# Coefficient of drag and surface smoothness

So i am working on a program that models the movement of a rocket through different planets. and i sm starting to get teach my self fluid dynamics. As i was reading a presentation by nasa about the forces that act on a rocket they got into shape effects on drag, i noticed from their equation Cd = D/(r * A * (V^2)/2)
"
The drag coefficient is a number which aerodynamicists use to model all of the complex dependencies
of drag on shape inclination, and some flow conditions. The drag coefficient (Cd) is
equal to the drag (D) divided by the quantity: density (r) times reference area (A) times one half
of the velocity (V) squared.
"
does not include the surface friction aspect of the problem, why is that, is this a simplified equation?

## Answers and Replies

boneh3ad
Science Advisor
Gold Member
Well first, you have to understand the nature of drag. There are a number of types depending on the speed regime. The three big types are form drag, viscous drag, and wave drag.

Form drag (some may call it pressure drag) has to do with the overall shape of the object and is a result of the pressure distribution that develops over an object as a result of a fluid flowing around it. For example, as a result of air flowing around a ball, there is going to be a higher pressure developing on the forward facing portion of the ball and a lower pressure on the back side, meaning an overall pressure force directed against the motion. This is form drag, and is what "the drag equation" typically covers. Depending on the shape and the speed, it may or may not be the most important type.

Viscous drag is what you above termed "surface friction." Friction, in the typical sense, doesn't really apply to fluids in the same way you think about it for solid objects. If you have been reading up on fluid mechanics, then perhaps you have come across the idea of viscosity? Basically, viscosity causes a fluid to "stick to" a surface in the sense that no matter how fast the object is moving through the fluid, the fluid sticks to the surface such that very close to the wall, the velocity of the fluid relative to the wall is zero. This is commonly called the no-slip condition. This means and any object traveling through the air is going to tend to pull a little bit of fluid along with it, which is associated with a force to give that fluid the tug that it needs. This is the nature of viscous drag.

The problem with viscous drag is that it is nearly impossible to accurately predict for most real-world examples. The magnitude of this force (measured in terms of shear stress) at a particular location is dependent on, among other things, the state of the boundary layer (whether it is laminar or turbulent). A turbulent boundary layer results in a larger shear stress at the wall and higher drag. The problem is that we don't have any real way of predicting exactly where along a surface the boundary layer transitions from laminar flow to turbulence, but unfortunately, when it does, the shear stress can increase by a factor of 10 or more. This can lead to very large errors in drag prediction due to simply not knowing the transition point. Viscous drag is the portion of drag which depends (partially) on surface roughness, as the surface roughness helps determine where transition occurs. The drag equation is effectively meaningless for this type of drag.

Wave drag is the last major type, but it only occurs in transonic flows or faster. It is the drag that arises from the formation of shocks and has to do with having to essentially push fluid away from the vehicle as it forces its way through air that can't quite react fast enough.

So yes, it is a simplified equation. It is a very simplified equation. However, it does tend to work reasonably for situations where form drag is most important, and in certain situations, even when viscous drag is important.