I think you understand my content perfectly, but perhaps completely misunderstood my intent. The explanation I provided is not “my” numbers, but rather an explanation, for our reader’s edification, of well accepted mathematical relationships equating power, drag, and velocity.Perhaps I misunderstand your content here?
But I just tried to compare your numbers to real world scenarios and I’m stuck with this 8x power increase for 2x speed increase equation.
How much power does it take for a Norton Commando to hit 30mph? Looking at mopeds etc I’m going to take a wild stab at somewhere around 5 BHP. Even if wrong, it’ll do to play with for now.
5 BHP at 30mph would then require 40 BHP at 60 mph. And 320 BHP at 120 mph.
Thats not right is it ?
Yes, your well-intentioned calculation is all correct. If it takes 5 HP to go 30 mph then it takes 320 HP to make your Commando go 120 mph. When you bring in cubic relationships stuff multiplies up in a hurry, as evidenced here. Your issue arises due to a poor assumption right out of the starting blocks with 5 HP required for 30 mph. Change this to about 0.75 HP and everything will work out for you.
Since you indicate an interest in “real world scenarios” perhaps we could leave Lambrettas behind and get back on the Norton track. We’ve got no shortage of contributors here that throw out 120 mph as a top speed for their stock CDO – and although that is debatable, please accept this number for the sake of this discussion. Please also accept that said Norton makes ~ 45 RWHP. Thus, we’ve set a stake in the ground equating 45 RWHP to 120 mph.
Now let’s move to a higher speed as described here for ELDO’s bike, which went 154 mph.
https://www.accessnorton.com/Norton...its-after-andy’s-154mph-bonneville-run.25886/
In this example speed increased by a factor of 1.28 (154/120 =1.28). Applying our cubic factor we come up with a power increase of 2.11X (1.28^3 = 2.11) required to increase speed from 120 mph to 154 mph. Applying this factor to the original 45 HP engine gives us 95 RWHP (45 * 2.11 = 95) to go 154 mph. What a coincidence, 95 RWHP just happens to be the RWHP of the Herb Becker prepared engine that powered the bike to 154 mph! Well, maybe it might be even more than a coincidence.
I can’t give any better or more convincing explanation than offered above. But Google is your friend, look, read, verify, etc.
file:///C:/Users/kurtc/Downloads/HP%20required%20to%20overcome%20Aero%20drag.pdf
Try a calculator.
http://www.wallaceracing.com/Calculate HP For Speed.php
In the end it will all lead to the same endpoint – the cubic factor.