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I hear what you are saying, but I don't agree with the way you are using the word, powerband.But I have no better wording either.
I think what you are getting at, is for a best mph, the car needs to trap at an rpm that has wrung the most out of the engine that it has to give, in as many gears as are in the tranny.That works well for an automatic, but a street car with a stick, takes time to shift,during which no power is being transmitted. There may be a benefit to limiting the number of shifts to 3 in an 80 mph stick-car. In a 110mph car 4 would probably be better.I'm just throwing numbers out there. In any case, you are always gonna want to gear it to trap well,in top gear.
--But I'm of the persuasion that the engine should be built with the tranny gear-spreads in mind. If you have a 4-gear tranny with tight ratios, you can make use of an engine with a narrow powerband. If you have a wide-ratio 3-gear tranny that really pulls the Rs down,she will need a wider powerband ,so it can pull itself back up out of the basement.
--My current combo was built for the A833 O/D box which requires a very wide powerband, cuz the splits leave the engine in the basement. The ratios are 3.09-1.67-1.00-.71 or .73. The splits are 54% and 60%. That means when I outshift at 7000, the Rs fall to 3780 and 4200. So that tranny needs a 3220/2800 rpm powerband. That's huge.
I realized right away that was no fun. So I slid a 4spd in there with a GearVendors behind it, which can be used as a splitter.The useable gear ratios with this combo are; 3.09(1st)-2.41(split)-1.92(2nd)-1.50(split)/1.39(3rd)-1.00(4th)-.78(O/D) The splits with this tranny are 78%,80%,78% for the first 4 ratios .Now I only need to outshift at 6400, to drop in at 5000. This reduces my powerband requirement to 1400rpm. This puts down a lot more average horsepower during the run. So now I don't need that 3000rpm powerband anymore.
In theory I could tighten up the LDA from it's current 110 to something like 104, and get more specific horsepower out of the combo, while giving up the tractor-like midrange and also giving up some off-the-line giddy-up. But with the 3.09 x 3.55 = 10.97 starter gear, getting off the line is not a problem.
And since the car has already gone 93 mph(1/8th) with this combo, I am certain it would go faster. But 93@6400 requires a trap gear combo of 5.42. Since I will be in 2nd over, which is 1.5 ratio, to trap well I would need 3.61s. Hence why I run 3.55s. They put me on the line at 6150, which is probably where it needs to be.
--So getting back to your example, with a 4500 rpm shift point, 80 mph trap, and a 904, and 4.56s.This tranny has ratios of 2.45-1.45-1.00, which gives a starter gear of 11.17, and equates to drops of 59% and 69%. This means that the Rs will drop to something like (0%TC slip),2655 and 3105.And that spits out a powerband requirement of 1845/1400. But if it was an A833 with ratios of 2.66-1.92-1.39-1.0; The starter gear would be 12.13, and the drops would be 72%,72%,72%; and the Rs would fall to 3240, making the powerband requirement just 1260.It doesn't sound like much, but the math says it's nearly 1/3 less Rs.
I think it should be readily apparent which tranny will pull a better mph.
The rear gear, in drag-racing, only helps you two times; through the traps, maximizing your MPH, and off the line. The rest of the time it gets lost in the total reduction number of; rear gear x tranny gear x splitter gear (if you have one), x engine torque, and becomes just part of the equation, getting you from here to there.
