On Wed, 27 Feb 2013 09:12:42 -0800 (PST), "
wrote:
On Feb 26, 9:53*pm, Ed Huntress wrote:
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
Thanks.
Ah an online calculator.
I was wondering how you got the aerodynamic drag and the rolling
resistance . But a good on line calculator would take the rolling
resistance into account.
Dan
I was lazy and looked for a calculator first. But I don't know the
source and so I didn't trust it.
The equation is something I had on hand. So, to check the online
calculator, I cancelled out the factors that would be the same at
different horsepower ratings and speeds on one particular bike (Cd, A,
k) and realized that the equation simplifies to something trivial, IF
you know both one particular speed and the horsepower required at that
speed.
Which happens rarely, but fortunately there is a lot of documentation
about it online because of the unusual agreement between Kawasaki and
the EU to speed-limit the bike to 300 km/hr. The magazines all wanted
to know what it will do without the governor, and there are several
road tests that came up with the 200 mph figure.
And that also happens to make sense in terms of the factors I
cancelled out. Those are pretty typical for a big bike with advanced
streamlining, like the Ninja.
Notice that the Honda that went 270+ did a bit better with less
horsepower (270 with 400 hp vs. 265 with 450), which also makes sense.
That Honda is engineered for one thing: setting a world record at
Bonneville. Its Cd probably is lower than that of any street bike.
Anyway, the online calculator checks out. Try varying the weight of
the bike a bit and see what the consequence is for different values of
rolling resistance (that's where the weight factor comes into play).
The speed varies very little, you'll notice. That also makes sense.
--
Ed Huntress