On Tue, 26 Feb 2013 17:05:16 -0800 (PST), "
wrote:
On Feb 26, 6:09*pm, Ed Huntress wrote:
However, speed is an exponential-ratio thing, and the record set with
one of the recent models was 231 mph. If a bike will go 200 mph with
190 hp, it will take 298 hp to go 231, and 450 hp to go 265.
--
Ed Huntress
Can you explain the math?
No. I used a speed shop's calculator and I'm not telling. g
Oh, all right....The horsepower required to maintain a specific speed:
P = 1/2 * Cd * A * k * v^3
P = horsepower required for the velocity in question
Cd = coefficient of drag
A = frontal area
k = constant to account for the density of air (or you can use the
actual number - 1.2g/m^3, if you watch your units throughout)
v = velocity
In addition, you have to work in the rolling resistance. For a
motorcycle with high-speed, hard tires, you can ignore it for these
purposes. I'll give you a shortcut for the formula in a minute.
I'll give you the site of a calculator but first, note the v^3. That's
the key to the whole thing, which leads people to overestimate how
fast they can go on, say, a Kawasaki Ninja with two or three hundred
horsepower. g
Here's the calculator.
http://www.apexgarage.com/tech/horsepower_calc.shtml
Knowing that the unregulated speed of a Ninja is 200 mph and it
achieves that with 190 hp, you can plug in any trial numbers you want
to get everything to work (I used Cd = 0.5; A = 7; weight 500 lb.) As
long as the relationship of these numbers isn't ridiculous, all you
need to know is what trial numbers give you 200 mph with 190 hp. Then
use those same trial values and try changing the speed. That will give
you the horsepower.
I tested the online calculator by using a shortcut of the real formula
on my own pocket calculator:
Original speed cubed over original horsepower = final speed cubed over
"x", where "x" is horsepower required.
Actually, I tested it by using the variable for speed, and assumed 450
horsepower, to test the online calculator. It works either way.
By knowing the original speed and horsepower, you can do away with
drag coefficient, frontal area, and air density. It's the relationship
between power and speed that you need, plus the "cube" factor for
velocity. The shortcut, or the online calculator, will give that to
you.
Have fun.
--
Ed Huntress
Dan