How could I extrapolate this weekend's stellar numbers to 1320' numbers?
Namely, the 3.70 and the 3.9x's.
Thanx
Good question -
I believe the answer is an explosion just before the quarter as the engine loses it's load just after 1000'.
But seriously, mathematically you could extrapolate using the good ole fashioned kinematic equations.
For simplicity and for the formulas to work, we would have to assume constant acceleration, and neglect wind resistance, rolling resistance etc.. In reality, this is not true, so the numbers I get are fantasy numbers.
A 3.70s time at 1000' gets an acceleration of 146.09 ft/s/s
With that acceleration rate, from a dead start over 1320 would take 4.25 seconds.
For speed, from a dead start that acceleration extrapolates to 423 mi/hr. This number hints at the inherent error of assuming constant acceleration, as in reality I'm sure there is a much higher acceleration rate early in the run, and it tails off later. Thinking of what the graph's would look like for constant vs varying acceleration vs time (especially later in the run), it makes sense that that last bit of time can throw off the mph by that much.
Great question as I've just been reviewing and thinking about different techniques as to how to approach this question without the assumptions.
The best way I can figure is to get the racepak data. Then you can have a graph of say the G load vs time. With that you can get graphs of the same data displayed differently, such as velocity vs time, or position vs time - all of which can be generated from the G load vs time.
You could curve fit some sort of polynomial trend line or whatever to extrapolate what the quarter could be - in fact, just the last couple points leading up to 1000' would be the most useful - but this method would have limitations based on the physical capabilities of the engine, but it would be better then what I assumed.
Even getting the incremental times I could use the basic kinematic formula to get better extrapolated data.
Also note, that even if there were no acceleration between 1000' and 1320', it takes 0.65 seconds to travel 320' at 334 mph... so add 0.65 to 3.70 and you get 4.35 - I don't remember what the record was for the quarter when they were running, but I think it was like 4.40 or something, so I guess even if it blew up at 1000' it would be a new quarter mile record.
With all that said, I think my first assumption (engine explosion) is likely what the result would have been considering the rules regarding gearing ratios and RPMs.