The Design of UAV Systems
3.2 Parasitic Drag
Other factors also create drag on an aircraft. These other origins of drag, which may be collectively grouped as ‘parasitic drag’, comprise skin friction drag, form drag, interference drag, momentum drag and cooling drag. The origins of these are discussed in detail in most books on aircraft aerodynamics.
An extensive treatise on this is given in Reference 3.1, which enables a designer, in the initial stages of a
Aerodynamics and Airframe Configurations 27
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0 5000 10,000 15,000 20,000
Altitude [m]
Air Density [kg/m3]
Figure 3.2 The standard atmosphere
project, to make a preliminary estimate of the total drag of an aircraft by calculating the drag contributed by the component parts and summing them.
Suffice it to say that parasitic drag varies, to first order, on an aircraft of defined configuration, with the air density and with the square of the airspeed.
Early in the design of an aircraft, its drag, along with other aerodynamic characteristics, will be measured in a wind tunnel and this will be reduced into a coefficient form by dividing the measured drag by the airspeed, air density and a reference area S, usually the main wing area in fixed-wing aircraft.
That is, the parasitic drag coefficient,CDp= Dp/1/2ρV2S, so that the parasitic drag may be estimated for any level flight condition using the expression:
Dp= qCDp.S (3.2)
where S is the wing area and q is the aerodynamic head: q=1/2ρV2.
There is, however, a further term which represents the increased drag which results from a wing being operated at higher incidence. This term is usually small until the wing approaches a stalled condition, when it becomes extremely large. It is caused by an increased skin friction and form drag as the wing incidence increases either to produce more lift or to fly more slowly. The increase generally trends as a function of the square of the lift coefficient CL, so that the parasitic drag equation then becomes:
Dp=
CDp+ kpCL2
q S. (3.3)
Combining the induced drag and the parasite drag gives the total drag of the aircraft.
Given that for a fixed configuration, the induced drag reduces as the square of the reciprocal of the airspeed, whilst the parasite drag varies with the square of the airspeed, then to obtain a reduction in
28 Unmanned Aircraft Systems
induced drag, the aircraft must fly faster but, in doing so, the parasite drag increases. Thus there is an intermediate airspeed, where the induced drag equals the parasitic drag and the total drag is a minimum.
The power used by the aircraft is equal to the product of total drag and the airspeed, so there is another airspeed at which the power used is a minimum.
There is yet another airspeed, usually faster than either of the former, at which the aircraft is at its most economic in terms of fuel used per distance travelled. All these values are different at different altitudes and they can be a significant determinant in the design of the aircraft, depending upon its operational roles and conditions.
Two basic criteria for flight at any given airspeed are that the wing produces sufficient lift to oppose the aircraft weight and that the thrust of the propulsor (propeller or jet) is equal to, or greater than, the total drag of the aircraft. For a fixed-wing aircraft, if there is a speed below which either of these criteria is not met, then the aircraft cannot sustain flight. This speed is the absolute minimum flight speed. However, it is not practical for the aircraft to attempt flight at this absolute minimum speed since any air turbulence or aircraft manoeuvre can increase the drag and/or reduce the lift, thus causing the aircraft to stall. A margin of speed above this is necessary to define a practical minimum flight speed Vmin. This important concept of a minimum flight speed will also determine the speed required for the aircraft to take off or be launched.
The lift produced by a wing is given by the equation
L = 1
2ρV2SCL (3.4)
where CLis a coefficient that determines the ability of the wing of area S to deflect the airstream. This coefficient, itself, is a function of the design of the wing section, the Reynolds number at which it is operating and the wing incidence, increasing in value with incidence and peaking at a value, CL.max.,
.beyond which it sharply reduces.
The value of the absolute minimum flight speed is obtained by rearranging Equation (3.5) as:
V = (2L/ρS CL. max .)1/2
but this provides no margin, as discussed above. A more realistic value of Vmincan be specified either by allowing a margin in speed or in lift coefficient. The latter approach is adopted by the author.
This results in a value of Vmingiven by:
Vmin= (2L/ρS Clo.)1/2 (3.5)
where CLo (operating CL) has been chosen to have a value of about 0.2 less than the CL.max for the selected aerofoil section. Note that this makes but little allowance for turbulent air or for manoeuvres and so refers to an absolute minimum speed at which the aircraft is able to maintain straight and level flight in smooth air. In that sense it is optimistic.
A typical, moderately cambered, section offers a CL.max of about 1.2 when used in practical wing construction and without flaps. Hence a value of 1.0 has been adopted.
Few UAV wings incorporate flaps as they represent complication and extra weight and cost. Although their deployment would produce an increase in lift coefficient, it would also add considerable drag. This would demand extra thrust and an increase in fuel-burn, neither effect desirable for take-off or in cruise flight. Their use is normally limited to the landing mode.
Equation (3.6) can be rewritten as:
Vmin= (2w/ρCLo)1/2 or
(2/ρ0)1/2(w/σ )1/2
(3.6)
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0 50 100 150 200 250 300
0 500 1000 1500 2000 2500 3000
Wing Loading [N/m2]
Minimum Flight Speed [m/s]
20,000 m
15,000 m
10,000 m 5,000 m Sea Level Global Hawk
Predator B
Figure 3.3 The variation of Vminwith aircraft wing loading
where w is the aircraft wing loading in N/m2,ρ0is the air density at sea-level standard conditions andσ is the relative air density at altitude.
The variation of Vmin with aircraft wing loading at several altitudes is shown in Figure 3.3 which covers wing loadings appropriate to the close-range, medium-range and MALE and HALE UAV. Figure 3.4 covers the lower values of Vmin, resulting from the wing loading relevant to the smaller mini and micro UAV.