Quote:
Originally Posted by dlavery
/edit/I just ran a few numbers out of curiosity. In a "perfect collision" situation (two full weight 151 pound robots hitting head-on at 9 fps, with one of the robots skewed so it impacts the other "corner first") the impact forces get pretty impressive. As the robots collide, they compress the pool noodles down to 20% of their original thickness in about 0.009259 seconds. At a closure velocity of 18 fps, this is a peak change in velocity of 1944 ft/sec/sec, or a 60.75-G impact. Since I said the robot impacted "corner first" I will posit an impact area of 1.5 square inches. Assuming the pool noodles absorb about 18% of the impact energy during compression (not too bad for material of this type), that still means that the localized impact pressure is right around 10,000 pounds per square inch. I haven't looked at the bending moment of 3/4-inch plywood on 12-inch support centers yet. But I am now really not surprised by what happened to the bumpers. /edit/
There is a reason for that rule. Don't count on it changing.
-dave
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Okay... seeing as how my other car is still on this planet, I'm a bit hesitant to question these numbers, but I was doing some calculations with our programmers this evening to figure out peak velocities and such and have to question the assumed closure velocity cited here.
We used the published value of static coefficient (.06) of friction to determine that a 150 lb (68kg) robot would have a normal force of 668n and a peak forward force of 40N. The mass of the robot, plus trailer, is 186lb, or 84kg, giving a peak accelleration of 0.47 m/s/s
Next we assumed that the effective length of the playing field was 15m. Although 54 feet works out to be 16.5m, or thereabouts, the length of the robot and trailer, as well as the driver station bumpers must be subtracted from the space available for picking up speed.
Assuming constant acelleration, of .47m/s/s over 15m, it should take a minimum of 8 seconds to cross the playing field from one end to the other, with a peak impact velocity of 3.76 m/s or... 12.3 feet per second.
Now this is the peak velocity of a robot hitting the end... but it is also the maximum impact velocity that any two robots could sustain. If each started out at one end of the playing field, they would meet in the middle, and would each only have reached 6.15 fps each, for a closing velocity of 12.3 fps, which is just 2/3 of the assumed 18 fps velocity impact. (Actually it would be lower than 12.3fps, as the effective length of the playing field would again be diminished by the length of the second robot/trailer combo unit.)
That isn't to say that some robots might not exceed the published coefficient of friction as the playing field wears, or that a 12 fps impact is something to be laughed off without concern... we'll be building a solid robot and strapping solid bumpers on it... we agree with the point of the post and if this were anything but FRC would probably just say "close enough, good enough" on the calculations, but the peak closure speed and resulting extreme G-forces didn't mesh with our calculations and we were wondering if we had somehow missed something.
Or, perhaps, if the 18fps impact velocity is based on actual testing of robots on regolith, then the published coefficients of friction don't provide an accurate estimation of robot performance. I know a few teams have posted suggesting that their experimental results for coefficients of friction are much higher than the published values.
Any suggestions?
Jason
<Edit> first assumption... that is not quite right. We assumed all of the weight of the trailer would be over the trailer wheels. Some of it will contribute to the normal force of the robot and thus improve traction and accelleration. Even assuming 100% of the trailer weight does so, however, peak accelleration is just .6 m/s/s and it takes 7 seconds to make the trip with a peak velocity of 14 fps. We're getting closer...
second assumption... we were assuming a straight line path from one end to the other... it may be possible to achieve a slightly higher peak velocity by taking a curved path along the playing surface... </edit>
<edit 2> third assumption in these calculations is that accelleration will take place on the regolith. Maybe, just maybe, if everything is right and teams are driving at least partly on the carpet, an 18 fps impact speed is a theoretically possible event </edit>