WHAT SHOULD THE CAMBER BE?
A mean camber line, such as those presented in Figs. 7.2 and 7.3, is designed to operate at one ideal design value of cj. Once the camber is determined, any symmetrical thickness form or envelope may be fitted to it to give an aerofoil which will operate most efficiently at the design ci.
For a racing model, it is first necessary to decide the speed at maximum power, straight and level. This may be measured from a real model in flight, or estimated for a new design, from previous experience. Then the model Cl may be worked out as described above. Knowing the Cl, the type of mean line required should be chosen from those in the tables (or from any similar source). Most of the NAC A mean lines are worked out for a design ci of unity. This allows the designer to arrive at the camber for his aerofoil by simple multiplication of the camber line ordinates in the NACA tables.
A worked example follows: the figures used are not intended to be representative of any modern racing model.
Model weight 1 kg. wing area 0.2 sq. metres, designed speed 20 metres per second.
„ , , „ lx 9.81 _ 9.81 _ . .
Model Cl и x 1 225 x 202 x 0.2 49.00 0-2
Hence the ordinates for the NACA a = 1 mean line may be multiplied throughout by
0. 200 to give the desired camber line.
For example, at 50% chord, the maximum camber point on this mean line, the camber should be:
.200 x 5.515 = 1.103, i. e. a 1.1% camber approx, for flight at this speed with this model
If the model is in a steep turn, the required lift force, and hence the effective weight, increase perhaps to three or four times die above. The formula then must be modified:
Cl (in steep turn) = 4 x.200 = .8, requiring a camber of.8 x 5.515 = 4.120%.
A flight speed of 50 metres/sec yields: 9.81
The required camber is then.032 x 5.515 = 0.177% and in the steep turn 0.708%. Cambers of less than 1% are thus required for pylon racing models with speeds over 180 k. p.h. or 100 m. p.h. Note also the width of the low drag range or ‘bucket’ on modem laminar flow symmetrical aerofoils (see Chapter 9).
THE POWER FACTOR DERIVATION
Lift in level flight may be taken as equal to weight Then by re-arranging the lift formula:
For a glider the rate of sink is given by V x Sin a where a is the glide angle. As the ratio of drag to lift is also (very nearly) equal to Sin a the above expressions may be combined:
Sinking speed =
Fig. A2 Chart showing variation of Reynolds number with air temperature and pressure [altitude].
The formulae in the right hand margin give the equations for Re extremes of winter and summer at near sea level. The shaded area indicates variations with seasons and altitudes up to 1000m (3281ft).
This is simplified as shown:
Sinking speed = / W 1 Cp _ / W Cp
V WpS X C1У1 CL V ^pS CL3/2
From tliis it is seen that two factors affect the sinking speed, one of these contains the wing loading, W/S, the other is the factor Ср/Сь3/2- To decrease the sinking speed, the wing loading W/S may be decreased, but this factor appears within a square root, so the effect of a large decrease of wing loading is relatively small. To obtain a larger improvement in sinking speed, Cp/CL15 must be reduced, or, what amounts to the same thing, Cl1 5/Cp must be increased. For steeper angles of glide, more than 10 degrees, the wing loading factor remains unchanged but the other factor is slightly modified to:
Cp (CL2 + Cp2)3/4
For a power model the lift formula is accurate for level flight, so the minimum power to sustain flight is arrived at thus: Power = force x distance in unit time
= Drag x Speed = DV
Drag = D = W-^ = (Formula for V is given above)
Power = W X/ ^ X S’R/7
‘V fcpS CL3/2
As with gliding, the wing loading, W/S, and the power factor must both be adjusted to achieve flight at minimum power. In addition, the weight alone plays a major part and the formula shows that a heavy model necessarily needs greater power for sustained flight