Quote:
Originally Posted by IKE
So, I was very inspired by some of the physics guys up above, and have a challenge:
Assume 16m dash (approx. 54 feet- robot length), and COF of 1.0. Also assume a 4 cim power-train at 300 Watts/CIM.
What weight is your bot so that you are just barely traction limited the moment you strike the other wall? Is this less than 4 cims & a battery?
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First of all THANK YOU for putting it in meters to spare me the conversions necessary to use watts and meters. However, there would be a missing variable in the necessary calculations if I am not mistaken, because we would need to know a time that it would take to travel said 16m. But I can solve for this with time as a variable anyway.
P
T = 4P
CIM
P = 1200 watts (~80 - 95 % efficient depending on number of gears, transmission, and other variables)
F
f = mgµ = m*9.8*1 = 9.8m
Work = Force * Distance = 9.8m * 16 = 156.8*m
time = Work / Power = 156.8*m / (between 960 and 1140) watts = between .138*m and .163*m seconds
so to solve for mass (in kg) it would work out to between 6.135 * t to 7.246 * t depending on the efficiency.
Of course, this all assumes that the robot would be constantly accelerating at the maximum possible value (no slipping/static friction) and that the robot would be able to keep getting faster and faster, but I'm pretty sure it would be impossible to gear 4 cims without a transmission such that they provided exactly maximum static frictional force and still could reach rotational speeds that would allow it to continue accelerating...would probably need really really small wheels, but not too sure about that one.