Drag-divergence Mach number
Mach number where drag rises sharply, a key transonic effect.
The drag-divergence Mach number marks the point where an airfoil’s aerodynamic drag starts to climb sharply as speed increases. This is a transonic effect, typically occurring above Mach 0.6, and it is distinct from the critical Mach number, though always greater than it. The drag coefficient can jump to more than ten times its low-speed value, peaking at Mach 1.0 and then dropping again after roughly Mach 1.2 in the supersonic regime.
The rapid drag rise comes from a shock wave forming on the airfoil’s upper surface, which can cause flow separation and adverse pressure gradients on the rear of the wing. This means aircraft designed for supersonic flight need substantial thrust. Early transonic and supersonic aircraft often used steep dives to gain extra acceleration through the high-drag region around Mach 1.0.
This steep drag increase fueled the false idea of an unbreakable sound barrier, as it seemed no foreseeable technology could provide enough thrust or control to overcome it. The Prandtl–Glauert rule, a popular analytical method, even predicted infinite drag at Mach 1.0.
Key advances that helped conquer this barrier include the Whitcomb area rule and the supercritical airfoil. A supercritical airfoil is shaped to push the drag-divergence Mach number significantly higher than the critical Mach number, allowing faster transonic cruise than earlier subsonic limits. Along with computational fluid dynamics, these innovations have reduced the drag increase factor to two or three for modern designs.
For a given family of propeller airfoils, the drag-divergence Mach number \( M_{\text{dd}} \) can be approximated by Korn’s relation:
\[ M_{\text{dd}} + \frac{1}{10} c_{l,\text{design}} + \frac{t}{c} = K \]
Here, \( c_{l,\text{design}} \) is the section’s design lift coefficient, \( t \) is the airfoil thickness at the section, \( c \) is the chord length, and \( K \) is a CFD-derived factor: 0.87 for conventional airfoils (6 series) and 0.95 for supercritical airfoils.
- Typical minimum value
- greater than 0.6
- Drag coefficient increase factor
- more than ten times its low-speed value
- Peak drag mach
- 1.0
- Supersonic regime onset
- above approximately Mach 1.2
- Korn relation k conventional airfoils
- 0.87
- Korn relation k supercritical airfoils
- 0.95
Lore & Background
The large increase in drag is caused by the formation of a shock wave on the upper surface of the airfoil, which can induce flow separation and adverse pressure gradients on the aft portion of the wing. This effect requires that aircraft intended to fly at supersonic speeds have a large amount of thrust. In early development of transonic and supersonic aircraft, a steep dive was often used to provide extra acceleration through the high-drag region around Mach 1.0.
The steep increase in drag gave rise to the popular false notion of an unbreakable sound barrier, because it seemed that no aircraft technology in the foreseeable future would have enough propulsive force or control authority to overcome it. One of the popular analytical methods for calculating drag at high speeds, the Prandtl–Glauert rule, predicts an infinite amount of drag at Mach 1.0.
Two of the important technological advancements that arose out of attempts to conquer the sound barrier were the Whitcomb area rule and the supercritical airfoil. A supercritical airfoil is shaped to make the drag-divergence Mach number significantly higher than the critical Mach number, allowing aircraft to cruise faster transonically than with previous subsonic cruise limits.
Reader's Guide
The drag-divergence Mach number is significant because it defines the onset of a dramatic drag increase that historically posed a major barrier to high-speed flight. The article notes that this increase can cause the drag coefficient to rise to more than ten times its low-speed value, necessitating large thrust for supersonic aircraft. Early pilots used steep dives to accelerate through the high-drag region around Mach 1.0. The phenomenon contributed to the false notion of an unbreakable sound barrier, reinforced by the Prandtl–Glauert rule's prediction of infinite drag at Mach 1.0. Technological responses included the Whitcomb area rule and the supercritical airfoil, which raises the drag-divergence Mach number relative to the critical Mach number. Modern computational fluid dynamics and these advancements have reduced the factor of increase in drag to two or three for modern aircraft designs. The drag-divergence Mach number can be approximated for propeller airfoils using Korn's relation, which incorporates the design lift coefficient, airfoil thickness-to-chord ratio, and a factor K (0.87 for conventional airfoils, 0.95 for supercritical airfoils). This parameter remains essential for transonic and supersonic aircraft design.
Did You Know?
- The drag-divergence Mach number is always greater than the critical Mach number.
- The drag coefficient typically peaks at Mach 1.0 and begins to decrease above approximately Mach 1.2.
- Korn's relation uses a factor K of 0.87 for conventional airfoils and 0.95 for supercritical airfoils.
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