horizontal. Now let's take a look at the equation:

Tube# = (Sv-1) x (Sh-1)

So let's input our values...

Tube# = (6-1) x (4-1)
=15

So our 6x4 plate has 15 tubes. If you have one lying around, take a look at it and you'll see it's right!

Now then, for some techniques (such as the Enjary joint) we need to know how many Tube Spaces there are. Let's look at our diagram again:

As you can see, the studs have turned grey and the tubes are now in white. The spaces between the tubes are highlighted in red. Now sometimes, counting those spaces can be tricky. No need to worry! I've got a formula for ye:

( ( (Sh-1)-1)x(Sv-1) ) + ( ( (Sv-1)-1)x(Sh-1) )

Substitute your horizontal stud numbers and vertical stud numbers...

( ( (4-1)-1)x(6-1) ) + ( ( (6-1)-1)x(4-1) )

...and you will get an answer of 22, which is correct! You can call this stud-gap number ǥ (for those of you who can't see it, it's a g with a cross through its tail).

I rest my case.

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