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I like coffee. I like to drive fast. These two don't usually go together, unless you like that coffee all over your floor because you tipped it over going around the corner.

If I have up to four cups of coffee in a typical coffee tray like below, what orientation should it be to allow me to go maximum speed? You may make the following assumptions:

  • The cups may or may not be the same size, but they can be ordered in descending order of size A B C D, where any adjacent letters may actually be equal, but earlier letters are guaranteed to be not less than later letters.
  • One or more cups may be empty.
  • Cups are conic sections (your normal coffee to-go cup) that scale upward but not outward (so they can all use the same size lid). In other words, the height of the cup may be considered to be a function of its mass.
  • Contents of the cup at least 98% water, although it is possible for some to have ice. (I don't know why she wants ice in her coffee, makes it simply disgusting, but that's none of my business...)
  • There are three important scenarios - turning left 90°, turning right°, and coming to a stop going straight. In the coming to a stop, coffee and time are the only important factors, my brakes are not.
  • I'm open to any physical parameters to adjust my coffee (my gut tells me placement in the tray and orientation to the direction of travel are most important), but it must be on a flat surface made of a typical floor mat on which sits a cardboard tray of three or four coffee cups. (If it were only one or two, I'd put them in my car's cup holders. If a one- or two- cup configuration is more stable than a three- or four- cup configuration, I can put the one or two least stable cups in my car's cup holders instead to guarantee they never spill. My experience has been one and two cup trays tip way too fast, so I suspect that won't be part of a solution... but you never know!)

How would an object which is fairly tall (relative to its base) have optimal balance in an environment which is constantly accelerating, decelerating, and following sharp curves?

Here's an image of a 3 cup configuration before it reaches my car: enter image description here

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So for starters you need to make sure the center of gravity is in the middle of the tray (so in you scenario of lighter/heavier cups, balance it out). This is assuming that you make as many right turns as left turns. If this is not the case, say 70% of your turns are right turns, then you would want to slightly offset the orientation so that it's not quite balanced. Also, this depends on your driving style.

If you prefer to have sharp deceleration and acceleration: Bracing it against a object would be preferable. Apart from that, I would suggest putting the third cup in front, in a the below formation (simply because rapid deceleration is less predictable (and controllable) than rapid acceleration

enter image description here

If you prefer sharp deceleration but can gradually accelerate: same formation, and bracing it would certainly help.

If you prefer sharp acceleration: Then the below formation would be most appropriate. As before, bracing would be useful. Also (this might be a greater risk than it's worth) consider placing a thin book under the back coffee cup. This will align it further backwards, making it more suitable for sharp acceleration (but more susceptible to deceleration)

enter image description here

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  • $\begingroup$ By the way, this assumes that you only have three cups. If you have four cups, then try to balance out the weight and orient it in this 45º rotation (it gives better stability in turning). $\endgroup$ Jan 21, 2016 at 22:09
  • $\begingroup$ So the grey circle is the lightest cup (which may or may not be empty)? $\endgroup$
    – corsiKa
    Jan 21, 2016 at 22:54
  • $\begingroup$ It can either be an empty cup, or no cup at all (though this does change stability a little bit. I would say that, if you have the option, ask for an extra cup if you only have 3 cups. Having that fourth cup would make bracing a lot easier. $\endgroup$ Jan 21, 2016 at 22:55
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If you have no means to change the inclination of the tray while you are driving, then the answer is: flat. You'll make as many left turns as right turns, so you can't favor left tilt vs right tilt. And you will speed up as well as slow down, so you can't favor forward tilt vs backward tilt.

The distribution of cups ... which cup goes where ... doesn't seem to make any difference either.

Just make sure that the cups are held firmly enough so that the don't tilt in response to acceleration, braking, or turning. I know that's not what you wanted to hear. Sorry.

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  • $\begingroup$ The orientation certainly matters - if I have two heavy cups and two light cups, I can put them criss cross to have better stability than a row of heavy and a row of light. So unless I misunderstand your answer, it's demonstrably incorrect. $\endgroup$
    – corsiKa
    Jan 21, 2016 at 21:49

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