Quote:
Originally Posted by JesseK
... 5-lbs of weight will spend over 75% of their climb time in the acceleration phase, resulting in a 6+ second climb....
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I'll ditto Gary here. Check your math on this one. I was thinking along similar lines two weeks ago and whipped up a spreadsheet to do all the numerical integration for me. The acceleration phase was stupidly short, in the tenths of a second. But we don't need a complicated spreadsheet to tell us that. If we gear for peak power, that's 1/2 stall torque. So full stall torque is 2 times the weight of the bot, is 1 g instantaneous acceleration at the beginning. When you get up to half your final speed, you're still doing 0.5g. At 3/4 final speed, it's still 1/4g, and so on.
In fact, if you toss out friction, this is a very nice linear system to model. The fact that your torque/force decreases linearly with your speed makes it just another damping term, so it actually works out to a simple mass-damper system with an external force. So if I wasn't so lazy, I could tell you the exact time constant based solely off the robot's mass and motor characteristics.