Hahaha I usually end up doing pages and pages of sketches before even presenting an idea to my team ( I have too much free time at school
)
Half of them end up being junk of course, and I can't do any of those kinds of advanced calculations (Yet), but my study hall time usually yields some pretty crazy stuff.
and then if I like it enough, I'll do a quick Google Sketchup model or something on my laptop (I'm still learning "real" CAD, but have gotten quite proficient with Sketchup)
Over the past year that I've been on the team, I've been trying to get other students do do more sketches, it seems they just want to wing it, and build as they go