OL I knew somebody would ask that. The energy ratio stays the same as the speed varies. The TKE depends on the square of the speed. The angular velocity varies directly as the speed and it, too, gets squared.
Just to be sure here are the numbers for 10 mi/hr (= 14.7 ft/sec = 2.3 rev/sec)
TKE = 1/2 X 1 lbm X (14.7 squared) ft ft/ sec/sec = 108 lbm ft ft /sec sec
W= 2 X pi radians/rev X 2.3 rev/sec = 14.6 rad/sec
RKE = 1/2 X .562 lbm ft ft X (14.6 squared) /sec sec = 59.8 lbm ft ft/sec sec
So the ratio is (59.8 + 108)/108 = 1.6 (to 3 figures it’s 1.55, but it was xmas and my 18 in lumped distance might be a little low, so I rounded up.)
Yes, it’s way, way more important to take weight off near the outside of the wheel/tire. Since the RKE varies as the square of radius of the mass from from the center, taking 1 pound off the tire tread (say at a radius of 10 in.) is about equal to taking 25 pounds off the hub (say at a radius of about 2 in.) (10/2) squared = 25!!!!!!
I didn’t want to do a bunch of detailed calculations figuring out the inertia of the wheel and tire. For my examples, I just assumed everything was lumped 1/2 in beyond the rim, at a diameter of 18 in. I admit this could be off, but as my favorite college professor said “the most important calculation an engineer does is the first one on the napkin. You don’t want 3 significant figures. you want the right order of magnitude and 1 significant number. You want to know if the answer is .06 or .6 or 6 or 60 or 6 million.” That’s what I’m after here.
I’ll look up the spreadsheet and try to figure out how it was done.
I’m not trying to figure out how to calculate the 0-60 time from scratch; that’s more complicated. That time depends on launch techique, how much power the engine has at different rpms, the gearing, how long it takes to shift, air drag, etc., etc., and the weights and inertias. I’m saying that given all the other stuff as equal (garfield’s stock runs), what can you expect just by reducing the weight and rotational inertia. And by a quick and easy calculation.
I don’t know what car/wheels/tires SCC was using. For now, for the
MCS, I stand by the 1.6 and the .2.
looking forward to your results.
(I wrote the posts out in Word. Copying them into this editor loses some punctuation and the fraction symbols, so I’m going to correct some of those in my original post, indicated by [ ] )
