Easy question about an aircraft's top speed

[Diresu]

I found an equation on Wikipedia that I believe will give me the top speed of a theoretical aircraft. Mission accomplished? Well... maybe not.

http://en.wikipedia.org/wiki/Drag_equation

D=.5P(V2)ACd
(V2 is supposed to mean V squared, and d is a subscript of C)

D is the force of drag,
ρ is the density of the fluid,
v is the velocity of the object relative to the fluid,
A is the reference area, and
Cd is the drag coefficient

I am trying to solve the equation on this page for V, but I've been out of college for 10 years so maybe that's my problem:

I came up with
V=SQRT((2D)/(PACd))

It looks correct to me but somehow I don't think I'm getting it correct because of the paragraph at the bottom of the page.

"Another interesting relation, though it is not part of the equation, is that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Since power is the rate of doing work, exerting four times the force at twice the speed requires eight times the power."

When I run my equation it's never an 8 to 1 ratio for power to speed. I've hosed something but I can't figure out what.

Any help would be greatly apreciated!

Thanks,

Al

 

[Diresu]

Just answered my own question

Geez after 2 hours of tearing my hair out I post a message and 5 minutes later I figure it out. DOH!

thanks anyway,

Al

 

[charng]

Dear Al,

Thank you for reaching out to me with your question about an aircraft's top speed. While the equation you found on Wikipedia may give you a theoretical estimate of an aircraft's top speed, there are many other factors that need to be considered in determining the actual top speed of an aircraft. These factors include the design and aerodynamics of the aircraft, the engine power and thrust, and even the altitude and air density in which the aircraft is flying.

Additionally, the drag equation you have referenced is a simplified version and does not take into account other forms of drag, such as skin friction drag or induced drag. It also assumes that the aircraft is flying at a constant speed, which is not always the case in real-life situations.

Furthermore, the paragraph at the bottom of the page highlights the concept of power being the rate of doing work, and how it increases exponentially with speed. This means that the power needed to maintain a certain speed increases significantly as the speed increases, which may not be reflected in your equation.

In order to accurately determine an aircraft's top speed, a combination of mathematical equations and experimental data is usually used. I would recommend consulting with an aerospace engineer or conducting further research to get a more accurate estimate.

I hope this helps clarify the limitations of the equation you found and the complexities involved in determining an aircraft's top speed.