# Aerodynamics of Control Line Models

### Drag and Power

The drag of a control line model is composed of the drag of the model and its control lines. Because of the circular motion and the fact that the the drag force depends on the square of the local velocity the calculation of the power requirements is more complicated than usual.

#### Drag and power of the model

The drag of the model can be calculated like for any flying aircraft. It is composed of zero lift drag D0 and lift dependent (induced) drag Di. For the drag of the model we obtain the well known formula

The power P required to pull the model through the air at a given flight speed can then be calculated from:

#### Drag and power of the control wires

Again we need the distribution of the local flow velocity at each radius station as already shown in the notes about flying on a circular path.

 Top view of a control line model, flying at velocity .

The local velocity at a radial position r (measured from the center post) is given by

 A segment of a control wire, having diameter d and length .

If we cut a control wire (having a diameter d) into small segments of length dl we can write for the drag contribution dD of such a piece at a radial station r

To obtain the power consumption we can multiply this expression with v(r):

In general the drag coefficient Cd is a function of the radius because the Reynolds number varies along the radius. If we look at typical values, we see, that this leads to a minor variation of Cd only, so that we can assume Cd=1.15 for all segments along the radius. Also we can safely assume that the wires have a constant diameter d, i.e. they are not tapered.

With these assumptions one can integrate (sum up) the power required by all segments to find the value for the whole wire:

The integration along the wire starts at the center post (r=0) and ends at the inboard wing tip (r=l-b/2). The calculation finally yields the following formula for the required power of one control line:

The total drag of the control lines can found by integration of dD along the radius and one finally obtains a useful result:

It can be shown, that this distributed drag force acts like a single drag force having the same magnitude, attached to a single point at 3/4 of the length of the control wire. This means that 3/4 of the drag force has to be compensated by engine thrust and 1/4 of the drag has to be carried at the center post (i.e. by the pilot).

#### Symbols and Abbreviations

Symbol Description Unit
D drag force N
P power W
S wing area m2
density of air kg/m3
b wing span m
d diameter of control wire m
l length of control wire m
v velocity m/s
Cd,0 zero lift drag coefficient -
Cd,i induced drag coefficient -

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