## Total drag

**Introduction**: Total drag is the sum of all forces working parallel to but opposed to thrust. Although there are numerous of factors affecting total drag it is common to subdivide these factors into 2 main factors, namely:

- induced drag (drag which is associated with the production of lift)
- parasite drag (drag which is not associated with lift production but mainly depends on aircraft shape or skin friction for example and is also known as zero lift drag)

Thereby, the boundary layer plays a significant role in how much drag is produced at different airspeeds.

**WAVE DRAG:**Wave drag is similar to parasitic drag but only occurs in conditions of supersonic flow. A body generating a shock wave feels this force as a consequence of pressure differences in the shock.

**The equation is:**

**Derivation:** The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object, according to a complicated (and not completely understood) law. Suppose that the variables involved – under some conditions – are the:

- speed u,
- fluid density ρ,
- viscosity ν of the fluid,
- size of the body, expressed in terms of its frontal area A, and
- Drag force FD.

**Using the algorithm of the Buckingham π theorem, these five variables can be reduced to two dimensionless parameters:**

- drag coefficient CD and
- Reynolds number Re.

Alternatively, the dimensionless parameters via direct manipulation of the underlying differential equations.That this is so becomes apparent when the drag force FD is expressed as part of a function of the other variables in the problem:

This rather odd form of expression is used because it does not assume a one-to-one relationship. Here, fa is some (as-yet-unknown) function that takes five arguments. Now the right-hand side is zero in any system of units; so it should be possible to express the relationship described by fa in terms of only dimensionless groups.There are many ways of combining the five arguments of fa to form dimensionless groups, but the Buckingham π theorem states that there will be two such groups. The most appropriate are the Reynolds number, given by

And the drag coefficient, given by

Thus the function of five variables may be replaced by another function of only two variables:

Where fb is some function of two arguments. The original law is then reduced to a law involving only these two numbers. Because the only unknown in the above equation is the drag force FD, it is possible to express it as

Or

And with

Thus the force is simply ½ ρ A u_{2} times some (as-yet-unknown) function fc of the Reynolds number Re – a considerably simpler system than the original five-argument function given above.

Dimensional analysis thus makes a very complex problem (trying to determine the behavior of a function of five variables) a much simpler one: the determination of the drag as a function of only one variable, the Reynolds number.