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Originally Posted by swamp2
Not so. It's sort of all about the R^2 value... Really.
There is only a 3% difference in the predictive capability of power to weight vs. trap and power to weight vs. ET. And in fact the model for ET actually has fewer outliers:
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For me, that 3% is essentially a yawning gap. At least it is out on a drag strip. I admit that numerically speaking, 3% is a relatively tiny amount.
Quote:
Originally Posted by swamp2
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Nice find! Thanks.
Quote:
Originally Posted by swamp2
As much as I thought the data would make a massively worse correlation (hence my challenge to Petros) the short answer is that is is way better than I expected. The data just happened to be present in the link above so I grabbed it and did the work.
We have to accept (observe) that average power correlates reasonably well with peak power. If that wasn't the case we would not have such a strong predictive power in this model. However, power and torque are certainly correlated as well. Of course since peak torque and peak power pretty well never occur at the same rpm we can't use the rigid relationship at a given rpm. However, not surprisingly peak torque and peak power as well as average power are all correlated. The R^2 value when running the regression is a surprisingly high, 0.78. Again that is compared to a 0.93 for trap speed vs. (peak) power to weight. So in short the torque to weight model is only capturing 15% less of the observed variation.
Last but not least, we should observe that despite this reasonable correlation this relationship is still entirely less CAUSAL than regressing vs. power to weight. Recall the important distinction between correlation vs. causation. The physics indicate we should observe a correlation in the power to weight case and we do. It just so happens that peak torque also correlates with peak power. There is no reason this has to be so, as evidenced by F1 cars that make absurd power with very little torque. And again we can do the thought experiment where we double peak torque and performance won't change appreciably, we can't do the same with power.
I won't be surprised if you have a more elegant way of explaining why the correlation is much better than expected.
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Sans elegance, three things:
First, taken across a plethora of data points, torque-to-weight will generally be a rough average percent (compared to power) across many internal combustion engines.
Second, expect the rough average to change as we move further into force-fed proliferation of engines, and particularly, force-fed diesels. In these cases, the torque-to-power relationship changes pretty dramatically, while quarter-mile performance changes only somewhat..
Lastly (and just in agreement), power and weight will be a strong predictor of quarter mile performance case by case, and torque and weight will not be. The fact that you've found a moderately loose relationship across a large number of cars is interesting, but no more than that.
Bruce