1021

Item 1021

OTHER: Aerodynamic - Drag - Parasitic [D_P]

The helicopter industry defines parasitic drag in terms of the equivalent flat plate area (equivalent unitary drag coefficient area) [f], which is the drag divided by the dynamic pressure (velocity pressure). f = D_P / q, in sq-ft.

Dynamic pressure; q = 1/2 (ρ * v²)

where (using SI units):

q = dynamic pressure in pascals. 1 pascal = 0.02088543 lb/ft²

ρ = fluid density in kg/m³ (e.g. density of air). 1 kg/m³ = 0.06242796 lb/ft²

v = fluid velocity in m/s. 1 m/s = 2.2369 mph

Coefficient's of Drag:

Flat plate C_D =1.28

Rectangle C_D = 0.75

Round tube/wire C_D = 0.5

Ellipse C_D = down to 0.25 (varies depending on ratio of thickness to length)

Airfoil section C_D = 0.10 to 0.04 (varies depending on section)

It appears that a streamlined shape having a 3/1 fineness ratio (NACA 0033) gives the best value of C_D , namely 0.045.

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The following values are of X-sections through the fuselage, which are being subjected to a downward airflow.

Prouty's Coefficient of Drag Values:

Use Prouty's cross-sectional shapes and drag coefficients when using his algorithm.

Circle C_D = 0.6

Ellipse C_D = 0.6 to 0.3

Rectangle C_D = 2.0

Airfoil (flat leading) C_D = 2.0 (2-dim) & 1.2 (3-dim)

For more shapes see [Source ~ RWP1 p.280]

Stepniewski's Coefficient of Drag Values; For more shapes see [Source ~ RWA p.40]

Misc.

If you make the coefficient of drag [C_D] equal to one, then the equivalent flat plate area [f] is entered into the drag area.

For an airplane wing: D_W = (ρ / 2) * V² * S * C_D . Where S is the area of the wing.

For a helicopter: D_p = f * q = f * (ρ / 2) * V².

"The number in my aero engineering text from college is 1.28 for a flat plate, and the NASA site shows the same value, but it varies somewhat with Reynolds number. Hoerner shows it at about 1.17 at 1.0E5 Reynolds, and higher at 1.0E2, perhaps about 1.28, but hard to read on the graph." ~ e-mail from Bill F.

"Data obtained during helicopter development show that the percentage of drag attributed only to the hub is greater than 22 percent of the entire aircraft drag for a representative configuration"

Wheeled landing gear appears to have approximately twice the drag of faired skids.

Streamline Drag:

The primary component of streamline drag is skin friction.

Bluff Body Drag:

Drag that is created mainly by the rotor hubs and landing gear. Much of this might be reduced in the UniCopter by fairing the fuselage and/or secondary gearbox into the rotor hub and streamlining the hub as much as possible.

Interference Drag:

Drag that is produced by the mixing of the flows past two objects that are either attached to, or are close to one another. Unless the flows meet smoothly, turbulence is created, which represents an energy loss resulting in increased drag. Reference the UniCopter's fuselage and two rotors.

Intersection Drag:

When two objects join, the amount of intersection drag depends on the angle they join at. Minimal drag is at 90 degrees, and the drag just goes up from there. Usually, designers compensate for the non-90 degree interface by using fairings that get bigger the faster the plane goes and the difference from the ideal 90-degree position.

Parasitic Drag - Blade:

An informative post by Nomadd on PPRuNe November 22, 2003:

Ideally an airfoil section should not have the parasitic drag but in reality, it will surely have some parasitic drag.
Parasitic drag is the sum of profile drag and interference drag.
Profile drag is sum of Skin friction and pressure drag
1. Usually the airfoil is designed to give the greatest decrease in Skin friction drag at low lift coefficients or in other words at high speeds
2. Pressure drag arises due to overall pressure distribution of an aircraft, it the difference between forces caused by high pressure on the forward portion and low pressure on the aft portion of the aircraft
3. Interference drag is caused by regions of turbulence at junctions
All the three factor above may be small for heli blades, will they be increasing more than reduction in induced drag?
Hard to answer that I suppose.

Algorithm for Force Required to Overcome Parasite Drag:

Working in MKS (metric) units
F = 1/2 ρ C_D A v²

Where
F is the force [in kilograms]
ρ (Greek letter "rho") is the density of air = 1.225 kg/m³ (1.225 grams/litre)
C_Dis the coefficient of drag; which is 0.04 for a streamline strut (NACA 0025), 1.0 for a round wire, 2.0 for flat wire or 1.5 for a parachute. For values for helicopter component shapes see [Source ~ RWP1 p.280].
A is the area of the surface [in square meters]
v is the velocity through the air [meters per second]

Working in (English) units
F = 1/2 ρ C_D A v²

Where
F is the force [in pounds]
ρ (Greek letter "rho") is the density of air = 0.002377 slugs/foot³(The paragraph below says to use pounds per cubic foot, which is actually = 0.0765 pounds/foot³, but it appears that the slugs/foot³ value is the correct one.)
C_D is the coefficient of drag; which is 0.04 for a streamline strut (NACA 0025), 1.0 for a round wire, 2.0 for flat wire or 1.5 for a parachute. For values for helicopter component shapes see [Source ~ RWP1 p.280].
A is the area of the surface [in square feet]
v is the velocity through the air [feet per second]. (To convert from miles per hour to feet per second; multiply mph by 1.4667)

General:

"However, noticeable improvements can be made by fairing the hub into the fuselage" ~ [Source ~ PHA p.168]. This is of particular interest to the UniCopter and of little relevance to the SynchroLite.

"Note that if the gross weight is equally shared by two rotors as in a tandem, side-by-side or synchcropter configuration, the total hub parasite drag area is likely to be 21/3 = 1.26 greater than one hub carrying all of the gross weight." ~ [ Source Report ~ An Overview of Autogyros and The McDonnell XV-1 Convertiplane , page 6]

Equivalent Flat Plate Area: [f] ~ Additional Information off the Web

The drag equation for a flat plate is the simple D = Cd*S*q where Cd is the flat plate drag of unity, S is equivalent flat plate area and q is aerodynamic pressure. q uses sub-factors of half air density, equal to .0012 at sea level, and of V^2, where V^2 is velocity in feet per second, squared. For estimate calculations, the drag of one square foot of flat plate at 100 knots, or 169 ft/sec, is 29 pounds.

Using the horsepower equation where 1 hp=550 ft-lbs/sec, the result is that a square foot of surface at 100 knots requires 29*169/550 = 8.9 HP/ sq. ft..

From: http://www.auf.asn.au/groundschool/umodule4.html

• The equation for calculation of the total parasite drag for an aircraft is:-

Parasite drag = C_Dp × 1/2V² × S newtons

Unlike the lift coefficient the parasite drag coefficient C_Dp is more or less a constant - the ratio of drag to dynamic pressure - and thus provides a means for comparing the relative aerodynamic cleanness of two aircraft. The coefficient is usually in the range 0.03 to 0.08.

• There is another value, the 'equivalent flat plate area' (FPA) used by aircraft, motor vehicle and structural engineers who are concerned with calculation of air resistance. FPA is often quoted in aviation magazines when comparing the parasite drag efficiency of an aircraft with other similar aircraft and it is usually stated in terms of square feet.

FPA is calculated as C_Dp times the wing area divided by the C_Dp for a flat plate. However it is assumed that the C_Dp for a flat plate held at 90° to the airstream = 1 (in fact it is about 20% greater but that is of no real consequence) so the flat plate C_Dp is omitted from the calculation, thus:

FPA = C_Dp × S ft²

For example the FPA for the run-of-the-mill two or four seater fixed undercarriage general aviation aeroplane would be around 6 ft² with C_Dp of 0.03 to 0.05 and the retractables around 4 - 5 ft² with C_Dp of 0.02 to 0.03. FPA of a very clean high performance general aviation aeroplane like a Mooney model is around 3 ft² with C_Dp about 0.015. Some very clean high performance kit-built aircraft have FPA less than 2. Note that FPA does not represent the frontal cross-section area of the aircraft.

Probably the smallest known FPA is not associated with a general aviation aircraft but with an owner designed and built ultralight! [not U.S. FAR Part 103 ultralight] Californian Mike Arnold's 65hp Rotax 582 powered AR-5 holds the world speed record, in the under 300 kg class, of 213 mph. This little dogfighter has an FPA of 0.88 ft² with C_Dp about 0.016 and demonstrates what can be achieved - an unmatchable 3.3 mph per hp - in an ultralight design when the designer/builder pays the utmost attention to detail - note the beautifully shaped engine cowling. So don't let anyone tell you ultralights have to be slow and draggy!

Last Revised: October 17, 2008