But I take it that you agree with the Strong Form of Golden Horsepower then? That the HP curve doesn't matter after all?
I actually think there's something missing in TBz's proposed proof, and the Strong Form doesn't hold after all.
The point is that although the "proof" seems to establish one particular transmission where absolute best acceleration is achieved, actually it is always possible to squeeze out a little more acceleration at lower speeds, therefore there are always certain kinds of acceleration competitions where the HP curve still matters.
The construction of counterexample is funny too. Remember the F0 at speeds under V0? Well it depends on the friction coefficient between the tire and the road, and what does the friction coefficient depend on? The weight at the driving wheels. If the car is two-wheel drive with transmission located near the driving wheels, increasing the weight of the transmission by an amount of X will increase F0 by a bigger factor than total vehicle weight, hence marginally increase acceleration below V0. Furthermore, it lowers the V0 where tires do not spin. During this brief moment, it is no longer always optimal to keep engine rpm at R0 (where HP is peak). And then an engine with better HP curve wins the acceleration test marginally, up to V0.
The analogy is: If you increase the final drive ratio of your transmission, you'll increase the likelihood of wheel spin, but then if you put a sandbag in your trunk, you reduce wheel spin and have faster acceleration (up to a point, after that the higher weight still hurts you).
I actually think there's something missing in TBz's proposed proof, and the Strong Form doesn't hold after all.
The point is that although the "proof" seems to establish one particular transmission where absolute best acceleration is achieved, actually it is always possible to squeeze out a little more acceleration at lower speeds, therefore there are always certain kinds of acceleration competitions where the HP curve still matters.
The construction of counterexample is funny too. Remember the F0 at speeds under V0? Well it depends on the friction coefficient between the tire and the road, and what does the friction coefficient depend on? The weight at the driving wheels. If the car is two-wheel drive with transmission located near the driving wheels, increasing the weight of the transmission by an amount of X will increase F0 by a bigger factor than total vehicle weight, hence marginally increase acceleration below V0. Furthermore, it lowers the V0 where tires do not spin. During this brief moment, it is no longer always optimal to keep engine rpm at R0 (where HP is peak). And then an engine with better HP curve wins the acceleration test marginally, up to V0.
The analogy is: If you increase the final drive ratio of your transmission, you'll increase the likelihood of wheel spin, but then if you put a sandbag in your trunk, you reduce wheel spin and have faster acceleration (up to a point, after that the higher weight still hurts you).
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