four-legged landers

[Damien_The_Unbeliever]

Sorry if this has been discussed before, I've taken a (quick) look through the archives and not seen anything.

Why do we prefer four-legged landers (Apollo LEM, Falcon 9 reusable) versus three-legged alternatives? If we want to ensure that all legs make contact, 3 legs are the only combination that work (with uneven surfaces). If we want some redundancy, why is 4 the right number?

[Dkmdlb]

Because the area of the square made by connecting the 4 points of the landing feet is much larger than the area of the triangle made by 3. It doesn't matter if all the legs make contact as long as the point on the ground directly under the center of mass falls within that square. And the benefits of the larger footprint outweigh the benefit of the 3-leg stability.

*EDIT* Here is an image:

[Ten Key]

Four legs provide more stability if your lander still has some horizontal velocity when it touches down-- four legs are less likely to tip over than three.

In the diagram Dkmdlb posted above, the green line can be interpreted as the "tipping distance". The longer the green line, the farther the lander has to tilt before it will fall over.

Edited January 29, 2015 by Ten Key

[linkxsc]

Try it out in ksp yourself. Make a lander, use 1 of the lander cans as the main portion, then try to land it with 3, 4, 6, 8 legs, and see how stable it is.

6 is usually the best btw, but you cant always find space for them what with other things attached like ladders.

[sal_vager]

Interestingly, the early designs for the Lunar lander included five legs, as this was thought to be safer if one leg should break.

But it was too heavy so they went with four

Edited January 29, 2015 by sal_vager

[Damien_The_Unbeliever]

Thanks,

I'm starting to get what you mean. But from your diagrams, five legs look better than four (and then smaller improvements after) - is it a trade-off/minuscule difference?

[magnemoe]

You are right about the three legs will always have three legs on ground however you will always use shock absorbers making this less of an issue, the extra leg is well worth the 50% increase radius from center of gravity, the other option would be to increase the reach of the three legs 50% and it would be more complex and heavier.

[Dkmdlb]

Adding extra legs gives diminishing returns. You see the difference between 3 and 4 legs is large, but the difference between 5 and 6 legs isn't very big at all, right?

But each of those extra legs is extra mass and complexity. Bad for landers.

[Louella]

concept for the Lunar Escape Device.