The Long Tall Model

That Kept Falling Over.

Because of this: (https://study.com/academy/lesson/law-of-the-lever-definition-formula-examples.html)

Someone on a forum I'm in had issues with a tall skinny item of which every attempt to print kept detaching when it got to a certain height and they thought their printer had a fault and were looking into stabilising the Z-axis lead screw and all sorts.

Hoping their issues have now been sorted out by the conversation we had.

The issue's a well known one - and the standard solution is to print it with a brim, or in extreme circumstances with a raft. And it's to do with levers, as the beginning link indicates. 

Quick example: 
I'm printing models of various antenna towers. The models are a pyramid shaped tower, a square section tower, and a square tube tower such as is used for cellphone antennas. Cases A, B, and C:

All the maths you need are the formula for levers (F1 x L1 = F2 x L2) and for surface area (L x W) of the base of each print. 

For this exercise let's assume that the models will include all the ground it's standing on and all are 15cm tall. 

I'll use lengths of  4cm, 2cm, and 1cm for L2 in cases A, B, and C respectively. L1 will be 15cm in every case, and we'll work on the forces once we have the maths.

So the surface area under each print comes to 16 square cm for case A, 4 square cm for case B, and 1 square cm  for case C. If we assume that it take about 5g of force to separate a model off the bed for each square cm that makes the breakaway force 80g for case A, 20g for Case B, and 5gm for case C.

So the F2 x L2 portion of the equations will be 80x4=320 for A, 16x2=32 for B, and 5x1=5 for C.

That means that at that point 15cm up, it would take 21g of sideways force to rotate the base off the print surface in case A, 2g in case B, and a force of just 0.3g in the case of the skinny model C.

Conclusion

A brim is attached to the bottom of the model and increases the surface area in contact with the print surface, increases the length of L2 which adjusts the lever ratio and makes it harder for the print head to pull the model over. As you could see, a small increase in the base makes a great deal of difference in the printability of a model. 

Try it - print a cylinder of 0.5cm diameter and 200cm tall (in vase mode if you like, for speed) and see how tall you can print it before it gets pulled over. Now add a brim of 0.5cm width all around and try again. I bet you won't get more than 5cm in the first case and probably a full print in the second.

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