# Velocity in Drag Equation

## Main Question or Discussion Point

While I understand this is a basic question, I am a beginner with regard to fluid dynamics etc. To start, say you have a propulsion system capable of X Newtons and a weight of Y kg. I realize max speed occurs at the point at which the force of drag is equal to the force of acceleration, and the aircraft will neither be accelerating nor decelerating (inertial motion will be achieved). Here is where my problem occurs: Fd (Force of Drag) is partially dependent upon velocity as V^2 is part of the equation. However, the drag coefficient is non-constant as it too relies upon velocity. Can X N/Y kg be the reference velocity to find the force of drag (assuming all other quantities are known) or does max speed simply have to be tested for in another way? I can test for Fd at different velocities, but have no idea how to plot this on a graph or set it equal to Fa as Cd also depends on velocity. Any help would be appreciated.

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Well there are few things you need to clear up before anyone can answer your question.

-Weight is not in kg. The unit kg is mass.
-Weight/Mass (N/kg) does not have the units of velocity. It has the units of acceleration.
-Maximum velocity is not achieved when Thrust = Drag. This condition is known as cruise. Cruise is when you are not accelerating and are at a constant Velocity.
-Cd is a coefficient and dimensionless. Setting Fd = Cd yields nothing useful.

Now to answer your last question, you can find cruise velocity if you other know things, such as cruise at angle of attack or cruise CL.

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First of all thanks for replying!
Alright (these match up to your responses):
-I realize kg is mass and am frankly embarrassed by this rudimentary mistake.
-I also realize force/mass=acceleration and I meant at a given time as acceleration*time=velocity.This was originally brash and illogical thinking regardless, and meant to demonstrate my futility in finding a solution. I don't have any idea what was going through mind.
-Inside my parameters (the aircraft has constant unwavering propulsion), I believe cruise to be my max velocity as this is the point at which the plane stops accelerating and the velocity is at it's highest. So, for all intensive purposes, are these phrases not interchangeable? Correct me if I'm wrong here.
-If I suggested I was setting Cd to Fd (I don't see where) I apologize as this was not properly conveyed. I was merely suggesting setting Fa equal to Fd. My concern was that both Fd and Cd are dependent upon velocity, so there is no way to calculate Fd given all other variables. What it boils down to is this: how can you find Fd at a specific velocity without testing if Cd changes with velocity. Is the only way to find Fd by testing at every different velocity you need, or is there a way to figure this out after only testing for Fd at one or two velocities? How can conclusive Cd values be predicted?

I think I was ambiguous in my last post. What I meant to ask was if in the drag equation you need to know Cd, how can you find this out without knowing Fd? It's almost like a contradiction:You need Cd to solve Fd, but you can't find Cd without knowing Fd. It's frustrating me to say the least.

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Drag is not a simple concept. Let's look at the case of incompressible flow for simplicity. In theis case, there are two sources of drags: skin friction (viscous drag) and pressure (form drag).

To find Cd for form drag is fairly easy. You just need to know the pressure distribution on the surface. The difficulty depends on the shape. You can generally find this value for most airfoils and most simple shapes in books such as "Theory of Wing Sections" or probably online somewhere.

Viscous drag is much more difficult and depends on many factors. For that you need to know boundary layer profiles all over the surface. Those are not simple to find. Viscous drag generally contributes around 20% of the drag on an airliner, so ignoring it would just give you a VERY rough estimate.

Why do I say this? The drag equation you cite is much more complicated
Than it looks.your best bet is trying to find Cd published somewhere.

Yeah that makes sense I realize the tough subject I'm getting into here. What about testing for the force of drag at different velocities with all other variables known (with the exception of Cd) and rearranging the equation to solve for Cd. Would plugging in the numbers in that manner yield a legitimate Cd at each velocity?

Yes that is a legitimate way to do it but be careful now, because CD also varies with angle of attack. So you would have to have a fixed angle of attack and vary your velocities.

Great! And that is perfect considering my experiment entails varying the angle of attack to see the effects. Thanks go guiding my thinking process as I'm only a junior in highschool with half a year of physics behind me.