Aircraft Drag: Types, Equations, and Reduction, Lecture notes of Aerospace Engineering

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MAE 154S Fall 2024

Lecture 3 - Drag

• Aircraft Drag

67 Photo Courtesy USAF

MAE 154S Fall 2024

Two types of drag

• All types of drag can be included in

these two groups:

• Skin friction drag
  • Caused by viscous shearing forces tangential to body’s surface
  • Influenced by Reynold’s number and surface roughness - Laminar flow leads to lower skin friction coefficients than turbulent flow
• Pressure Drag
  • Caused by pressure distribution normal to body’s surface
  • Dependent on Reynold’s number, projected frontal area. - Laminar flow can lead to an adverse pressure gradient that increases drag
• In general, both skin friction and form

drag are difficult to predict, so

experimental wind tunnel tests often

are required to obtain accurate

predictions

68 Concorde

MAE 154S Fall 2024

D =

ρ V

SC

Dp

ρ V

SC

Di

Drag Equations

70

D

D V SC

= r

C

D

= C

DP

C

L

π Ae

If flying straight, then lift

equals weight (L = W).

€ W = L = 1 2 ρ V 2 SC L € CL = 2 W ρ V 2 S Parasite Drag (^) Induced Drag

If L=W, parasite drag is proportional to V

, while

induced drag is proportional to 1/V

𝐶!,# ∝ 1 𝑉 $

MAE 154S Fall 2024

Drag vs. Velocity when L=W

71 Total Drag Parasite Drag Induced Drag Aircraft data: W= 3200 lbs, S = 300 ft^2 , CD=0.02+0.05CL*^2 , ρ=0.00238 slug/ft^3 Parasite drag makes up most of the drag at high speeds, while induced drag dominates at low speeds

MAE 154S Fall 2024

Trim Drag

• Drag due to control surface deflections that are needed to balance aircraft moments
• CG locations strongly influence trim drag
  • CG too far forward may result in increased trim drag, as

more down-lift on tail would be required to balance the

moments about CG (leads to increased induced drag at tail

and wing)

73

Tail lift

MAC

Elevator deflects up, producing down lift and pitch up moment

Wing lift

MAE 154S Fall 2024

Designing for Drag Reduction

• Reducing Skin Friction

• Laminar airfoils can be used, but not always very realistic depending

on the materials and construction tolerances being used

• Wetted area should be minimized, usually by having the fuselage taper

in the back. However, useful volume of fuselage is sacrificed

• Can consider optimum fineness ratio for fuselage. However, this

usually isn’t very realistic either. Most aircraft fuselages are longer to

provide sufficient moment arms for tail control surfaces

74 Lancair 360 Photo by Omoo

MAE 154S Fall 2024

Laminar Airfoils

• Laminar airfoils are shaped to prevent or delay the onset of turbulent

flow in order to reduce skin friction

• Laminar airflow is difficult to produce
  • Airfoil must be very smooth to promote laminar flow
• For laminar airfoils, favorable pressure conditions only exist for a

narrow CL and AoA range, leading to a “drag bucket” on the drag polar

76

MAE 154S Fall 2024

Turbulators

• Although laminar flow leads to reduced skin friction drag, laminar

flow tends to separate easier than turbulent flow

• Flow separation is usually a lot worse than skin friction drag
• Some aircraft intentionally trip the flow to initiate turbulent flow.

This thickens the boundary layer and helps delay or prevent flow

separation

77

MAE 154S Fall 2024

Winglets

• Winglets alter the structure of

the trailing vortex system

• Sidewash velocity produces an

angle of attack acting on the

winglet

• Outward flow from beneath the wing, inward flow on top
• Lift force acting on winglet can have a forward component that counteracts some of the drag 79 Airbus A319 wingtip fence Photo Courtesy NASA Photo by D. Nehrener

MAE 154S Fall 2024 Vought V-173 “Flying Pancake” (1942)

• Very unorthodox design: disc-shaped body serves as the lifting

surface

• A disc wing such as this has a very low aspect ratio, which typically leads to very high induced drag
• Large propellers were used to cancel the effect of the wingtip vortices by rotating in the opposite direction. This allowed the wing to be much smaller, which has improved maneuverability and increased structural strength 80 Photo Courtesy USAF^ Photo Courtesy USAF

MAE 154S Fall 2024

Transonic Area Rule

• At higher speeds, shock waves form on the aircraft body and cause wave drag
• Shockwaves can be reduced if the cross-sectional area of the aircraft changes gradually across its length, and it turns out this effect is largely independent of the aircraft shape
• One way to follow this area rule is to reduce the fuselage cross-section where the wing is placed (Coke bottle shape) 82 Photo Courtesy USAF

MAE 154S Fall 2024

Transonic Area Rule

83 Early version of the F-102 Delta Dagger with its straight fuselage design. Aircraft performance was disappointing – designed to fly Mach 1.2 but could not exceed Mach 1 Later variants of the Delta Dagger followed the transonic area rule

MAE 154S Fall 2024

Supercritical Airfoil

• At transonic speeds, drag for a given lift coefficient can be reduced if using a supercritical airfoil
• Airfoil shape results in a more rearward location and decrease in the strength of the shock wave
• Onset of boundary layer separation is also delayed to a higher Mach number
• Lift is lost due to reducing the upper surface curvature, but this is made up for by the supersonic flow on the upper surface, and by the large camber on the rear portion of the airfoil 85 Image Courtesy of NASA

MAE 154S Fall 2024 Wing Sweep for Transonic Aircraft

• Critical mach number is dependant on airspeed normal to leading edge
• Wing sweep increases critical mach number by reducing the velocity component normal to leading edge
• Allows for higher speeds before drag divergence occurs 86

V

Vnormal

Vnormal= V cos Λ